mirror of https://github.com/CGAL/cgal
Fix conflicts
This commit is contained in:
Maxime Gimeno
commit
95c2045eb6
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@ -1297,7 +1297,7 @@ void Scene::refine_loop()
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return;
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}
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std::cout << "Loop subdivision...";
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CGAL::Subdivision_method_3::Loop_subdivision(*m_pPolyhedron, 1);
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CGAL::Subdivision_method_3::Loop_subdivision(*m_pPolyhedron);
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std::cout << "done (" << m_pPolyhedron->size_of_facets() << " facets)" << std::endl;
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clear_internal_data();
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@ -1,5 +1,5 @@
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#include <iostream>
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#include <boost/iterator.hpp>
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#include <boost/iterator/iterator_adaptor.hpp>
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#include <CGAL/Simple_cartesian.h>
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#include <CGAL/AABB_tree.h>
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@ -31,10 +31,18 @@
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#include <boost/type_traits/is_same.hpp>
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#include <boost/variant/apply_visitor.hpp>
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#if BOOST_VERSION >= 105000
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#include <boost/heap/priority_queue.hpp>
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# if defined(BOOST_MSVC)
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# pragma warning(push)
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# pragma warning(disable: 4996)
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# endif
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# include <boost/heap/priority_queue.hpp>
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# if defined(BOOST_MSVC)
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# pragma warning(pop)
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# endif
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#else
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#include <queue>
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# include <queue>
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#endif
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#include <CGAL/assertions.h>
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namespace CGAL {
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@ -325,27 +325,27 @@ efficiency.
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The following example illustrates the construction of `AlgebraicKernel_d_1::Algebraic_real_1`
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using `AlgebraicKernel_d_1::Construct_algebraic_real_1`:
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<SMALL>\cgalExample{Algebraic_kernel_d/Construct_algebraic_real_1.cpp}</SMALL>
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\cgalExample{Algebraic_kernel_d/Construct_algebraic_real_1.cpp}
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\subsection CGALAK1Solving Solving Univariate Polynomials
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The following example illustrates the construction of `AlgebraicKernel_d_1::Algebraic_real_1`
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using `AlgebraicKernel_d_1::Solve_1`: <SMALL>\cgalExample{Algebraic_kernel_d/Solve_1.cpp} </SMALL>
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using `AlgebraicKernel_d_1::Solve_1`: \cgalExample{Algebraic_kernel_d/Solve_1.cpp}
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\subsection CGALAK1EGCompare_1 Comparison and Approximation of Algebraic Real Numbers
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The following example illustrates the comparison of `AlgebraicKernel_d_1::Algebraic_real_1` numbers:
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<SMALL>\cgalExample{Algebraic_kernel_d/Compare_1.cpp}</SMALL>
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\cgalExample{Algebraic_kernel_d/Compare_1.cpp}
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\subsection CGALAK1EGIsolate_1 Isolation of Algebraic Real Numbers with respect to roots of other polynomials
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The following example illustrates the isolation of `AlgebraicKernel_d_1::Algebraic_real_1` numbers:
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<SMALL>\cgalExample{Algebraic_kernel_d/Isolate_1.cpp}</SMALL>
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\cgalExample{Algebraic_kernel_d/Isolate_1.cpp}
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\subsection CGALAK1EGSign_at_1 Interplay with Polynomials
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The following example illustrates the sign evaluation of `AlgebraicKernel_d_1::Algebraic_real_1` numbers in polynomials:
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<SMALL>\cgalExample{Algebraic_kernel_d/Sign_at_1.cpp}</SMALL>
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\cgalExample{Algebraic_kernel_d/Sign_at_1.cpp}
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\section Algebraic_kernel_dDesign Design and Implementation History
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@ -1524,17 +1524,11 @@ compute_intermediate_values_and_slices() const {
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#if CGAL_ACK_DEBUG_FLAG
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CGAL_ACK_DEBUG_PRINT << "Prepare intermediate slices.." << std::flush;
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#endif
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std::size_t size = event_x_coordinates().size()+1;
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this->ptr()->intermediate_values=std::vector<Lazy_bound>();
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this->ptr()->intermediate_slices=std::vector<Lazy_status_line_CPA_1>();
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for(size_type i=0;
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i<=static_cast<size_type>(event_x_coordinates().size());
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i++) {
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this->ptr()->intermediate_values.get().push_back(Lazy_bound());
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this->ptr()->intermediate_slices.get().push_back
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(Lazy_status_line_CPA_1());
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}
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this->ptr()->intermediate_values.get().resize(size);
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this->ptr()->intermediate_slices.get().resize(size);
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#if CGAL_ACK_DEBUG_FLAG
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CGAL_ACK_DEBUG_PRINT << "done" << std::endl;
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#endif
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@ -2209,10 +2209,10 @@ representing line segments.
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A polyline can be constructed given one of the following inputs:
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- <b>A range of \a points</b>, where two succeeding points in the
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- <b>A range of <em>points</em></b>, where two succeeding points in the
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range represent the endpoints of a segment of the polyline.
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- <b>A range of \a segments</b>. Note that , if the types
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- <b>A range of <em>segments</em></b>. Note that , if the types
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`SubcurveTraits_2::Curve_2` and `SubcurveTraits_2::X_monotone_curve_2` are
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not the same, then when `Make_x_monotone_2` is invoked the segments
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that compose the polyline will be broken into \f$x\f$-monotone
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@ -167,7 +167,7 @@ virtual void before_detach ();
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issued immediately after the observer has been detached from its
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arrangement instance.
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*/
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virtual void after_attach ();
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virtual void after_detach ();
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/// @}
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@ -197,7 +197,7 @@ function(run_test_alt name datafile)
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set(command ${name} ${datafile} ${ARGN})
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string(MAKE_C_IDENTIFIER "${name} ${ARGV4} ${ARGV5}" test_name)
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add_test(NAME ${test_name} COMMAND ${command}
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WORKING_DIRECTORY ${CGAL_CURRENT_SOURCE_DIR})
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WORKING_DIRECTORY ${CMAKE_CURRENT_SOURCE_DIR})
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set_property(TEST "${test_name}"
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APPEND PROPERTY DEPENDS "compilation_of__${name}")
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if(POLICY CMP0066) # CMake 3.7 or later
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@ -708,6 +708,7 @@ user might encounter.
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## I/O Functions ##
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- \link PkgBGLIOFct CGAL::read_off() \endlink
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- \link PkgBGLIOFct CGAL::write_off() \endlink
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- \link PkgBGLIOFct CGAL::write_wrl() \endlink
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*/
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Binary file not shown.
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After Width: | Height: | Size: 7.6 KiB |
Binary file not shown.
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After Width: | Height: | Size: 5.7 KiB |
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@ -25,10 +25,10 @@ int main()
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Point_3(1,-1,-1),
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Point_3(1,1,-1),
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Point_3(-1,1,-1),
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Point_3(-1,1,1),
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Point_3(-1,-1,1),
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Point_3(1,-1,1),
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Point_3(1,1,1),
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Point_3(-1,1,1),
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sm
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);
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@ -45,10 +45,10 @@ int main()
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Point_3(0.5,-0.5,-0.5),
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Point_3(0.5,0.5,-0.5),
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Point_3(-0.5,0.5,-0.5),
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Point_3(-0.5,0.5,0.5),
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Point_3(-0.5,-0.5,0.5),
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Point_3(0.5,-0.5,0.5),
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Point_3(0.5,0.5,0.5),
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Point_3(-0.5,0.5,0.5),
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poly
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);
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pvertex_descriptor pvd = * vertices(pmesh).first;
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@ -585,8 +585,16 @@ add_face(const VertexRange& vr, Graph& g)
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std::vector<vertex_descriptor> vertices(vr.begin(), vr.end()); // quick and dirty copy
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unsigned int n = (unsigned int)vertices.size();
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//check that every vertex is unique
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std::sort(vertices.begin(), vertices.end());
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if(std::adjacent_find(vertices.begin(), vertices.end()) != vertices.end()){
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return boost::graph_traits<Graph>::null_face();
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}
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std::copy(vr.begin(), vr.end(), vertices.begin());
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// don't allow degenerated faces
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CGAL_assertion(n > 2);
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if(n <= 2){
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return boost::graph_traits<Graph>::null_face();
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}
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std::vector<halfedge_descriptor> halfedges(n);
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std::vector<bool> is_new(n);
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@ -837,6 +837,8 @@ make_quad(const P& p0, const P& p1, const P& p2, const P& p3, Graph& g)
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* \ingroup PkgBGLHelperFct
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* \brief Creates an isolated hexahedron
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* with its vertices initialized to `p0`, `p1`, ...\ , and `p7`, and adds it to the graph `g`.
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* \image html hexahedron.png
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* \image latex hexahedron.png
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* \returns the halfedge that has the target vertex associated with `p0`, in the face with the vertices with the points `p0`, `p1`, `p2`, and `p3`.
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**/
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template<typename Graph, typename P>
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@ -868,16 +870,16 @@ make_hexahedron(const P& p0, const P& p1, const P& p2, const P& p3,
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ppmap[v6] = p6;
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ppmap[v7] = p7;
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halfedge_descriptor ht = internal::make_quad(v7, v4, v5, v6, g);
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halfedge_descriptor hb = prev(internal::make_quad(v1, v0, v3, v2, g),g);
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halfedge_descriptor ht = internal::make_quad(v4, v5, v6, v7, g);
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halfedge_descriptor hb = prev(internal::make_quad(v0, v3, v2, v1, g),g);
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for(int i=0; i <4; i++){
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halfedge_descriptor h = halfedge(add_edge(g),g);
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set_target(h,target(hb,g),g);
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set_next(h,opposite(hb,g),g);
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set_next(opposite(next(ht,g),g),h,g);
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set_next(opposite(prev(ht,g),g),h,g);
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h = opposite(h,g);
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set_target(h,target(ht,g),g);
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set_next(h,opposite(ht,g),g);
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set_target(h,source(prev(ht,g),g),g);
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set_next(h,opposite(next(next(ht,g),g),g),g);
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set_next(opposite(next(hb,g),g),h,g);
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hb = next(hb,g);
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ht = prev(ht,g);
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@ -892,6 +894,8 @@ make_hexahedron(const P& p0, const P& p1, const P& p2, const P& p3,
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* \ingroup PkgBGLHelperFct
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* \brief Creates an isolated tetrahedron
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* with its vertices initialized to `p0`, `p1`, `p2`, and `p3`, and adds it to the graph `g`.
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* \image html tetrahedron.png
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* \image latex tetrahedron.png
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* \returns the halfedge that has the target vertex associated with `p0`, in the face with the vertices with the points `p0`, `p1`, and `p2`.
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**/
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template<typename Graph, typename P>
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@ -36,6 +36,89 @@
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#include <CGAL/boost/graph/named_function_params.h>
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namespace CGAL {
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/*!
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\ingroup PkgBGLIOFct
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writes the graph `g` in the wrl format (VRML 2.0).
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\cgalNamedParamsBegin
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* \cgalParamBegin{vertex_point_map} the property map with the points associated to the vertices of `g`.
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* If this parameter is omitted, an internal property map for
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* `CGAL::vertex_point_t` should be available in `FaceGraph`\cgalParamEnd
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* \cgalNamedParamsEnd
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*/
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template <typename FaceGraph, typename NamedParameters>
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bool write_wrl(std::ostream& os,
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const FaceGraph& g,
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const NamedParameters& np)
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{
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typedef typename boost::graph_traits<FaceGraph>::vertex_descriptor vertex_descriptor;
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typedef typename boost::graph_traits<FaceGraph>::face_descriptor face_descriptor;
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typedef typename boost::graph_traits<FaceGraph>::vertices_size_type vertices_size_type;
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typename Polygon_mesh_processing::GetVertexPointMap<FaceGraph, NamedParameters>::const_type
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vpm = choose_param(get_param(np, internal_np::vertex_point),
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get_const_property_map(CGAL::vertex_point, g));
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boost::container::flat_map<vertex_descriptor,vertices_size_type> reindex;
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int n = 0;
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os << "#VRML V2.0 utf8\n"
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"Group {\n"
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"children [\n"
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"Shape {\n"
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"appearance DEF A1 Appearance {\n"
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"material Material {\n"
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"diffuseColor .6 .5 .9\n"
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"}\n"
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"}\n"
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"appearance\n"
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"Appearance {\n"
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"material DEF Material Material {}\n"
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"}\n"
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"}\n"
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"Group {\n"
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"children [\n"
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"Shape {\n"
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"appearance Appearance { material USE Material }\n"
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"geometry IndexedFaceSet {\n"
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"convex FALSE\n"
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"solid FALSE\n"
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"coord Coordinate {\n"
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"point [\n";
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BOOST_FOREACH(vertex_descriptor v, vertices(g)){
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os << get(vpm,v) << ",\n";
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reindex[v]=n++;
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}
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os << "] #point\n"
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"} #coord Coordinate\n"
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"coordIndex [\n";
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BOOST_FOREACH(face_descriptor f, faces(g)){
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BOOST_FOREACH(vertex_descriptor v, vertices_around_face(halfedge(f,g),g)){
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os << reindex[v] << ",";
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}
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os << "-1,\n";
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}
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os << "] #coordIndex\n"
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"} #geometry\n"
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"} #Shape\n"
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"] #children\n"
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"} #group\n"
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"]\n"
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"}\n";
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return os.good();
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}
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template <typename FaceGraph>
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bool write_wrl(std::ostream& os,
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const FaceGraph& g)
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{
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return write_wrl(os, g,
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parameters::all_default());
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}
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/*!
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\ingroup PkgBGLIOFct
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writes the graph `g` in the OFF format.
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|
|
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@ -97,6 +97,8 @@ create_single_source_cgal_program( "test_graph_traits.cpp" )
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create_single_source_cgal_program( "test_Properties.cpp" )
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create_single_source_cgal_program( "test_wrl.cpp" )
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if(OpenMesh_FOUND)
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target_link_libraries( test_clear PRIVATE ${OPENMESH_LIBRARIES})
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target_link_libraries( test_Euler_operations PRIVATE ${OPENMESH_LIBRARIES})
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|
|
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@ -132,7 +132,7 @@ int main()
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assert(CGAL::is_triangle_mesh(m));
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assert(CGAL::is_valid_polygon_mesh(m));
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m.clear();
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hd = CGAL::make_hexahedron(a,b,c,d,aa,bb,cc,dd,m);
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hd = CGAL::make_hexahedron(a,b,c,d,dd,aa,bb,cc,m);
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assert(CGAL::is_hexahedron(hd,m));
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assert(CGAL::is_quad_mesh(m));
|
||||
assert(CGAL::is_valid_polygon_mesh(m));
|
||||
|
|
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|||
|
|
@ -0,0 +1,18 @@
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|||
#include <CGAL/Simple_cartesian.h>
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||||
#include <CGAL/Surface_mesh.h>
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||||
#include <CGAL/boost/graph/helpers.h>
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||||
#include <CGAL/boost/graph/io.h>
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||||
#include <iostream>
|
||||
|
||||
typedef CGAL::Simple_cartesian<double> Kernel;
|
||||
typedef Kernel::Point_3 Point;
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||||
typedef CGAL::Surface_mesh<Point> Mesh;
|
||||
|
||||
int main()
|
||||
{
|
||||
Mesh sm;
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||||
|
||||
CGAL::make_tetrahedron(Point(0,0,0), Point(1,0,0), Point(1,1,0), Point(0,0,1), sm);
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CGAL::write_wrl(std::cout, sm);
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||||
return 0;
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||||
}
|
||||
|
|
@ -74,7 +74,7 @@ polygon vertices is referred to as the polygon <B>(outer) boundary</B>.
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|||
|
||||
<LI>A polygon whose curves are pairwise disjoint in their interior, and whose vertices' degree equals two is defined as a <B>Simple polygon</B>. Such a polygon has a well-defined interior and exterior and is topologically equivalent to a disk. Note that while traversing the edges of the relatively simple polygon illustrated above (B), no curve is crossed over.
|
||||
|
||||
<LI>A <B>Relatively simple</B> polygon allows vertices with a degree\f$\gt 2\f$, but all of its edges are disjoint in their interior. Furthermore, it must be an orientable polygon. Namely when it is inserted into an arrangement and its outer boundary is traversed, the same face is adjacent to all of the halfedges (no crossing over any curve during the traversal).
|
||||
<LI>A <B>Relatively simple</B> polygon allows vertices with a degree\f$> 2\f$, but all of its edges are disjoint in their interior. Furthermore, it must be an orientable polygon. Namely when it is inserted into an arrangement and its outer boundary is traversed, the same face is adjacent to all of the halfedges (no crossing over any curve during the traversal).
|
||||
Note that while polygon C has the same curves as polygon B, traversal of the curves leads to crossing over a previously traversed curve, and is therefore neither simple nor relatively simple.
|
||||
|
||||
<LI>A polygon in our context must be relatively simple and its outer boundary vertices must be ordered in a counterclockwise direction around the interior of the polygon.
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||||
|
|
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|||
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@ -13,28 +13,28 @@ x\in\E^d \mid x^T E x + x^T e + \eta\leq 0 \}\f$, where \f$ E\f$ is some
|
|||
positive definite matrix from the set \f$ \mathbb{R}^{d\times d}\f$, \f$ e\f$ is some
|
||||
real \f$ d\f$-vector, and \f$ \eta\in\mathbb{R}\f$. A pointset \f$ P\subseteq \E^d\f$ is
|
||||
called <I>full-dimensional</I> if its affine hull has dimension \f$ d\f$.
|
||||
For a finite, full-dimensional pointset \f$ P\f$ we denote by \f$ \mel(P)\f$ the
|
||||
For a finite, full-dimensional pointset \f$ P\f$ we denote by \f$ (P)\f$ the
|
||||
smallest ellipsoid that contains all points of \f$ P\f$; this ellipsoid
|
||||
exists and is unique.
|
||||
|
||||
For a given finite and full-dimensional pointset \f$ P\subset \E^d\f$ and a
|
||||
real number \f$ \epsilon\ge 0\f$, we say that an ellipsoid \f$ {\cal
|
||||
E}\subset\E^d\f$ is an <I>\f$ (1+\epsilon)\f$-appoximation</I> to \f$ \mel(P)\f$ if
|
||||
\f$ P\subset {\cal E}\f$ and \f$ \vol({\cal E}) \leq (1+\epsilon)
|
||||
\vol(\mel(P))\f$. In other words, an \f$ (1+\epsilon)\f$-approximation to
|
||||
\f$ \mel(P)\f$ is an enclosing ellipsoid whose volume is by at most a
|
||||
E}\subset\E^d\f$ is an <I>\f$ (1+\epsilon)\f$-appoximation</I> to \f$ (P)\f$ if
|
||||
\f$ P\subset {\cal E}\f$ and \f$ ({\cal E}) \leq (1+\epsilon)
|
||||
((P))\f$. In other words, an \f$ (1+\epsilon)\f$-approximation to
|
||||
\f$ (P)\f$ is an enclosing ellipsoid whose volume is by at most a
|
||||
factor of \f$ 1+\epsilon\f$ larger than the volume of the smallest
|
||||
enclosing ellipsoid of \f$ P\f$.
|
||||
|
||||
Given this notation, an object of class `Approximate_min_ellipsoid_d` represents an
|
||||
\f$ (1+\epsilon)\f$-approximation to \f$ \mel(P)\f$ for a given finite and
|
||||
\f$ (1+\epsilon)\f$-approximation to \f$ (P)\f$ for a given finite and
|
||||
full-dimensional multiset of points \f$ P\subset\E^d\f$ and a real constant
|
||||
\f$ \epsilon>0\f$.\cgalFootnote{A <I>multiset</I> is a set where elements may have multiplicity greater than \f$ 1\f$.} When an
|
||||
`Approximate_min_ellipsoid_d<Traits>` object is constructed, an
|
||||
iterator over the points \f$ P\f$ and the number \f$ \epsilon\f$ have to be
|
||||
specified; the number \f$ \epsilon\f$ defines the <I>desired
|
||||
approximation ratio</I> \f$ 1+\epsilon\f$. The underlying algorithm will then
|
||||
try to compute an \f$ (1+\epsilon)\f$-approximation to \f$ \mel(P)\f$, and one of
|
||||
try to compute an \f$ (1+\epsilon)\f$-approximation to \f$ (P)\f$, and one of
|
||||
the following two cases takes place.
|
||||
<UL>
|
||||
<LI>The algorithm determines that \f$ P\f$ is not full-dimensional (see
|
||||
|
|
@ -44,7 +44,7 @@ the following two cases takes place.
|
|||
in all cases decide correctly whether \f$ P\f$ is full-dimensional or
|
||||
not. If `is_full_dimensional()` returns `false`, the points
|
||||
lie in such a "thin" subspace of \f$ \E^d\f$ that the algorithm is
|
||||
incapable of computing an approximation to \f$ \mel(P)\f$. More
|
||||
incapable of computing an approximation to \f$ (P)\f$. More
|
||||
precisely, if `is_full_dimensional()` returns `false`, there
|
||||
exist two parallel hyperplanes in \f$ \E^d\f$ with the points \f$ P\f$ in
|
||||
between so that the distance \f$ \delta\f$ between the hyperplanes is
|
||||
|
|
@ -55,7 +55,7 @@ If \f$ P\f$ is not full-dimensional, linear algebra techniques should be
|
|||
used to determine an affine subspace \f$ S\f$ of \f$ \E^d\f$ that contains the
|
||||
points \f$ P\f$ as a (w.r.t.\ \f$ S\f$) full-dimensional pointset; once \f$ S\f$ is
|
||||
determined, the algorithm can be invoked again to compute an
|
||||
approximation to (the lower-dimensional) \f$ \mel(P)\f$ in \f$ S\f$. Since
|
||||
approximation to (the lower-dimensional) \f$ (P)\f$ in \f$ S\f$. Since
|
||||
`is_full_dimensional()` might (due to rounding errors, see
|
||||
above) return `false` even though \f$ P\f$ is full-dimensional, the
|
||||
lower-dimensional subspace \f$ S\f$ containing \f$ P\f$ need not exist.
|
||||
|
|
@ -66,7 +66,7 @@ ellipsoid of the projected points within \f$ H\f$; the fitting can be
|
|||
done for instance using the `linear_least_squares_fitting()`
|
||||
function from the \cgal package `Principal_component_analysis`.
|
||||
<LI>The algorithm determines that \f$ P\f$ is full-dimensional. In this
|
||||
case, it provides an approximation \f$ {\cal E}\f$ to \f$ \mel(P)\f$, but
|
||||
case, it provides an approximation \f$ {\cal E}\f$ to \f$ (P)\f$, but
|
||||
depending on the input problem (i.e., on the pair \f$ (P,\epsilon)\f$),
|
||||
it may not have achieved the desired approximation ratio but merely
|
||||
some <I>worse</I> approximation ratio \f$ 1+\epsilon'>1+\epsilon\f$. The
|
||||
|
|
@ -126,7 +126,7 @@ Cholesky-decomposition. The algorithm's running time is
|
|||
|
||||
To illustrate the usage of `Approximate_min_ellipsoid_d` we give two examples in 2D. The
|
||||
first program generates a random set \f$ P\subset\E^2\f$ and outputs the
|
||||
points and a \f$ 1.01\f$-approximation of \f$ \mel(P)\f$ as an EPS-file, which
|
||||
points and a \f$ 1.01\f$-approximation of \f$ (P)\f$ as an EPS-file, which
|
||||
you can view using <TT>gv</TT>, for instance. (In both examples you can
|
||||
change the variables `n` and `d` to experiment with the code.)
|
||||
|
||||
|
|
@ -204,7 +204,7 @@ typedef unspecified_type Axis_direction_iterator;
|
|||
/*!
|
||||
|
||||
initializes `ame` to an \f$ (1+\epsilon)\f$-approximation of
|
||||
\f$ \mel(P)\f$ with \f$ P\f$ being the set of points in the range
|
||||
\f$ (P)\f$ with \f$ P\f$ being the set of points in the range
|
||||
[`first`,`last`). The number \f$ \epsilon\f$ in this will
|
||||
be at most `eps`, if possible. However, due to the
|
||||
limited precision in the algorithm's underlying arithmetic, it
|
||||
|
|
@ -260,7 +260,7 @@ unsigned int number_of_points( ) const;
|
|||
returns a number
|
||||
\f$ \epsilon'\f$ such that the computed approximation is (under exact
|
||||
arithmetic) guaranteed to be an \f$ (1+\epsilon')\f$-approximation to
|
||||
\f$ \mel(P)\f$.
|
||||
\f$ (P)\f$.
|
||||
\pre `ame.is_full_dimensional() == true`.
|
||||
\post \f$ \epsilon'>0\f$.
|
||||
*/
|
||||
|
|
@ -404,7 +404,7 @@ bool is_full_dimensional( ) const;
|
|||
/// An object `ame` is valid iff <UL> <LI>`ame` contains all points of
|
||||
/// its defining set \f$ P\f$, <LI>`ame` is an \f$
|
||||
/// (1+\epsilon')\f$-approximation to the smallest ellipsoid \f$
|
||||
/// \mel(P)\f$ of \f$ P\f$, <LI>The ellipsoid represented by `ame`
|
||||
/// (P)\f$ of \f$ P\f$, <LI>The ellipsoid represented by `ame`
|
||||
/// fulfills the inclusion ( \ref eqapproximate_min_ellipsoid_incl
|
||||
/// ). </UL>
|
||||
/// @{
|
||||
|
|
@ -426,7 +426,7 @@ bool is_valid( bool verbose = false) const;
|
|||
/*!
|
||||
|
||||
Writes the points \f$ P\f$ and the computed approximation to
|
||||
\f$ \mel(P)\f$ as an EPS-file under pathname `name`. \pre The dimension of points \f$ P\f$ must be \f$ 2\f$.
|
||||
\f$ (P)\f$ as an EPS-file under pathname `name`. \pre The dimension of points \f$ P\f$ must be \f$ 2\f$.
|
||||
<I>Note:</I> this
|
||||
routine is provided as a debugging routine; future version of
|
||||
\cgal might not provide it anymore.
|
||||
|
|
|
|||
|
|
@ -360,7 +360,20 @@ class Min_ellipse_2 {
|
|||
|
||||
// default constructor
|
||||
inline
|
||||
Min_ellipse_2( const Traits& traits = Traits())
|
||||
Min_ellipse_2()
|
||||
: n_support_points( 0)
|
||||
{
|
||||
// allocate support points' array
|
||||
support_points = new Point[ 5];
|
||||
|
||||
// initialize ellipse
|
||||
tco.ellipse.set();
|
||||
|
||||
CGAL_optimisation_postcondition( is_empty());
|
||||
}
|
||||
|
||||
inline
|
||||
Min_ellipse_2( const Traits& traits )
|
||||
: tco( traits), n_support_points( 0)
|
||||
{
|
||||
// allocate support points' array
|
||||
|
|
|
|||
|
|
@ -168,7 +168,7 @@ unsigned int ImageIO_limit_len(size_t to_be_read)
|
|||
CGAL_INLINE_FUNCTION
|
||||
size_t ImageIO_write(const _image *im, const void *buf, size_t len) {
|
||||
size_t to_be_written = len;
|
||||
int l = -1;
|
||||
std::ptrdiff_t l = -1;
|
||||
char *b = (char*)buf;
|
||||
|
||||
switch(im->openMode) {
|
||||
|
|
|
|||
|
|
@ -63,6 +63,7 @@ read_vtk_image_data(vtkImageData* vtk_image)
|
|||
_image* image = ::_initImage();
|
||||
const int* dims = vtk_image->GetDimensions();
|
||||
const double* spacing = vtk_image->GetSpacing();
|
||||
const double* offset = vtk_image->GetOrigin();
|
||||
image->vectMode = VM_SCALAR;
|
||||
image->xdim = dims[0];
|
||||
image->ydim = dims[1];
|
||||
|
|
@ -71,6 +72,9 @@ read_vtk_image_data(vtkImageData* vtk_image)
|
|||
image->vx = spacing[0];
|
||||
image->vy = spacing[1];
|
||||
image->vz = spacing[2];
|
||||
image->tx = offset[0];
|
||||
image->ty = offset[1];
|
||||
image->tz = offset[2];
|
||||
image->endianness = ::_getEndianness();
|
||||
int vtk_type = vtk_image->GetScalarType();
|
||||
if(vtk_type == VTK_SIGNED_CHAR) vtk_type = VTK_CHAR;
|
||||
|
|
|
|||
|
|
@ -28,6 +28,7 @@
|
|||
|
||||
#include <CGAL/determinant.h>
|
||||
#include <CGAL/number_utils.h>
|
||||
#include <boost/type_traits/is_integral.hpp>
|
||||
|
||||
namespace CGAL {
|
||||
|
||||
|
|
@ -284,7 +285,16 @@ line_get_pointC2(const FT &a, const FT &b, const FT &c, int i,
|
|||
{
|
||||
if (CGAL_NTS is_zero(b))
|
||||
{
|
||||
x = (-b-c)/a + i * b;
|
||||
// Laurent Rineau, 2018/12/07: I add this CGAL_assume to calm
|
||||
// down a warning from MSVC 2017:
|
||||
// > include\cgal\constructions\kernel_ftc2.h(287) :
|
||||
// > warning C4723: potential divide by 0
|
||||
// The test `!boost::is_integral<FT>::value` is there to avoid
|
||||
// that `a != 0` is tested on anything but integral types, for
|
||||
// performance reasons.
|
||||
CGAL_assume(!boost::is_integral<FT>::value || a != FT(0));
|
||||
|
||||
x = -c/a;
|
||||
y = 1 - i * a;
|
||||
}
|
||||
else
|
||||
|
|
|
|||
|
|
@ -38,6 +38,7 @@
|
|||
# pragma warning(disable:4267)
|
||||
# pragma warning(disable:4275)
|
||||
# pragma warning(disable:4251)
|
||||
# pragma warning(disable:4996)
|
||||
#endif
|
||||
|
||||
#include <CGAL/Classification/internal/auxiliary/random-forest/node-gini.hpp>
|
||||
|
|
|
|||
|
|
@ -93,7 +93,7 @@ function(configure_doxygen_package CGAL_PACKAGE_NAME)
|
|||
file(APPEND ${CGAL_DOC_PACKAGE_DEFAULTS} "STRIP_FROM_INC_PATH = ${CGAL_PACKAGE_DOC_DIR}/\n")
|
||||
file(APPEND ${CGAL_DOC_PACKAGE_DEFAULTS} "STRIP_FROM_INC_PATH += ${CGAL_PACKAGE_DIR}/include/\n")
|
||||
file(APPEND ${CGAL_DOC_PACKAGE_DEFAULTS} "ALIASES += \"cgalPkgDescriptionBegin{2}=\\details \"\n")
|
||||
file(APPEND ${CGAL_DOC_PACKAGE_DEFAULTS} "ALIASES += \"cgalPkgManuals{2}=<BR>\"\n")
|
||||
file(APPEND ${CGAL_DOC_PACKAGE_DEFAULTS} "ALIASES += \"cgalPkgManuals{2}=<div class=\\\"PkgManuals\\\"></div>\"\n")
|
||||
file(APPEND ${CGAL_DOC_PACKAGE_DEFAULTS} "INPUT = ${CGAL_PACKAGE_DOC_DIR}\n")
|
||||
if(NOT EXISTS "${CGAL_PACKAGE_DOC_DIR}/CGAL")
|
||||
# This package has in-source documentation.
|
||||
|
|
|
|||
|
|
@ -250,9 +250,9 @@ ALIASES = "sc{1}=<span style=\"font-variant: small-caps;\">\1</sp
|
|||
"cgalFigureBegin{8}=\anchor fig__\1 \n <CENTER> <TABLE border=0> <TR> <TD> \image html \2 \n \image latex \2 \"\" width=2.1cm \n </TD> <TD> \image html \3 \n \image latex \3 \"\" width=2.1cm \n </TD> <TD> \image html \4 \n \image latex \4 \"\" width=2.1cm \n </TD> <TD> \image html \5 \n \image latex \5 \"\" width=2.1cm \n </TD> <TD> \image html \6 \n \image latex \6 \"\" width=2.1cm \n </TD> <TD> \image html \7 \n \image latex \7 \"\" width=2.1cm \n </TD> <TD> \image html \8 \n \image latex \8 \"\" width=2.1cm \n </TD> </TR> </TABLE> </CENTER> \htmlonly <div class=\"cgal_figure_caption\"> \endhtmlonly \n \latexonly \n \endlatexonly \ref fig__\1" \
|
||||
"cgalFigureBegin{9}=\anchor fig__\1 \n <CENTER> <TABLE border=0> <TR> <TD> \image html \2 \n \image latex \2 \"\" width=1.9cm \n </TD> <TD> \image html \3 \n \image latex \3 \"\" width=1.9cm \n </TD> <TD> \image html \4 \n \image latex \4 \"\" width=1.9cm \n </TD> <TD> \image html \5 \n \image latex \5 \"\" width=1.9cm \n </TD> <TD> \image html \6 \n \image latex \6 \"\" width=1.9cm \n </TD> <TD> \image html \7 \n \image latex \7 \"\" width=1.9cm \n </TD> <TD> \image html \8 \n \image latex \8 \"\" width=1.9cm \n </TD> <TD> \image html \9 \n \image latex \9 \"\" width=1.9cm \n </TD> </TR> </TABLE> </CENTER> \htmlonly <div class=\"cgal_figure_caption\"> \endhtmlonly \n \latexonly \n \endlatexonly \ref fig__\1" \
|
||||
"cgalFigureBegin{10}=\anchor fig__\1 \n <CENTER> <TABLE border=0> <TR> <TD> \image html \2 \n \image latex \2 \"\" width=1.6cm \n </TD> <TD> \image html \3 \n \image latex \3 \"\" width=1.6cm \n </TD> <TD> \image html \4 \n \image latex \4 \"\" width=1.6cm \n </TD> <TD> \image html \5 \n \image latex \5 \"\" width=1.6cm \n </TD> <TD> \image html \6 \n \image latex \6 \"\" width=1.6cm \n </TD> <TD> \image html \7 \n \image latex \7 \"\" width=1.6cm \n </TD> <TD> \image html \8 \n \image latex \8 \"\" width=1.6cm \n </TD> <TD> \image html \9 \n \image latex \9 \"\" width=1.6cm \n </TD> <TD> \image html \10 \n \image latex \10 \"\" width=1.6cm \n </TD> </TR> </TABLE> </CENTER> \htmlonly <div class=\"cgal_figure_caption\"> \endhtmlonly \n \latexonly \n \endlatexonly \ref fig__\1" \
|
||||
"cgalFigureEnd=\htmlonly </div> \endhtmlonly <br>" \
|
||||
"cgalFigureEnd=\htmlonly </div> <br> \endhtmlonly" \
|
||||
"cgalFigureCaptionBegin{1}=\htmlonly <div class=\"cgal_figure_caption\"> \endhtmlonly \ref fig__\1" \
|
||||
"cgalFigureCaptionEnd=\htmlonly </div> \endhtmlonly <br>" \
|
||||
"cgalFigureCaptionEnd=\htmlonly </div> <br> \endhtmlonly" \
|
||||
"cgalConcept=\details <div id=\"CGALConcept\"></div>\n \brief" \
|
||||
"cgalConceptNamespace=\details <div id=\"CGALConceptNS\"></div>\n \brief" \
|
||||
"cgalRefines=\xrefitem refines \"Refines\" \"Refinement Relationships\"" \
|
||||
|
|
|
|||
|
|
@ -1,4 +1,4 @@
|
|||
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
|
||||
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "https://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
|
||||
<html xmlns="http://www.w3.org/1999/xhtml">
|
||||
<head>
|
||||
<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
|
||||
|
|
|
|||
|
|
@ -1,5 +1,5 @@
|
|||
<!-- HTML header for doxygen 1.8.13-->
|
||||
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
|
||||
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "https://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
|
||||
<html xmlns="http://www.w3.org/1999/xhtml">
|
||||
<head>
|
||||
<link rel="icon" type="image/png" href="$relpath$../Manual/g-196x196-doc.png"/>
|
||||
|
|
|
|||
|
|
@ -1,5 +1,5 @@
|
|||
<!-- HTML header for doxygen 1.8.13-->
|
||||
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
|
||||
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "https://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
|
||||
<html xmlns="http://www.w3.org/1999/xhtml">
|
||||
<head>
|
||||
<link rel="icon" type="image/png" href="$relpath$../Manual/g-196x196-doc.png" />
|
||||
|
|
|
|||
|
|
@ -242,29 +242,29 @@ ALIASES = "sc{1}=<span style=\"font-variant: small-caps;\">\1</sp
|
|||
"cgalExample{1}=<br><b>File</b> \ref \1 \include \1" \
|
||||
"cgalFigureAnchor{1}=\anchor fig__\1" \
|
||||
"cgalFigureRef{1}=\ref fig__\1" \
|
||||
"cgalFigureBegin{2}=\anchor fig__\1 ^^ \image html \2 ^^ \image latex \2 \"\" width=15cm ^^ \htmlonly <div class=\"cgal_figure_caption\"> \endhtmlonly \latexonly ^^ \endlatexonly ^^ \ref fig__\1" \
|
||||
"cgalFigureBegin{3}=\anchor fig__\1 ^^ <CENTER> <TABLE border=0> <TR> <TD> \image html \2 ^^ \image latex \2 \"\" width=7.5cm ^^ </TD> <TD> \image html \3 ^^ \image latex \3 \"\" width=7.5cm ^^ </TD> </TR> </TABLE> </CENTER> \htmlonly <div class=\"cgal_figure_caption\"> \endhtmlonly ^^ \latexonly ^^ \endlatexonly \ref fig__\1" \
|
||||
"cgalFigureBegin{4}=\anchor fig__\1 ^^ <CENTER> <TABLE border=0> <TR> <TD> \image html \2 ^^ \image latex \2 \"\" width=5cm ^^ </TD> <TD> \image html \3 ^^ \image latex \3 \"\" width=5cm ^^ </TD> <TD> \image html \4 ^^ \image latex \4 \"\" width=5cm ^^ </TD> </TR> </TABLE> </CENTER> \htmlonly <div class=\"cgal_figure_caption\"> \endhtmlonly ^^ \latexonly ^^ \endlatexonly \ref fig__\1" \
|
||||
"cgalFigureBegin{5}=\anchor fig__\1 ^^ <CENTER> <TABLE border=0> <TR> <TD> \image html \2 ^^ \image latex \2 \"\" width=3.75cm ^^ </TD> <TD> \image html \3 ^^ \image latex \3 \"\" width=3.75cm ^^ </TD> <TD> \image html \4 ^^ \image latex \4 \"\" width=3.75cm ^^ </TD> <TD> \image html \5 ^^ \image latex \5 \"\" width=3.75cm ^^ </TD> </TR> </TABLE> </CENTER> \htmlonly <div class=\"cgal_figure_caption\"> \endhtmlonly ^^ \latexonly ^^ \endlatexonly \ref fig__\1" \
|
||||
"cgalFigureBegin{6}=\anchor fig__\1 ^^ <CENTER> <TABLE border=0> <TR> <TD> \image html \2 ^^ \image latex \2 \"\" width=3cm ^^ </TD> <TD> \image html \3 ^^ \image latex \3 \"\" width=3cm ^^ </TD> <TD> \image html \4 ^^ \image latex \4 \"\" width=3cm ^^ </TD> <TD> \image html \5 ^^ \image latex \5 \"\" width=3cm ^^ </TD> <TD> \image html \6 ^^ \image latex \6 \"\" width=3cm ^^ </TD> </TR> </TABLE> </CENTER> \htmlonly <div class=\"cgal_figure_caption\"> \endhtmlonly ^^ \latexonly ^^ \endlatexonly \ref fig__\1" \
|
||||
"cgalFigureBegin{7}=\anchor fig__\1 ^^ <CENTER> <TABLE border=0> <TR> <TD> \image html \2 ^^ \image latex \2 \"\" width=2.5cm ^^ </TD> <TD> \image html \3 ^^ \image latex \3 \"\" width=2.5cm ^^ </TD> <TD> \image html \4 ^^ \image latex \4 \"\" width=2.5cm ^^ </TD> <TD> \image html \5 ^^ \image latex \5 \"\" width=2.5cm ^^ </TD> <TD> \image html \6 ^^ \image latex \6 \"\" width=2.5cm ^^ </TD> <TD> \image html \7 ^^ \image latex \7 \"\" width=2.5cm ^^ </TD> </TR> </TABLE> </CENTER> \htmlonly <div class=\"cgal_figure_caption\"> \endhtmlonly ^^ \latexonly ^^ \endlatexonly \ref fig__\1" \
|
||||
"cgalFigureBegin{8}=\anchor fig__\1 ^^ <CENTER> <TABLE border=0> <TR> <TD> \image html \2 ^^ \image latex \2 \"\" width=2.1cm ^^ </TD> <TD> \image html \3 ^^ \image latex \3 \"\" width=2.1cm ^^ </TD> <TD> \image html \4 ^^ \image latex \4 \"\" width=2.1cm ^^ </TD> <TD> \image html \5 ^^ \image latex \5 \"\" width=2.1cm ^^ </TD> <TD> \image html \6 ^^ \image latex \6 \"\" width=2.1cm ^^ </TD> <TD> \image html \7 ^^ \image latex \7 \"\" width=2.1cm ^^ </TD> <TD> \image html \8 ^^ \image latex \8 \"\" width=2.1cm ^^ </TD> </TR> </TABLE> </CENTER> \htmlonly <div class=\"cgal_figure_caption\"> \endhtmlonly ^^ \latexonly ^^ \endlatexonly \ref fig__\1" \
|
||||
"cgalFigureBegin{9}=\anchor fig__\1 ^^ <CENTER> <TABLE border=0> <TR> <TD> \image html \2 ^^ \image latex \2 \"\" width=1.9cm ^^ </TD> <TD> \image html \3 ^^ \image latex \3 \"\" width=1.9cm ^^ </TD> <TD> \image html \4 ^^ \image latex \4 \"\" width=1.9cm ^^ </TD> <TD> \image html \5 ^^ \image latex \5 \"\" width=1.9cm ^^ </TD> <TD> \image html \6 ^^ \image latex \6 \"\" width=1.9cm ^^ </TD> <TD> \image html \7 ^^ \image latex \7 \"\" width=1.9cm ^^ </TD> <TD> \image html \8 ^^ \image latex \8 \"\" width=1.9cm ^^ </TD> <TD> \image html \9 ^^ \image latex \9 \"\" width=1.9cm ^^ </TD> </TR> </TABLE> </CENTER> \htmlonly <div class=\"cgal_figure_caption\"> \endhtmlonly ^^ \latexonly ^^ \endlatexonly \ref fig__\1" \
|
||||
"cgalFigureBegin{10}=\anchor fig__\1 ^^ <CENTER> <TABLE border=0> <TR> <TD> \image html \2 ^^ \image latex \2 \"\" width=1.6cm ^^ </TD> <TD> \image html \3 ^^ \image latex \3 \"\" width=1.6cm ^^ </TD> <TD> \image html \4 ^^ \image latex \4 \"\" width=1.6cm ^^ </TD> <TD> \image html \5 ^^ \image latex \5 \"\" width=1.6cm ^^ </TD> <TD> \image html \6 ^^ \image latex \6 \"\" width=1.6cm ^^ </TD> <TD> \image html \7 ^^ \image latex \7 \"\" width=1.6cm ^^ </TD> <TD> \image html \8 ^^ \image latex \8 \"\" width=1.6cm ^^ </TD> <TD> \image html \9 ^^ \image latex \9 \"\" width=1.6cm ^^ </TD> <TD> \image html \10 ^^ \image latex \10 \"\" width=1.6cm ^^ </TD> </TR> </TABLE> </CENTER> \htmlonly <div class=\"cgal_figure_caption\"> \endhtmlonly ^^ \latexonly ^^ \endlatexonly \ref fig__\1" \
|
||||
"cgalFigureEnd=\htmlonly </div> \endhtmlonly <br>" \
|
||||
"cgalFigureCaptionBegin{1}=\htmlonly <div class=\"cgal_figure_caption\"> \endhtmlonly \ref fig__\1" \
|
||||
"cgalFigureCaptionEnd=\htmlonly </div> \endhtmlonly <br>" \
|
||||
"cgalFigureBegin{2}=\anchor fig__\1 ^^ \image html \2 ^^ \image latex \2 \"\" width=15cm ^^ \htmlonly[block] <div class=\"cgal_figure_caption\"> \endhtmlonly \latexonly ^^ \endlatexonly ^^ \ref fig__\1" \
|
||||
"cgalFigureBegin{3}=\anchor fig__\1 ^^ <CENTER> <TABLE border=0> <TR> <TD> \image html \2 ^^ \image latex \2 \"\" width=7.5cm ^^ </TD> <TD> \image html \3 ^^ \image latex \3 \"\" width=7.5cm ^^ </TD> </TR> </TABLE> </CENTER> \htmlonly[block] <div class=\"cgal_figure_caption\"> \endhtmlonly ^^ \latexonly ^^ \endlatexonly \ref fig__\1" \
|
||||
"cgalFigureBegin{4}=\anchor fig__\1 ^^ <CENTER> <TABLE border=0> <TR> <TD> \image html \2 ^^ \image latex \2 \"\" width=5cm ^^ </TD> <TD> \image html \3 ^^ \image latex \3 \"\" width=5cm ^^ </TD> <TD> \image html \4 ^^ \image latex \4 \"\" width=5cm ^^ </TD> </TR> </TABLE> </CENTER> \htmlonly[block] <div class=\"cgal_figure_caption\"> \endhtmlonly ^^ \latexonly ^^ \endlatexonly \ref fig__\1" \
|
||||
"cgalFigureBegin{5}=\anchor fig__\1 ^^ <CENTER> <TABLE border=0> <TR> <TD> \image html \2 ^^ \image latex \2 \"\" width=3.75cm ^^ </TD> <TD> \image html \3 ^^ \image latex \3 \"\" width=3.75cm ^^ </TD> <TD> \image html \4 ^^ \image latex \4 \"\" width=3.75cm ^^ </TD> <TD> \image html \5 ^^ \image latex \5 \"\" width=3.75cm ^^ </TD> </TR> </TABLE> </CENTER> \htmlonly[block] <div class=\"cgal_figure_caption\"> \endhtmlonly ^^ \latexonly ^^ \endlatexonly \ref fig__\1" \
|
||||
"cgalFigureBegin{6}=\anchor fig__\1 ^^ <CENTER> <TABLE border=0> <TR> <TD> \image html \2 ^^ \image latex \2 \"\" width=3cm ^^ </TD> <TD> \image html \3 ^^ \image latex \3 \"\" width=3cm ^^ </TD> <TD> \image html \4 ^^ \image latex \4 \"\" width=3cm ^^ </TD> <TD> \image html \5 ^^ \image latex \5 \"\" width=3cm ^^ </TD> <TD> \image html \6 ^^ \image latex \6 \"\" width=3cm ^^ </TD> </TR> </TABLE> </CENTER> \htmlonly[block] <div class=\"cgal_figure_caption\"> \endhtmlonly ^^ \latexonly ^^ \endlatexonly \ref fig__\1" \
|
||||
"cgalFigureBegin{7}=\anchor fig__\1 ^^ <CENTER> <TABLE border=0> <TR> <TD> \image html \2 ^^ \image latex \2 \"\" width=2.5cm ^^ </TD> <TD> \image html \3 ^^ \image latex \3 \"\" width=2.5cm ^^ </TD> <TD> \image html \4 ^^ \image latex \4 \"\" width=2.5cm ^^ </TD> <TD> \image html \5 ^^ \image latex \5 \"\" width=2.5cm ^^ </TD> <TD> \image html \6 ^^ \image latex \6 \"\" width=2.5cm ^^ </TD> <TD> \image html \7 ^^ \image latex \7 \"\" width=2.5cm ^^ </TD> </TR> </TABLE> </CENTER> \htmlonly[block] <div class=\"cgal_figure_caption\"> \endhtmlonly ^^ \latexonly ^^ \endlatexonly \ref fig__\1" \
|
||||
"cgalFigureBegin{8}=\anchor fig__\1 ^^ <CENTER> <TABLE border=0> <TR> <TD> \image html \2 ^^ \image latex \2 \"\" width=2.1cm ^^ </TD> <TD> \image html \3 ^^ \image latex \3 \"\" width=2.1cm ^^ </TD> <TD> \image html \4 ^^ \image latex \4 \"\" width=2.1cm ^^ </TD> <TD> \image html \5 ^^ \image latex \5 \"\" width=2.1cm ^^ </TD> <TD> \image html \6 ^^ \image latex \6 \"\" width=2.1cm ^^ </TD> <TD> \image html \7 ^^ \image latex \7 \"\" width=2.1cm ^^ </TD> <TD> \image html \8 ^^ \image latex \8 \"\" width=2.1cm ^^ </TD> </TR> </TABLE> </CENTER> \htmlonly[block] <div class=\"cgal_figure_caption\"> \endhtmlonly ^^ \latexonly ^^ \endlatexonly \ref fig__\1" \
|
||||
"cgalFigureBegin{9}=\anchor fig__\1 ^^ <CENTER> <TABLE border=0> <TR> <TD> \image html \2 ^^ \image latex \2 \"\" width=1.9cm ^^ </TD> <TD> \image html \3 ^^ \image latex \3 \"\" width=1.9cm ^^ </TD> <TD> \image html \4 ^^ \image latex \4 \"\" width=1.9cm ^^ </TD> <TD> \image html \5 ^^ \image latex \5 \"\" width=1.9cm ^^ </TD> <TD> \image html \6 ^^ \image latex \6 \"\" width=1.9cm ^^ </TD> <TD> \image html \7 ^^ \image latex \7 \"\" width=1.9cm ^^ </TD> <TD> \image html \8 ^^ \image latex \8 \"\" width=1.9cm ^^ </TD> <TD> \image html \9 ^^ \image latex \9 \"\" width=1.9cm ^^ </TD> </TR> </TABLE> </CENTER> \htmlonly[block] <div class=\"cgal_figure_caption\"> \endhtmlonly ^^ \latexonly ^^ \endlatexonly \ref fig__\1" \
|
||||
"cgalFigureBegin{10}=\anchor fig__\1 ^^ <CENTER> <TABLE border=0> <TR> <TD> \image html \2 ^^ \image latex \2 \"\" width=1.6cm ^^ </TD> <TD> \image html \3 ^^ \image latex \3 \"\" width=1.6cm ^^ </TD> <TD> \image html \4 ^^ \image latex \4 \"\" width=1.6cm ^^ </TD> <TD> \image html \5 ^^ \image latex \5 \"\" width=1.6cm ^^ </TD> <TD> \image html \6 ^^ \image latex \6 \"\" width=1.6cm ^^ </TD> <TD> \image html \7 ^^ \image latex \7 \"\" width=1.6cm ^^ </TD> <TD> \image html \8 ^^ \image latex \8 \"\" width=1.6cm ^^ </TD> <TD> \image html \9 ^^ \image latex \9 \"\" width=1.6cm ^^ </TD> <TD> \image html \10 ^^ \image latex \10 \"\" width=1.6cm ^^ </TD> </TR> </TABLE> </CENTER> \htmlonly[block] <div class=\"cgal_figure_caption\"> \endhtmlonly ^^ \latexonly ^^ \endlatexonly \ref fig__\1" \
|
||||
"cgalFigureEnd=\htmlonly[block] </div> \endhtmlonly <br>" \
|
||||
"cgalFigureCaptionBegin{1}=\htmlonly[block] <div class=\"cgal_figure_caption\"> \endhtmlonly \ref fig__\1" \
|
||||
"cgalFigureCaptionEnd=\htmlonly[block] </div> \endhtmlonly <br>" \
|
||||
"cgalConcept=\details <div id=\"CGALConcept\"></div>^^ \brief" \
|
||||
"cgalConceptNamespace=\details <div id=\"CGALConceptNS\"></div>^^ \brief" \
|
||||
"cgalRefines=\xrefitem refines \"Refines\" \"Refinement Relationships\"" \
|
||||
"cgalModels=\xrefitem models \"Is Model Of\" \"Is Model Relationships\"" \
|
||||
"cgalGeneralizes=\xrefitem generalizes \"Generalizes\" \"Generalization Relationships\"" \
|
||||
"cgalHasModel=\xrefitem hasModels \"Has Models\" \"Has Model Relationships\"" \
|
||||
"cgalDebugBegin=\htmlonly <div class=\"CGALDebug\"> <div>Debugging Support</div> \endhtmlonly ^^" \
|
||||
"cgalDebugEnd=\htmlonly </div> \endhtmlonly" \
|
||||
"cgalDebugBegin=\htmlonly[block] <div class=\"CGALDebug\"> <div>Debugging Support</div> \endhtmlonly ^^" \
|
||||
"cgalDebugEnd=\htmlonly[block] </div> \endhtmlonly" \
|
||||
"cgalDebugFunction=This is a function for debugging purpose." \
|
||||
"cgalAdvancedBegin=\htmlonly <div class=\"CGALAdvanced\"> <div>Advanced</div> \endhtmlonly ^^" \
|
||||
"cgalAdvancedEnd=\htmlonly </div> \endhtmlonly" \
|
||||
"cgalAdvancedBegin=\htmlonly[block] <div class=\"CGALAdvanced\"> <div>Advanced</div> \endhtmlonly ^^" \
|
||||
"cgalAdvancedEnd=\htmlonly[block] </div> \endhtmlonly" \
|
||||
"cgalAdvancedFunction=This is an advanced function." \
|
||||
"cgalAdvancedClass=This is an advanced class." \
|
||||
"cgalRequiresCPP11=\warning This function requires a C++11 compiler." \
|
||||
|
|
@ -287,11 +287,11 @@ ALIASES = "sc{1}=<span style=\"font-variant: small-caps;\">\1</sp
|
|||
"cgalModifEnd=\htmlonly </div> \endhtmlonly \latexonly END MODIFICATIONS \endlatexonly" \
|
||||
"cgalPkgBib{1}=<B>BibTeX:</B> <a href=\"../Manual/how_to_cite_cgal.html#\1-${CGAL_RELEASE_YEAR_ID}\">\1-${CGAL_RELEASE_YEAR_ID}</a><BR>" \
|
||||
"cgalFootnote{1}=<span class=\"footnote\">\1</span>" \
|
||||
"cgalAutoToc=\htmlonly <div id=\"autotoc\" class=\"toc\"></div> \endhtmlonly" \
|
||||
"cgalAutoToc=\htmlonly[block] <div id=\"autotoc\" class=\"toc\"></div> \endhtmlonly" \
|
||||
"cgalTagTrue=\link CGAL::Tag_true `CGAL::Tag_true`\endlink" \
|
||||
"cgalTagFalse=\link CGAL::Tag_false `CGAL::Tag_false`\endlink" \
|
||||
"cgalHeading{1}= <B>\1</B><BR>" \
|
||||
"cgalClassifedRefPages=\htmlonly <h2 class=\"groupheader\">Classified Reference Pages</h2> \endhtmlonly" \
|
||||
"cgalClassifedRefPages=\htmlonly[block] <h2 class=\"groupheader\">Classified Reference Pages</h2> \endhtmlonly" \
|
||||
"cgalCite{1}=<!-- -->\cite \1"
|
||||
|
||||
# This tag can be used to specify a number of word-keyword mappings (TCL only).
|
||||
|
|
|
|||
|
|
@ -1,4 +1,4 @@
|
|||
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
|
||||
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "https://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
|
||||
<html xmlns="http://www.w3.org/1999/xhtml">
|
||||
<head>
|
||||
<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
|
||||
|
|
|
|||
|
|
@ -1,5 +1,5 @@
|
|||
<!-- HTML header for doxygen 1.8.13-->
|
||||
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
|
||||
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "https://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
|
||||
<html xmlns="http://www.w3.org/1999/xhtml">
|
||||
<head>
|
||||
<link rel="icon" type="image/png" href="$relpath$../Manual/g-196x196-doc.png"/>
|
||||
|
|
|
|||
|
|
@ -1,5 +1,5 @@
|
|||
<!-- HTML header for doxygen 1.8.13-->
|
||||
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
|
||||
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "https://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
|
||||
<html xmlns="http://www.w3.org/1999/xhtml">
|
||||
<head>
|
||||
<link rel="icon" type="image/png" href="$relpath$../Manual/g-196x196-doc.png"/>
|
||||
|
|
|
|||
|
|
@ -1,4 +1,4 @@
|
|||
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
|
||||
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "https://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
|
||||
<html xmlns="http://www.w3.org/1999/xhtml">
|
||||
<head>
|
||||
<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
|
||||
|
|
|
|||
|
|
@ -1,4 +1,4 @@
|
|||
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
|
||||
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "https://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
|
||||
<html xmlns="http://www.w3.org/1999/xhtml">
|
||||
<head>
|
||||
<link rel="icon" type="image/png" href="$relpath$../Manual/g-196x196-doc.png"/>
|
||||
|
|
|
|||
|
|
@ -1,4 +1,4 @@
|
|||
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
|
||||
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "https://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
|
||||
<html xmlns="http://www.w3.org/1999/xhtml">
|
||||
<head>
|
||||
<link rel="icon" type="image/png" href="$relpath$../Manual/g-196x196-doc.png"/>
|
||||
|
|
|
|||
|
|
@ -62,7 +62,7 @@ def conceptify_ns(d):
|
|||
def write_out_html(d, fn):
|
||||
f = codecs.open(fn, 'w', encoding='utf-8')
|
||||
# this is the normal doxygen doctype, which is thrown away by pyquery
|
||||
f.write('<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">\n')
|
||||
f.write('<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "https://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">\n')
|
||||
f.write('<html xmlns=\"http://www.w3.org/1999/xhtml\">')
|
||||
f.write(d.html())
|
||||
f.write('\n')
|
||||
|
|
|
|||
|
|
@ -277,7 +277,7 @@ triangle (2D and 3D) and in tetrahedra (3D). Basically, in order to generate
|
|||
a random point in a \f$N\f$-simplex (a triangle for \f$N = 2\f$, and tetrahedron
|
||||
for \f$N = 3\f$), we generate numbers \f$a_1,a_2,\ldots,a_N\f$ identically and independently
|
||||
uniformly distributed in \f$(0,1)\f$, we sort them, we let \f$a_0 = 0\f$ and \f$a_{N+1} = 1\f$,
|
||||
and then \f$a_{i+1}−a_i\f$, for \f$i = 1,\ldots,N\f$ becomes its
|
||||
and then \f$a_{i+1}-a_i\f$, for \f$i = 1,\ldots,N\f$ becomes its
|
||||
barycentric coordinates with respect to the simplex.
|
||||
|
||||
Maxime Gimemo introduced the random generators on 2D and 3D triangle meshes.
|
||||
|
|
|
|||
|
|
@ -151,6 +151,7 @@ void
|
|||
Random_points_in_cube_d<P>::
|
||||
generate_point() {
|
||||
typedef typename Kernel_traits<P>::Kernel::RT RT;
|
||||
CGAL_assume(dimension>0);
|
||||
std::vector<RT> coord(dimension);
|
||||
for(int i=0; i<dimension; ++i)
|
||||
coord[i]=RT(this->d_range * ( 2 * this->_rnd.get_double() - 1.0));
|
||||
|
|
|
|||
|
|
@ -288,8 +288,10 @@ int main()
|
|||
Polyhedron polyhedron;
|
||||
|
||||
// A cube
|
||||
make_hexahedron(Point_3(-0.5,-0.5,-0.5), Point_3(0.5,-0.5,-0.5), Point_3(0.5,0.5,-0.5), Point_3(-0.5,0.5,-0.5),
|
||||
Point_3(-0.5,0.5,0.5), Point_3(-0.5,-0.5,0.5), Point_3(0.5,-0.5,0.5), Point_3(0.5,0.5,0.5),
|
||||
make_hexahedron(
|
||||
Point_3(-0.5,-0.5,-0.5), Point_3(0.5,-0.5,-0.5), Point_3(0.5,0.5,-0.5),
|
||||
Point_3(-0.5,0.5,-0.5), Point_3(-0.5,0.5,0.5), Point_3(-0.5,-0.5,0.5),
|
||||
Point_3(0.5,-0.5,0.5), Point_3(0.5,0.5,0.5),
|
||||
polyhedron);
|
||||
|
||||
boost::graph_traits<Polyhedron>::halfedge_descriptor facets[6];
|
||||
|
|
|
|||
|
|
@ -363,19 +363,6 @@ operator<<(Geomview_stream& gs, const Bbox_2& b);
|
|||
Geomview_stream&
|
||||
operator<<(Geomview_stream& gs, const Bbox_3& b);
|
||||
|
||||
/*!
|
||||
Inserts the bounding box `b` into the stream `gs`.
|
||||
\relates Geomview_stream
|
||||
*/
|
||||
Geomview_stream&
|
||||
operator<<(Geomview_stream& gs, const Bbox_3& b);
|
||||
|
||||
/*!
|
||||
Inserts the bounding box `b` into the stream `gs`.
|
||||
\relates Geomview_stream
|
||||
*/
|
||||
Geomview_stream&
|
||||
operator<<(Geomview_stream& gs, const Bbox_3& b);
|
||||
|
||||
/// @}
|
||||
|
||||
|
|
|
|||
|
|
@ -54,6 +54,10 @@ Release date: March 2019
|
|||
`Arr_polyline_traits_2`, `Arr_polycurve_traits_2`, and
|
||||
`Arr_polycurve_basic_traits_2`.
|
||||
|
||||
### CGAL and the Boost Graph Library (BGL)
|
||||
|
||||
- Add function `write_wrl()` for writing into VRML 2.0 format.
|
||||
|
||||
Release 4.13
|
||||
------------
|
||||
|
||||
|
|
|
|||
|
|
@ -42,7 +42,7 @@ endif()
|
|||
|
||||
# Process a list, and replace items contains a file pattern (like
|
||||
# `*.off`) by the sublist that corresponds to the globbing of the
|
||||
# pattern in the directory `${CGAL_CURRENT_SOURCE_DIR}`.
|
||||
# pattern in the directory `${CMAKE_CURRENT_SOURCE_DIR}`.
|
||||
#
|
||||
#
|
||||
# For example: the `file
|
||||
|
|
@ -71,7 +71,7 @@ function(expand_list_with_globbing list_name)
|
|||
list(GET input_list ${n} item_n)
|
||||
# message(STATUS "argument ${n} is ${item_n}")
|
||||
if(item_n MATCHES ".*\\*.*")
|
||||
file(GLOB files RELATIVE ${CGAL_CURRENT_SOURCE_DIR} ${item_n})
|
||||
file(GLOB files RELATIVE ${CMAKE_CURRENT_SOURCE_DIR} ${item_n})
|
||||
list(APPEND output_list ${files})
|
||||
else()
|
||||
list(APPEND output_list ${item_n})
|
||||
|
|
@ -97,7 +97,7 @@ function(cgal_setup_test_properties test_name)
|
|||
endif()
|
||||
set_property(TEST "${test_name}"
|
||||
APPEND PROPERTY LABELS "${PROJECT_NAME}")
|
||||
# message(STATUS " working dir: ${CGAL_CURRENT_SOURCE_DIR}")
|
||||
# message(STATUS " working dir: ${CMAKE_CURRENT_SOURCE_DIR}")
|
||||
set_property(TEST "${test_name}"
|
||||
PROPERTY WORKING_DIRECTORY ${CMAKE_CURRENT_SOURCE_DIR})
|
||||
if(exe_name)
|
||||
|
|
@ -198,7 +198,7 @@ function(cgal_add_test exe_name)
|
|||
return()
|
||||
endif()
|
||||
# message("Add test ${test_name}")
|
||||
set(cin_file "${CGAL_CURRENT_SOURCE_DIR}/${exe_name}.cin")
|
||||
set(cin_file "${CMAKE_CURRENT_SOURCE_DIR}/${exe_name}.cin")
|
||||
if(NOT ARGS AND EXISTS ${cin_file})
|
||||
add_test(NAME ${test_name}
|
||||
COMMAND ${TIME_COMMAND} ${CMAKE_COMMAND}
|
||||
|
|
@ -213,11 +213,11 @@ function(cgal_add_test exe_name)
|
|||
else()
|
||||
if(NOT ARGS AND NOT cgal_add_test_TEST_NAME)
|
||||
if(ARGC GREATER 2 AND ARGV2)
|
||||
set(cmd_file "${CGAL_CURRENT_SOURCE_DIR}/${ARGV2}.cmd")
|
||||
set(cmd_file "${CMAKE_CURRENT_SOURCE_DIR}/${ARGV2}.cmd")
|
||||
elseif(ARGC GREATER 1 AND ARGV1 AND NOT EXISTS ${cmd_file})
|
||||
set(cmd_file "${CGAL_CURRENT_SOURCE_DIR}/${ARGV1}.cmd")
|
||||
set(cmd_file "${CMAKE_CURRENT_SOURCE_DIR}/${ARGV1}.cmd")
|
||||
elseif(NOT EXISTS ${cmd_file})
|
||||
set(cmd_file "${CGAL_CURRENT_SOURCE_DIR}/${exe_name}.cmd")
|
||||
set(cmd_file "${CMAKE_CURRENT_SOURCE_DIR}/${exe_name}.cmd")
|
||||
endif()
|
||||
if(EXISTS ${cmd_file})
|
||||
file(STRINGS "${cmd_file}" CMD_LINES)
|
||||
|
|
|
|||
|
|
@ -9,11 +9,6 @@ include(${CGAL_MODULES_DIR}/CGAL_Macros.cmake)
|
|||
|
||||
cgal_setup_module_path()
|
||||
|
||||
# Save the current source directory. That variable can be changed by
|
||||
# a `CMakeLists.txt`, for `CMakeLists.txt` files that are created in
|
||||
# the binary directory.
|
||||
set(CGAL_CURRENT_SOURCE_DIR ${CMAKE_CURRENT_SOURCE_DIR})
|
||||
|
||||
if(NOT USE_CGAL_FILE_INCLUDED)
|
||||
set(USE_CGAL_FILE_INCLUDED 1)
|
||||
|
||||
|
|
|
|||
|
|
@ -11,11 +11,6 @@ get_filename_component(CGAL_CONFIG_DIR "${CMAKE_CURRENT_LIST_FILE}" PATH)
|
|||
|
||||
set(CGAL_HEADER_ONLY TRUE)
|
||||
|
||||
# Save the current source directory. That variable can be changed by
|
||||
# a `CMakeLists.txt`, for `CMakeLists.txt` files that are created in
|
||||
# the binary directory.
|
||||
set(CGAL_CURRENT_SOURCE_DIR ${CMAKE_CURRENT_SOURCE_DIR})
|
||||
|
||||
function(cgal_detect_branch_build VAR_NAME)
|
||||
if(IS_DIRECTORY ${CGAL_CONFIG_DIR}/../../../../Installation/package_info/Installation/)
|
||||
set(${VAR_NAME} TRUE PARENT_SCOPE)
|
||||
|
|
@ -73,6 +68,9 @@ include(${CGAL_MODULES_DIR}/CGAL_CreateSingleSourceCGALProgram.cmake)
|
|||
include(${CGAL_MODULES_DIR}/CGAL_Macros.cmake)
|
||||
include(${CGAL_MODULES_DIR}/CGAL_Common.cmake)
|
||||
|
||||
set(CGAL_USE_FILE ${CGAL_MODULES_DIR}/UseCGAL.cmake)
|
||||
|
||||
|
||||
if(CGAL_BUILDING_LIBS)
|
||||
foreach(comp ${CGAL_FIND_COMPONENTS})
|
||||
if(CGAL_${comp}_FOUND)
|
||||
|
|
@ -146,8 +144,6 @@ endforeach()
|
|||
# Temporary? Change the CMAKE module path
|
||||
cgal_setup_module_path()
|
||||
|
||||
set(CGAL_USE_FILE ${CGAL_MODULES_DIR}/UseCGAL.cmake)
|
||||
|
||||
include("${CGAL_MODULES_DIR}/CGAL_parse_version_h.cmake")
|
||||
cgal_parse_version_h( "${CGAL_INSTALLATION_PACKAGE_DIR}/include/CGAL/version.h"
|
||||
"CGAL_VERSION_NAME"
|
||||
|
|
|
|||
|
|
@ -199,7 +199,7 @@ Monge_via_jet_fitting();
|
|||
This operator performs all the computations. The \f$ N\f$ input points are
|
||||
given by the `InputIterator` parameters which value-type are
|
||||
`Data_kernel::Point_3`, `d` is the degree of the fitted
|
||||
polynomial, `d'` is the degree of the expected Monge
|
||||
polynomial, \c d' is the degree of the expected Monge
|
||||
coefficients. \pre \f$ N \geq N_{d}:=(d+1)(d+2)/2\f$, \f$ 1 \leq d' \leq\min(d,4) \f$.
|
||||
*/
|
||||
template <class InputIterator> Monge_form
|
||||
|
|
|
|||
|
|
@ -77,13 +77,11 @@ the surface can locally be written as the graph of a bivariate
|
|||
function. Letting \f$ h.o.t.\f$ stand for <I>higher order terms</I>, one
|
||||
has :
|
||||
|
||||
\f[
|
||||
\begin{equation}
|
||||
\f{equation}{
|
||||
z(x,y)=J_{B,d}(x,y) + h.o.t. \ ; \quad
|
||||
J_{B,d}(x,y)=\ccSum{k=0}{d}{(\ccSum{i=0}{i}{
|
||||
\frac{B_{k-i,i}x^{k-i}y^{i}}{i!(k-i)!}})}.
|
||||
\end{equation}
|
||||
\f]
|
||||
\f}
|
||||
|
||||
The degree \f$ d\f$ polynomial \f$ J_{B,d}\f$ is the Taylor expansion of the
|
||||
function \f$ z\f$, and is called its <I>\f$ d\f$-jet</I>. Notice that a \f$ d\f$-jet contains
|
||||
|
|
@ -343,12 +341,10 @@ The fitting process consists of finding the coefficients
|
|||
\f$ A_{i,j}\f$ of the degree \f$ d\f$ polynomial
|
||||
|
||||
\anchor eqanswer
|
||||
\f[
|
||||
\begin{equation}
|
||||
\f{equation}{
|
||||
J_{A,d}= \ccSum{k=0}{d}{(\ccSum{i=0}{k}{
|
||||
\frac{A_{k-i,i}x^{k-i}y^{i}}{i!(k-i)!}})}.
|
||||
\end{equation}
|
||||
\f]
|
||||
\f}
|
||||
|
||||
Denote \f$ p_i=(x_i,y_i,z_i), \ i=1,\ldots , N\f$ the coordinates of the
|
||||
sample points of \f$ P^+\f$.
|
||||
|
|
@ -362,7 +358,7 @@ given by
|
|||
A = & (A_{0,0}, A_{1,0},A_{0,1}, \ldots , A_{0,d})^T \\
|
||||
Z= &(z_1, z_2,\ldots , z_N)^T \\
|
||||
M= &(1,x_i,\ y_i,\ \frac{x_i^2}{2},\ldots ,
|
||||
\ \frac{x_iy_i^{d-1}}{(d-1)!},\ \frac{y_i^d}{d!})_{i=1,...,N}\\
|
||||
\ \frac{x_iy_i^{d-1}}{(d-1)!},\ \frac{y_i^d}{d!})_{i=1,...,N}
|
||||
\f}
|
||||
|
||||
The equations for interpolation become \f$ MA=Z\f$. For approximation, the
|
||||
|
|
@ -395,8 +391,7 @@ The number \f$ r\f$, which is the number of non zero singular values, is
|
|||
strictly lower than \f$ N_d\f$ if the system is under constrained. In any
|
||||
case, the unique solution which minimize \f$ ||A||_2\f$ is given by:
|
||||
|
||||
\f[
|
||||
\begin{equation}
|
||||
\f{equation}{
|
||||
A= V
|
||||
\left( \begin{array}{cc}
|
||||
D_r^{-1} & 0_{N_d-r,\ r}\\
|
||||
|
|
@ -404,8 +399,7 @@ D_r^{-1} & 0_{N_d-r,\ r}\\
|
|||
\end{array}
|
||||
\right)
|
||||
U^TZ.
|
||||
\end{equation}
|
||||
\f]
|
||||
\f}
|
||||
|
||||
One can provide the condition number of the matrix \f$ M\f$ (after
|
||||
preconditioning) which is the ratio of the maximal and the minimal
|
||||
|
|
@ -491,22 +485,18 @@ We use explicit formula. The implicit equation of the fitted
|
|||
polynomial surface in the fitting-basis with origin the point
|
||||
\f$ (0,0,A_{0,0})\f$ is \f$ Q=0\f$ with
|
||||
|
||||
\f[
|
||||
\begin{equation}
|
||||
\f{equation}{
|
||||
Q=-w-A_{0,0} +\ccSum{i,j}{}{\frac{A_{i,j}u^iv^j}{i!j!}}.
|
||||
\end{equation}
|
||||
\f]
|
||||
\f}
|
||||
|
||||
The equation in the Monge basis is obtained by substituting \f$ (u,v,w)\f$
|
||||
by \f$ P^T_{F\rightarrow M}(x,y,z)\f$. Denote \f$ f(x,y,z)=0\f$ this implicit
|
||||
equation. By definition of the Monge basis, we have locally (at
|
||||
\f$ (0,0,0)\f$)
|
||||
|
||||
\f[
|
||||
\begin{equation}
|
||||
\f{equation}{
|
||||
f(x,y,z)=0 \Leftrightarrow z=g(x,y)
|
||||
\end{equation}
|
||||
\f]
|
||||
\f}
|
||||
|
||||
and the Taylor expansion of \f$ g\f$ at \f$ (0,0)\f$ are the Monge coefficients
|
||||
sought.
|
||||
|
|
@ -526,7 +516,7 @@ f_{0,0,1} ^{2}}}
|
|||
\\
|
||||
&b_1=g_{2,1}=-{\frac {- f_{0,1,1} f_{2,0,0} + f_{2,1,0} f_{0,0,1} }{ f_{0,0,1} ^{2}}}
|
||||
\\
|
||||
& .... \\
|
||||
& ....
|
||||
\f}
|
||||
|
||||
|
||||
|
|
|
|||
|
|
@ -40,7 +40,7 @@ _test_io_for(const T& t)
|
|||
}
|
||||
|
||||
std::ifstream iFile(TEST_FILENAME, std::ios::in);
|
||||
T u;
|
||||
T u = t;
|
||||
iFile >> u;
|
||||
assert(!iFile.fail());
|
||||
assert(u == t);
|
||||
|
|
|
|||
|
|
@ -28,7 +28,7 @@
|
|||
int main()
|
||||
{
|
||||
try {
|
||||
CGAL::Point_3<CGAL::Epick> a, b, c, d;
|
||||
CGAL::Point_3<CGAL::Epick> a(CGAL::ORIGIN), b(a), c(a), d(a);
|
||||
CGAL::squared_radius(a, b, c, d);
|
||||
} catch(...) {}
|
||||
return EXIT_SUCCESS;
|
||||
|
|
|
|||
|
|
@ -96,8 +96,8 @@ InputIterator first, InputIterator last);
|
|||
introduces a
|
||||
variable `v` of type `Vector_d<Kernel>` in dimension `d`
|
||||
initialized to the vector with homogeneous coordinates as defined by
|
||||
`H = set [first,last)` and `D`: \f$ (\pmH[0],
|
||||
\pmH[1], \ldots, \pmH[d-1], \pmD)\f$. The sign
|
||||
`H = set [first,last)` and `D`: \f$ (\pm H_0,
|
||||
\pm H_1, \ldots, \pm H_{D-1}, \pm H_D)\f$. The sign
|
||||
chosen is the sign of \f$ D\f$.
|
||||
|
||||
\pre `D` is non-zero, the iterator range defines a \f$ d\f$-tuple of `RT`.
|
||||
|
|
|
|||
|
|
@ -314,7 +314,9 @@ struct Tester
|
|||
// Test edge iterators
|
||||
//-------------------------------------------------------
|
||||
std::cout << "Test edge iterators\n";
|
||||
const Edge& edge_to_modify = *(c3t3.edges_in_complex_begin());
|
||||
typename C3t3::Edges_in_complex_iterator eit = c3t3.edges_in_complex_begin();
|
||||
assert(eit != c3t3.edges_in_complex_end());
|
||||
const Edge& edge_to_modify = *eit;
|
||||
c3t3.remove_from_complex(edge_to_modify);
|
||||
c3t3.add_to_complex(edge_to_modify,curve_index_bis);
|
||||
|
||||
|
|
|
|||
|
|
@ -40,8 +40,15 @@
|
|||
#endif
|
||||
|
||||
#ifdef CGAL_USE_BOOST_BIMAP
|
||||
# if defined(BOOST_MSVC)
|
||||
# pragma warning(push)
|
||||
# pragma warning(disable: 4996)
|
||||
# endif
|
||||
#include <CGAL/boost/bimap.hpp>
|
||||
#include <boost/bimap/multiset_of.hpp>
|
||||
# if defined(BOOST_MSVC)
|
||||
# pragma warning(pop)
|
||||
# endif
|
||||
#endif
|
||||
|
||||
namespace CGAL {
|
||||
|
|
|
|||
|
|
@ -71,6 +71,23 @@ VVector convert(const CGAL::Vector_3<R>& v)
|
|||
CGAL::to_double(v.y()),
|
||||
CGAL::to_double(v.z())); }
|
||||
|
||||
template <typename R>
|
||||
VVector normalize_and_convert(const CGAL::Vector_3<R>& v)
|
||||
{
|
||||
typename R::FT xa = CGAL::abs(v.x());
|
||||
typename R::FT ya = CGAL::abs(v.y());
|
||||
typename R::FT za = CGAL::abs(v.z());
|
||||
typename R::FT m = (std::max)((std::max)(xa,ya),za);
|
||||
if (m==0) {
|
||||
return VVector(0,0,0);
|
||||
} else {
|
||||
double xd = CGAL::to_double(v.x()/m);
|
||||
double yd = CGAL::to_double(v.y()/m);
|
||||
double zd = CGAL::to_double(v.z()/m);
|
||||
VVector u(xd,yd,zd);
|
||||
return u / CGAL_NTS sqrt(u*u) ; // normalize
|
||||
}
|
||||
}
|
||||
|
||||
const double refinement_angle = 0.1;
|
||||
const double shrink_fac = 0.995;
|
||||
|
|
@ -80,8 +97,7 @@ class Approximator {
|
|||
|
||||
public:
|
||||
static VPoint approximate(const CGAL::Sphere_point<R>& p) {
|
||||
VVector v = convert(p-CGAL::ORIGIN);
|
||||
v = v / CGAL_NTS sqrt(v*v) ; // normalize
|
||||
VVector v = normalize_and_convert(p-CGAL::ORIGIN);
|
||||
return CGAL::ORIGIN+v;
|
||||
}
|
||||
|
||||
|
|
|
|||
|
|
@ -350,6 +350,11 @@ public:
|
|||
f->mark() == true);
|
||||
}
|
||||
|
||||
bool is_sphere() const
|
||||
{
|
||||
return is_plane();
|
||||
}
|
||||
|
||||
void extract_complement()
|
||||
{ CGAL_NEF_TRACEN("extract complement");
|
||||
if ( this->is_shared() ) clone_rep();
|
||||
|
|
@ -390,7 +395,7 @@ public:
|
|||
CGAL_forall_svertices(v,D) v->mark() = true;
|
||||
CGAL_forall_sedges(e,D) e->mark() = true;
|
||||
CGAL_forall_sfaces(f,D) f->mark() = false;
|
||||
if ( D.has_shalfloop() ) D.shalfloop()->mark() = D.shalfoop()->twin() = true;
|
||||
if ( D.has_shalfloop() ) D.shalfloop()->mark() = D.shalfoop()->twin()->mark() = true;
|
||||
D.simplify();
|
||||
}
|
||||
|
||||
|
|
|
|||
|
|
@ -70,6 +70,7 @@ template<class NT_,class Dim_,class Max_dim_=Dim_> struct Array_vector {
|
|||
CGAL_assertion(d<=d_);
|
||||
//TODO: optimize for forward iterators
|
||||
Vector a;
|
||||
CGAL_assume(f!=e);
|
||||
std::copy(f,e,a.begin());
|
||||
return a;
|
||||
}
|
||||
|
|
|
|||
|
|
@ -149,7 +149,6 @@ public:
|
|||
/// @{
|
||||
Construct_point_2 construct_point_2_object();
|
||||
Construct_vector_2 construct_vector_2_object();
|
||||
Construct_vector_2 construct_vector_2_object();
|
||||
Construct_line_2 construct_line_2_object();
|
||||
Construct_translated_point_2 construct_translated_point_2_object();
|
||||
Construct_scaled_vector_2 construct_scaled_vector_2_object();
|
||||
|
|
|
|||
|
|
@ -772,7 +772,6 @@ get_positions_with_vertex_at_extremity(const Bare_point& known_point,
|
|||
<< " inverted order ? " << std::boolalpha << inverted_return_order << std::endl;
|
||||
#endif
|
||||
|
||||
CGAL_precondition(known_point != Bare_point());
|
||||
CGAL_precondition(!domain_.is_loop(curve_index));
|
||||
CGAL_precondition(extremity_points.size() == 2);
|
||||
|
||||
|
|
|
|||
|
|
@ -33,6 +33,11 @@
|
|||
|
||||
namespace CGAL {
|
||||
|
||||
#if defined(BOOST_MSVC)
|
||||
# pragma warning(push)
|
||||
# pragma warning(disable:4003) // not enough actual parameters for macro
|
||||
#endif
|
||||
|
||||
// see <CGAL/config.h>
|
||||
CGAL_PRAGMA_DIAG_PUSH
|
||||
// see <CGAL/boost/parameter.h>
|
||||
|
|
@ -120,6 +125,10 @@ BOOST_PARAMETER_FUNCTION(
|
|||
|
||||
CGAL_PRAGMA_DIAG_POP
|
||||
|
||||
#if defined(BOOST_MSVC)
|
||||
# pragma warning(pop)
|
||||
#endif
|
||||
|
||||
} // namespace CGAL
|
||||
|
||||
#endif // CGAL_OPTIMIZE_PERIODIC_3_MESH_3_H
|
||||
|
|
|
|||
|
|
@ -116,7 +116,6 @@ void project_points(C3T3& c3t3,
|
|||
const Weighted_point& vh_wp = c3t3.triangulation().point(vh);
|
||||
const Bare_point& vh_p = cp(vh_wp);
|
||||
const Bare_point new_point = helper.project_on_surface(vh, vh_p);
|
||||
CGAL_assertion(new_point != Bare_point());
|
||||
|
||||
const FT sq_d = CGAL::squared_distance(new_point, vh_p);
|
||||
|
||||
|
|
@ -144,6 +143,11 @@ void project_points(C3T3& c3t3,
|
|||
|
||||
} // namespace internal
|
||||
|
||||
#if defined(BOOST_MSVC)
|
||||
# pragma warning(push)
|
||||
# pragma warning(disable:4003) // not enough actual parameters for macro
|
||||
#endif
|
||||
|
||||
// see <CGAL/config.h>
|
||||
CGAL_PRAGMA_DIAG_PUSH
|
||||
// see <CGAL/boost/parameter.h>
|
||||
|
|
@ -181,6 +185,10 @@ BOOST_PARAMETER_FUNCTION(
|
|||
|
||||
CGAL_PRAGMA_DIAG_POP
|
||||
|
||||
#if defined(BOOST_MSVC)
|
||||
# pragma warning(pop)
|
||||
#endif
|
||||
|
||||
/**
|
||||
* @brief This function refines the mesh c3t3 wrt domain & criteria
|
||||
*
|
||||
|
|
|
|||
|
|
@ -156,7 +156,7 @@ private:
|
|||
|
||||
virtual void assign (PLY_element& element, typename Point_set::Index index)
|
||||
{
|
||||
Type t;
|
||||
Type t{};
|
||||
element.assign (t, m_name.c_str());
|
||||
put(m_pmap, index, t);
|
||||
}
|
||||
|
|
|
|||
|
|
@ -35,7 +35,7 @@ public:
|
|||
/// The circle type, only required if you want to detect tori
|
||||
typedef unspecified_type Circle_2;
|
||||
/// The 2D vector type, only required if you want to detect tori
|
||||
typedef unspecified_type Vector_3;
|
||||
typedef unspecified_type Vector_2;
|
||||
|
||||
/// The number type of the Cartesian coordinates of types Point_3
|
||||
typedef unspecified_type FT;
|
||||
|
|
|
|||
|
|
@ -440,6 +440,58 @@ corefine_and_compute_boolean_operations(
|
|||
return CGAL::make_array(true, true, true, true);
|
||||
}
|
||||
|
||||
// handle case of empty meshes (isolated vertices are ignored)
|
||||
if (faces(tm1).empty())
|
||||
{
|
||||
if(faces(tm2).empty())
|
||||
{
|
||||
for (int i=0; i<4; ++i)
|
||||
if (output[i] != boost::none)
|
||||
clear(*(*output[i]));
|
||||
return CGAL::make_array(true, true, true, true);
|
||||
}
|
||||
// tm2 is not empty
|
||||
if (output[Corefinement::UNION] != boost::none)
|
||||
if (&tm2 != *output[Corefinement::UNION])
|
||||
copy_face_graph(tm2,
|
||||
*(*output[Corefinement::UNION]),
|
||||
parameters::vertex_point_map(vpm2),
|
||||
parameters::vertex_point_map(*cpp11::get<Corefinement::UNION>(vpm_out_tuple)));
|
||||
if (output[Corefinement::INTERSECTION] != boost::none)
|
||||
clear(*(*output[Corefinement::INTERSECTION]));
|
||||
if (output[Corefinement::TM1_MINUS_TM2] != boost::none)
|
||||
clear(*(*output[Corefinement::TM1_MINUS_TM2]));
|
||||
if (output[Corefinement::TM2_MINUS_TM1] != boost::none)
|
||||
if (&tm2 != *output[Corefinement::TM2_MINUS_TM1])
|
||||
copy_face_graph(tm2,
|
||||
*(*output[Corefinement::TM2_MINUS_TM1]),
|
||||
parameters::vertex_point_map(vpm2),
|
||||
parameters::vertex_point_map(*cpp11::get<Corefinement::TM2_MINUS_TM1>(vpm_out_tuple)));
|
||||
return CGAL::make_array(true, true, true, true);
|
||||
}
|
||||
else
|
||||
if (faces(tm2).empty())
|
||||
{
|
||||
// tm1 is not empty
|
||||
if (output[Corefinement::UNION] != boost::none)
|
||||
if (&tm1 != *output[Corefinement::UNION])
|
||||
copy_face_graph(tm1,
|
||||
*(*output[Corefinement::UNION]),
|
||||
parameters::vertex_point_map(vpm1),
|
||||
parameters::vertex_point_map(*cpp11::get<Corefinement::UNION>(vpm_out_tuple)));
|
||||
if (output[Corefinement::INTERSECTION] != boost::none)
|
||||
clear(*(*output[Corefinement::INTERSECTION]));
|
||||
if (output[Corefinement::TM2_MINUS_TM1] != boost::none)
|
||||
clear(*(*output[Corefinement::TM2_MINUS_TM1]));
|
||||
if (output[Corefinement::TM1_MINUS_TM2] != boost::none)
|
||||
if (&tm1 != *output[Corefinement::TM1_MINUS_TM2])
|
||||
copy_face_graph(tm1,
|
||||
*(*output[Corefinement::TM1_MINUS_TM2]),
|
||||
parameters::vertex_point_map(vpm1),
|
||||
parameters::vertex_point_map(*cpp11::get<Corefinement::TM1_MINUS_TM2>(vpm_out_tuple)));
|
||||
return CGAL::make_array(true, true, true, true);
|
||||
}
|
||||
|
||||
// Edge is-constrained maps
|
||||
//for input meshes
|
||||
typedef typename boost::lookup_named_param_def <
|
||||
|
|
|
|||
|
|
@ -115,13 +115,15 @@ void fill_pairs(const Halfedge& he,
|
|||
++set_it->second.first; // increase the multiplicity
|
||||
if(set_it->second.first == 2)
|
||||
{
|
||||
set_it->second.second = halfedge_pairs.size(); // set the id of the pair in the vector
|
||||
halfedge_pairs.push_back( std::make_pair(set_it->first, he) );
|
||||
if ( get(vpmap, source(he,pmesh))==get(vpmap, target(set_it->first,pmesh)) &&
|
||||
get(vpmap, target(he,pmesh))==get(vpmap, source(set_it->first,pmesh)) )
|
||||
{
|
||||
set_it->second.second = halfedge_pairs.size(); // set the id of the pair in the vector
|
||||
halfedge_pairs.push_back( std::make_pair(set_it->first, he) );
|
||||
manifold_halfedge_pairs.push_back(true);
|
||||
}
|
||||
else
|
||||
manifold_halfedge_pairs.push_back(false);
|
||||
}
|
||||
else
|
||||
if ( set_it->second.first > 2 )
|
||||
|
|
|
|||
|
|
@ -118,6 +118,20 @@ void test_surface_mesh_cc(const char* fname)
|
|||
std::cout << "OK\n";
|
||||
}
|
||||
|
||||
void bug_test()
|
||||
{
|
||||
typedef CGAL::Simple_cartesian<double> K;
|
||||
typedef K::Point_3 Point_3;
|
||||
CGAL::Surface_mesh<Point_3> tm;
|
||||
|
||||
CGAL::make_triangle(Point_3(0,0,0), Point_3(1,0,0), Point_3(0,1,0), tm);
|
||||
CGAL::make_triangle(Point_3(0,0,0), Point_3(1,0,0), Point_3(0,1,0), tm);
|
||||
CGAL::make_triangle(Point_3(0,0,0), Point_3(1,0,0), Point_3(0,1,0), tm);
|
||||
CGAL::make_triangle(Point_3(0,0,0), Point_3(1,0,0), Point_3(0,1,0), tm);
|
||||
|
||||
CGAL::Polygon_mesh_processing::stitch_borders(tm);
|
||||
}
|
||||
|
||||
int main()
|
||||
{
|
||||
test_stitch_boundary_cycles("data_stitching/boundary_cycle.off");
|
||||
|
|
@ -150,5 +164,7 @@ int main()
|
|||
test_surface_mesh("data_stitching/non_manifold.off");
|
||||
test_surface_mesh_cc("data_stitching/nm_cubes.off");
|
||||
|
||||
bug_test();
|
||||
|
||||
return EXIT_SUCCESS;
|
||||
}
|
||||
|
|
|
|||
|
|
@ -1,5 +1,8 @@
|
|||
#ifdef _MSC_VER
|
||||
# pragma warning(disable:4244) // conversion with loss of data
|
||||
# pragma warning(disable:4996) // boost_1_65_1\boost/iostreams/positioning.hpp(96):
|
||||
// warning C4996: 'std::fpos<_Mbstatet>::seekpos': warning STL4019:
|
||||
// The member std::fpos::seekpos() is non-Standard
|
||||
#endif
|
||||
|
||||
#include "Volume_plane.h"
|
||||
|
|
|
|||
|
|
@ -34,6 +34,8 @@ typedef Kernel::Point_3 Point;
|
|||
|
||||
namespace euler = CGAL::Euler;
|
||||
using namespace CGAL::Three;
|
||||
namespace params = CGAL::parameters;
|
||||
|
||||
class Q_DECL_EXPORT Basic_generator_plugin :
|
||||
public QObject,
|
||||
public Polyhedron_demo_plugin_helper
|
||||
|
|
@ -548,7 +550,7 @@ void Basic_generator_plugin::generateSphere()
|
|||
typedef typename boost::property_map<typename Facegraph_item::Face_graph, CGAL::vertex_point_t>::type VPMap;
|
||||
if(precision !=0)
|
||||
CGAL::Subdivision_method_3::Sqrt3_subdivision(sphere,
|
||||
precision);
|
||||
params::number_of_iterations(precision));
|
||||
VPMap vpmap = get(CGAL::vertex_point, sphere);
|
||||
//emplace the points back on the sphere
|
||||
BOOST_FOREACH(typename boost::graph_traits<typename Facegraph_item::Face_graph>::vertex_descriptor vd, vertices(sphere))
|
||||
|
|
|
|||
|
|
@ -877,7 +877,7 @@ Polyhedron_demo_mean_curvature_flow_skeleton_plugin::createContractedItem(Scene_
|
|||
{
|
||||
if(!item)
|
||||
return;
|
||||
if(item->mcs == NULL)
|
||||
if(item->mcs != NULL)
|
||||
delete item->mcs;
|
||||
double omega_H = ui->omega_H->value();
|
||||
double omega_P = ui->omega_P->value();
|
||||
|
|
|
|||
|
|
@ -11,7 +11,10 @@
|
|||
#include "Scene_surface_mesh_item.h"
|
||||
#include "SMesh_type.h"
|
||||
#include <CGAL/subdivision_method_3.h>
|
||||
|
||||
using namespace CGAL::Three;
|
||||
namespace params = CGAL::parameters;
|
||||
|
||||
class Polyhedron_demo_subdivision_methods_plugin :
|
||||
public QObject,
|
||||
public Polyhedron_demo_plugin_helper
|
||||
|
|
@ -81,7 +84,7 @@ void Polyhedron_demo_subdivision_methods_plugin::apply_loop(FaceGraphItem* item,
|
|||
time.start();
|
||||
messages->information("Loop subdivision...");
|
||||
QApplication::setOverrideCursor(Qt::WaitCursor);
|
||||
CGAL::Subdivision_method_3::Loop_subdivision(*graph, nb_steps);
|
||||
CGAL::Subdivision_method_3::Loop_subdivision(*graph, params::number_of_iterations(nb_steps));
|
||||
messages->information(QString("ok (%1 ms)").arg(time.elapsed()));
|
||||
QApplication::restoreOverrideCursor();
|
||||
item->invalidateOpenGLBuffers();
|
||||
|
|
@ -113,7 +116,7 @@ void Polyhedron_demo_subdivision_methods_plugin::apply_catmullclark(FaceGraphIte
|
|||
time.start();
|
||||
messages->information("Catmull-Clark subdivision...");
|
||||
QApplication::setOverrideCursor(Qt::WaitCursor);
|
||||
CGAL::Subdivision_method_3::CatmullClark_subdivision(*graph, nb_steps);
|
||||
CGAL::Subdivision_method_3::CatmullClark_subdivision(*graph, params::number_of_iterations(nb_steps));
|
||||
messages->information(QString("ok (%1 ms)").arg(time.elapsed()));
|
||||
QApplication::restoreOverrideCursor();
|
||||
item->invalidateOpenGLBuffers();
|
||||
|
|
@ -143,7 +146,7 @@ void Polyhedron_demo_subdivision_methods_plugin::apply_sqrt3(FaceGraphItem* item
|
|||
time.start();
|
||||
messages->information("Sqrt-3 subdivision...");
|
||||
QApplication::setOverrideCursor(Qt::WaitCursor);
|
||||
CGAL::Subdivision_method_3::Sqrt3_subdivision(*graph, nb_steps);
|
||||
CGAL::Subdivision_method_3::Sqrt3_subdivision(*graph, params::number_of_iterations(nb_steps));
|
||||
messages->information(QString("ok (%1 ms)").arg(time.elapsed()));
|
||||
QApplication::restoreOverrideCursor();
|
||||
item->invalidateOpenGLBuffers();
|
||||
|
|
@ -175,7 +178,7 @@ void Polyhedron_demo_subdivision_methods_plugin::apply_doosabin(FaceGraphItem* i
|
|||
time.start();
|
||||
messages->information("Doo-Sabin subdivision...");
|
||||
QApplication::setOverrideCursor(Qt::WaitCursor);
|
||||
CGAL::Subdivision_method_3::DooSabin_subdivision(*graph, nb_steps);
|
||||
CGAL::Subdivision_method_3::DooSabin_subdivision(*graph, params::number_of_iterations(nb_steps));
|
||||
messages->information(QString("ok (%1 ms)").arg(time.elapsed()));
|
||||
QApplication::restoreOverrideCursor();
|
||||
item->invalidateOpenGLBuffers();
|
||||
|
|
|
|||
|
|
@ -225,7 +225,7 @@ void Scene::refine_loop()
|
|||
return;
|
||||
}
|
||||
std::cout << "Loop subdivision...";
|
||||
CGAL::Subdivision_method_3::Loop_subdivision(*m_pPolyhedron, 1);
|
||||
CGAL::Subdivision_method_3::Loop_subdivision(*m_pPolyhedron);
|
||||
std::cout << "done (" << m_pPolyhedron->size_of_facets() << " facets)" << std::endl;
|
||||
}
|
||||
|
||||
|
|
|
|||
|
|
@ -495,9 +495,9 @@ then \f$\lambda_i\geq 0\f$ (\f$\lambda_i\leq 0\f$, respectively).
|
|||
<LI>
|
||||
\f[
|
||||
\begin{array}{llll}
|
||||
&&\geq 0 & \mbox{if \f$u_j=\infty\f$} \\
|
||||
&&\geq 0 & \mbox{if $u_j=\infty$} \\
|
||||
\qplambda^T A_j &\quad \\
|
||||
&&\leq 0 & \mbox{if \f$l_j=-\infty\f$.}
|
||||
&&\leq 0 & \mbox{if $l_j=-\infty$}.
|
||||
\end{array}
|
||||
\f]
|
||||
<LI> \f[\qplambda^T\qpb \quad<\quad \ccSum{j: \qplambda^TA_j <0}{}{ \qplambda^TA_j u_j }
|
||||
|
|
@ -508,12 +508,12 @@ then \f$\lambda_i\geq 0\f$ (\f$\lambda_i\leq 0\f$, respectively).
|
|||
that there is a feasible solution \f$\qpx\f$. Then we get
|
||||
\f[
|
||||
\begin{array}{lcll}
|
||||
0 &\geq& \qplambda^T(A\qpx -\qpb) & \mbox{(by \f$A\qpx\qprel \qpb\f$ and 1.)} \\
|
||||
0 &\geq& \qplambda^T(A\qpx -\qpb) & \mbox{(by $A\qpx\qprel \qpb$ and 1.)} \\
|
||||
&=& \ccSum{j: \qplambda^TA_j <0}{}{ \qplambda^TA_j x_j }
|
||||
\quad+\quad \ccSum{j: \qplambda^TA_j >0}{}{ \qplambda^TA_j x_j} - \qplambda^T \qpb \\
|
||||
&\geq& \ccSum{j: \qplambda^TA_j <0}{}{ \qplambda^TA_j u_j }
|
||||
\quad+\quad \ccSum{j: \qplambda^TA_j >0}{}{ \qplambda^TA_j l_j} - \qplambda^T \qpb &
|
||||
\mbox{(by \f$\qpl\leq \qpx \leq \qpu\f$ and 2.)} \\
|
||||
\mbox{(by $\qpl\leq \qpx \leq \qpu$ and 2.)} \\
|
||||
&>& 0 & \mbox{(by 3.)},
|
||||
\end{array}
|
||||
\f]
|
||||
|
|
@ -547,9 +547,9 @@ solution of (QP). The program (QP) is unbounded if an \f$n\f$-vector
|
|||
then \f$(A\qpw)_i\leq 0\f$ (\f$(A\qpw)_i\geq 0, (A\qpw)_i=0\f$, respectively).
|
||||
<LI> \f[
|
||||
\begin{array}{llll}
|
||||
&&\geq 0 & \mbox{if \f$l_j\f$ is finite} \\
|
||||
&&\geq 0 & \mbox{if $l_j$ is finite} \\
|
||||
w_j &\quad \\
|
||||
&&\leq 0 & \mbox{if \f$u_j\f$ is finite.}
|
||||
&&\leq 0 & \mbox{if $u_j$ is finite.}
|
||||
\end{array}
|
||||
\f]
|
||||
<LI> \f$\qpw^TD\qpw=0\f$ and \f$(\qpc^T+2{\qpx^*}^TD)\qpw<0\f$.
|
||||
|
|
|
|||
|
|
@ -1,3 +1,5 @@
|
|||
@INCLUDE = ${CGAL_DOC_PACKAGE_DEFAULTS}
|
||||
|
||||
PROJECT_NAME = "CGAL ${CGAL_DOC_VERSION} - Linear and Quadratic Programming Solver"
|
||||
|
||||
EXCLUDE = ${CGAL_PACKAGE_DOC_DIR}/fig_src
|
||||
|
|
|
|||
|
|
@ -528,7 +528,7 @@ when we use the homogeneous representations of the points: if
|
|||
\f$ q_1,\ldots,q_n,q\in\mathbb{R}^{d+1}\f$ are homogeneous coordinates for
|
||||
\f$ p_1,\ldots,p_n,p\f$ with positive homogenizing coordinates
|
||||
\f$ h_1,\ldots,h_n,h\f$, we have
|
||||
\f[$q_j = h_j \cdot (p_j \mid 1) \mbox{~for all $j$, and~} q = h \cdot
|
||||
\f[q_j = h_j \cdot (p_j \mid 1) \mbox{~for all $j$, and~} q = h \cdot
|
||||
(p\mid 1).\f] Now, nonnegative \f$\lambda_1,\ldots,\lambda_n\f$ are
|
||||
suitable coefficients for a convex combination if and only if
|
||||
\f[\ccSum{j=1}{n}{~ \lambda_j(p_j \mid 1)} = (p\mid 1), \f]
|
||||
|
|
|
|||
|
|
@ -113,20 +113,16 @@ The Taylor expansion of \f$ k_1\f$ (resp. \f$ k_2\f$) along the max
|
|||
by \f$ x\f$ (resp. \f$ y\f$) are:
|
||||
|
||||
\anchor eqtaylor_along_line
|
||||
\f[
|
||||
\begin{equation}
|
||||
\f{equation}{
|
||||
k_1(x) = k_1 + b_0x + \frac{P_1}{2(k_1-k_2)}x^2 + ... , \quad \quad \quad
|
||||
P_1= 3b_1^2+(k_1-k_2)(c_0-3k_1^3).
|
||||
\end{equation}
|
||||
\f]
|
||||
\f}
|
||||
|
||||
\anchor eqtaylor_along_red_line
|
||||
\f[
|
||||
\begin{equation}
|
||||
\f{equation}{
|
||||
k_2(y) = k_2 + b_3y + \frac{P_2}{2(k_2-k_1)}y^2 + ... , \quad \quad \quad
|
||||
P_2= 3b_2^2+(k_2-k_1)(c_4-3k_2^3).
|
||||
\end{equation}
|
||||
\f]
|
||||
\f}
|
||||
|
||||
Notice also that switching from one to the other of the two
|
||||
afore-mentioned coordinate systems reverts the sign of all the odd
|
||||
|
|
|
|||
|
|
@ -58,6 +58,10 @@ public:
|
|||
template < class T >
|
||||
class In_place_list_base {
|
||||
public:
|
||||
In_place_list_base()
|
||||
: next_link(NULL), prev_link(NULL)
|
||||
{}
|
||||
|
||||
T* next_link; // forward pointer
|
||||
T* prev_link; // backwards pointer
|
||||
//friend class internal::In_place_list_iterator<T, Alloc>;
|
||||
|
|
|
|||
|
|
@ -3,9 +3,24 @@
|
|||
zmodload zsh/stat
|
||||
set -e
|
||||
|
||||
git=git
|
||||
if [ "x$1" = "x--help" -o "x$1" = "x-h" ]; then
|
||||
cat <<EOF
|
||||
Usage: $0
|
||||
[HEAD] [BASE]
|
||||
|
||||
base=${1:-HEAD}
|
||||
List the commits in the range BASE..HEAD, with --first-parent
|
||||
and show for each the weight of the commit.
|
||||
|
||||
[HEAD] is the head of the branch you want to display.
|
||||
Its default value is 'HEAD'.
|
||||
|
||||
[BASE] is the base of the range. Its default value is 'cgal/master'.
|
||||
EOF
|
||||
exit 0
|
||||
fi
|
||||
|
||||
commit=${1:-HEAD}
|
||||
base=${2:-cgal/master}
|
||||
|
||||
function reset() {
|
||||
git update-ref -d refs/cgal/git-show-content
|
||||
|
|
@ -14,7 +29,7 @@ function reset() {
|
|||
|
||||
trap reset ERR EXIT KILL TERM INT
|
||||
|
||||
for c in $(git --no-pager log --pretty='%h' --first-parent cgal/master..$base); do
|
||||
for c in $(git --no-pager log --pretty='%h' --first-parent ${base}..${commit}); do
|
||||
git update-ref refs/cgal/git-show-content $c
|
||||
git bundle create bundle ${c}^..refs/cgal/git-show-content > /dev/null 2>&1
|
||||
gzip -f bundle
|
||||
|
|
|
|||
|
|
@ -26,7 +26,8 @@ int main()
|
|||
assert( ifs );
|
||||
|
||||
SDG2 sdg;
|
||||
SDG2::Site_2 site;
|
||||
SDG2::Site_2 site =
|
||||
SDG2::Site_2::construct_site_2(K::Point_2(CGAL::ORIGIN));
|
||||
|
||||
// read the sites and insert them in the segment Delaunay graph
|
||||
while ( ifs >> site ) {
|
||||
|
|
|
|||
|
|
@ -17,7 +17,8 @@ bool test_info(SDG& sdg, const char* fname)
|
|||
assert( ifs );
|
||||
|
||||
sdg.clear();
|
||||
typename SDG::Site_2 site;
|
||||
typename SDG::Site_2 site =
|
||||
SDG::Site_2::construct_site_2(typename SDG::Point_2(CGAL::ORIGIN));
|
||||
|
||||
// read the sites and insert them in the segment Delaunay graph
|
||||
int info_id = 1;
|
||||
|
|
|
|||
|
|
@ -30,7 +30,8 @@ int main( int argc, char *argv[] )
|
|||
assert( ifs );
|
||||
|
||||
SDG2 sdg;
|
||||
SDG2::Site_2 site;
|
||||
SDG2::Site_2 site =
|
||||
SDG2::Site_2::construct_site_2(Rep::Point_2(CGAL::ORIGIN));
|
||||
|
||||
// read the sites and insert them in the segment Delaunay graph
|
||||
while ( ifs >> site ) {
|
||||
|
|
|
|||
|
|
@ -160,7 +160,7 @@ namespace CGAL {
|
|||
|
||||
Implements the <I>midpoint of max spread</I> splitting rule.
|
||||
A rectangle is cut through \f$ (\mathrm{Mind}+\mathrm{Maxd})/2\f$ orthogonal
|
||||
to the dimension with the maximum point spread \f$ [\mathrm{Mind},\matrm{Maxd}]\f$.
|
||||
to the dimension with the maximum point spread \f$ [\mathrm{Mind},\mathrm{Maxd}]\f$.
|
||||
|
||||
\cgalHeading{Parameters}
|
||||
|
||||
|
|
|
|||
|
|
@ -166,6 +166,7 @@ namespace CGAL {
|
|||
inline FT
|
||||
min_coord(int i) const
|
||||
{
|
||||
CGAL_assume(i<D::value);
|
||||
CGAL_assertion(lower_.size() != 0);
|
||||
return lower_[i];
|
||||
}
|
||||
|
|
@ -173,6 +174,7 @@ namespace CGAL {
|
|||
inline FT
|
||||
max_coord(int i) const
|
||||
{
|
||||
CGAL_assume(i<D::value);
|
||||
return upper_[i];
|
||||
}
|
||||
|
||||
|
|
|
|||
|
|
@ -95,10 +95,13 @@ namespace parameters = CGAL::parameters;
|
|||
|
||||
#ifndef DOXYGEN_RUNNING
|
||||
// Backward compatibility
|
||||
#ifndef CGAL_NO_DEPRECATED_CODE
|
||||
template <class PolygonMesh>
|
||||
void CatmullClark_subdivision(PolygonMesh& pmesh, int step = 1) {
|
||||
CGAL_DEPRECATED_MSG("you are using the deprecated API of CatmullClark_subdivision(), please update your code")
|
||||
void CatmullClark_subdivision(PolygonMesh& pmesh, int step) {
|
||||
PQQ(pmesh, CatmullClark_mask_3<PolygonMesh>(&pmesh, get(vertex_point,pmesh)), step);
|
||||
}
|
||||
#endif
|
||||
#endif
|
||||
|
||||
/*!
|
||||
|
|
@ -138,14 +141,22 @@ void CatmullClark_subdivision(PolygonMesh& pmesh, const NamedParameters& np) {
|
|||
internal::PQQ_1step(pmesh, vpm, mask);
|
||||
}
|
||||
|
||||
template <class PolygonMesh>
|
||||
void CatmullClark_subdivision(PolygonMesh& pmesh)
|
||||
{
|
||||
CatmullClark_subdivision(pmesh, CGAL::parameters::all_default());
|
||||
}
|
||||
// -----------------------------------------------------------------------------
|
||||
|
||||
#ifndef DOXYGEN_RUNNING
|
||||
// backward compatibility
|
||||
#ifndef CGAL_NO_DEPRECATED_CODE
|
||||
template <class PolygonMesh>
|
||||
void Loop_subdivision(PolygonMesh& pmesh, int step = 1) {
|
||||
CGAL_DEPRECATED_MSG("you are using the deprecated API of Loop_subdivision(), please update your code")
|
||||
void Loop_subdivision(PolygonMesh& pmesh, int step) {
|
||||
PTQ(pmesh, Loop_mask_3<PolygonMesh>(&pmesh, get(vertex_point,pmesh)) , step);
|
||||
}
|
||||
#endif
|
||||
#endif
|
||||
|
||||
/*!
|
||||
|
|
@ -183,15 +194,23 @@ void Loop_subdivision(PolygonMesh& pmesh, const NamedParameters& np) {
|
|||
internal::PTQ_1step(pmesh, vpm, mask);
|
||||
}
|
||||
|
||||
template <class PolygonMesh>
|
||||
void Loop_subdivision(PolygonMesh& pmesh)
|
||||
{
|
||||
Loop_subdivision(pmesh, CGAL::parameters::all_default());
|
||||
}
|
||||
// -----------------------------------------------------------------------------
|
||||
|
||||
#ifndef DOXYGEN_RUNNING
|
||||
// backward compatibility
|
||||
#ifndef CGAL_NO_DEPRECATED_CODE
|
||||
template <class PolygonMesh>
|
||||
void DooSabin_subdivision(PolygonMesh& pmesh, int step = 1) {
|
||||
CGAL_DEPRECATED_MSG("you are using the deprecated API of DooSabin_subdivision(), please update your code")
|
||||
void DooSabin_subdivision(PolygonMesh& pmesh, int step) {
|
||||
DQQ(pmesh, DooSabin_mask_3<PolygonMesh>(&pmesh, get(vertex_point, pmesh)), step);
|
||||
}
|
||||
#endif
|
||||
#endif
|
||||
|
||||
/*!
|
||||
*
|
||||
|
|
@ -227,16 +246,24 @@ void DooSabin_subdivision(PolygonMesh& pmesh, const NamedParameters& np) {
|
|||
for(unsigned int i = 0; i < step; i++)
|
||||
internal::DQQ_1step(pmesh, vpm, mask);
|
||||
}
|
||||
|
||||
|
||||
template <class PolygonMesh>
|
||||
void DooSabin_subdivision(PolygonMesh& pmesh)
|
||||
{
|
||||
DooSabin_subdivision(pmesh, CGAL::parameters::all_default());
|
||||
}
|
||||
// -----------------------------------------------------------------------------
|
||||
|
||||
#ifndef DOXYGEN_RUNNING
|
||||
// backward compatibility
|
||||
#ifndef CGAL_NO_DEPRECATED_CODE
|
||||
template <class PolygonMesh>
|
||||
void Sqrt3_subdivision(PolygonMesh& pmesh, int step = 1) {
|
||||
CGAL_DEPRECATED_MSG("you are using the deprecated API of Sqrt3_subdivision(), please update your code")
|
||||
void Sqrt3_subdivision(PolygonMesh& pmesh, int step) {
|
||||
Sqrt3(pmesh, Sqrt3_mask_3<PolygonMesh>(&pmesh, get(vertex_point,pmesh)), step);
|
||||
}
|
||||
#endif
|
||||
#endif
|
||||
|
||||
/*!
|
||||
*
|
||||
|
|
@ -277,7 +304,12 @@ void Sqrt3_subdivision(PolygonMesh& pmesh, const NamedParameters& np) {
|
|||
for(unsigned int i = 0; i < step; i++)
|
||||
internal::Sqrt3_1step(pmesh, vpm, mask, (i%2==1));
|
||||
}
|
||||
|
||||
|
||||
template <class PolygonMesh>
|
||||
void Sqrt3_subdivision(PolygonMesh& pmesh)
|
||||
{
|
||||
Sqrt3_subdivision(pmesh, CGAL::parameters::all_default());
|
||||
}
|
||||
/// @}
|
||||
|
||||
} // namespace Subdivision_method_3
|
||||
|
|
|
|||
|
|
@ -57,7 +57,7 @@ void test_Subdivision_surface_3() {
|
|||
Polyhedron P;
|
||||
mesh >> P;
|
||||
|
||||
Subdivision_method_3::CatmullClark_subdivision(P,TEST_DEPTH);
|
||||
Subdivision_method_3::CatmullClark_subdivision(P);
|
||||
assert(CGAL::is_valid_polygon_mesh(P));
|
||||
}
|
||||
|
||||
|
|
@ -68,7 +68,7 @@ void test_Subdivision_surface_3() {
|
|||
Polyhedron P;
|
||||
mesh >> P;
|
||||
|
||||
Subdivision_method_3::CatmullClark_subdivision(P,TEST_DEPTH);
|
||||
Subdivision_method_3::CatmullClark_subdivision(P);
|
||||
assert(CGAL::is_valid_polygon_mesh(P));
|
||||
}
|
||||
|
||||
|
|
@ -80,7 +80,7 @@ void test_Subdivision_surface_3() {
|
|||
Polyhedron P;
|
||||
mesh >> P;
|
||||
|
||||
Subdivision_method_3::Loop_subdivision(P,TEST_DEPTH);
|
||||
Subdivision_method_3::Loop_subdivision(P);
|
||||
assert(CGAL::is_valid_polygon_mesh(P));
|
||||
}
|
||||
|
||||
|
|
@ -91,7 +91,7 @@ void test_Subdivision_surface_3() {
|
|||
Polyhedron P;
|
||||
mesh >> P;
|
||||
|
||||
Subdivision_method_3::Loop_subdivision(P,TEST_DEPTH);
|
||||
Subdivision_method_3::Loop_subdivision(P);
|
||||
assert(CGAL::is_valid_polygon_mesh(P));
|
||||
}
|
||||
|
||||
|
|
@ -102,7 +102,7 @@ void test_Subdivision_surface_3() {
|
|||
Polyhedron P;
|
||||
mesh >> P;
|
||||
|
||||
Subdivision_method_3::DooSabin_subdivision(P,TEST_DEPTH);
|
||||
Subdivision_method_3::DooSabin_subdivision(P);
|
||||
assert(CGAL::is_valid_polygon_mesh(P));
|
||||
}
|
||||
|
||||
|
|
@ -113,7 +113,7 @@ void test_Subdivision_surface_3() {
|
|||
Polyhedron P;
|
||||
mesh >> P;
|
||||
|
||||
Subdivision_method_3::Sqrt3_subdivision(P,TEST_DEPTH);
|
||||
Subdivision_method_3::Sqrt3_subdivision(P);
|
||||
assert(CGAL::is_valid_polygon_mesh(P));
|
||||
}
|
||||
}
|
||||
|
|
@ -129,7 +129,7 @@ void test_Subdivision_surface_3_SM() {
|
|||
Polyhedron P;
|
||||
mesh >> P;
|
||||
|
||||
Subdivision_method_3::CatmullClark_subdivision(P,TEST_DEPTH);
|
||||
Subdivision_method_3::CatmullClark_subdivision(P);
|
||||
assert(CGAL::is_valid_polygon_mesh(P));
|
||||
}
|
||||
|
||||
|
|
@ -140,7 +140,7 @@ void test_Subdivision_surface_3_SM() {
|
|||
Polyhedron P;
|
||||
mesh >> P;
|
||||
|
||||
Subdivision_method_3::CatmullClark_subdivision(P,TEST_DEPTH);
|
||||
Subdivision_method_3::CatmullClark_subdivision(P);
|
||||
assert(CGAL::is_valid_polygon_mesh(P));
|
||||
}
|
||||
|
||||
|
|
@ -152,7 +152,7 @@ void test_Subdivision_surface_3_SM() {
|
|||
Polyhedron P;
|
||||
mesh >> P;
|
||||
|
||||
Subdivision_method_3::Loop_subdivision(P,TEST_DEPTH);
|
||||
Subdivision_method_3::Loop_subdivision(P);
|
||||
assert(CGAL::is_valid_polygon_mesh(P));
|
||||
}
|
||||
|
||||
|
|
@ -163,7 +163,7 @@ void test_Subdivision_surface_3_SM() {
|
|||
Polyhedron P;
|
||||
mesh >> P;
|
||||
|
||||
Subdivision_method_3::Loop_subdivision(P,TEST_DEPTH);
|
||||
Subdivision_method_3::Loop_subdivision(P);
|
||||
assert(CGAL::is_valid_polygon_mesh(P));
|
||||
}
|
||||
|
||||
|
|
@ -174,7 +174,7 @@ void test_Subdivision_surface_3_SM() {
|
|||
Polyhedron P;
|
||||
mesh >> P;
|
||||
|
||||
Subdivision_method_3::DooSabin_subdivision(P,TEST_DEPTH);
|
||||
Subdivision_method_3::DooSabin_subdivision(P);
|
||||
assert(CGAL::is_valid_polygon_mesh(P, true));
|
||||
}
|
||||
|
||||
|
|
@ -185,7 +185,7 @@ void test_Subdivision_surface_3_SM() {
|
|||
Polyhedron P;
|
||||
mesh >> P;
|
||||
|
||||
Subdivision_method_3::DooSabin_subdivision(P,TEST_DEPTH);
|
||||
Subdivision_method_3::DooSabin_subdivision(P);
|
||||
assert(CGAL::is_valid_polygon_mesh(P));
|
||||
}
|
||||
|
||||
|
|
@ -196,7 +196,7 @@ void test_Subdivision_surface_3_SM() {
|
|||
Polyhedron P;
|
||||
mesh >> P;
|
||||
|
||||
Subdivision_method_3::Sqrt3_subdivision(P,TEST_DEPTH);
|
||||
Subdivision_method_3::Sqrt3_subdivision(P);
|
||||
assert(CGAL::is_valid_polygon_mesh(P));
|
||||
}
|
||||
|
||||
|
|
@ -207,7 +207,7 @@ void test_Subdivision_surface_3_SM() {
|
|||
Polyhedron P;
|
||||
mesh >> P;
|
||||
|
||||
Subdivision_method_3::Sqrt3_subdivision(P,TEST_DEPTH);
|
||||
Subdivision_method_3::Sqrt3_subdivision(P);
|
||||
assert(CGAL::is_valid_polygon_mesh(P));
|
||||
}
|
||||
}
|
||||
|
|
@ -284,7 +284,7 @@ void test_Subdivision_surface_3_SM_NP() {
|
|||
Polyhedron P;
|
||||
mesh >> P;
|
||||
|
||||
Subdivision_method_3::DooSabin_subdivision(P,TEST_DEPTH);
|
||||
Subdivision_method_3::DooSabin_subdivision(P,Subdivision_method_3::parameters::number_of_iterations(TEST_DEPTH));
|
||||
assert(CGAL::is_valid_polygon_mesh(P));
|
||||
}
|
||||
|
||||
|
|
|
|||
|
|
@ -0,0 +1,362 @@
|
|||
#include <CGAL/internal/disable_deprecation_warnings_and_errors.h>
|
||||
// ============================================================================
|
||||
//
|
||||
// Copyright (c) 2005-2006, 2017 Le-Jeng Shiue
|
||||
//
|
||||
// This software and related documentation is part of an INTERNAL release
|
||||
// of the Computational Geometry Algorithms Library (CGAL). It is not
|
||||
// intended for general use.
|
||||
//
|
||||
// ----------------------------------------------------------------------------
|
||||
//
|
||||
// release : $CGAL_Revision: $
|
||||
// release_date : $CGAL_Date: $
|
||||
//
|
||||
// file : test/Subdivision_method_3/test_Subdivision_method_3.C
|
||||
// package : Subdivision_method_3
|
||||
// chapter : Subdivision Method
|
||||
//
|
||||
// revision : $Id$
|
||||
// revision_date : $Date$
|
||||
//
|
||||
// author(s) : Le-Jeng Shiue <Andy.Shiue@gmail.com>
|
||||
//
|
||||
// Test subdivision methods
|
||||
// ============================================================================
|
||||
|
||||
#include <CGAL/Simple_cartesian.h>
|
||||
#include <CGAL/Polyhedron_3.h>
|
||||
#include <CGAL/Surface_mesh.h>
|
||||
|
||||
#include <CGAL/subdivision_method_3.h>
|
||||
|
||||
#include <iostream>
|
||||
#include <fstream>
|
||||
#include <cassert>
|
||||
|
||||
using namespace std;
|
||||
using namespace CGAL;
|
||||
|
||||
#define TEST_DEPTH (3)
|
||||
|
||||
//#define TESTMESH_GENERAL "data/??.off"
|
||||
|
||||
#define TESTMESH_QUAD "data/corner.off"
|
||||
#define TESTMESH_QUAD_OPEN "data/corner_with_hole.off"
|
||||
|
||||
#define TESTMESH_TRI "data/quint_tris.off"
|
||||
#define TESTMESH_TRI_OPEN "data/nefertiti.off"
|
||||
|
||||
void test_Subdivision_surface_3() {
|
||||
typedef CGAL::Simple_cartesian<double> Kernel;
|
||||
typedef CGAL::Polyhedron_3<Kernel> Polyhedron;
|
||||
|
||||
// test Catmull-Clark subdivision on quad mesh
|
||||
{
|
||||
ifstream mesh(TESTMESH_QUAD);
|
||||
|
||||
Polyhedron P;
|
||||
mesh >> P;
|
||||
|
||||
Subdivision_method_3::CatmullClark_subdivision(P,TEST_DEPTH);
|
||||
assert(CGAL::is_valid_polygon_mesh(P));
|
||||
}
|
||||
|
||||
// test Catmull-Clark subdivision on 'opened' quad mesh
|
||||
{
|
||||
ifstream mesh(TESTMESH_QUAD_OPEN);
|
||||
|
||||
Polyhedron P;
|
||||
mesh >> P;
|
||||
|
||||
Subdivision_method_3::CatmullClark_subdivision(P,TEST_DEPTH);
|
||||
assert(CGAL::is_valid_polygon_mesh(P));
|
||||
}
|
||||
|
||||
|
||||
// test Loop subdivision on tri mesh
|
||||
{
|
||||
ifstream mesh(TESTMESH_TRI);
|
||||
|
||||
Polyhedron P;
|
||||
mesh >> P;
|
||||
|
||||
Subdivision_method_3::Loop_subdivision(P,TEST_DEPTH);
|
||||
assert(CGAL::is_valid_polygon_mesh(P));
|
||||
}
|
||||
|
||||
// test Loop subdivision on 'opened' tri mesh
|
||||
{
|
||||
ifstream mesh(TESTMESH_TRI_OPEN);
|
||||
|
||||
Polyhedron P;
|
||||
mesh >> P;
|
||||
|
||||
Subdivision_method_3::Loop_subdivision(P,TEST_DEPTH);
|
||||
assert(CGAL::is_valid_polygon_mesh(P));
|
||||
}
|
||||
|
||||
// test Doo-Sabin subdivision on general mesh
|
||||
{
|
||||
ifstream mesh(TESTMESH_TRI_OPEN);
|
||||
|
||||
Polyhedron P;
|
||||
mesh >> P;
|
||||
|
||||
Subdivision_method_3::DooSabin_subdivision(P,TEST_DEPTH);
|
||||
assert(CGAL::is_valid_polygon_mesh(P));
|
||||
}
|
||||
|
||||
// test Sqrt-3 subdivision on tri mesh
|
||||
{
|
||||
ifstream mesh(TESTMESH_TRI);
|
||||
|
||||
Polyhedron P;
|
||||
mesh >> P;
|
||||
|
||||
Subdivision_method_3::Sqrt3_subdivision(P,TEST_DEPTH);
|
||||
assert(CGAL::is_valid_polygon_mesh(P));
|
||||
}
|
||||
}
|
||||
|
||||
void test_Subdivision_surface_3_SM() {
|
||||
typedef CGAL::Simple_cartesian<double> Kernel;
|
||||
typedef CGAL::Surface_mesh<Kernel::Point_3> Polyhedron;
|
||||
|
||||
// test Catmull-Clark subdivision on quad mesh
|
||||
{
|
||||
ifstream mesh(TESTMESH_QUAD);
|
||||
|
||||
Polyhedron P;
|
||||
mesh >> P;
|
||||
|
||||
Subdivision_method_3::CatmullClark_subdivision(P,TEST_DEPTH);
|
||||
assert(CGAL::is_valid_polygon_mesh(P));
|
||||
}
|
||||
|
||||
// test Catmull-Clark subdivision on 'opened' quad mesh
|
||||
{
|
||||
ifstream mesh(TESTMESH_QUAD_OPEN);
|
||||
|
||||
Polyhedron P;
|
||||
mesh >> P;
|
||||
|
||||
Subdivision_method_3::CatmullClark_subdivision(P,TEST_DEPTH);
|
||||
assert(CGAL::is_valid_polygon_mesh(P));
|
||||
}
|
||||
|
||||
|
||||
// test Loop subdivision on tri mesh
|
||||
{
|
||||
ifstream mesh(TESTMESH_TRI);
|
||||
|
||||
Polyhedron P;
|
||||
mesh >> P;
|
||||
|
||||
Subdivision_method_3::Loop_subdivision(P,TEST_DEPTH);
|
||||
assert(CGAL::is_valid_polygon_mesh(P));
|
||||
}
|
||||
|
||||
// test Loop subdivision on 'opened' tri mesh
|
||||
{
|
||||
ifstream mesh(TESTMESH_TRI_OPEN);
|
||||
|
||||
Polyhedron P;
|
||||
mesh >> P;
|
||||
|
||||
Subdivision_method_3::Loop_subdivision(P,TEST_DEPTH);
|
||||
assert(CGAL::is_valid_polygon_mesh(P));
|
||||
}
|
||||
|
||||
// test Doo-Sabin subdivision on general mesh
|
||||
{
|
||||
ifstream mesh(TESTMESH_TRI_OPEN);
|
||||
|
||||
Polyhedron P;
|
||||
mesh >> P;
|
||||
|
||||
Subdivision_method_3::DooSabin_subdivision(P,TEST_DEPTH);
|
||||
assert(CGAL::is_valid_polygon_mesh(P, true));
|
||||
}
|
||||
|
||||
// test Doo-Sabin subdivision on 'opened' quad mesh
|
||||
{
|
||||
ifstream mesh(TESTMESH_QUAD_OPEN);
|
||||
|
||||
Polyhedron P;
|
||||
mesh >> P;
|
||||
|
||||
Subdivision_method_3::DooSabin_subdivision(P,TEST_DEPTH);
|
||||
assert(CGAL::is_valid_polygon_mesh(P));
|
||||
}
|
||||
|
||||
// test Sqrt-3 subdivision on tri mesh
|
||||
{
|
||||
ifstream mesh(TESTMESH_TRI);
|
||||
|
||||
Polyhedron P;
|
||||
mesh >> P;
|
||||
|
||||
Subdivision_method_3::Sqrt3_subdivision(P,TEST_DEPTH);
|
||||
assert(CGAL::is_valid_polygon_mesh(P));
|
||||
}
|
||||
|
||||
// test Sqrt-3 subdivision on 'opened' tri mesh
|
||||
{
|
||||
ifstream mesh(TESTMESH_TRI_OPEN);
|
||||
|
||||
Polyhedron P;
|
||||
mesh >> P;
|
||||
|
||||
Subdivision_method_3::Sqrt3_subdivision(P,TEST_DEPTH);
|
||||
assert(CGAL::is_valid_polygon_mesh(P));
|
||||
}
|
||||
}
|
||||
|
||||
void test_Subdivision_surface_3_SM_NP() {
|
||||
typedef CGAL::Simple_cartesian<double> Kernel;
|
||||
typedef CGAL::Surface_mesh<Kernel::Point_3> Polyhedron;
|
||||
|
||||
// test Catmull-Clark subdivision on quad mesh
|
||||
{
|
||||
ifstream mesh(TESTMESH_QUAD);
|
||||
|
||||
Polyhedron P;
|
||||
mesh >> P;
|
||||
|
||||
Subdivision_method_3::CatmullClark_subdivision(P,Subdivision_method_3::parameters::vertex_point_map(get(vertex_point, P))
|
||||
.number_of_iterations(TEST_DEPTH));
|
||||
assert(CGAL::is_valid_polygon_mesh(P));
|
||||
}
|
||||
|
||||
// test Catmull-Clark subdivision on 'opened' quad mesh
|
||||
{
|
||||
ifstream mesh(TESTMESH_QUAD_OPEN);
|
||||
|
||||
Polyhedron P;
|
||||
mesh >> P;
|
||||
|
||||
Subdivision_method_3::CatmullClark_subdivision(P,Subdivision_method_3::parameters::vertex_point_map(get(vertex_point, P))
|
||||
.number_of_iterations(TEST_DEPTH));
|
||||
assert(CGAL::is_valid_polygon_mesh(P));
|
||||
}
|
||||
|
||||
|
||||
// test Loop subdivision on tri mesh
|
||||
{
|
||||
ifstream mesh(TESTMESH_TRI);
|
||||
|
||||
Polyhedron P;
|
||||
mesh >> P;
|
||||
|
||||
Subdivision_method_3::Loop_subdivision(P,Subdivision_method_3::parameters::vertex_point_map(get(vertex_point, P))
|
||||
.number_of_iterations(TEST_DEPTH));
|
||||
assert(CGAL::is_valid_polygon_mesh(P));
|
||||
}
|
||||
|
||||
// test Loop subdivision on 'opened' tri mesh
|
||||
{
|
||||
ifstream mesh(TESTMESH_TRI_OPEN);
|
||||
|
||||
Polyhedron P;
|
||||
mesh >> P;
|
||||
|
||||
Subdivision_method_3::Loop_subdivision(P,Subdivision_method_3::parameters::vertex_point_map(get(vertex_point, P))
|
||||
.number_of_iterations(TEST_DEPTH));
|
||||
assert(CGAL::is_valid_polygon_mesh(P));
|
||||
}
|
||||
|
||||
// test Doo-Sabin subdivision on 'opened' tri mesh
|
||||
{
|
||||
ifstream mesh(TESTMESH_TRI_OPEN);
|
||||
|
||||
Polyhedron P;
|
||||
mesh >> P;
|
||||
|
||||
Subdivision_method_3::DooSabin_subdivision(P,Subdivision_method_3::parameters::vertex_point_map(get(vertex_point, P))
|
||||
.number_of_iterations(TEST_DEPTH));
|
||||
assert(CGAL::is_valid_polygon_mesh(P));
|
||||
}
|
||||
|
||||
// test Doo-Sabin subdivision on 'opened' quad mesh
|
||||
{
|
||||
ifstream mesh(TESTMESH_QUAD_OPEN);
|
||||
|
||||
Polyhedron P;
|
||||
mesh >> P;
|
||||
|
||||
Subdivision_method_3::DooSabin_subdivision(P,TEST_DEPTH);
|
||||
assert(CGAL::is_valid_polygon_mesh(P));
|
||||
}
|
||||
|
||||
// test Sqrt-3 subdivision on tri mesh
|
||||
{
|
||||
ifstream mesh(TESTMESH_TRI);
|
||||
|
||||
Polyhedron P;
|
||||
mesh >> P;
|
||||
|
||||
Subdivision_method_3::Sqrt3_subdivision(P,Subdivision_method_3::parameters::vertex_point_map(get(vertex_point, P))
|
||||
.number_of_iterations(TEST_DEPTH));
|
||||
|
||||
assert(CGAL::is_valid_polygon_mesh(P));
|
||||
}
|
||||
|
||||
// test Sqrt-3 subdivision on 'opened' tri mesh
|
||||
{
|
||||
ifstream mesh(TESTMESH_TRI_OPEN);
|
||||
|
||||
Polyhedron P;
|
||||
mesh >> P;
|
||||
|
||||
Subdivision_method_3::Sqrt3_subdivision(P,Subdivision_method_3::parameters::vertex_point_map(get(vertex_point, P))
|
||||
.number_of_iterations(TEST_DEPTH));
|
||||
|
||||
std::ofstream out("out_0.off");
|
||||
out << P;
|
||||
|
||||
assert(CGAL::is_valid_polygon_mesh(P));
|
||||
}
|
||||
|
||||
// test Sqrt-3 subdivision on 'opened' tri mesh & with external property map
|
||||
{
|
||||
ifstream mesh(TESTMESH_TRI_OPEN);
|
||||
|
||||
Polyhedron P;
|
||||
mesh >> P;
|
||||
|
||||
typedef Kernel::Point_3 Point;
|
||||
typedef Kernel::Vector_3 Vector;
|
||||
|
||||
typedef boost::graph_traits<Polyhedron>::vertex_descriptor vertex_descriptor;
|
||||
typedef boost::unordered_map<vertex_descriptor, Kernel::Point_3> Point_pmap;
|
||||
typedef boost::associative_property_map<Point_pmap> APM;
|
||||
typedef boost::property_map<Polyhedron, CGAL::vertex_point_t>::type VPM;
|
||||
|
||||
Point_pmap um;
|
||||
APM apm(um);
|
||||
VPM vpm = get(vertex_point, P);
|
||||
|
||||
// some arbitrary new coordinates (different from the internal vpm)
|
||||
BOOST_FOREACH(vertex_descriptor vd, vertices(P)) {
|
||||
boost::property_traits<VPM>::reference pt = get(vpm, vd);
|
||||
Vector v = pt - Point(0., 0., -3.);
|
||||
put(apm, vd, pt + 0.5*v);
|
||||
}
|
||||
|
||||
Subdivision_method_3::Sqrt3_subdivision(P,
|
||||
Subdivision_method_3::parameters::vertex_point_map(apm)
|
||||
.number_of_iterations(TEST_DEPTH));
|
||||
|
||||
assert(CGAL::is_valid_polygon_mesh(P));
|
||||
}
|
||||
}
|
||||
|
||||
int main() {
|
||||
test_Subdivision_surface_3();
|
||||
test_Subdivision_surface_3_SM();
|
||||
test_Subdivision_surface_3_SM_NP();
|
||||
std::cerr << "Done" << std::endl;
|
||||
return 0;
|
||||
}
|
||||
// EOF //
|
||||
|
|
@ -2159,10 +2159,18 @@ private: //------------------------------------------------------- private data
|
|||
std::string off;
|
||||
is >> sm_skip_comments;
|
||||
is >> off;
|
||||
CGAL_assertion( (off == "OFF") || (off == "COFF") || (off == "NOFF") || (off == "CNOFF"));
|
||||
|
||||
if(! (
|
||||
(off == "OFF") || (off == "COFF") || (off == "NOFF") || (off == "CNOFF")
|
||||
)
|
||||
)
|
||||
{
|
||||
is.setstate(std::ios::failbit);
|
||||
return false;
|
||||
}
|
||||
is >> n >> f >> e;
|
||||
|
||||
if(!is){
|
||||
return false;
|
||||
}
|
||||
sm.reserve(sm.num_vertices()+n, sm.num_faces()+2*f, sm.num_edges()+e);
|
||||
std::vector<Vertex_index> vertexmap(n);
|
||||
P p;
|
||||
|
|
@ -2219,6 +2227,10 @@ private: //------------------------------------------------------- private data
|
|||
for(int i=0; i < f; i++){
|
||||
is >> sm_skip_comments;
|
||||
is >> d;
|
||||
if(!is){
|
||||
sm.clear();
|
||||
return false;
|
||||
}
|
||||
vr.resize(d);
|
||||
for(std::size_t j=0; j<d; j++){
|
||||
is >> vi;
|
||||
|
|
@ -2555,6 +2567,11 @@ void
|
|||
Surface_mesh<P>::
|
||||
collect_garbage(F& funct)
|
||||
{
|
||||
if (!has_garbage())
|
||||
{
|
||||
return;
|
||||
}
|
||||
|
||||
int i, i0, i1,
|
||||
nV(num_vertices()),
|
||||
nE(num_edges()),
|
||||
|
|
|
|||
|
|
@ -255,12 +255,10 @@ The <em>Laplacian representation</em> (referred to as <em>Laplace coordinates</e
|
|||
of a vertex in a surface mesh is one way to <em>encode</em> the local neighborhood of a vertex in the surface mesh.
|
||||
In this representation, a vertex \f$ \mathbf{v}_i \f$ is associated a 3D vector defined as:
|
||||
|
||||
\f[
|
||||
\begin{equation}
|
||||
\f{equation}{
|
||||
L(\mathbf{v}_i) = \sum_{\mathbf{v}_j \in N(\mathbf{v}_i)} w_{ij}(\mathbf{v}_i - \mathbf{v}_j),
|
||||
\label{eq:lap_open}
|
||||
\end{equation}
|
||||
\f]
|
||||
\f}
|
||||
|
||||
where:
|
||||
- \f$N(\mathbf{v}_i)\f$ denotes the set of vertices adjacent to \f$\mathbf{v}_i\f$;
|
||||
|
|
@ -282,12 +280,10 @@ Laplacian representation of \f$ v_i \f$ with uniform weights: the red square ver
|
|||
|
||||
Considering a surface mesh with \f$n\f$ vertices, it is possible to define its <i>Laplacian representation</i> \f$\Delta\f$ as a \f$n \times 3\f$ matrix:
|
||||
|
||||
\f[
|
||||
\begin{equation}
|
||||
\f{equation}{
|
||||
\mathbf{L}\mathbf{V} = \Delta,
|
||||
\label{eq:lap_system}
|
||||
\end{equation}
|
||||
\f]
|
||||
\f}
|
||||
|
||||
where:
|
||||
- \f$\mathbf{L}\f$ is a \f$n \times n\f$ sparse matrix, referred to as the <em>Laplacian matrix</em>. Its elements \f$ m_{ij} \f$, \f$i,j \in \{1 \dots n\} \f$ are defined as follows:
|
||||
|
|
@ -313,8 +309,7 @@ This package supports hard constraints, that is, target positions of control ver
|
|||
|
||||
Given a surface mesh deformation system with a ROI made of \f$ n \f$ vertices and \f$ k \f$ control vertices, we consider the following linear system:
|
||||
|
||||
\f[
|
||||
\begin{equation}
|
||||
\f{equation}{
|
||||
\left[
|
||||
\begin{array}{ccc}
|
||||
\mathbf{L}_f\\
|
||||
|
|
@ -329,8 +324,7 @@ Given a surface mesh deformation system with a ROI made of \f$ n \f$ vertices an
|
|||
\end{array}
|
||||
\right],
|
||||
\label{eq:lap_energy_system}
|
||||
\end{equation}
|
||||
\f]
|
||||
\f}
|
||||
|
||||
where:
|
||||
- \f$\mathbf{V}\f$ is a \f$n \times 3\f$ matrix denoting the unknowns of the system that represent the vertex coordinates after deformation. The system is built so that the \f$ k \f$ last rows correspond to the control vertices.
|
||||
|
|
@ -348,14 +342,12 @@ preserves the Laplacian representation of the surface mesh restricted to the unc
|
|||
Given a surface mesh \f$M\f$ with \f$ n \f$ vertices \f$ \{\mathbf{v}_i\} i \in \{1 \dots n \} \f$ and some deformation
|
||||
constraints, we consider the following energy function:
|
||||
|
||||
\f[
|
||||
\begin{equation}
|
||||
\f{equation}{
|
||||
\sum_{\mathbf{v}_i \in M}
|
||||
\sum_{\mathbf{v}_j \in N(\mathbf{v}_i)} w_{ij}
|
||||
\left\| (\mathbf{v}'_i - \mathbf{v}'_j) - \mathbf{R}_i(\mathbf{v}_i - \mathbf{v}_j) \right\|^2,
|
||||
\label{eq:arap_energy}
|
||||
\end{equation}
|
||||
\f]
|
||||
\f}
|
||||
|
||||
where:
|
||||
- \f$\mathbf{R}_i\f$ is a \f$ 3 \times 3 \f$ rotation matrix
|
||||
|
|
@ -387,12 +379,10 @@ Each such term of the energy is minimized by using a two-step optimization appro
|
|||
In the first step, the positions of the vertices are considered as fixed so that the rotation matrices are the only unknowns.
|
||||
|
||||
For the vertex \f$\mathbf{v}_i\f$, we consider the covariance matrix \f$\mathbf{S}_i\f$:
|
||||
\f[
|
||||
\begin{equation}
|
||||
\f{equation}{
|
||||
\mathbf{S}_i = \sum_{\mathbf{v}_j \in N(\mathbf{v}_i)} w_{ij} (\mathbf{v}_i - \mathbf{v}_j)(\mathbf{v}'_i - \mathbf{v}'_j)^T,
|
||||
\label{eq:cov_matrix}
|
||||
\end{equation}
|
||||
\f]
|
||||
\f}
|
||||
|
||||
It was shown \cgalCite{Sorkine2009LeastSquaresRigid} that minimizing the energy contribution of
|
||||
\f$\mathbf{v}_i\f$ in Eq. \f$\eqref{eq:arap_energy}\f$ is equivalent to maximizing the trace of the matrix
|
||||
|
|
@ -404,13 +394,11 @@ In the second step, the rotation matrices are substituted into the partial deriv
|
|||
with respect to \f$\mathbf{v}'_i\f$. Assuming the weights are symmetric, setting the derivative to zero results in the
|
||||
following equation:
|
||||
|
||||
\f[
|
||||
\begin{equation}
|
||||
\f{equation}{
|
||||
\sum_{\mathbf{v}_j \in N(\mathbf{v}_i)} w_{ij}(\mathbf{v}'_i - \mathbf{v}'_j) =
|
||||
\sum_{\mathbf{v}_j \in N(\mathbf{v}_i)} w_{ij} \frac{(\mathbf{R}_i + \mathbf{R}_j)}{2} (\mathbf{v}_i - \mathbf{v}_j).
|
||||
\label{eq:lap_ber}
|
||||
\end{equation}
|
||||
\f]
|
||||
\f}
|
||||
|
||||
The left-hand side of this equation corresponds to the one of Eq.\f$\eqref{eq:lap_open}\f$,
|
||||
and we can set \f$\Delta\f$ to be the right-hand side.
|
||||
|
|
@ -428,13 +416,11 @@ The original algorithm \cgalCite{Sorkine2007AsRigidAs} we described assumes that
|
|||
|
||||
- the weight between two vertices is symmetric. In order to support asymmetric weights in our implementation,
|
||||
we slightly change Eq. \f$\eqref{eq:lap_ber}\f$ to:
|
||||
\f[
|
||||
\begin{equation}
|
||||
\f{equation}{
|
||||
\sum_{\mathbf{v}_j \in N(\mathbf{v}_i)} (w_{ij} + w_{ji})(\mathbf{v}'_i - \mathbf{v}'_j) =
|
||||
\sum_{\mathbf{v}_j \in N(\mathbf{v}_i)} (w_{ij}\mathbf{R}_i + w_{ji}\mathbf{R}_j)(\mathbf{v}_i - \mathbf{v}_j).
|
||||
\label{eq:lap_ber_asym}
|
||||
\end{equation}
|
||||
\f]
|
||||
\f}
|
||||
|
||||
- The energy contribution of each vertex is positive. If the weight between two vertices is always positive, this is always the case.
|
||||
However, when using the cotangent weighting scheme (the default in our implementation), if the sum of the angles opposite to an edge is greater than \f$ \pi \f$,
|
||||
|
|
@ -448,14 +434,12 @@ A method minimizing another energy function is described next to avoid the latte
|
|||
The elastic energy function proposed by \cgalCite{Chao2010SimpleGeomModel} additionally takes into account
|
||||
all the opposite edges in the facets incident to a vertex. The energy function to minimize becomes:
|
||||
|
||||
\f[
|
||||
\begin{equation}
|
||||
\f{equation}{
|
||||
\sum_{\mathbf{v}_i \in M}
|
||||
\sum_{(\mathbf{v}_j, \mathbf{v}_k) \in E(\mathbf{v}_i)} w_{jk}
|
||||
\left\| (\mathbf{v}'_j - \mathbf{v}'_k) - \mathbf{R}_i(\mathbf{v}_j - \mathbf{v}_k) \right\|^2,
|
||||
\label{eq:arap_energy_rims}
|
||||
\end{equation}
|
||||
\f]
|
||||
\f}
|
||||
|
||||
where \f$E(\mathbf{v}_i)\f$ consists of the set of edges incident to \f$\mathbf{v}_i\f$ (the <em>spokes</em>) and
|
||||
the set of edges in the link (the <em>rims</em>) of \f$\mathbf{v}_i\f$ in the surface mesh \f$M\f$
|
||||
|
|
@ -470,23 +454,19 @@ The method to get the new positions of the unconstrained vertices is similar to
|
|||
method explained in \ref SMD_Overview_ARAP.
|
||||
For the first step, the Eq. \f$\eqref{eq:cov_matrix}\f$ is modified to take into account the edges in \f$E(\mathbf{v}_i)\f$:
|
||||
|
||||
\f[
|
||||
\begin{equation}
|
||||
\f{equation}{
|
||||
\mathbf{S}_i = \sum_{(\mathbf{v}_j, \mathbf{v}_k) \in E(\mathbf{v}_i)} w_{jk} (\mathbf{v}_j - \mathbf{v}_k)(\mathbf{v}'_j - \mathbf{v}'_k)^T,
|
||||
\label{eq:cov_matrix_sr}
|
||||
\end{equation}
|
||||
\f]
|
||||
\f}
|
||||
|
||||
For the second step, setting partial derivative of Eq. \f$\eqref{eq:arap_energy_rims}\f$ to zero with
|
||||
respect to \f$\mathbf{v}_i\f$ gives the following equation:
|
||||
|
||||
\f[
|
||||
\begin{equation}
|
||||
\f{equation}{
|
||||
\sum_{\mathbf{v}_j \in N(\mathbf{v}_i)} (w_{ij} + w_{ji})(\mathbf{v}'_i - \mathbf{v}'_j) =
|
||||
\sum_{\mathbf{v}_j \in N(\mathbf{v}_i)} \frac{w_{ij}(\mathbf{R}_i + \mathbf{R}_j + \mathbf{R}_m) + w_{ji}(\mathbf{R}_i + \mathbf{R}_j + \mathbf{R}_n)}{3} (\mathbf{v}_i - \mathbf{v}_j).
|
||||
\label{eq:lap_ber_rims}
|
||||
\end{equation}
|
||||
\f]
|
||||
\f}
|
||||
|
||||
where \f$\mathbf{R}_m\f$ and \f$\mathbf{R}_n\f$ are the rotation matrices of the vertices \f$\mathbf{v}_m\f$,
|
||||
\f$\mathbf{v}_n\f$ which are the opposite vertices of the edge \f$\mathbf{v}_i \mathbf{v}_j\f$
|
||||
|
|
@ -504,14 +484,12 @@ The implementation in this package uses the cotangent weights by default (negati
|
|||
\subsection SMD_Overview_SRE_ARAP Smoothed Rotation Enhanced As-Rigid-As Possible (SR_ARAP) Deformation
|
||||
Using 1-ring elements, SR-ARAP adds a bending element to Eq. \f$\eqref{eq:arap_energy}\f$:
|
||||
|
||||
\f[
|
||||
\begin{equation}
|
||||
\f{equation}{
|
||||
\sum_{\mathbf{v}_i \in M}
|
||||
\sum_{\mathbf{v}_j \in N(\mathbf{v}_i)} w_{ij}
|
||||
\left\| (\mathbf{v}'_i - \mathbf{v}'_j) - \mathbf{R}_i(\mathbf{v}_i - \mathbf{v}_j) \right\|^2 + \alpha A \left\| \mathbf{R}_i - \mathbf{R}_j \right\|^2_F
|
||||
\label{eq:sre_arap_energy}
|
||||
\end{equation}
|
||||
\f]
|
||||
\f}
|
||||
|
||||
where
|
||||
- \f$\alpha=0.02\f$ is a weighting coefficient.
|
||||
|
|
|
|||
|
|
@ -93,8 +93,8 @@ template < class Refs, class Point, class ID, class vertex_descriptor>
|
|||
struct Skel_HDS_vertex_type : public HalfedgeDS_vertex_max_base_with_id<Refs, Point, ID>
|
||||
{
|
||||
typedef HalfedgeDS_vertex_max_base_with_id<Refs, Point, ID> Base;
|
||||
Skel_HDS_vertex_type() : Base (), is_fixed(false) {}
|
||||
Skel_HDS_vertex_type( Point const& p) : Base(p), is_fixed(false) {}
|
||||
Skel_HDS_vertex_type() : Base (), pole(ORIGIN), is_fixed(false) {}
|
||||
Skel_HDS_vertex_type( Point const& p) : Base(p), pole(ORIGIN), is_fixed(false) {}
|
||||
std::vector<vertex_descriptor> vertices;
|
||||
Point pole;
|
||||
bool is_fixed;
|
||||
|
|
|
|||
|
|
@ -266,7 +266,7 @@ Triangulation_line_face_circulator_2(const Point& pp,
|
|||
int in;
|
||||
switch(pqs) {
|
||||
case LEFT_TURN:
|
||||
*this = Line_face_circulator();
|
||||
pos = Face_handle();
|
||||
return;
|
||||
case COLLINEAR:
|
||||
fn = fc->neighbor(i);
|
||||
|
|
@ -306,7 +306,7 @@ Triangulation_line_face_circulator_2(const Point& pp,
|
|||
|
||||
// if line (p,q) does not intersect the convex hull in an edge
|
||||
// the circulator has a singular value
|
||||
*this=Line_face_circulator();
|
||||
pos=Face_handle();
|
||||
return;
|
||||
}
|
||||
|
||||
|
|
@ -368,7 +368,7 @@ Triangulation_line_face_circulator_2(const Point& pp,
|
|||
return;
|
||||
} else {
|
||||
// singular value
|
||||
*this = Line_face_circulator();
|
||||
pos=Face_handle();
|
||||
return;
|
||||
}
|
||||
case LEFT_TURN :
|
||||
|
|
|
|||
|
|
@ -129,7 +129,6 @@ does not require preprocessing is advantageous.
|
|||
The following example shows how to obtain the regularized and non-regularized visibility regions.
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\cgalFigureBegin{simple_example, simple_example.png}
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The visibility region of \f$ q \f$ in a simple polygon: (1) non-regularized visibility; and (2) regularized visibility.
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\cgalFigureEnd
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\cgalExample{Visibility_2/simple_polygon_visibility_2.cpp}
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Loading…
Reference in New Issue