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cgal/Kernel_d/test/Kernel_d/interface-test.cpp

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//---------------------------------------------------------------------
// file generated by notangle from noweb/Kernel_d-tests.lw
// please debug or modify noweb file
// coding: M. Seel
//---------------------------------------------------------------------
#include <CGAL/basic.h>
#include <CGAL/Homogeneous_d.h>
#include <CGAL/Cartesian_d.h>
#include <CGAL/constructions_d.h>
#include <CGAL/predicates_d.h>
#include <CGAL/double.h>
#include <CGAL/test_macros.h>
#ifdef CGAL_USE_LEDA
#include <CGAL/leda_integer.h>
#include <CGAL/leda_rational.h>
typedef leda_integer RT_;
typedef leda_rational FT_;
#else
#ifdef CGAL_USE_GMP
#include <CGAL/Gmpz.h>
#include <CGAL/Quotient.h>
typedef CGAL::Gmpz RT_;
typedef CGAL::Quotient<RT_> FT_;
#else
typedef double RT_;
typedef double FT_;
#endif
#endif
int main()
{ SETDTHREAD(2);
CGAL::set_pretty_mode ( std::cerr );
CGAL_TEST_START;
{ // Homogeneous Kernel
typedef CGAL::Homogeneous_d<RT_> Kernel;
typedef Kernel::RT RT;
typedef Kernel::FT FT;
typedef Kernel::LA LA;
typedef CGAL::Point_d<Kernel> Point;
typedef CGAL::Vector_d<Kernel> Vector;
typedef CGAL::Direction_d<Kernel> Direction;
typedef CGAL::Hyperplane_d<Kernel> Hyperplane;
typedef CGAL::Sphere_d<Kernel> Sphere;
typedef CGAL::Segment_d<Kernel> Segment;
typedef CGAL::Ray_d<Kernel> Ray;
typedef CGAL::Line_d<Kernel> Line;
typedef LA::Vector IVector;
bool DOIO=true;
{
/* some construction test */
int IV1[] = {1,0,1};
int IV2[] = {0,1};
IVector iv1(IV1,IV1+3), iv2(IV2,IV2+2);
Point p0(2,CGAL::ORIGIN), p1(2,IV1,IV1+3),
p2(2,iv2.begin(),iv2.end(),1),
p3(2), p4(p1), p5(2,iv2.begin(),iv2.end(),1);
CGAL_TEST(p0 == p3 && p1 == p4 && p2 == p5); // op==
CGAL_TEST(p0 != p1 && p0 != p2); // op!=
CGAL_TEST(p0 == CGAL::ORIGIN);
if (DOIO) CGAL_IO_TEST(p1,p4,CGAL::IO::ASCII); p4 = p1;
CGAL_TEST(p4.dimension()==p1.dimension()); // dimension()
CGAL_TEST(p4.dimension()!=Point(3).dimension()); // dimension()
/* some input and access test */
CGAL_TEST(p1.hx()==RT(1) && p1.hy()==RT(0) && p1.hw()!=RT(0));
CGAL_TEST(p1.hx()==p1.homogeneous(0) &&
p1.hy()==p1.homogeneous(1) &&
p1.hw()==p1.homogeneous(2)); // hx,hy,hw
CGAL_TEST(p1.x()==FT(1) && p1.y()==FT(0)); // x(),y()
CGAL_TEST(p1.x()==p1[0] && p1.y()==p1[1]); // x(),y()
CGAL_TEST(p1.x()==p1.cartesian(0) && p1.y()==p1.cartesian(1)); // x(),y()
Point::Homogeneous_const_iterator hcit; int i;
for (i=0, hcit = p1.homogeneous_begin();
hcit != p1.homogeneous_end(); ++i, ++hcit)
CGAL_TEST(*hcit == iv1[i]);
Point::Homogeneous_const_iterator hit;
Point::Cartesian_const_iterator cit;
Kernel::Cartesian_const_iterator_d cit_begin =
Kernel().construct_cartesian_const_iterator_d_object()(p1);
Kernel::Cartesian_const_iterator_d cit_end =
Kernel().construct_cartesian_const_iterator_d_object()(p1, 1);
for (i=0,hit=p1.homogeneous_begin(),cit=p1.cartesian_begin();
i<p1.dimension(); ++hit,++cit,++i) {
CGAL_TEST(p1.homogeneous(i)==*hit);
CGAL_TEST(p1.cartesian(i)==*cit);
CGAL_TEST(p1.cartesian(i)==*cit_begin);
cit_begin++;
}
CGAL_TEST(cit==p1.cartesian_end());
CGAL_TEST(cit_begin==cit_end);
CGAL_TEST(p1.homogeneous(p1.dimension())==*hit);
CGAL_TEST(++hit == p1.homogeneous_end());
/* the geometric operations and predicates */
CGAL_TEST(CGAL::project_along_d_axis(
CGAL::lift_to_paraboloid(p1)) == p1); // lift and project
Vector vi(7,8,1);
CGAL_TEST(CGAL::midpoint(p1+vi,p1-vi)==p1);
CGAL_TEST(CGAL::squared_distance(p1,p1+vi)==vi.squared_length());
std::vector<Point> A = make_vector(p0,p1,p2);
CGAL_TEST(CGAL::orientation(A.begin(),A.end())==CGAL::POSITIVE);
p3 = Point(1,1,2);
CGAL_TEST(CGAL::side_of_oriented_sphere(A.begin(),A.end(),p3) ==
CGAL::ON_POSITIVE_SIDE);
CGAL_TEST(CGAL::side_of_bounded_sphere(A.begin(),A.end(),p3) ==
CGAL::ON_BOUNDED_SIDE);
p3 = Point(1,1,1);
CGAL_TEST(CGAL::side_of_oriented_sphere(A.begin(),A.end(),p3) ==
CGAL::ON_ORIENTED_BOUNDARY);
CGAL_TEST(CGAL::side_of_bounded_sphere(A.begin(),A.end(),p3) ==
CGAL::ON_BOUNDARY);
p3 = Point(2,2,1);
CGAL_TEST(CGAL::side_of_oriented_sphere(A.begin(),A.end(),p3) ==
CGAL::ON_NEGATIVE_SIDE);
CGAL_TEST(CGAL::side_of_bounded_sphere(A.begin(),A.end(),p3) ==
CGAL::ON_UNBOUNDED_SIDE);
CGAL_TEST(CGAL::side_of_bounded_sphere(A.begin(),A.end(),p3) ==
CGAL::ON_UNBOUNDED_SIDE);
Point B[2] = { p1, p2 };
CGAL_TEST(CGAL::affine_rank(B,B+2)==1);
CGAL_TEST(CGAL::contained_in_affine_hull(B,B+2,Point(1,1,2)));
CGAL_TEST(CGAL::contained_in_affine_hull(B,B+2,Point(1,1,2)+5*(p1-p2)));
CGAL_TEST(CGAL::contained_in_simplex(B,B+2,Point(1,1,2)));
CGAL_TEST(!CGAL::contained_in_simplex(B,B+2,Point(5,5,1)));
CGAL_TEST(!CGAL::contained_in_simplex(B,B+2,Point(1,1,2)+5*(p1-p2)));
CGAL_TEST(CGAL::contained_in_simplex(A.begin(),A.end(),Point(1,1,3)));
CGAL_TEST(!CGAL::contained_in_simplex(A.begin(),A.end(),Point(5,5,1)));
CGAL_TEST(CGAL::affinely_independent(B,B+2));
CGAL_TEST(CGAL::affinely_independent(A.begin(),A.end()));
A.push_back(Point(1,1));
CGAL_TEST(!CGAL::affinely_independent(A.begin(),A.end()));
CGAL_TEST(CGAL::compare_lexicographically(p0,p1)==CGAL::SMALLER);
CGAL_TEST(CGAL::lexicographically_smaller(p0,p1));
CGAL_TEST(CGAL::lexicographically_smaller_or_equal(p0,p1));
CGAL_TEST(CGAL::compare_lexicographically(p1,p0)==CGAL::LARGER);
CGAL_TEST(CGAL::compare_lexicographically(p1,p1)==CGAL::EQUAL);
}
{
/* some construction test */
Point p0(3); // the origin
Vector e1 = Vector(3,Vector::Base_vector(),0);
int IV1[] = {0,1,0,1};
int IV2[] = {0,0,1};
IVector iv1(IV1,IV1+4), iv2(IV2,IV2+3);
// the first unit vector
Point p1(p0 + e1),
p2(3,iv1.begin(),iv1.end()),
p3(3,iv2.begin(),iv2.end(),1),
p4(3);
CGAL_TEST(CGAL::compare_lexicographically(p0,p4)==CGAL::EQUAL);
CGAL_TEST(CGAL::compare_lexicographically(p0,p1)==CGAL::SMALLER);
CGAL_TEST(CGAL::compare_lexicographically(p3,p0)==CGAL::LARGER);
CGAL_TEST(p1.cartesian(0)==FT(1));
CGAL_TEST(p1[1]==FT(0));
CGAL_TEST(p1.homogeneous(0)==Kernel::RT(1));
CGAL_TEST( (p1 - CGAL::ORIGIN) == e1);
CGAL_TEST(CGAL::squared_distance(Point(1,1,1,1),p0)==FT(3));
CGAL_TEST(p1-p0==e1);
CGAL_TEST(p1+e1==Point(2,0,0,1));
CGAL_TEST(p1-e1==p0);
Point p5(3);
CGAL_TEST((p5+=e1)==p1);
CGAL_TEST((p5-=e1)==p0);
/* orientation, sphere position, simplex position */
std::vector<Point> A = make_vector(p0,p1,p2,p4);
CGAL_TEST(CGAL::orientation(A.begin(),A.end())==CGAL::ZERO);
A[3] = p3;
CGAL_TEST(CGAL::orientation(A.begin(),A.end())==CGAL::POSITIVE);
std::swap(A[2],A[3]);
CGAL_TEST(CGAL::orientation(A.begin(),A.end())==CGAL::NEGATIVE);
p4 = Point(1,1,1,2);
std::swap(A[2],A[3]);
CGAL_TEST(CGAL::side_of_oriented_sphere(A.begin(),A.end(),p4)
== CGAL::ON_POSITIVE_SIDE);
p4 = Point(1,1,1,1);
CGAL_TEST(CGAL::side_of_oriented_sphere(A.begin(),A.end(),p4)
== CGAL::ON_ORIENTED_BOUNDARY);
p4 = Point(2,2,2,1);
CGAL_TEST(CGAL::side_of_oriented_sphere(A.begin(),A.end(),p4)
== CGAL::ON_NEGATIVE_SIDE);
std::swap(A[2],A[3]);
p4 = Point(1,1,1,2);
CGAL_TEST(CGAL::side_of_bounded_sphere(A.begin(),A.end(),p4)
== CGAL::ON_BOUNDED_SIDE);
p4 = Point(1,1,1,1);
CGAL_TEST(CGAL::side_of_bounded_sphere(A.begin(),A.end(),p4)
== CGAL::ON_BOUNDARY);
p4 = Point(2,2,2,1);
CGAL_TEST(CGAL::side_of_bounded_sphere(A.begin(),A.end(),p4)
== CGAL::ON_UNBOUNDED_SIDE);
std::swap(A[2],A[3]);
p4 = Point(1,1,1,3);
CGAL_TEST(CGAL::contained_in_simplex(A.begin(),A.end(),p4));
p4 = Point(1,1,1,2);
CGAL_TEST(!CGAL::contained_in_simplex(A.begin(),A.end(),p4));
p4 = Point(1,1,1,1);
CGAL_TEST(!CGAL::contained_in_simplex(A.begin(),A.end(),p4));
/* affine hull, independence and rank */
std::vector<Point> B = make_vector(p1,p2,p3);
p4 = CGAL::midpoint(p1,p2);
CGAL_TEST(CGAL::contained_in_affine_hull(B.begin(),B.end(),p4));
p4 = p0;
CGAL_TEST(!CGAL::contained_in_affine_hull(B.begin(),B.end(),p0));
A[0] = Point(3,3,3,1);
CGAL_TEST(CGAL::affinely_independent(A.begin(),A.end()));
CGAL_TEST(CGAL::affine_rank(A.begin(),A.end())==3);
A[3] = CGAL::midpoint(CGAL::midpoint(A[0],A[1]),A[2]);
CGAL_TEST(!CGAL::affinely_independent(A.begin(),A.end()));
// degenerate_simplex
CGAL_TEST(CGAL::affine_rank(A.begin(),A.end())==2);
// full_simplex
}
{
/* construction and access */
int IV1[] = {1,2,3,1};
int IV2[] = {3,2,1};
IVector i1(IV1,IV1+4), i2(IV2,IV2+3);
Vector a0(3),
a1(3,i1.begin(),i1.end()),
a2(3,i2.begin(),i2.end(),1),
a3(6,4,2,2), a4(1,0,1), a5(1,1,6), a6(a1);
CGAL_TEST((a1==a6 && a3==a2));
CGAL_TEST((a0!=a1 && a0!=a4));
if (DOIO) CGAL_IO_TEST(a1,a6,CGAL::IO::ASCII); a6 = a1;
CGAL_TEST(a2.dimension()==a3.dimension());
CGAL_TEST(a3.dimension()!=a4.dimension());
CGAL_TEST(a4.hx()==RT(1) && a4.hy()==RT(0) && a4.hw()!=RT(0));
CGAL_TEST(a4.x()==FT(1) && a4.y()==FT(0));
CGAL_TEST(Kernel::make_FT(a3.homogeneous(1),a3.homogeneous(3))==FT(2));
CGAL_TEST(a3.cartesian(1)==FT(2));
CGAL_TEST(a3[0]==FT(3));
CGAL_TEST(a3.direction()==Direction(3,2,1));
Vector::Homogeneous_const_iterator hit;
Vector::Cartesian_const_iterator cit; int i;
for (i=0,hit=a1.homogeneous_begin(),cit=a1.cartesian_begin();
i<a1.dimension(); ++hit,++cit,++i) {
CGAL_TEST(a1.homogeneous(i)==*hit);
CGAL_TEST(a1.cartesian(i)==*cit);
}
CGAL_TEST(cit==a1.cartesian_end());
CGAL_TEST(a1.homogeneous(a1.dimension())==*hit);
CGAL_TEST(++hit == a1.homogeneous_end());
/* arithmetical operations and compare */
CGAL_TEST(Vector::cmp(a0,a1)==CGAL::SMALLER);
CGAL_TEST(Vector::cmp(a1,Vector(1,2,3,1))==CGAL::EQUAL);
CGAL_TEST(Vector::cmp(a1,Vector(-1,0,0,1))==CGAL::LARGER);
CGAL_TEST(2*a1==Vector(2,4,6,1));
CGAL_TEST(Kernel::make_FT(2,3)*a4==Vector(2,0,3));
CGAL_TEST(a3/2==Vector(3,2,1,2));
CGAL_TEST(a3/Kernel::make_FT(2,3)==Vector(9,6,3,2));
Vector a7(a1);
a7*=2;
a7*=Kernel::make_FT(3,2);
CGAL_TEST(3*a1==a7);
a7/=Kernel::make_FT(3,4);
a7/=4;
CGAL_TEST(a1==a7);
CGAL_TEST(a4*a4==FT(1));
CGAL_TEST(a4.squared_length()==FT(1));
CGAL_TEST(a1+a2==Vector(4,4,4,1));
CGAL_TEST(a1-a2==Vector(-2,0,2,1));
Vector eins(1,1,1,1);
a7 = a1;
CGAL_TEST((a7+=eins)==a1+eins);
CGAL_TEST((a7-=eins)==a1);
CGAL_TEST(a1-2*a1==-a1);
CGAL_TEST(a0.is_zero());
/* some linear algebra */
std::vector<Vector> P12 = make_vector(a1,a2);
CGAL_TEST(CGAL::contained_in_linear_hull(P12.begin(),P12.end(),a1+a2));
Vector z_off = a1 + Vector(3,Vector::Base_vector(),2);
CGAL_TEST(!CGAL::contained_in_linear_hull(P12.begin(),P12.end(),z_off));
std::vector<Vector> NLI = make_vector(a1,a2,a1+a2),
LI = make_vector(a1,a2,z_off);
CGAL_TEST(CGAL::linearly_independent(LI.begin(),LI.end()));
CGAL_TEST(!CGAL::linearly_independent(NLI.begin(),NLI.end()));
CGAL_TEST(CGAL::linear_rank(LI.begin(),LI.end())==3);
CGAL_TEST(CGAL::linear_rank(NLI.begin(),NLI.end())==2);
std::vector<Vector> LB(3);
std::vector<Vector>::iterator last =
CGAL::linear_base(NLI.begin(),NLI.end(),LB.begin());
CGAL_TEST(CGAL::linearly_independent(LB.begin(),last));
}
{
/* construction and access */
int IV1[] = {1,5,-3,2};
int IV2[] = {1,1,0};
IVector iv1(IV1,IV1+4), iv2(IV2,IV2+3);
Direction d0(3), d1(3,iv1.begin(),iv1.end()),
d2(3,iv2.begin(),iv2.end()),
d31(1,1,1), d32(1,1),
d4 = Direction(3,Direction::Base_direction(),2),
d5(d0);
CGAL_TEST(d0==d5);
CGAL_TEST(d2==Direction(2,2,0));
CGAL_TEST(d31!=d32 && d2!=d1)
if (DOIO) CGAL_IO_TEST(d1,d5,CGAL::IO::ASCII); d5=d1;
CGAL_TEST(d2.dimension()==d1.dimension());
CGAL_TEST(d31.dimension()!=d32.dimension());
CGAL_TEST(d1.dx()==d1.delta(0));
CGAL_TEST(d1.dy()==d1.delta(1));
CGAL_TEST(d1.dz()==d1.delta(2));
CGAL_TEST(d1.dy()==d1[1]);
CGAL_TEST(d4.delta(0)==RT(0) && d4.delta(2)==RT(1));
CGAL_TEST(d4==-Direction(0,0,-1));
CGAL_TEST(d4==Direction(0,0,-1).opposite());
CGAL_TEST(Direction::cmp(d0,d2)==CGAL::SMALLER);
Direction::Delta_const_iterator it; int i;
for (i=0,it=d1.deltas_begin(); i<d1.dimension(); ++it,++i) {
CGAL_TEST(d1.delta(i)==*it);
}
CGAL_TEST(it==d1.deltas_end());
}
{
/* construction and access */
int IV1[] = {1,2,3,4};
int IV2[] = {-4,-3,-2};
IVector vi1(IV1,IV1+4);
IVector vi2(IV2,IV2+3);
// two ivec inits
Point p1(CGAL::ORIGIN + Vector(3,Vector::Base_vector(),0)),
p2(CGAL::ORIGIN + Vector(3,Vector::Base_vector(),1)),
p3(CGAL::ORIGIN + Vector(3,Vector::Base_vector(),2));
// one three point init
Direction dir(1,1,1);
Point o(-1,-1,-1,1), org(3);
// one dir init
Hyperplane h0(3,vi1.begin(),vi1.end());
Hyperplane h1(3,vi2.begin(),vi2.end(),1);
std::vector<Point> V = make_vector(p1,p2,p3);
Hyperplane h2(V.begin(),V.end(),o,CGAL::ON_NEGATIVE_SIDE);
V = make_vector(org,org,org);
Hyperplane h3(V.begin(),V.end(),o,CGAL::ON_POSITIVE_SIDE);
Hyperplane h4(p1,-dir);
Hyperplane h5(1,2,3,4);
Hyperplane h6(1,0,1);
Hyperplane h7(h0);
Hyperplane h8(3);
CGAL_TEST((h5==h0 && h7==h0));
CGAL_TEST((h1!=h0 && h7!=h6));
CGAL_TEST((h2.dimension()==h5.dimension() &&
h2.dimension()!=h6.dimension()));
CGAL_TEST((h5.coefficient(1)==RT(2) && h5[2]==RT(3)));
CGAL_TEST((vi1 == h0.coefficient_vector()));
CGAL_TEST(h2.orthogonal_vector()*(p2-p1) == FT(0) );
CGAL_TEST(h2.orthogonal_direction()==dir);
CGAL_TEST(h2.value_at(o)<FT(0));
CGAL_TEST(h2.value_at(p3)==FT(0));
CGAL_TEST(h2.value_at(p3+dir.vector())>FT(0));
CGAL_TEST(h2.oriented_side(o)==CGAL::ON_NEGATIVE_SIDE);
CGAL_TEST(h2.oriented_side(p3)==CGAL::ON_ORIENTED_BOUNDARY);
CGAL_TEST(h2.oriented_side(p3+dir.vector())==CGAL::ON_POSITIVE_SIDE);
CGAL_TEST(h3.oriented_side(o)==CGAL::ON_POSITIVE_SIDE);
CGAL_TEST(h4.has_on(p1));
CGAL_TEST(h3.has_on(org));
CGAL_TEST(!h5.has_on(p1));
CGAL_TEST(h3.has_on_positive_side(o));
if (DOIO) CGAL_IO_TEST(h0,h8,CGAL::IO::ASCII); h8=h0;
Hyperplane::Coefficient_const_iterator it; int i;
for (i=0,it=h5.coefficients_begin();
i<=h5.dimension(); ++it,++i) {
CGAL_TEST(h5.coefficient(i)==*it);
}
CGAL_TEST(it==h5.coefficients_end());
// all kind of |HyperplaneHd<integer>| inits
/* compares and other operations */
CGAL_TEST(Hyperplane::strong_cmp(h0,h1)>0);
CGAL_TEST(Hyperplane::strong_cmp(h1,h0)<0);
CGAL_TEST(Hyperplane::strong_cmp(h0,h5)==0);
CGAL_TEST(Hyperplane::strong_cmp(h4,h2)<0);
CGAL_TEST(Hyperplane::weak_cmp(h4,h2)==0);
CGAL_TEST(Hyperplane::weak_cmp(h0,h1)>0);
CGAL_TEST(Hyperplane::weak_cmp(h1,h0)<0);
CGAL_TEST(h4!=h2 && CGAL::weak_equality(h4,h2));
}
{
Point p(-1,-1,-1,1);
Point q(1,-1,-1,1);
Point r(-1,1,-1,1);
Point s(1,1,1,1);
std::vector< Point > A = make_vector(p,q,r,s);
Sphere S1(3,A.begin(),A.end()), S2(3), S3(S1), S4 = S1;
CGAL_TEST(S1 == S3 && S1 == S4 && S1 != S2);
CGAL_TEST(S1.dimension()==3);
CGAL_TEST(S1.point(0)==p);
CGAL_TEST(S2.is_degenerate());
CGAL_TEST(S1.orientation()==CGAL::POSITIVE);
CGAL_TEST(S2.orientation()==CGAL::ZERO);
CGAL_TEST(S1.is_legal() && S2.is_legal());
A[2]=A[3];
Sphere S5 = Sphere(3,A.begin(),A.end());
CGAL_TEST((!S5.is_legal()));
Point origin(0,0,0,1);
CGAL_TEST((S1.center()==origin));
CGAL_TEST(S1.has_on_bounded_side(origin));
CGAL_TEST(S1.has_on_positive_side(origin));
CGAL_TEST(!S1.has_on_unbounded_side(origin));
CGAL_TEST(S1.has_on_unbounded_side(Point(2,0,0,1)));
CGAL_TEST(S1.has_on_negative_side(Point(2,0,0,1)));
CGAL_TEST(S1.has_on_boundary(Point(1,-1,1,1)));
CGAL_TEST(S1.oriented_side(origin)==CGAL::ON_POSITIVE_SIDE);
CGAL_TEST(S1.bounded_side(origin)==CGAL::ON_BOUNDED_SIDE);
Vector v(1,0,0,1);
std::vector< Point > B = make_vector(p+v,q+v,r+v,s+v);
CGAL_TEST( (S1+v) == Sphere(3,B.begin(),B.end()) );
CGAL_TEST( CGAL::weak_equality(S1.opposite(),S1) );
if (DOIO) CGAL_IO_TEST(S1,S3,CGAL::IO::ASCII); S3 = S1;
}
{
Point p1(-5,1), p2(5,1);
Vector v(0,5);
Segment s0, s1(p1,p2), s2(p1,v),
s3(Point(-1,-1),Point(5,5)),
s4(Point(1,1,2),Point(5,5,3)),
s5(Point(0,0,1),Point(4,4,1)),
s6(s1);
CGAL_TEST(s6==s1&&s2!=s1&&s5!=s2);
CGAL_TEST(s5.dimension()==2 && s2.dimension()==s3.dimension());
CGAL_TEST(s1.source()==p1 && s1.target()==p2);
CGAL_TEST(s1.vertex(0)==p1 && s1.vertex(1)==p2);
CGAL_TEST(s1.point(0)==p1 && s1.point(1)==p2);
CGAL_TEST(s1[0]==p1 && s1[1]==p2);
CGAL_TEST(s1.opposite()==Segment(p2,p1));
CGAL_TEST((s1.min)()==p1 && (s1.max)()==p2);
CGAL_TEST(s2.vector()==v);
CGAL_TEST(s2.direction()==v.direction());
CGAL_TEST(s1.supporting_line()==Line(p1,p2));
CGAL_TEST((s1 + v)==Segment(Point(-5,6),Point(5,6)));
s6 = Segment(Point(0,0),Point(10,10));
Point p3(10,0);
CGAL_TEST(s6.squared_length()==FT(200));
CGAL_TEST(s6.has_on(Point(5,5)));
CGAL_TEST(Segment(Point(1,1),Point(1,1)).is_degenerate());
CGAL_TEST(CGAL::weak_equality(s1,s1.opposite()));
CGAL_TEST(CGAL::parallel(s6,s6+v));
CGAL_TEST(CGAL::common_endpoint(s1,s2,p3)&&p3==p1);
if (DOIO) CGAL_IO_TEST(s1,s6,CGAL::IO::ASCII); s6 = s1;
}
{
Point p1(2), p2(5,0);
Segment s(Point(1,-1),Point(1,5));
Direction dir(1,0);
Ray r0, r1(p1,p2), r2(p1,dir), r3(s), r4(r1);
Point p3(3), p4(1,1,1,1);
Ray r6(p3,p4);
CGAL_TEST(r1==r4&&r1==r2);
CGAL_TEST(r1!=r3);
CGAL_TEST(r0.dimension()==0&&r1.dimension()==2&&r6.dimension()==3);
CGAL_TEST(r1.source()==p1);
CGAL_TEST(r1.point(0)==p1&&r1.point(1)==p2);
CGAL_TEST(r1.opposite()==Ray(p1,-dir));
CGAL_TEST(r2.direction()==dir);
CGAL_TEST(r1.supporting_line()==r2.supporting_line());
Ray r7(p1+Vector(1,-1),dir);
CGAL_TEST(r1+Vector(1,-1) == r7);
CGAL_TEST(r1.has_on(Point(10,0))&&!r1.has_on(Point(-10,0)));
CGAL_TEST(CGAL::parallel(r1,(r2+Vector(0,1)).opposite()));
if (DOIO) CGAL_IO_TEST(r1,r4,CGAL::IO::ASCII); r4 = r1;
}
{
Point origin(2), p1(5,0), p2(0,5), p3(3,3,2);
Direction dir(7,0);
Vector v(0,2);
Segment s(Point(1,-2),Point(1,2));
Ray r(origin, p3);
Line l1(origin,p1), l2(origin,dir), l3(s), l4(r), l5(l1), l6;
CGAL_TEST(l1==l5&&l1==l2);
CGAL_TEST(l1!=l3&&l1!=l6);
CGAL_TEST(l1.dimension()==2&&l6.dimension()==0);
CGAL_TEST(l1.point(0)==origin&&l1.point(1)==p1);
CGAL_TEST(l1.opposite()==Line(p1,-dir));
CGAL_TEST(l2.direction()==dir);
CGAL_TEST(l1+v==Line(origin+v,dir));
CGAL_TEST(l1.projection(Point(1,1))==Point(1,0));
CGAL_TEST(l1.has_on(Point(3,0))&&!l1.has_on(p2));
CGAL_TEST(CGAL::weak_equality(l1,l1.opposite())&&l1!=l1.opposite());
CGAL_TEST(CGAL::parallel(l2,Line(p2,dir)));
if (DOIO) CGAL_IO_TEST(l1,l5,CGAL::IO::ASCII); l5 = l1;
}
}
{ // Cartesian Kernel
typedef CGAL::Cartesian_d<FT_> Kernel;
typedef Kernel::FT FT;
typedef Kernel::RT RT;
typedef Kernel::LA LA;
typedef CGAL::Point_d<Kernel> Point;
typedef CGAL::Vector_d<Kernel> Vector;
typedef CGAL::Direction_d<Kernel> Direction;
typedef CGAL::Hyperplane_d<Kernel> Hyperplane;
typedef CGAL::Sphere_d<Kernel> Sphere;
typedef CGAL::Segment_d<Kernel> Segment;
typedef CGAL::Ray_d<Kernel> Ray;
typedef CGAL::Line_d<Kernel> Line;
typedef LA::Vector IVector;
bool DOIO=false;
{
/* some construction test */
int IV1[] = {1,0,1};
int IV2[] = {0,1};
IVector iv1(IV1,IV1+3), iv2(IV2,IV2+2);
Point p0(2,CGAL::ORIGIN), p1(2,IV1,IV1+3),
p2(2,iv2.begin(),iv2.end(),1),
p3(2), p4(p1), p5(2,iv2.begin(),iv2.end(),1);
CGAL_TEST(p0 == p3 && p1 == p4 && p2 == p5); // op==
CGAL_TEST(p0 != p1 && p0 != p2); // op!=
CGAL_TEST(p0 == CGAL::ORIGIN);
if (DOIO) CGAL_IO_TEST(p1,p4,CGAL::IO::ASCII); p4 = p1;
CGAL_TEST(p4.dimension()==p1.dimension()); // dimension()
CGAL_TEST(p4.dimension()!=Point(3).dimension()); // dimension()
/* some input and access test */
CGAL_TEST(p1.hx()==RT(1) && p1.hy()==RT(0) && p1.hw()!=RT(0));
CGAL_TEST(p1.hx()==p1.homogeneous(0) &&
p1.hy()==p1.homogeneous(1) &&
p1.hw()==p1.homogeneous(2)); // hx,hy,hw
CGAL_TEST(p1.x()==FT(1) && p1.y()==FT(0)); // x(),y()
CGAL_TEST(p1.x()==p1[0] && p1.y()==p1[1]); // x(),y()
CGAL_TEST(p1.x()==p1.cartesian(0) && p1.y()==p1.cartesian(1)); // x(),y()
Point::Homogeneous_const_iterator hcit; int i;
for (i=0, hcit = p1.homogeneous_begin();
hcit != p1.homogeneous_end(); ++i, ++hcit)
CGAL_TEST(*hcit == iv1[i]);
Point::Homogeneous_const_iterator hit;
Point::Cartesian_const_iterator cit;
Kernel::Cartesian_const_iterator_d cit_begin =
Kernel().construct_cartesian_const_iterator_d_object()(p1);
Kernel::Cartesian_const_iterator_d cit_end =
Kernel().construct_cartesian_const_iterator_d_object()(p1, 1);
for (i=0,hit=p1.homogeneous_begin(),cit=p1.cartesian_begin();
i<p1.dimension(); ++hit,++cit,++i) {
CGAL_TEST(p1.homogeneous(i)==*hit);
CGAL_TEST(p1.cartesian(i)==*cit);
CGAL_TEST(p1.cartesian(i)==*cit_begin);
cit_begin++;
}
CGAL_TEST(cit==p1.cartesian_end());
CGAL_TEST(cit_begin==cit_end);
CGAL_TEST(p1.homogeneous(p1.dimension())==*hit);
CGAL_TEST(++hit == p1.homogeneous_end());
/* the geometric operations and predicates */
CGAL_TEST(CGAL::project_along_d_axis(
CGAL::lift_to_paraboloid(p1)) == p1); // lift and project
Vector vi(7,8,1);
CGAL_TEST(CGAL::midpoint(p1+vi,p1-vi)==p1);
CGAL_TEST(CGAL::squared_distance(p1,p1+vi)==vi.squared_length());
std::vector<Point> A = make_vector(p0,p1,p2);
CGAL_TEST(CGAL::orientation(A.begin(),A.end())==CGAL::POSITIVE);
p3 = Point(1,1,2);
CGAL_TEST(CGAL::side_of_oriented_sphere(A.begin(),A.end(),p3) ==
CGAL::ON_POSITIVE_SIDE);
CGAL_TEST(CGAL::side_of_bounded_sphere(A.begin(),A.end(),p3) ==
CGAL::ON_BOUNDED_SIDE);
p3 = Point(1,1,1);
CGAL_TEST(CGAL::side_of_oriented_sphere(A.begin(),A.end(),p3) ==
CGAL::ON_ORIENTED_BOUNDARY);
CGAL_TEST(CGAL::side_of_bounded_sphere(A.begin(),A.end(),p3) ==
CGAL::ON_BOUNDARY);
p3 = Point(2,2,1);
CGAL_TEST(CGAL::side_of_oriented_sphere(A.begin(),A.end(),p3) ==
CGAL::ON_NEGATIVE_SIDE);
CGAL_TEST(CGAL::side_of_bounded_sphere(A.begin(),A.end(),p3) ==
CGAL::ON_UNBOUNDED_SIDE);
CGAL_TEST(CGAL::side_of_bounded_sphere(A.begin(),A.end(),p3) ==
CGAL::ON_UNBOUNDED_SIDE);
Point B[2] = { p1, p2 };
CGAL_TEST(CGAL::affine_rank(B,B+2)==1);
CGAL_TEST(CGAL::contained_in_affine_hull(B,B+2,Point(1,1,2)));
CGAL_TEST(CGAL::contained_in_affine_hull(B,B+2,Point(1,1,2)+5*(p1-p2)));
CGAL_TEST(CGAL::contained_in_simplex(B,B+2,Point(1,1,2)));
CGAL_TEST(!CGAL::contained_in_simplex(B,B+2,Point(5,5,1)));
CGAL_TEST(!CGAL::contained_in_simplex(B,B+2,Point(1,1,2)+5*(p1-p2)));
CGAL_TEST(CGAL::contained_in_simplex(A.begin(),A.end(),Point(1,1,3)));
CGAL_TEST(!CGAL::contained_in_simplex(A.begin(),A.end(),Point(5,5,1)));
CGAL_TEST(CGAL::affinely_independent(B,B+2));
CGAL_TEST(CGAL::affinely_independent(A.begin(),A.end()));
A.push_back(Point(1,1));
CGAL_TEST(!CGAL::affinely_independent(A.begin(),A.end()));
CGAL_TEST(CGAL::compare_lexicographically(p0,p1)==CGAL::SMALLER);
CGAL_TEST(CGAL::lexicographically_smaller(p0,p1));
CGAL_TEST(CGAL::lexicographically_smaller_or_equal(p0,p1));
CGAL_TEST(CGAL::compare_lexicographically(p1,p0)==CGAL::LARGER);
CGAL_TEST(CGAL::compare_lexicographically(p1,p1)==CGAL::EQUAL);
}
{
/* some construction test */
Point p0(3); // the origin
Vector e1 = Vector(3,Vector::Base_vector(),0);
int IV1[] = {0,1,0,1};
int IV2[] = {0,0,1};
IVector iv1(IV1,IV1+4), iv2(IV2,IV2+3);
// the first unit vector
Point p1(p0 + e1),
p2(3,iv1.begin(),iv1.end()),
p3(3,iv2.begin(),iv2.end(),1),
p4(3);
CGAL_TEST(CGAL::compare_lexicographically(p0,p4)==CGAL::EQUAL);
CGAL_TEST(CGAL::compare_lexicographically(p0,p1)==CGAL::SMALLER);
CGAL_TEST(CGAL::compare_lexicographically(p3,p0)==CGAL::LARGER);
CGAL_TEST(p1.cartesian(0)==FT(1));
CGAL_TEST(p1[1]==FT(0));
CGAL_TEST(p1.homogeneous(0)==Kernel::RT(1));
CGAL_TEST( (p1 - CGAL::ORIGIN) == e1);
CGAL_TEST(CGAL::squared_distance(Point(1,1,1,1),p0)==FT(3));
CGAL_TEST(p1-p0==e1);
CGAL_TEST(p1+e1==Point(2,0,0,1));
CGAL_TEST(p1-e1==p0);
Point p5(3);
CGAL_TEST((p5+=e1)==p1);
CGAL_TEST((p5-=e1)==p0);
/* orientation, sphere position, simplex position */
std::vector<Point> A = make_vector(p0,p1,p2,p4);
CGAL_TEST(CGAL::orientation(A.begin(),A.end())==CGAL::ZERO);
A[3] = p3;
CGAL_TEST(CGAL::orientation(A.begin(),A.end())==CGAL::POSITIVE);
std::swap(A[2],A[3]);
CGAL_TEST(CGAL::orientation(A.begin(),A.end())==CGAL::NEGATIVE);
p4 = Point(1,1,1,2);
std::swap(A[2],A[3]);
CGAL_TEST(CGAL::side_of_oriented_sphere(A.begin(),A.end(),p4)
== CGAL::ON_POSITIVE_SIDE);
p4 = Point(1,1,1,1);
CGAL_TEST(CGAL::side_of_oriented_sphere(A.begin(),A.end(),p4)
== CGAL::ON_ORIENTED_BOUNDARY);
p4 = Point(2,2,2,1);
CGAL_TEST(CGAL::side_of_oriented_sphere(A.begin(),A.end(),p4)
== CGAL::ON_NEGATIVE_SIDE);
std::swap(A[2],A[3]);
p4 = Point(1,1,1,2);
CGAL_TEST(CGAL::side_of_bounded_sphere(A.begin(),A.end(),p4)
== CGAL::ON_BOUNDED_SIDE);
p4 = Point(1,1,1,1);
CGAL_TEST(CGAL::side_of_bounded_sphere(A.begin(),A.end(),p4)
== CGAL::ON_BOUNDARY);
p4 = Point(2,2,2,1);
CGAL_TEST(CGAL::side_of_bounded_sphere(A.begin(),A.end(),p4)
== CGAL::ON_UNBOUNDED_SIDE);
std::swap(A[2],A[3]);
p4 = Point(1,1,1,3);
CGAL_TEST(CGAL::contained_in_simplex(A.begin(),A.end(),p4));
p4 = Point(1,1,1,2);
CGAL_TEST(!CGAL::contained_in_simplex(A.begin(),A.end(),p4));
p4 = Point(1,1,1,1);
CGAL_TEST(!CGAL::contained_in_simplex(A.begin(),A.end(),p4));
/* affine hull, independence and rank */
std::vector<Point> B = make_vector(p1,p2,p3);
p4 = CGAL::midpoint(p1,p2);
CGAL_TEST(CGAL::contained_in_affine_hull(B.begin(),B.end(),p4));
p4 = p0;
CGAL_TEST(!CGAL::contained_in_affine_hull(B.begin(),B.end(),p0));
A[0] = Point(3,3,3,1);
CGAL_TEST(CGAL::affinely_independent(A.begin(),A.end()));
CGAL_TEST(CGAL::affine_rank(A.begin(),A.end())==3);
A[3] = CGAL::midpoint(CGAL::midpoint(A[0],A[1]),A[2]);
CGAL_TEST(!CGAL::affinely_independent(A.begin(),A.end()));
// degenerate_simplex
CGAL_TEST(CGAL::affine_rank(A.begin(),A.end())==2);
// full_simplex
}
{
/* construction and access */
int IV1[] = {1,2,3,1};
int IV2[] = {3,2,1};
IVector i1(IV1,IV1+4), i2(IV2,IV2+3);
Vector a0(3),
a1(3,i1.begin(),i1.end()),
a2(3,i2.begin(),i2.end(),1),
a3(6,4,2,2), a4(1,0,1), a5(1,1,6), a6(a1);
CGAL_TEST((a1==a6 && a3==a2));
CGAL_TEST((a0!=a1 && a0!=a4));
if (DOIO) CGAL_IO_TEST(a1,a6,CGAL::IO::ASCII); a6 = a1;
CGAL_TEST(a2.dimension()==a3.dimension());
CGAL_TEST(a3.dimension()!=a4.dimension());
CGAL_TEST(a4.hx()==RT(1) && a4.hy()==RT(0) && a4.hw()!=RT(0));
CGAL_TEST(a4.x()==FT(1) && a4.y()==FT(0));
CGAL_TEST(Kernel::make_FT(a3.homogeneous(1),a3.homogeneous(3))==FT(2));
CGAL_TEST(a3.cartesian(1)==FT(2));
CGAL_TEST(a3[0]==FT(3));
CGAL_TEST(a3.direction()==Direction(3,2,1));
Vector::Homogeneous_const_iterator hit;
Vector::Cartesian_const_iterator cit; int i;
for (i=0,hit=a1.homogeneous_begin(),cit=a1.cartesian_begin();
i<a1.dimension(); ++hit,++cit,++i) {
CGAL_TEST(a1.homogeneous(i)==*hit);
CGAL_TEST(a1.cartesian(i)==*cit);
}
CGAL_TEST(cit==a1.cartesian_end());
CGAL_TEST(a1.homogeneous(a1.dimension())==*hit);
CGAL_TEST(++hit == a1.homogeneous_end());
/* arithmetical operations and compare */
CGAL_TEST(Vector::cmp(a0,a1)==CGAL::SMALLER);
CGAL_TEST(Vector::cmp(a1,Vector(1,2,3,1))==CGAL::EQUAL);
CGAL_TEST(Vector::cmp(a1,Vector(-1,0,0,1))==CGAL::LARGER);
CGAL_TEST(2*a1==Vector(2,4,6,1));
CGAL_TEST(Kernel::make_FT(2,3)*a4==Vector(2,0,3));
CGAL_TEST(a3/2==Vector(3,2,1,2));
CGAL_TEST(a3/Kernel::make_FT(2,3)==Vector(9,6,3,2));
Vector a7(a1);
a7*=2;
a7*=Kernel::make_FT(3,2);
CGAL_TEST(3*a1==a7);
a7/=Kernel::make_FT(3,4);
a7/=4;
CGAL_TEST(a1==a7);
CGAL_TEST(a4*a4==FT(1));
CGAL_TEST(a4.squared_length()==FT(1));
CGAL_TEST(a1+a2==Vector(4,4,4,1));
CGAL_TEST(a1-a2==Vector(-2,0,2,1));
Vector eins(1,1,1,1);
a7 = a1;
CGAL_TEST((a7+=eins)==a1+eins);
CGAL_TEST((a7-=eins)==a1);
CGAL_TEST(a1-2*a1==-a1);
CGAL_TEST(a0.is_zero());
/* some linear algebra */
std::vector<Vector> P12 = make_vector(a1,a2);
CGAL_TEST(CGAL::contained_in_linear_hull(P12.begin(),P12.end(),a1+a2));
Vector z_off = a1 + Vector(3,Vector::Base_vector(),2);
CGAL_TEST(!CGAL::contained_in_linear_hull(P12.begin(),P12.end(),z_off));
std::vector<Vector> NLI = make_vector(a1,a2,a1+a2),
LI = make_vector(a1,a2,z_off);
CGAL_TEST(CGAL::linearly_independent(LI.begin(),LI.end()));
CGAL_TEST(!CGAL::linearly_independent(NLI.begin(),NLI.end()));
CGAL_TEST(CGAL::linear_rank(LI.begin(),LI.end())==3);
CGAL_TEST(CGAL::linear_rank(NLI.begin(),NLI.end())==2);
std::vector<Vector> LB(3);
std::vector<Vector>::iterator last =
CGAL::linear_base(NLI.begin(),NLI.end(),LB.begin());
CGAL_TEST(CGAL::linearly_independent(LB.begin(),last));
}
{
/* construction and access */
int IV1[] = {1,5,-3,2};
int IV2[] = {1,1,0};
IVector iv1(IV1,IV1+4), iv2(IV2,IV2+3);
Direction d0(3), d1(3,iv1.begin(),iv1.end()),
d2(3,iv2.begin(),iv2.end()),
d31(1,1,1), d32(1,1),
d4 = Direction(3,Direction::Base_direction(),2),
d5(d0);
CGAL_TEST(d0==d5);
CGAL_TEST(d2==Direction(2,2,0));
CGAL_TEST(d31!=d32 && d2!=d1)
if (DOIO) CGAL_IO_TEST(d1,d5,CGAL::IO::ASCII); d5=d1;
CGAL_TEST(d2.dimension()==d1.dimension());
CGAL_TEST(d31.dimension()!=d32.dimension());
CGAL_TEST(d1.dx()==d1.delta(0));
CGAL_TEST(d1.dy()==d1.delta(1));
CGAL_TEST(d1.dz()==d1.delta(2));
CGAL_TEST(d1.dy()==d1[1]);
CGAL_TEST(d4.delta(0)==RT(0) && d4.delta(2)==RT(1));
CGAL_TEST(d4==-Direction(0,0,-1));
CGAL_TEST(d4==Direction(0,0,-1).opposite());
CGAL_TEST(Direction::cmp(d0,d2)==CGAL::SMALLER);
Direction::Delta_const_iterator it; int i;
for (i=0,it=d1.deltas_begin(); i<d1.dimension(); ++it,++i) {
CGAL_TEST(d1.delta(i)==*it);
}
CGAL_TEST(it==d1.deltas_end());
}
{
/* construction and access */
int IV1[] = {1,2,3,4};
int IV2[] = {-4,-3,-2};
IVector vi1(IV1,IV1+4);
IVector vi2(IV2,IV2+3);
// two ivec inits
Point p1(CGAL::ORIGIN + Vector(3,Vector::Base_vector(),0)),
p2(CGAL::ORIGIN + Vector(3,Vector::Base_vector(),1)),
p3(CGAL::ORIGIN + Vector(3,Vector::Base_vector(),2));
// one three point init
Direction dir(1,1,1);
Point o(-1,-1,-1,1), org(3);
// one dir init
Hyperplane h0(3,vi1.begin(),vi1.end());
Hyperplane h1(3,vi2.begin(),vi2.end(),1);
std::vector<Point> V = make_vector(p1,p2,p3);
Hyperplane h2(V.begin(),V.end(),o,CGAL::ON_NEGATIVE_SIDE);
V = make_vector(org,org,org);
Hyperplane h3(V.begin(),V.end(),o,CGAL::ON_POSITIVE_SIDE);
Hyperplane h4(p1,-dir);
Hyperplane h5(1,2,3,4);
Hyperplane h6(1,0,1);
Hyperplane h7(h0);
Hyperplane h8(3);
CGAL_TEST((h5==h0 && h7==h0));
CGAL_TEST((h1!=h0 && h7!=h6));
CGAL_TEST((h2.dimension()==h5.dimension() &&
h2.dimension()!=h6.dimension()));
CGAL_TEST((h5.coefficient(1)==RT(2) && h5[2]==RT(3)));
CGAL_TEST((vi1 == h0.coefficient_vector()));
CGAL_TEST(h2.orthogonal_vector()*(p2-p1) == FT(0) );
CGAL_TEST(h2.orthogonal_direction()==dir);
CGAL_TEST(h2.value_at(o)<FT(0));
CGAL_TEST(h2.value_at(p3)==FT(0));
CGAL_TEST(h2.value_at(p3+dir.vector())>FT(0));
CGAL_TEST(h2.oriented_side(o)==CGAL::ON_NEGATIVE_SIDE);
CGAL_TEST(h2.oriented_side(p3)==CGAL::ON_ORIENTED_BOUNDARY);
CGAL_TEST(h2.oriented_side(p3+dir.vector())==CGAL::ON_POSITIVE_SIDE);
CGAL_TEST(h3.oriented_side(o)==CGAL::ON_POSITIVE_SIDE);
CGAL_TEST(h4.has_on(p1));
CGAL_TEST(h3.has_on(org));
CGAL_TEST(!h5.has_on(p1));
CGAL_TEST(h3.has_on_positive_side(o));
if (DOIO) CGAL_IO_TEST(h0,h8,CGAL::IO::ASCII); h8=h0;
Hyperplane::Coefficient_const_iterator it; int i;
for (i=0,it=h5.coefficients_begin();
i<=h5.dimension(); ++it,++i) {
CGAL_TEST(h5.coefficient(i)==*it);
}
CGAL_TEST(it==h5.coefficients_end());
// all kind of |HyperplaneHd<integer>| inits
/* compares and other operations */
CGAL_TEST(Hyperplane::strong_cmp(h0,h1)>0);
CGAL_TEST(Hyperplane::strong_cmp(h1,h0)<0);
CGAL_TEST(Hyperplane::strong_cmp(h0,h5)==0);
CGAL_TEST(Hyperplane::strong_cmp(h4,h2)<0);
CGAL_TEST(Hyperplane::weak_cmp(h4,h2)==0);
CGAL_TEST(Hyperplane::weak_cmp(h0,h1)>0);
CGAL_TEST(Hyperplane::weak_cmp(h1,h0)<0);
CGAL_TEST(h4!=h2 && CGAL::weak_equality(h4,h2));
}
{
Point p(-1,-1,-1,1);
Point q(1,-1,-1,1);
Point r(-1,1,-1,1);
Point s(1,1,1,1);
std::vector< Point > A = make_vector(p,q,r,s);
Sphere S1(3,A.begin(),A.end()), S2(3), S3(S1), S4 = S1;
CGAL_TEST(S1 == S3 && S1 == S4 && S1 != S2);
CGAL_TEST(S1.dimension()==3);
CGAL_TEST(S1.point(0)==p);
CGAL_TEST(S2.is_degenerate());
CGAL_TEST(S1.orientation()==CGAL::POSITIVE);
CGAL_TEST(S2.orientation()==CGAL::ZERO);
CGAL_TEST(S1.is_legal() && S2.is_legal());
A[2]=A[3];
Sphere S5 = Sphere(3,A.begin(),A.end());
CGAL_TEST((!S5.is_legal()));
Point origin(0,0,0,1);
CGAL_TEST((S1.center()==origin));
CGAL_TEST(S1.has_on_bounded_side(origin));
CGAL_TEST(S1.has_on_positive_side(origin));
CGAL_TEST(!S1.has_on_unbounded_side(origin));
CGAL_TEST(S1.has_on_unbounded_side(Point(2,0,0,1)));
CGAL_TEST(S1.has_on_negative_side(Point(2,0,0,1)));
CGAL_TEST(S1.has_on_boundary(Point(1,-1,1,1)));
CGAL_TEST(S1.oriented_side(origin)==CGAL::ON_POSITIVE_SIDE);
CGAL_TEST(S1.bounded_side(origin)==CGAL::ON_BOUNDED_SIDE);
Vector v(1,0,0,1);
std::vector< Point > B = make_vector(p+v,q+v,r+v,s+v);
CGAL_TEST( (S1+v) == Sphere(3,B.begin(),B.end()) );
CGAL_TEST( CGAL::weak_equality(S1.opposite(),S1) );
if (DOIO) CGAL_IO_TEST(S1,S3,CGAL::IO::ASCII); S3 = S1;
}
{
Point p1(-5,1), p2(5,1);
Vector v(0,5);
Segment s0, s1(p1,p2), s2(p1,v),
s3(Point(-1,-1),Point(5,5)),
s4(Point(1,1,2),Point(5,5,3)),
s5(Point(0,0,1),Point(4,4,1)),
s6(s1);
CGAL_TEST(s6==s1&&s2!=s1&&s5!=s2);
CGAL_TEST(s5.dimension()==2 && s2.dimension()==s3.dimension());
CGAL_TEST(s1.source()==p1 && s1.target()==p2);
CGAL_TEST(s1.vertex(0)==p1 && s1.vertex(1)==p2);
CGAL_TEST(s1.point(0)==p1 && s1.point(1)==p2);
CGAL_TEST(s1[0]==p1 && s1[1]==p2);
CGAL_TEST(s1.opposite()==Segment(p2,p1));
CGAL_TEST((s1.min)()==p1 && (s1.max)()==p2);
CGAL_TEST(s2.vector()==v);
CGAL_TEST(s2.direction()==v.direction());
CGAL_TEST(s1.supporting_line()==Line(p1,p2));
CGAL_TEST((s1 + v)==Segment(Point(-5,6),Point(5,6)));
s6 = Segment(Point(0,0),Point(10,10));
Point p3(10,0);
CGAL_TEST(s6.squared_length()==FT(200));
CGAL_TEST(s6.has_on(Point(5,5)));
CGAL_TEST(Segment(Point(1,1),Point(1,1)).is_degenerate());
CGAL_TEST(CGAL::weak_equality(s1,s1.opposite()));
CGAL_TEST(CGAL::parallel(s6,s6+v));
CGAL_TEST(CGAL::common_endpoint(s1,s2,p3)&&p3==p1);
if (DOIO) CGAL_IO_TEST(s1,s6,CGAL::IO::ASCII); s6 = s1;
}
{
Point p1(2), p2(5,0);
Segment s(Point(1,-1),Point(1,5));
Direction dir(1,0);
Ray r0, r1(p1,p2), r2(p1,dir), r3(s), r4(r1);
Point p3(3), p4(1,1,1,1);
Ray r6(p3,p4);
CGAL_TEST(r1==r4&&r1==r2);
CGAL_TEST(r1!=r3);
CGAL_TEST(r0.dimension()==0&&r1.dimension()==2&&r6.dimension()==3);
CGAL_TEST(r1.source()==p1);
CGAL_TEST(r1.point(0)==p1&&r1.point(1)==p2);
CGAL_TEST(r1.opposite()==Ray(p1,-dir));
CGAL_TEST(r2.direction()==dir);
CGAL_TEST(r1.supporting_line()==r2.supporting_line());
Ray r7(p1+Vector(1,-1),dir);
CGAL_TEST(r1+Vector(1,-1) == r7);
CGAL_TEST(r1.has_on(Point(10,0))&&!r1.has_on(Point(-10,0)));
CGAL_TEST(CGAL::parallel(r1,(r2+Vector(0,1)).opposite()));
if (DOIO) CGAL_IO_TEST(r1,r4,CGAL::IO::ASCII); r4 = r1;
}
{
Point origin(2), p1(5,0), p2(0,5), p3(3,3,2);
Direction dir(7,0);
Vector v(0,2);
Segment s(Point(1,-2),Point(1,2));
Ray r(origin, p3);
Line l1(origin,p1), l2(origin,dir), l3(s), l4(r), l5(l1), l6;
CGAL_TEST(l1==l5&&l1==l2);
CGAL_TEST(l1!=l3&&l1!=l6);
CGAL_TEST(l1.dimension()==2&&l6.dimension()==0);
CGAL_TEST(l1.point(0)==origin&&l1.point(1)==p1);
CGAL_TEST(l1.opposite()==Line(p1,-dir));
CGAL_TEST(l2.direction()==dir);
CGAL_TEST(l1+v==Line(origin+v,dir));
CGAL_TEST(l1.projection(Point(1,1))==Point(1,0));
CGAL_TEST(l1.has_on(Point(3,0))&&!l1.has_on(p2));
CGAL_TEST(CGAL::weak_equality(l1,l1.opposite())&&l1!=l1.opposite());
CGAL_TEST(CGAL::parallel(l2,Line(p2,dir)));
if (DOIO) CGAL_IO_TEST(l1,l5,CGAL::IO::ASCII); l5 = l1;
}
}
CGAL_TEST_END;
}
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