mirror of https://github.com/CGAL/cgal
PCA: update doc and description
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\begin{ccPkgDescription}{Principal Component Analysis\label{Pkg:PrincipalComponentAnalysisD}}
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\ccPkgHowToCiteCgal{cgal:ap-pcad-08}
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\ccPkgSummary{This package provides functions to compute global information about the shape of a set of 2D or 3D objects. It provides the computation of axis-aligned bounding boxes for sets of bounded objects, and barycenters of weighted point sets. In addition, it provides computation of centroids (center of mass) and linear least squares fitting for point sets as well as for sets of other bounded objects. More specifically, it is possible to fit 2D lines to 2D segments, circles, disks, iso rectangles and triangles, as well as to fit 3D lines or 3D planes to 3D segments, triangles, iso cuboids, tetrahedra, spheres and balls. The common interface to these functions takes an iterator range of objects.}
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\ccPkgSummary{This package provides functions to compute global information about the shape of a set of 2D or 3D objects. It provides the computation of axis-aligned bounding boxes for point sets, and barycenters of weighted point sets. In addition, it provides computation of centroids (center of mass) and linear least squares fitting for point sets as well as for sets of other bounded objects. More specifically, it is possible to fit 2D lines to 2D segments, circles, disks, iso rectangles and triangles, as well as to fit 3D lines or 3D planes to 3D segments, triangles, iso cuboids, tetrahedra, spheres and balls. The common interface to these functions takes an iterator range of objects.}
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%\ccPkgDependsOn{}
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\ccPkgIntroducedInCGAL{3.2}
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@ -5,16 +5,16 @@ In the following example we use \stl\ containers of 2D points and 3D points, and
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\ccIncludeExampleCode{Principal_component_analysis/bounding_box.cpp}
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\subsection{Centroid of 2D and 3D Objects}
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In the following example we use \stl\ containers of 2D and 3D points and 3D triangles, and compute their centroid. The kernel from which the input points originate is automatically deduced by the function. The dimension tag indicates the dimension of the objects being fitted (0 for points, and 2 for triangles). Note that it is also possible to compute the centroid of the triangle edges (3D segments) by specifying 1 as dimension tag, and of the triangle vertices (3D points) by specifying 0 as dimension tag. \ccIncludeExampleCode{Principal_component_analysis/centroid.cpp}
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In the following example we use \stl\ containers of 2D, 3D points and 3D triangles, and compute their centroid. The kernel from which the input objects originate is automatically deduced by the function. The dimension tag indicates the dimension of the objects being fitted (0 for points, 2 for triangles). Note that it is also possible to compute the centroid of the triangle edges (3D segments) by specifying 1 as dimension tag, and to compute the centroid of the triangle vertices (3D points) by specifying 0 as dimension tag. \ccIncludeExampleCode{Principal_component_analysis/centroid.cpp}
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\subsection{Barycenter of a Set of Weighted Points}
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In the following example we use \stl\ containers of 2D and 3D weighted points, and compute their barycenter. The kernel from which the input points originate is automatically deduced by the function. \ccIncludeExampleCode{Principal_component_analysis/barycenter.cpp}
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In the following example we use \stl\ containers of 2D and 3D weighted points, and compute their barycenter. The kernel from which the input weighted points originate is automatically deduced by the function. \ccIncludeExampleCode{Principal_component_analysis/barycenter.cpp}
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\subsection{Least Squares Fitting of a Line to a 2D Point Set}
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In the following example we use a \stl\ container of 2D points, and compute the best fitting line in the least squares sense. The kernel from which the input points originate is automatically deduced by the function.
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\ccIncludeExampleCode{Principal_component_analysis/linear_least_squares_fitting_points_2.cpp}
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\subsection{Least Squares Fitting of a Line and a Plane to a 3D Triangle Set}
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In the following example we use a \stl\ container of 3D triangles, and compute the best fitting line and plane in the least squares sense. The kernel from which the input points originate is automatically deduced by the function. Note that we can fit either the whole triangles, the triangle edges or the triangle vertices.
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In the following example we use a \stl\ container of 3D triangles, and compute the best fitting line and plane in the least squares sense. The kernel from which the input triangles originate is automatically deduced by the function. Note that we can fit either the whole triangles, the triangle edges or the triangle vertices.
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\ccIncludeExampleCode{Principal_component_analysis/linear_least_squares_fitting_triangles_3.cpp}
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@ -11,17 +11,7 @@
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\ccChapterAuthor{Pierre Alliez, Sylvain Pion and Ankit Gupta}
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This \cgal\ package provides functions to compute global information
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about the shape of a set of 2D or 3D objects. It provides the
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computation of axis-aligned bounding boxes for sets of bounded
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objects, and barycenters of weighted point sets. In addition, it
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provides computation of centroids (center of mass) and linear least
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squares fitting for point sets as well as for sets of other bounded
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objects. More specifically, it is possible to fit 2D lines to 2D
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segments, circles, disks, iso rectangles and triangles, as well as to
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fit 3D lines or 3D planes to 3D segments, triangles, iso cuboids,
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tetrahedra, spheres and balls. The common interface to these functions
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takes an iterator range of objects.
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This \cgal\ package provides functions to compute global information about the shape of a set of 2D or 3D objects. It provides the computation of axis-aligned bounding boxes for point sets, and barycenters of weighted point sets. In addition, it provides computation of centroids (center of mass) and linear least squares fitting for point sets as well as for sets of other bounded objects. More specifically, it is possible to fit 2D lines to 2D segments, circles, disks, iso rectangles and triangles, as well as to fit 3D lines or 3D planes to 3D segments, triangles, iso cuboids, tetrahedra, spheres and balls. The common interface to these functions takes an iterator range of objects.
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\section{Classified Reference Pages}
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@ -2,6 +2,6 @@ Package Principal Component Analysis
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- provides functions for linear fitting (in the least squares sense)
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of sets of 2D and 3D kernel objects.
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- some basic shape analysis functions :
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bounding_box()
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centroid()
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barycenter() only for sets of weighted points
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bounding_box() for point sets.
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centroid() for sets of 2D and 3D kernel objects.
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barycenter() only for sets of weighted points.
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