119 lines
5.5 KiB
C
119 lines
5.5 KiB
C
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#ifndef IGL_FAST_WINDING_NUMBER
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#define IGL_FAST_WINDING_NUMBER
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#include "igl_inline.h"
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#include <Eigen/Core>
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#include <vector>
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namespace igl
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{
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// Generate the precomputation for the fast winding number for point data
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// [Barill et. al 2018].
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//
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// Given a set of 3D points P, with normals N, areas A, along with octree
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// data, and an expansion order, we define a taylor series expansion at each
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// octree cell.
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//
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// The octree data is designed to come from igl::octree, and the areas
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// (if not obtained at scan time), may be calculated using
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// igl::copyleft::cgal::point_areas.
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//
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// Inputs:
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// P #P by 3 list of point locations
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// N #P by 3 list of point normals
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// A #P by 1 list of point areas
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// point_indices a vector of vectors, where the ith entry is a vector of
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// the indices into P that are the ith octree cell's points
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// CH #OctreeCells by 8, where the ith row is the indices of
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// the ith octree cell's children
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// expansion_order the order of the taylor expansion. We support 0,1,2.
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// Outputs:
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// CM #OctreeCells by 3 list of each cell's center of mass
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// R #OctreeCells by 1 list of each cell's maximum distance of any point
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// to the center of mass
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// EC #OctreeCells by #TaylorCoefficients list of expansion coefficients.
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// (Note that #TaylorCoefficients = ∑_{i=1}^{expansion_order} 3^i)
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//
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template <typename DerivedP, typename DerivedA, typename DerivedN,
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typename Index, typename DerivedCH, typename DerivedCM, typename DerivedR,
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typename DerivedEC>
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IGL_INLINE void fast_winding_number(const Eigen::MatrixBase<DerivedP>& P,
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const Eigen::MatrixBase<DerivedN>& N,
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const Eigen::MatrixBase<DerivedA>& A,
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const std::vector<std::vector<Index> > & point_indices,
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const Eigen::MatrixBase<DerivedCH>& CH,
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const int expansion_order,
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Eigen::PlainObjectBase<DerivedCM>& CM,
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Eigen::PlainObjectBase<DerivedR>& R,
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Eigen::PlainObjectBase<DerivedEC>& EC);
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// Evaluate the fast winding number for point data, having already done the
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// the precomputation
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//
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// Inputs:
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// P #P by 3 list of point locations
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// N #P by 3 list of point normals
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// A #P by 1 list of point areas
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// point_indices a vector of vectors, where the ith entry is a vector of
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// the indices into P that are the ith octree cell's points
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// CH #OctreeCells by 8, where the ith row is the indices of
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// the ith octree cell's children
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// CM #OctreeCells by 3 list of each cell's center of mass
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// R #OctreeCells by 1 list of each cell's maximum distance of any point
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// to the center of mass
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// EC #OctreeCells by #TaylorCoefficients list of expansion coefficients.
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// (Note that #TaylorCoefficients = ∑_{i=1}^{expansion_order} 3^i)
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// Q #Q by 3 list of query points for the winding number
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// beta This is a Barnes-Hut style accuracy term that separates near feild
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// from far field. The higher the beta, the more accurate and slower
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// the evaluation. We reccommend using a beta value of 2. Note that
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// for a beta value ≤ 0, we use the direct evaluation, rather than
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// the fast approximation
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// Outputs:
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// WN #Q by 1 list of windinng number values at each query point
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//
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template <typename DerivedP, typename DerivedA, typename DerivedN,
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typename Index, typename DerivedCH, typename DerivedCM, typename DerivedR,
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typename DerivedEC, typename DerivedQ, typename BetaType,
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typename DerivedWN>
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IGL_INLINE void fast_winding_number(const Eigen::MatrixBase<DerivedP>& P,
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const Eigen::MatrixBase<DerivedN>& N,
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const Eigen::MatrixBase<DerivedA>& A,
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const std::vector<std::vector<Index> > & point_indices,
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const Eigen::MatrixBase<DerivedCH>& CH,
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const Eigen::MatrixBase<DerivedCM>& CM,
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const Eigen::MatrixBase<DerivedR>& R,
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const Eigen::MatrixBase<DerivedEC>& EC,
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const Eigen::MatrixBase<DerivedQ>& Q,
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const BetaType beta,
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Eigen::PlainObjectBase<DerivedWN>& WN);
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// Evaluate the fast winding number for point data, with default expansion
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// order and beta (both are set to 2).
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//
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// This function performes the precomputation and evaluation all in one.
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// If you need to acess the precomuptation for repeated evaluations, use the
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// two functions designed for exposed precomputation (described above).
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//
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// Inputs:
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// P #P by 3 list of point locations
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// N #P by 3 list of point normals
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// A #P by 1 list of point areas
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// Q #Q by 3 list of query points for the winding number
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// Outputs:
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// WN #Q by 1 list of windinng number values at each query point
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//
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template <typename DerivedP, typename DerivedA, typename DerivedN,
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typename DerivedQ, typename DerivedWN>
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IGL_INLINE void fast_winding_number(const Eigen::MatrixBase<DerivedP>& P,
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const Eigen::MatrixBase<DerivedN>& N,
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const Eigen::MatrixBase<DerivedA>& A,
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const Eigen::MatrixBase<DerivedQ>& Q,
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Eigen::PlainObjectBase<DerivedWN>& WN
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);
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}
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#ifndef IGL_STATIC_LIBRARY
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# include "fast_winding_number.cpp"
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#endif
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#endif
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