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214 lines
8.3 KiB
214 lines
8.3 KiB
1 year ago
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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 "FastWindingNumberForSoups.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 (if not
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/// 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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/// @param[in] P #P by 3 list of point locations
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/// @param[in] N #P by 3 list of point normals
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/// @param[in] A #P by 1 list of point areas
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/// @param[in] 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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/// @param[in] 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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/// @param[in] expansion_order the order of the taylor expansion. We support 0,1,2.
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/// @param[out] CM #OctreeCells by 3 list of each cell's center of mass
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/// @param[out] 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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/// @param[out] 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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/// \see copyleft::cgal::point_areas, knn
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template <
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typename DerivedP,
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typename DerivedA,
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typename DerivedN,
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typename Index,
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typename DerivedCH,
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typename DerivedCM,
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typename DerivedR,
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typename DerivedEC>
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IGL_INLINE void fast_winding_number(
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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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/// @param[in] P #P by 3 list of point locations
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/// @param[in] N #P by 3 list of point normals
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/// @param[in] A #P by 1 list of point areas
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/// @param[in] 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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/// @param[in] 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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/// @param[in] CM #OctreeCells by 3 list of each cell's center of mass
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/// @param[in] 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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/// @param[in] 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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/// @param[in] Q #Q by 3 list of query points for the winding number
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/// @param[in] 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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/// @param[out] WN #Q by 1 list of windinng number values at each query point
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template <
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typename DerivedP,
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typename DerivedA,
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typename DerivedN,
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typename Index,
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typename DerivedCH,
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typename DerivedCM,
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typename DerivedR,
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typename DerivedEC,
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typename DerivedQ,
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typename BetaType,
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typename DerivedWN>
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IGL_INLINE void fast_winding_number(
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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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/// \overload
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///
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/// \brief Evaluate the fast winding number for point data without caching the
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/// precomputation.
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template <
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typename DerivedP,
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typename DerivedA,
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typename DerivedN,
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typename DerivedQ,
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typename BetaType,
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typename DerivedWN>
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IGL_INLINE void fast_winding_number(
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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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const int expansion_order,
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const BetaType beta,
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Eigen::PlainObjectBase<DerivedWN>& WN);
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/// \overload
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template <
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typename DerivedP,
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typename DerivedA,
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typename DerivedN,
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typename DerivedQ,
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typename DerivedWN>
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IGL_INLINE void fast_winding_number(
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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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/// @private
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namespace FastWindingNumber {
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/// @private
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namespace HDK_Sample{
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/// @private
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template <typename T1, typename T2> class UT_SolidAngle;} }
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/// Structure for caching precomputation for fast winding number for triangle
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/// soups
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struct FastWindingNumberBVH {
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/// @private
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FastWindingNumber::HDK_Sample::UT_SolidAngle<float,float> ut_solid_angle;
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// Need copies of these so they stay alive between calls.
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/// @private
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std::vector<FastWindingNumber::HDK_Sample::UT_Vector3T<float> > U;
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std::vector<int> F;
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};
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/// Compute approximate winding number of a triangle soup mesh according to
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/// "Fast Winding Numbers for Soups and Clouds" [Barill et al. 2018].
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///
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/// @param[in] V #V by 3 list of mesh vertex positions
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/// @param[in] F #F by 3 list of triangle mesh indices into rows of V
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/// @param[in] Q #Q by 3 list of query positions
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/// @param[out] W #Q list of winding number values
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template <
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typename DerivedV,
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typename DerivedF,
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typename DerivedQ,
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typename DerivedW>
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IGL_INLINE void fast_winding_number(
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const Eigen::MatrixBase<DerivedV> & V,
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const Eigen::MatrixBase<DerivedF> & F,
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const Eigen::MatrixBase<DerivedQ> & Q,
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Eigen::PlainObjectBase<DerivedW> & W);
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/// Precomputation for computing approximate winding numbers of a triangle
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/// soup.
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///
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/// @param[in] V #V by 3 list of mesh vertex positions
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/// @param[in] F #F by 3 list of triangle mesh indices into rows of V
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/// @param[in] order Taylor series expansion order to use (e.g., 2)
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/// @param[out] fwn_bvh Precomputed bounding volume hierarchy
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///
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template <
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typename DerivedV,
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typename DerivedF>
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IGL_INLINE void fast_winding_number(
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const Eigen::MatrixBase<DerivedV> & V,
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const Eigen::MatrixBase<DerivedF> & F,
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const int order,
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FastWindingNumberBVH & fwn_bvh);
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/// After precomputation, compute winding number at a each of many points in a
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/// list.
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///
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/// @param[in] fwn_bvh Precomputed bounding volume hierarchy
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/// @param[in] accuracy_scale parameter controlling accuracy (e.g., 2)
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/// @param[in] Q #Q by 3 list of query positions
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/// @param[out] W #Q list of winding number values
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template <
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typename DerivedQ,
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typename DerivedW>
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IGL_INLINE void fast_winding_number(
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const FastWindingNumberBVH & fwn_bvh,
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const float accuracy_scale,
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const Eigen::MatrixBase<DerivedQ> & Q,
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Eigen::PlainObjectBase<DerivedW> & W);
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/// After precomputation, compute winding number at a single point
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///
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/// @param[in] fwn_bvh Precomputed bounding volume hierarchy
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/// @param[in] accuracy_scale parameter controlling accuracy (e.g., 2)
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/// @param[in] p single position
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/// @return w winding number of this point
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template <typename Derivedp>
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IGL_INLINE typename Derivedp::Scalar fast_winding_number(
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const FastWindingNumberBVH & fwn_bvh,
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const float accuracy_scale,
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const Eigen::MatrixBase<Derivedp> & p);
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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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