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Document ClosestPointQueries
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‎source/pbat/geometry/ClosestPointQueries.h‎

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#ifndef PBAT_GEOMETRY_CLOSESTPOINTQUERIES_H
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/**
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* @file ClosestPointQueries.h
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* @author Quoc-Minh Ton-That ([email protected])
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* @brief This file contains functions to answer closest point queries.
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* @date 2025-02-12
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*
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* @copyright Copyright (c) 2025
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*
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*/
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#ifndef PBAT_GEOMETRY_CLOSESTPOINTQUERIES_H
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#define PBAT_GEOMETRY_CLOSESTPOINTQUERIES_H
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#include "pbat/HostDevice.h"
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namespace pbat {
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namespace geometry {
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/**
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* @brief This namespace contains functions to answer closest point queries.
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*/
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namespace ClosestPointQueries {
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namespace mini = math::linalg::mini;
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/**
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* @brief Obtain the point on the plane (P,n) closest to the point X.
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* @param X
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* @param P
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* @param n
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* @return
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* @param X Query point
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* @param P Point on the plane
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* @param n Normal of the plane
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* @return Point on the plane closest to X
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*/
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template <mini::CMatrix TMatrixX, mini::CMatrix TMatrixP, mini::CMatrix TMatrixN>
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PBAT_HOST_DEVICE mini::SVector<typename TMatrixX::ScalarType, TMatrixX::kRows>
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PointOnPlane(TMatrixX const& X, TMatrixP const& P, TMatrixN const& n);
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PBAT_HOST_DEVICE auto PointOnPlane(TMatrixX const& X, TMatrixP const& P, TMatrixN const& n)
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-> mini::SVector<typename TMatrixX::ScalarType, TMatrixX::kRows>;
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/**
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* @brief Obtain the point on the line segment PQ closest to the point X.
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* @param X
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* @param P
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* @param Q
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* @return
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* @param X Query point
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* @param P Start point of the line segment
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* @param Q End point of the line segment
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* @return Point on the line segment closest to X
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*/
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template <mini::CMatrix TMatrixX, mini::CMatrix TMatrixP, mini::CMatrix TMatrixQ>
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PBAT_HOST_DEVICE mini::SVector<typename TMatrixX::ScalarType, TMatrixX::kRows>
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PointOnLineSegment(TMatrixX const& X, TMatrixP const& P, TMatrixQ const& Q);
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PBAT_HOST_DEVICE auto PointOnLineSegment(TMatrixX const& X, TMatrixP const& P, TMatrixQ const& Q)
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-> mini::SVector<typename TMatrixX::ScalarType, TMatrixX::kRows>;
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/**
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* @brief Obtain the point on the axis-aligned bounding box (AABB) defined by the lower
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* and upper corners closest to the point P.
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* @param P
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* @param L
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* @param U
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* @return
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* and upper corners closest to the point X.
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* @param X Query point
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* @param L Lower corner of the AABB
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* @param U Upper corner of the AABB
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* @return Point on the AABB closest to X
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*/
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template <mini::CMatrix TMatrixX, mini::CMatrix TMatrixL, mini::CMatrix TMatrixU>
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PBAT_HOST_DEVICE mini::SVector<typename TMatrixX::ScalarType, TMatrixX::kRows>
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PointOnAxisAlignedBoundingBox(TMatrixX const& X, TMatrixL const& L, TMatrixU const& U);
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PBAT_HOST_DEVICE auto
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PointOnAxisAlignedBoundingBox(TMatrixX const& X, TMatrixL const& L, TMatrixU const& U)
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-> mini::SVector<typename TMatrixX::ScalarType, TMatrixX::kRows>;
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/**
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* @brief Obtain the point on the triangle ABC closest to the point P in barycentric coordinates.
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* @param P
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* @param A
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* @param B
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* @param C
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* @return
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* @param P Query point
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* @param A Vertex A of the triangle
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* @param B Vertex B of the triangle
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* @param C Vertex C of the triangle
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* @return Barycentric coordinates of the point in the triangle closest to P
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*/
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template <
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mini::CMatrix TMatrixP,
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mini::CMatrix TMatrixA,
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mini::CMatrix TMatrixB,
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mini::CMatrix TMatrixC>
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PBAT_HOST_DEVICE mini::SVector<typename TMatrixP::ScalarType, 3>
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UvwPointInTriangle(TMatrixP const& P, TMatrixA const& A, TMatrixB const& B, TMatrixC const& C);
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PBAT_HOST_DEVICE auto
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UvwPointInTriangle(TMatrixP const& P, TMatrixA const& A, TMatrixB const& B, TMatrixC const& C)
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-> mini::SVector<typename TMatrixP::ScalarType, 3>;
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/**
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* @brief Obtain the point on the triangle ABC closest to the point P.
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* @param P
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* @param A
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* @param B
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* @param C
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* @return
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* @param P Query point
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* @param A Vertex A of the triangle
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* @param B Vertex B of the triangle
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* @param C Vertex C of the triangle
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* @return Point in the triangle closest to P
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*/
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template <
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mini::CMatrix TMatrixP,
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mini::CMatrix TMatrixA,
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mini::CMatrix TMatrixB,
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mini::CMatrix TMatrixC>
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PBAT_HOST_DEVICE mini::SVector<typename TMatrixP::ScalarType, TMatrixP::kRows>
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PointInTriangle(TMatrixP const& P, TMatrixA const& A, TMatrixB const& B, TMatrixC const& C);
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PBAT_HOST_DEVICE auto
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PointInTriangle(TMatrixP const& P, TMatrixA const& A, TMatrixB const& B, TMatrixC const& C)
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-> mini::SVector<typename TMatrixP::ScalarType, TMatrixP::kRows>;
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/**
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* @brief Obtain the point in the tetrahedron ABCD closest to the point P. The order of ABCD
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* must be such that all faces ABC, ACD, ADB and BDC are oriented with outwards pointing normals
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* when viewed from outside the tetrahedron.
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* @param P
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* @param A
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* @param B
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* @param C
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* @param D
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* @return
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* @param P Query point
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* @param A Vertex A of the tetrahedron
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* @param B Vertex B of the tetrahedron
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* @param C Vertex C of the tetrahedron
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* @param D Vertex D of the tetrahedron
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* @return Point in the tetrahedron closest to P
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*/
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template <
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mini::CMatrix TMatrixP,
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mini::CMatrix TMatrixA,
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mini::CMatrix TMatrixB,
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mini::CMatrix TMatrixC,
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mini::CMatrix TMatrixD>
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PBAT_HOST_DEVICE mini::SVector<typename TMatrixP::ScalarType, TMatrixP::kRows> PointInTetrahedron(
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PBAT_HOST_DEVICE auto PointInTetrahedron(
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TMatrixP const& P,
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TMatrixA const& A,
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TMatrixB const& B,
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TMatrixC const& C,
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TMatrixD const& D);
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TMatrixD const& D) -> mini::SVector<typename TMatrixP::ScalarType, TMatrixP::kRows>;
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template <mini::CMatrix TMatrixX, mini::CMatrix TMatrixP, mini::CMatrix TMatrixN>
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PBAT_HOST_DEVICE mini::SVector<typename TMatrixX::ScalarType, TMatrixX::kRows>
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PointOnPlane(TMatrixX const& X, TMatrixP const& P, TMatrixN const& n)
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PBAT_HOST_DEVICE auto PointOnPlane(TMatrixX const& X, TMatrixP const& P, TMatrixN const& n)
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-> mini::SVector<typename TMatrixX::ScalarType, TMatrixX::kRows>
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{
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using namespace std;
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using ScalarType = typename TMatrixX::ScalarType;
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}
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template <mini::CMatrix TMatrixX, mini::CMatrix TMatrixP, mini::CMatrix TMatrixQ>
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PBAT_HOST_DEVICE mini::SVector<typename TMatrixX::ScalarType, TMatrixX::kRows>
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PointOnLineSegment(TMatrixX const& X, TMatrixP const& P, TMatrixQ const& Q)
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PBAT_HOST_DEVICE auto PointOnLineSegment(TMatrixX const& X, TMatrixP const& P, TMatrixQ const& Q)
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-> mini::SVector<typename TMatrixX::ScalarType, TMatrixX::kRows>
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{
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using ScalarType = typename TMatrixX::ScalarType;
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using namespace std;
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}
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template <mini::CMatrix TMatrixX, mini::CMatrix TMatrixL, mini::CMatrix TMatrixU>
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PBAT_HOST_DEVICE mini::SVector<typename TMatrixX::ScalarType, TMatrixX::kRows>
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PBAT_HOST_DEVICE auto
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PointOnAxisAlignedBoundingBox(TMatrixX const& P, TMatrixL const& L, TMatrixU const& U)
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-> mini::SVector<typename TMatrixX::ScalarType, TMatrixX::kRows>
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{
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using namespace std;
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/**
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mini::CMatrix TMatrixA,
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mini::CMatrix TMatrixB,
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mini::CMatrix TMatrixC>
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PBAT_HOST_DEVICE mini::SVector<typename TMatrixP::ScalarType, 3>
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PBAT_HOST_DEVICE auto
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UvwPointInTriangle(TMatrixP const& P, TMatrixA const& A, TMatrixB const& B, TMatrixC const& C)
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-> mini::SVector<typename TMatrixP::ScalarType, 3>
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{
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using ScalarType = typename TMatrixP::ScalarType;
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/**
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mini::CMatrix TMatrixA,
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mini::CMatrix TMatrixB,
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mini::CMatrix TMatrixC>
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PBAT_HOST_DEVICE mini::SVector<typename TMatrixP::ScalarType, TMatrixP::kRows>
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PBAT_HOST_DEVICE auto
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PointInTriangle(TMatrixP const& P, TMatrixA const& A, TMatrixB const& B, TMatrixC const& C)
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-> mini::SVector<typename TMatrixP::ScalarType, TMatrixP::kRows>
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{
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auto uvw = UvwPointInTriangle(P, A, B, C);
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return A * uvw(0) + B * uvw(1) + C * uvw(2);
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mini::CMatrix TMatrixB,
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mini::CMatrix TMatrixC,
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mini::CMatrix TMatrixD>
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PBAT_HOST_DEVICE mini::SVector<typename TMatrixP::ScalarType, TMatrixP::kRows> PointInTetrahedron(
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PBAT_HOST_DEVICE auto PointInTetrahedron(
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TMatrixP const& P,
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TMatrixA const& A,
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TMatrixB const& B,
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TMatrixC const& C,
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TMatrixD const& D)
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TMatrixD const& D) -> mini::SVector<typename TMatrixP::ScalarType, TMatrixP::kRows>
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{
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using ScalarType = typename TMatrixP::ScalarType;
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auto constexpr kRows = TMatrixP::kRows;

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