PointTriangleCcd.h File Reference

Point-triangle continuous collision detection (CCD) implementation. More...

#include "IntersectionQueries.h"
#include "pbat/HostDevice.h"
#include "pbat/math/linalg/mini/Concepts.h"
#include "pbat/math/linalg/mini/Matrix.h"
#include "pbat/math/linalg/mini/Reductions.h"
#include "pbat/math/polynomial/Roots.h"
#include <array>
#include <cmath>

Go to the source code of this file.

Namespaces
namespace	pbat
	The main namespace of the library.
namespace	pbat::geometry
	Geometric queries, quantities and data structures.

Functions
template<math::linalg::mini::CReadableVectorizedMatrix TXT, math::linalg::mini::CReadableVectorizedMatrix TAT, math::linalg::mini::CReadableVectorizedMatrix TBT, math::linalg::mini::CReadableVectorizedMatrix TCT, math::linalg::mini::CReadableVectorizedMatrix TX, math::linalg::mini::CReadableVectorizedMatrix TA, math::linalg::mini::CReadableVectorizedMatrix TB, math::linalg::mini::CReadableVectorizedMatrix TC, class TScalar = typename TX::ScalarType>
PBAT_HOST_DEVICE std::array< TScalar, 4 >	pbat::geometry::detail::PointTriangleCcdUnivariatePolynomial (TXT const &XT, TAT const &AT, TBT const &BT, TCT const &CT, TX const &X, TA const &A, TB const &B, TC const &C)
	Computes the univariate linearly swept point-triangle co-planarity polynomial.
template<math::linalg::mini::CReadableVectorizedMatrix TXT, math::linalg::mini::CReadableVectorizedMatrix TAT, math::linalg::mini::CReadableVectorizedMatrix TBT, math::linalg::mini::CReadableVectorizedMatrix TCT, math::linalg::mini::CReadableVectorizedMatrix TX, math::linalg::mini::CReadableVectorizedMatrix TA, math::linalg::mini::CReadableVectorizedMatrix TB, math::linalg::mini::CReadableVectorizedMatrix TC, class TScalar = typename TXT::ScalarType>
PBAT_HOST_DEVICE auto	pbat::geometry::PointTriangleCcd (TXT const &XT, TAT const &AT, TBT const &BT, TCT const &CT, TX const &X, TA const &A, TB const &B, TC const &C) -> math::linalg::mini::SVector< TScalar, 4 >
	Computes the time of impact \( t^* \) and barycentric coordinates \( \mathbf{\beta} \) of the intersection point between a point and a triangle moving along a linear trajectory.

Detailed Description

Point-triangle continuous collision detection (CCD) implementation.

Author

Quoc-Minh Ton-That (tonth.nosp@m.at.q.nosp@m.uocmi.nosp@m.nh@g.nosp@m.mail..nosp@m.com)

Date

2025-03-27

Copyright

Copyright (c) 2025

Function Documentation

PointTriangleCcdUnivariatePolynomial()

template<math::linalg::mini::CReadableVectorizedMatrix TXT, math::linalg::mini::CReadableVectorizedMatrix TAT, math::linalg::mini::CReadableVectorizedMatrix TBT, math::linalg::mini::CReadableVectorizedMatrix TCT, math::linalg::mini::CReadableVectorizedMatrix TX, math::linalg::mini::CReadableVectorizedMatrix TA, math::linalg::mini::CReadableVectorizedMatrix TB, math::linalg::mini::CReadableVectorizedMatrix TC, class TScalar = typename TX::ScalarType>

PBAT_HOST_DEVICE std::array< TScalar, 4 > pbat::geometry::detail::PointTriangleCcdUnivariatePolynomial	(	TXT const &	XT,
		TAT const &	AT,
		TBT const &	BT,
		TCT const &	CT,
		TX const &	X,
		TA const &	A,
		TB const &	B,
		TC const &	C )

Computes the univariate linearly swept point-triangle co-planarity polynomial.

\[\langle \mathbf{n}(t), \mathbf{q}(t) \rangle = 0 , \]

where \( \mathbf{n}(t) = (\mathbf{b}(t) - \mathbf{a}) \times (\mathbf{c}(t) - \mathbf{a}) \) and \( \mathbf{q}(t) = \mathbf{x}(t) - \mathbf{a} \)

Note

Code-generated from python/geometry/ccd.py

Template Parameters

TXT	Type of the input matrix XT
TAT	Type of the input matrix AT
TBT	Type of the input matrix BT
TCT	Type of the input matrix CT
TX	Type of the input matrix X
TA	Type of the input matrix A
TB	Type of the input matrix B
TC	Type of the input matrix C
TScalar	Type of the scalar

Parameters

XT	Matrix of the initial positions of the point
AT	Matrix of the initial positions of the triangle vertex A
BT	Matrix of the initial positions of the triangle vertex B
CT	Matrix of the initial positions of the triangle vertex C
X	Matrix of the final positions of the point
A	Matrix of the final positions of the triangle vertex A
B	Matrix of the final positions of the triangle vertex B
C	Matrix of the final positions of the triangle vertex C

Returns

4-vector containing the coefficients of the polynomial in increasing order