EdgeEdgeCcd.h File Reference

Edge-edge continuous collision detection (CCD) implementation. More...

#include "pbat/HostDevice.h"
#include "pbat/geometry/ClosestPointQueries.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 TP1T, math::linalg::mini::CReadableVectorizedMatrix TQ1T, math::linalg::mini::CReadableVectorizedMatrix TP2T, math::linalg::mini::CReadableVectorizedMatrix TQ2T, math::linalg::mini::CReadableVectorizedMatrix TP1, math::linalg::mini::CReadableVectorizedMatrix TQ1, math::linalg::mini::CReadableVectorizedMatrix TP2, math::linalg::mini::CReadableVectorizedMatrix TQ2, class TScalar = typename TP1T::ScalarType>
PBAT_HOST_DEVICE std::array< TScalar, 4 >	pbat::geometry::detail::EdgeEdgeCcdUnivariatePolynomial (TP1T const &P1T, TQ1T const &Q1T, TP2T const &P2T, TQ2T const &Q2T, TP1 const &P1, TQ1 const &Q1, TP2 const &P2, TQ2 const &Q2)
	Computes the univariate linearly swept edge-edge co-planarity polynomial.
template<math::linalg::mini::CReadableVectorizedMatrix TP1T, math::linalg::mini::CReadableVectorizedMatrix TQ1T, math::linalg::mini::CReadableVectorizedMatrix TP2T, math::linalg::mini::CReadableVectorizedMatrix TQ2T, math::linalg::mini::CReadableVectorizedMatrix TP1, math::linalg::mini::CReadableVectorizedMatrix TQ1, math::linalg::mini::CReadableVectorizedMatrix TP2, math::linalg::mini::CReadableVectorizedMatrix TQ2, class TScalar = typename TP1T::ScalarType>
PBAT_HOST_DEVICE auto	pbat::geometry::EdgeEdgeCcd (TP1T const &P1T, TQ1T const &Q1T, TP2T const &P2T, TQ2T const &Q2T, TP1 const &P1, TQ1 const &Q1, TP2 const &P2, TQ2 const &Q2) -> math::linalg::mini::SVector< TScalar, 3 >
	Computes the time of impact \( t^* \) and barycentric coordinates \( \mathbf{\beta} \) of the intersection point between an edge \( (P1,Q1) \) and another edge \( (P2,Q2) \) moving along a linear trajectory.

Detailed Description

Edge-edge 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

EdgeEdgeCcdUnivariatePolynomial()

template<math::linalg::mini::CReadableVectorizedMatrix TP1T, math::linalg::mini::CReadableVectorizedMatrix TQ1T, math::linalg::mini::CReadableVectorizedMatrix TP2T, math::linalg::mini::CReadableVectorizedMatrix TQ2T, math::linalg::mini::CReadableVectorizedMatrix TP1, math::linalg::mini::CReadableVectorizedMatrix TQ1, math::linalg::mini::CReadableVectorizedMatrix TP2, math::linalg::mini::CReadableVectorizedMatrix TQ2, class TScalar = typename TP1T::ScalarType>

PBAT_HOST_DEVICE std::array< TScalar, 4 > pbat::geometry::detail::EdgeEdgeCcdUnivariatePolynomial	(	TP1T const &	P1T,
		TQ1T const &	Q1T,
		TP2T const &	P2T,
		TQ2T const &	Q2T,
		TP1 const &	P1,
		TQ1 const &	Q1,
		TP2 const &	P2,
		TQ2 const &	Q2 )

Computes the univariate linearly swept edge-edge co-planarity polynomial.

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

where \( \mathbf{n}(t) = (\mathbf{q}_1(t) - \mathbf{p}_1(t)) \times (\mathbf{q}_2(t) - \mathbf{p}_2(t)) \) and \( \mathbf{q}(t) = \mathbf{x}(t) - \mathbf{p}_1(t) \)

Note

Code-generated from python/geometry/ccd.py

Template Parameters

TP1T	Type of the input matrix P1T
TQ1T	Type of the input matrix Q1T
TP2T	Type of the input matrix P2T
TQ2T	Type of the input matrix Q2T
TP1	Type of the input matrix P1
TQ1	Type of the input matrix Q1
TP2	Type of the input matrix P2
TQ2	Type of the input matrix Q2
TScalar	Type of the scalar

Parameters

P1T	Matrix of the initial positions of the point P on edge 1
Q1T	Matrix of the initial positions of the point Q on edge 1
P2T	Matrix of the initial positions of the point P on edge 2
Q2T	Matrix of the initial positions of the point Q on edge 2
P1	Matrix of the final positions of the point P on edge 1
Q1	Matrix of the final positions of the point Q on edge 1
P2	Matrix of the final positions of the point P on edge 2
Q2	Matrix of the final positions of the point Q on edge 2

Returns

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