pbat::geometry::IntersectionQueries Namespace Reference

This namespace contains functions to answer intersection queries. More...

Functions
template<mini::CMatrix TMatrixAP, mini::CMatrix TMatrixAB, mini::CMatrix TMatrixAC>
PBAT_HOST_DEVICE auto	TriangleBarycentricCoordinates (TMatrixAP const &AP, TMatrixAB const &AB, TMatrixAC const &AC) -> mini::SMatrix< typename TMatrixAP::ScalarType, 3, 1 >
	Computes the barycentric coordinates of point P with respect to the triangle spanned by vertices A, B, and C.
template<mini::CMatrix TMatrixP, mini::CMatrix TMatrixA, mini::CMatrix TMatrixB, mini::CMatrix TMatrixC>
PBAT_HOST_DEVICE auto	TriangleBarycentricCoordinates (TMatrixP const &P, TMatrixA const &A, TMatrixB const &B, TMatrixC const &C) -> mini::SVector< typename TMatrixP::ScalarType, 3 >
	Computes the barycentric coordinates of point P with respect to the triangle spanned by vertices A, B, and C.
template<mini::CMatrix TMatrixL1, mini::CMatrix TMatrixU1, mini::CMatrix TMatrixL2, mini::CMatrix TMatrixU2>
PBAT_HOST_DEVICE auto	AxisAlignedBoundingBoxes (TMatrixL1 const &L1, TMatrixU1 const &U1, TMatrixL2 const &L2, TMatrixU2 const &U2) -> mini::SMatrix< typename TMatrixL1::ScalarType, TMatrixL1::Rows, 2 >
	Computes the intersection volume between 2 axis aligned bounding boxes.
template<mini::CMatrix TMatrixP, mini::CMatrix TMatrixQ, mini::CMatrix TMatrixC>
PBAT_HOST_DEVICE auto	LineSegmentSphere (TMatrixP const &P, TMatrixQ const &Q, TMatrixC const &C, typename TMatrixC::ScalarType R) -> std::optional< mini::SVector< typename TMatrixP::ScalarType, TMatrixP::kRows > >
	Computes the intersection point, if any, between a line segment PQ and a sphere (C,r).
template<mini::CMatrix TMatrixP, mini::CMatrix TMatrixQ, mini::CMatrix TMatrixA, mini::CMatrix TMatrixB, mini::CMatrix TMatrixC>
PBAT_HOST_DEVICE auto	LineSegmentPlane3D (TMatrixP const &P, TMatrixQ const &Q, TMatrixA const &A, TMatrixB const &B, TMatrixC const &C) -> std::optional< mini::SVector< typename TMatrixP::ScalarType, TMatrixP::kRows > >
	Computes the intersection point, if any, between a line including points P,Q and the plane spanned by triangle ABC, in 3D.
template<mini::CMatrix TMatrixP, mini::CMatrix TMatrixQ, mini::CMatrix TMatrixN>
PBAT_HOST_DEVICE auto	LineSegmentPlane3D (TMatrixP const &P, TMatrixQ const &Q, TMatrixN const &n, typename TMatrixN::ScalarType d) -> std::optional< mini::SVector< typename TMatrixP::ScalarType, TMatrixP::kRows > >
	Computes the intersection point, if any, between a line including points P,Q and the plane (n,d), in 3D.
template<mini::CMatrix TMatrixP, mini::CMatrix TMatrixQ, mini::CMatrix TMatrixA, mini::CMatrix TMatrixB, mini::CMatrix TMatrixC>
PBAT_HOST_DEVICE auto	UvwLineTriangle3D (TMatrixP const &P, TMatrixQ const &Q, TMatrixA const &A, TMatrixB const &B, TMatrixC const &C) -> std::optional< mini::SVector< typename TMatrixP::ScalarType, 3 > >
	Computes the intersection point, if any, between a line including points P,Q and a triangle ABC, in 3D.
template<mini::CMatrix TMatrixP, mini::CMatrix TMatrixQ, mini::CMatrix TMatrixA, mini::CMatrix TMatrixB, mini::CMatrix TMatrixC>
PBAT_HOST_DEVICE auto	UvwLineSegmentTriangle3D (TMatrixP const &P, TMatrixQ const &Q, TMatrixA const &A, TMatrixB const &B, TMatrixC const &C) -> std::optional< mini::SVector< typename TMatrixP::ScalarType, 4 > >
	Computes the intersection point, if any, between a line segment delimited by points P,Q and a triangle ABC, in 3D.
template<mini::CMatrix TMatrixA1, mini::CMatrix TMatrixB1, mini::CMatrix TMatrixC1, mini::CMatrix TMatrixA2, mini::CMatrix TMatrixB2, mini::CMatrix TMatrixC2>
PBAT_HOST_DEVICE auto	UvwTriangles3D (TMatrixA1 const &A1, TMatrixB1 const &B1, TMatrixC1 const &C1, TMatrixA2 const &A2, TMatrixB2 const &B2, TMatrixC2 const &C2) -> std::array< std::optional< mini::SVector< typename TMatrixA1::ScalarType, 3 > >, 6u >
	Computes intersection points between 3 edges (as line segments) of triangle A1B1C1 and triangle A2B2C2, and intersection points between 3 edges (as line segments) of triangle A2B2C2 and triangle A1B1C1, in 3D.

Detailed Description

This namespace contains functions to answer intersection queries.

Function Documentation

AxisAlignedBoundingBoxes()

template<mini::CMatrix TMatrixL1, mini::CMatrix TMatrixU1, mini::CMatrix TMatrixL2, mini::CMatrix TMatrixU2>

PBAT_HOST_DEVICE auto pbat::geometry::IntersectionQueries::AxisAlignedBoundingBoxes	(	TMatrixL1 const &	L1,
		TMatrixU1 const &	U1,
		TMatrixL2 const &	L2,
		TMatrixU2 const &	U2 ) -> mini::SMatrix<typename TMatrixL1::ScalarType, TMatrixL1::Rows, 2>

Computes the intersection volume between 2 axis aligned bounding boxes.

Template Parameters

TMatrixL1	Matrix type of the lower bound of AABB 1
TMatrixU1	Matrix type of the upper bound of AABB 1
TMatrixL2	Matrix type of the lower bound of AABB 2
TMatrixU2	Matrix type of the upper bound of AABB 2

Parameters

L1	The lower bound of AABB 1
U1	The upper bound of AABB 1
L2	The lower bound of AABB 2
U2	The upper bound of AABB 2

Returns

The intersection volume between the 2 AABBs

LineSegmentPlane3D() [1/2]

template<mini::CMatrix TMatrixP, mini::CMatrix TMatrixQ, mini::CMatrix TMatrixA, mini::CMatrix TMatrixB, mini::CMatrix TMatrixC>

PBAT_HOST_DEVICE auto pbat::geometry::IntersectionQueries::LineSegmentPlane3D	(	TMatrixP const &	P,
		TMatrixQ const &	Q,
		TMatrixA const &	A,
		TMatrixB const &	B,
		TMatrixC const &	C ) -> std::optional<mini::SVector<typename TMatrixP::ScalarType, TMatrixP::kRows>>

Computes the intersection point, if any, between a line including points P,Q and the plane spanned by triangle ABC, in 3D.

Template Parameters

TMatrixP	Matrix type of the point P
TMatrixQ	Matrix type of the point Q
TMatrixA	Matrix type of the vertex A
TMatrixB	Matrix type of the vertex B
TMatrixC	Matrix type of the vertex C

Parameters

P	The start point of the line
Q	The end point of the line
A	Vertex A of the triangle
B	Vertex B of the triangle
C	Vertex C of the triangle

Returns

The intersection point, if any

LineSegmentPlane3D() [2/2]

template<mini::CMatrix TMatrixP, mini::CMatrix TMatrixQ, mini::CMatrix TMatrixN>

PBAT_HOST_DEVICE auto pbat::geometry::IntersectionQueries::LineSegmentPlane3D	(	TMatrixP const &	P,
		TMatrixQ const &	Q,
		TMatrixN const &	n,
		typename TMatrixN::ScalarType	d ) -> std::optional<mini::SVector<typename TMatrixP::ScalarType, TMatrixP::kRows>>

Computes the intersection point, if any, between a line including points P,Q and the plane (n,d), in 3D.

Template Parameters

TMatrixP	Matrix type of the point P
TMatrixQ	Matrix type of the point Q
TMatrixN	Matrix type of the normal vector of the plane

Parameters

P	The start point of the line
Q	The end point of the line
n	The normal vector of the plane
d	The distance from the origin to the plane

Returns

The intersection point, if any

LineSegmentSphere()

template<mini::CMatrix TMatrixP, mini::CMatrix TMatrixQ, mini::CMatrix TMatrixC>

PBAT_HOST_DEVICE auto pbat::geometry::IntersectionQueries::LineSegmentSphere	(	TMatrixP const &	P,
		TMatrixQ const &	Q,
		TMatrixC const &	C,
		typename TMatrixC::ScalarType	R ) -> std::optional<mini::SVector<typename TMatrixP::ScalarType, TMatrixP::kRows>>

Computes the intersection point, if any, between a line segment PQ and a sphere (C,r).

If there are 2 intersection points, returns the one closest to P along PQ.

Parameters

P	The start point of the line segment
Q	The end point of the line segment
C	The center of the sphere
R	The radius of the sphere

Returns

The intersection point, if any

TriangleBarycentricCoordinates() [1/2]

template<mini::CMatrix TMatrixAP, mini::CMatrix TMatrixAB, mini::CMatrix TMatrixAC>

PBAT_HOST_DEVICE auto pbat::geometry::IntersectionQueries::TriangleBarycentricCoordinates	(	TMatrixAP const &	AP,
		TMatrixAB const &	AB,
		TMatrixAC const &	AC ) -> mini::SMatrix<typename TMatrixAP::ScalarType, 3, 1>

Computes the barycentric coordinates of point P with respect to the triangle spanned by vertices A, B, and C.

Template Parameters

TMatrixAP	Matrix type of the vector from A to P
TMatrixAB	Matrix type of the vector from A to B
TMatrixAC	Matrix type of the vector from A to C

Parameters

AP	The vector from A to P
AB	The vector from A to B
AC	The vector from A to C

Returns

The barycentric coordinates of P with respect to the triangle ABC

Precondition

AP, AB, and AC are coplanar

TriangleBarycentricCoordinates() [2/2]

template<mini::CMatrix TMatrixP, mini::CMatrix TMatrixA, mini::CMatrix TMatrixB, mini::CMatrix TMatrixC>

PBAT_HOST_DEVICE auto pbat::geometry::IntersectionQueries::TriangleBarycentricCoordinates	(	TMatrixP const &	P,
		TMatrixA const &	A,
		TMatrixB const &	B,
		TMatrixC const &	C ) -> mini::SVector<typename TMatrixP::ScalarType, 3>

Computes the barycentric coordinates of point P with respect to the triangle spanned by vertices A, B, and C.

Template Parameters

TMatrixP	Matrix type of the point P
TMatrixA	Matrix type of the vertex A
TMatrixB	Matrix type of the vertex B
TMatrixC	Matrix type of the vertex C

Parameters

P	Point from which to compute barycentric coordinates.
A	Vertex A of the triangle
B	Vertex B of the triangle
C	Vertex C of the triangle

Returns

The barycentric coordinates of P with respect to the triangle ABC

Precondition

P is in the plane spanned by triangle ABC.

UvwLineSegmentTriangle3D()

template<mini::CMatrix TMatrixP, mini::CMatrix TMatrixQ, mini::CMatrix TMatrixA, mini::CMatrix TMatrixB, mini::CMatrix TMatrixC>

PBAT_HOST_DEVICE auto pbat::geometry::IntersectionQueries::UvwLineSegmentTriangle3D	(	TMatrixP const &	P,
		TMatrixQ const &	Q,
		TMatrixA const &	A,
		TMatrixB const &	B,
		TMatrixC const &	C ) -> std::optional<mini::SVector<typename TMatrixP::ScalarType, 4>>

Computes the intersection point, if any, between a line segment delimited by points P,Q and a triangle ABC, in 3D.

Template Parameters

TMatrixP	Matrix type of the point P
TMatrixQ	Matrix type of the point Q
TMatrixA	Matrix type of the vertex A
TMatrixB	Matrix type of the vertex B
TMatrixC	Matrix type of the vertex C

Parameters

P	The start point of the line segment
Q	The end point of the line segment
A	Vertex A of the triangle
B	Vertex B of the triangle
C	Vertex C of the triangle

Returns

The intersection point as a 4-vector, if any, where the last 3 elements are the barycentric coordinates of the intersection point with respect to the triangle ABC, and the first element is the barycentric coordinate of the intersection point with respect to line segment PQ

UvwLineTriangle3D()

template<mini::CMatrix TMatrixP, mini::CMatrix TMatrixQ, mini::CMatrix TMatrixA, mini::CMatrix TMatrixB, mini::CMatrix TMatrixC>

PBAT_HOST_DEVICE auto pbat::geometry::IntersectionQueries::UvwLineTriangle3D	(	TMatrixP const &	P,
		TMatrixQ const &	Q,
		TMatrixA const &	A,
		TMatrixB const &	B,
		TMatrixC const &	C ) -> std::optional<mini::SVector<typename TMatrixP::ScalarType, 3>>

Computes the intersection point, if any, between a line including points P,Q and a triangle ABC, in 3D.

Template Parameters

TMatrixP	Matrix type of the point P
TMatrixQ	Matrix type of the point Q
TMatrixA	Matrix type of the vertex A
TMatrixB	Matrix type of the vertex B
TMatrixC	Matrix type of the vertex C

Parameters

P	The start point of the line
Q	The end point of the line
A	Vertex A of the triangle
B	Vertex B of the triangle
C	Vertex C of the triangle

Returns

The intersection point, if any

See [5] section 5.3.4

UvwTriangles3D()

template<mini::CMatrix TMatrixA1, mini::CMatrix TMatrixB1, mini::CMatrix TMatrixC1, mini::CMatrix TMatrixA2, mini::CMatrix TMatrixB2, mini::CMatrix TMatrixC2>

PBAT_HOST_DEVICE auto pbat::geometry::IntersectionQueries::UvwTriangles3D	(	TMatrixA1 const &	A1,
		TMatrixB1 const &	B1,
		TMatrixC1 const &	C1,
		TMatrixA2 const &	A2,
		TMatrixB2 const &	B2,
		TMatrixC2 const &	C2 ) -> std::array<std::optional<mini::SVector<typename TMatrixA1::ScalarType, 3>>, 6u>

Computes intersection points between 3 edges (as line segments) of triangle A1B1C1 and triangle A2B2C2, and intersection points between 3 edges (as line segments) of triangle A2B2C2 and triangle A1B1C1, in 3D.

Template Parameters

TMatrixA1	Matrix type of the vertex A1 of triangle 1
TMatrixB1	Matrix type of the vertex B1 of triangle 1
TMatrixC1	Matrix type of the vertex C1 of triangle 1
TMatrixA2	Matrix type of the vertex A2 of triangle 2
TMatrixB2	Matrix type of the vertex B2 of triangle 2
TMatrixC2	Matrix type of the vertex C2 of triangle 2

Parameters

A1	Vertex A of triangle 1
B1	Vertex B of triangle 1
C1	Vertex C of triangle 1
A2	Vertex A of triangle 2
B2	Vertex B of triangle 2
C2	Vertex C of triangle 2

Returns

The intersection points, if any