Some functions to perform various intersection calculations with 3D line segments. More...

#include <csgeom/math3d.h>

Static Public Member Functions
static bool	BoxBox (const csBox3 &box1, const csBox3 &box2)
	Test if two boxes intersect.
static bool	BoxFrustum (const csBox3 &box, const csPlane3 *frustum, uint32 inClipMask, uint32 &outClipMask)
	Intersect an AABB with a frustum.
static bool	BoxFrustum (const csBox3 &box, const csFrustum *frustum)
	Intersect an AABB with a frustum.
static bool	BoxPlane (const csBox3 &box, const csPlane3 &plane)
	Test if a plane intersects with a box.
static bool	BoxPlane (const csBox3 &box, const csVector3 &normal, const csVector3 &vert)
	Test if a plane intersects with a box.
static int	BoxSegment (const csBox3 &box, const csSegment3 &segment, csVector3 &isect, float *pr=0, bool use_ray=false)
	Intersect a segment or ray with a box.
static bool	BoxSphere (const csBox3 &box, const csVector3 &center, float sqradius)
	Test if a box intersects with a sphere.
static bool	BoxTriangle (const csBox3 &box, const csVector3 &tri0, const csVector3 &tri1, const csVector3 &tri2)
	Test if a triangle intersects with a box.
static bool	ClipSegmentBox (csSegment3 &segment, const csBox3 &box, bool use_ray=false)
	Clip a segment or ray to a box.
static csPtr< csFrustum >	FrustumFrustum (const csFrustum &f1, const csFrustum &f2)
	Calculate intersection of two frustums.
static csPtr< csFrustum >	FrustumFrustum (const csFrustum &f1, csVector3 *poly, int num)
	Calculate intersection of two frustums.
static bool	PlaneAxisPlane (const csPlane3 &p1, int nr, float pos, csPlane2 &isect)
	Intersect a regular plane and an axis aligned plane and return the intersection (line) as a 2D plane.
static bool	PlanePolygon (const csPlane3 &plane, csPoly3D *poly, csSegment3 &segment)
	Intersect a plane with a 3D polygon and return the line segment corresponding with this intersection.
static bool	PlaneXPlane (const csPlane3 &p1, float x2, csPlane2 &isect)
	Intersect a regular plane and an axis aligned plane and return the intersection (line) as a 2D plane.
static bool	PlaneYPlane (const csPlane3 &p1, float y2, csPlane2 &isect)
	Intersect a regular plane and an axis aligned plane and return the intersection (line) as a 2D plane.
static bool	PlaneZPlane (const csPlane3 &p1, float z2, csPlane2 &isect)
	Intersect a regular plane and an axis aligned plane and return the intersection (line) as a 2D plane.
static float	SegmentAxisPlane (const csVector3 &u, const csVector3 &v, int nr, float pos, csVector3 &isect)
	Intersect a 3D segment with an axis aligned plane and return the intersection (fails if segment is parallel to the plane), and returns the distance from u to the intersection point.
static int	SegmentFrustum (csPlane3 *planes, int num_planes, csSegment3 &seg)
	Intersect a segment with a frustum (given as a set of planes).
static bool	SegmentPlane (const csVector3 &u, const csVector3 &v, const csVector3 &normal, const csVector3 &a, csVector3 &isect, float &dist)
	Intersect a 3D segment with a plane.
static bool	SegmentPlane (const csPlane3 &plane, csSegment3 &segment)
	Intersect a 3D segment with a plane.
static bool	SegmentPlane (const csVector3 &u, const csVector3 &v, const csPlane3 &p, csVector3 &isect, float &dist)
	Intersect a 3D segment with a plane.
static bool	SegmentPlanes (const csVector3 &u, const csVector3 &v, const csPlane3 *planes, int length, csVector3 &isect, float &dist)
	If a number of planes enclose a convex space (with their normals pointing outwards).
static bool	SegmentPolygon (const csSegment3 &seg, const csPoly3D &poly, const csPlane3 &poly_plane, csVector3 &isect)
	Intersect a 3D segment with a polygon.
static bool	SegmentTriangle (const csSegment3 &seg, const csVector3 &tr1, const csVector3 &tr2, const csVector3 &tr3, csVector3 &isect)
	Intersect a 3D segment with a triangle.
static float	SegmentXFrustum (const csVector3 &u, const csVector3 &v, float A, csVector3 &isect)
	Intersect a 3D segment with the frustum plane Ax + z = 0.
static float	SegmentXFrustum (const csSegment3 &uv, float A, csVector3 &isect)
	Intersect a 3D segment with the frustum plane Ax + z = 0.
static float	SegmentXPlane (const csVector3 &u, const csVector3 &v, float xval, csVector3 &isect)
	Intersect a 3D segment with the plane x = xval.
static float	SegmentXPlane (const csSegment3 &uv, float xval, csVector3 &isect)
	Intersect a 3D segment with the plane x = xval.
static float	SegmentYFrustum (const csVector3 &u, const csVector3 &v, float B, csVector3 &isect)
	Intersect a 3D segment with the frustum plane By + z = 0.
static float	SegmentYFrustum (const csSegment3 &uv, float B, csVector3 &isect)
	Intersect a 3D segment with the frustum plane By + z = 0.
static float	SegmentYPlane (const csVector3 &u, const csVector3 &v, float yval, csVector3 &isect)
	Intersect a 3D segment with the plane y = yval.
static float	SegmentYPlane (const csSegment3 &uv, float yval, csVector3 &isect)
	Intersect a 3D segment with the plane y = yval.
static float	SegmentZ0Plane (const csVector3 &v1, const csVector3 &v2, csVector3 &isect)
	Intersect a 3D segment with the z = 0 plane.
static float	SegmentZ0Plane (const csSegment3 &uv, csVector3 &isect)
	Intersect a 3D segment with the z = 0 plane.
static float	SegmentZPlane (const csVector3 &u, const csVector3 &v, float zval, csVector3 &isect)
	Intersect a 3D segment with the plane z = zval.
static float	SegmentZPlane (const csSegment3 &uv, float zval, csVector3 &isect)
	Intersect a 3D segment with the plane z = zval.
static bool	ThreePlanes (const csPlane3 &p1, const csPlane3 &p2, const csPlane3 &p3, csVector3 &isect)
	Intersect 3 planes to get the point that is part of all three planes.
static bool	TriangleTriangle (const csVector3 tri1[3], const csVector3 tri2[3])
	Test intersection between two triangles.
static bool	TriangleTriangle (const csVector3 tri1[3], const csVector3 tri2[3], csSegment3 &isectline, bool &coplanar)
	Calculate intersection between two triangles and return it in isectline.

Detailed Description

Some functions to perform various intersection calculations with 3D line segments.

This is a static class and contains only static member functions.

Definition at line 261 of file math3d.h.

Member Function Documentation

static bool csIntersect3::BoxBox	(	const csBox3 &	box1,
		const csBox3 &	box2
	)		`[inline, static]`

Test if two boxes intersect.

Definition at line 648 of file math3d.h.

static bool csIntersect3::BoxFrustum	(	const csBox3 &	box,
		const csPlane3 *	frustum,
		uint32	inClipMask,
		uint32 &	outClipMask
	)		`[static]`

Intersect an AABB with a frustum.

The frustum may contain up to 32 planes. Active planes are defined using the 'inClipMask'. It will return true if AABB is visible in frustum. If the AABB intersects with the frustum then 'outClipMask' will contain the mask for all planes intersecting with the AABB. This can be used as 'inClipMask' for subsequent frustum tests with children of the AABB (i.e. other AABB inside this AABB).

static bool csIntersect3::BoxFrustum	(	const csBox3 &	box,
		const csFrustum *	frustum
	)		`[static]`

Intersect an AABB with a frustum.

static bool csIntersect3::BoxPlane	(	const csBox3 &	box,
		const csPlane3 &	plane
	)		`[static]`

Test if a plane intersects with a box.

static bool csIntersect3::BoxPlane	(	const csBox3 &	box,
		const csVector3 &	normal,
		const csVector3 &	vert
	)		`[static]`

Test if a plane intersects with a box.

'vert' is one point on the plane.

static int csIntersect3::BoxSegment	(	const csBox3 &	box,
		const csSegment3 &	segment,
		csVector3 &	isect,
		float *	pr = `0`,
		bool	use_ray = `false`
	)		`[static]`

Intersect a segment or ray with a box.

If the segment starts inside the box then isect will return the start of the segment.

Parameters:

box	The box with which to perform the intersection.
segment	The intersection candidate.
isect	The returned intersection point.
pr	If not null then a number between 0 and 1 (or bigger then 1 in case we are doing ray testing) is returned which corresponds to the position on the segment or ray. If we were in the box this this function will return CS_BOX_INSIDE. In this case 'isect' will be set to the start of the segment and *pr to 0.
use_ray	if true then the test is done as if the segment is a ray starting at the start of the segment and going in the direction of the end of the segment. Default is false.

Returns:: one of CS_BOX_SIDE_... if it intersects, CS_BOX_INSIDE if inside, or -1 otherwise.

static bool csIntersect3::BoxSphere	(	const csBox3 &	box,
		const csVector3 &	center,
		float	sqradius
	)		`[static]`

Test if a box intersects with a sphere.

The intersection is not computed. The sphere is given with squared radius.

static bool csIntersect3::BoxTriangle	(	const csBox3 &	box,
		const csVector3 &	tri0,
		const csVector3 &	tri1,
		const csVector3 &	tri2
	)		`[static]`

Test if a triangle intersects with a box.

static bool csIntersect3::ClipSegmentBox	(	csSegment3 &	segment,
		const csBox3 &	box,
		bool	use_ray = `false`
	)		`[static]`

Clip a segment or ray to a box.

Parameters:

segment	Is the segment or ray. It will be modified (if this routine returns true) to give the clipped segment.
box	is the box to clip against.
use_ray	if true then the test is done with a ray instead of a segment. Default is false.

static csPtr<csFrustum> csIntersect3::FrustumFrustum	(	const csFrustum &	f1,
		const csFrustum &	f2
	)		`[inline, static]`

Calculate intersection of two frustums.

Definition at line 656 of file math3d.h.

static csPtr<csFrustum> csIntersect3::FrustumFrustum	(	const csFrustum &	f1,
		csVector3 *	poly,
		int	num
	)		`[inline, static]`

Calculate intersection of two frustums.

Definition at line 665 of file math3d.h.

static bool csIntersect3::PlaneAxisPlane	(	const csPlane3 &	p1,
		int	nr,
		float	pos,
		csPlane2 &	isect
	)		`[inline, static]`

Intersect a regular plane and an axis aligned plane and return the intersection (line) as a 2D plane.

This intersection is defined on the axis aligned plane.

Returns:: false if there is no intersection.

Definition at line 409 of file math3d.h.

static bool csIntersect3::PlanePolygon	(	const csPlane3 &	plane,
		csPoly3D *	poly,
		csSegment3 &	segment
	)		`[static]`

Intersect a plane with a 3D polygon and return the line segment corresponding with this intersection.

Returns true if there is an intersection. If false then 'segment' will not be valid.

static bool csIntersect3::PlaneXPlane	(	const csPlane3 &	p1,
		float	x2,
		csPlane2 &	isect
	)		`[static]`

Intersect a regular plane and an axis aligned plane and return the intersection (line) as a 2D plane.

This intersection is defined on the axis aligned plane.

Returns:: false if there is no intersection.

static bool csIntersect3::PlaneYPlane	(	const csPlane3 &	p1,
		float	y2,
		csPlane2 &	isect
	)		`[static]`

Intersect a regular plane and an axis aligned plane and return the intersection (line) as a 2D plane.

This intersection is defined on the axis aligned plane.

Returns:: false if there is no intersection.

static bool csIntersect3::PlaneZPlane	(	const csPlane3 &	p1,
		float	z2,
		csPlane2 &	isect
	)		`[static]`

Intersect a regular plane and an axis aligned plane and return the intersection (line) as a 2D plane.

This intersection is defined on the axis aligned plane.

Returns:: false if there is no intersection.

static float csIntersect3::SegmentAxisPlane	(	const csVector3 &	u,
		const csVector3 &	v,
		int	nr,
		float	pos,
		csVector3 &	isect
	)		`[inline, static]`

Intersect a 3D segment with an axis aligned plane and return the intersection (fails if segment is parallel to the plane), and returns the distance from u to the intersection point.

The intersection point is returned in isect.

Definition at line 525 of file math3d.h.

static int csIntersect3::SegmentFrustum	(	csPlane3 *	planes,
		int	num_planes,
		csSegment3 &	seg
	)		`[static]`

Intersect a segment with a frustum (given as a set of planes).

Returns the clipped segment (i.e. the part of the segment that is visible in the frustum). Returns -1 if the segment is entirely outside the frustum. Returns 0 if the segment is not modified and returns 1 otherwise. The input segment will be modified. @@ WARNING! This function may not work completely ok. It has only barely been tested and is now unused.

static bool csIntersect3::SegmentPlane	(	const csVector3 &	u,
		const csVector3 &	v,
		const csVector3 &	normal,
		const csVector3 &	a,
		csVector3 &	isect,
		float &	dist
	)		`[static]`

Intersect a 3D segment with a plane.

Returns:: true if there is an intersection, with the intersection point returned in isect.

static bool csIntersect3::SegmentPlane	(	const csPlane3 &	plane,
		csSegment3 &	segment
	)		`[static]`

Intersect a 3D segment with a plane.

Returns:: true if there is an intersection, segment updated to reflect the clipped part.

static bool csIntersect3::SegmentPlane	(	const csVector3 &	u,
		const csVector3 &	v,
		const csPlane3 &	p,
		csVector3 &	isect,
		float &	dist
	)		`[static]`

Intersect a 3D segment with a plane.

Returns true if there is an intersection, with the intersection point returned in isect. The distance from u to the intersection point is returned in dist. The distance that is returned is a normalized distance with respect to the given input vector. i.e. a distance of 0.5 means that the intersection point is halfway u and v. There are two cases in which this method will return false:

If the plane and the segment are parallel, then 'dist' will be set equal to 0, and 'isect' equal to 'v'.
If the segment does not cross the plane (i.e. if 'dist'>1+epsilon or 'dist'<-epsilon, where epsilon is a very small value near to zero) then 'isect's value is (0, 0, 0).

Remarks:: 'p' is the plane, expressed as: A x + B y + C z + D = 0 , where (A,B,C) is the normal vector of the plane. 'u' and 'v' are the start (U point) and the end (V point) of the segment. 'isect' is searched along the segment U + x (V - U); the unknown 'x' value is got by: x = [(A,B,C) * U + D ] / (A,B,C) * (U - V), where * is the dot product.

static bool csIntersect3::SegmentPlanes	(	const csVector3 &	u,
		const csVector3 &	v,
		const csPlane3 *	planes,
		int	length,
		csVector3 &	isect,
		float &	dist
	)		`[static]`

If a number of planes enclose a convex space (with their normals pointing outwards).

Returns:: true if they are intersected by a segment. isect contains the closest intersection point. dist contains the distance to that point (with distance between u and v being 1)

static bool csIntersect3::SegmentPolygon	(	const csSegment3 &	seg,
		const csPoly3D &	poly,
		const csPlane3 &	poly_plane,
		csVector3 &	isect
	)		`[static]`

Intersect a 3D segment with a polygon.

Returns:: true if there is an intersection. In that case the intersection point will be in 'isect'. Note that this function doesn't do backface culling.

static bool csIntersect3::SegmentTriangle	(	const csSegment3 &	seg,
		const csVector3 &	tr1,
		const csVector3 &	tr2,
		const csVector3 &	tr3,
		csVector3 &	isect
	)		`[static]`

Intersect a 3D segment with a triangle.

Returns:: true if there is an intersection. In that case the intersection point will be in 'isect'.

static float csIntersect3::SegmentXFrustum	(	const csVector3 &	u,
		const csVector3 &	v,
		float	A,
		csVector3 &	isect
	)		`[static]`

Intersect a 3D segment with the frustum plane Ax + z = 0.

Assumes an intersection, and returns the intersection point in isect.

static float csIntersect3::SegmentXFrustum	(	const csSegment3 &	uv,
		float	A,
		csVector3 &	isect
	)		`[inline, static]`

Intersect a 3D segment with the frustum plane Ax + z = 0.

Assumes an intersection, and returns the intersection point in isect.

Definition at line 548 of file math3d.h.

static float csIntersect3::SegmentXPlane	(	const csVector3 &	u,
		const csVector3 &	v,
		float	xval,
		csVector3 &	isect
	)		`[static]`

Intersect a 3D segment with the plane x = xval.

Assumes that there is an intersection (fails if the segment is parallel to the plane), and returns the distance from u to the intersection point. The intersection point is returned in isect.

static float csIntersect3::SegmentXPlane	(	const csSegment3 &	uv,
		float	xval,
		csVector3 &	isect
	)		`[inline, static]`

Intersect a 3D segment with the plane x = xval.

Assumes that there is an intersection (fails if the segment is parallel to the plane), and returns the distance from u to the intersection point. The intersection point is returned in isect.

Definition at line 461 of file math3d.h.

static float csIntersect3::SegmentYFrustum	(	const csVector3 &	u,
		const csVector3 &	v,
		float	B,
		csVector3 &	isect
	)		`[static]`

Intersect a 3D segment with the frustum plane By + z = 0.

Assumes an intersection, and returns the intersection point in isect.

static float csIntersect3::SegmentYFrustum	(	const csSegment3 &	uv,
		float	B,
		csVector3 &	isect
	)		`[inline, static]`

Intersect a 3D segment with the frustum plane By + z = 0.

Assumes an intersection, and returns the intersection point in isect.

Definition at line 565 of file math3d.h.

static float csIntersect3::SegmentYPlane	(	const csVector3 &	u,
		const csVector3 &	v,
		float	yval,
		csVector3 &	isect
	)		`[static]`

Intersect a 3D segment with the plane y = yval.

Assumes that there is an intersection (fails if the segment is parallel to the plane), and returns the distance from u to the intersection point. The intersection point is returned in isect.

static float csIntersect3::SegmentYPlane	(	const csSegment3 &	uv,
		float	yval,
		csVector3 &	isect
	)		`[inline, static]`

Intersect a 3D segment with the plane y = yval.

Assumes that there is an intersection (fails if the segment is parallel to the plane), and returns the distance from u to the intersection point. The intersection point is returned in isect.

Definition at line 486 of file math3d.h.

static float csIntersect3::SegmentZ0Plane	(	const csVector3 &	v1,
		const csVector3 &	v2,
		csVector3 &	isect
	)		`[static]`

Intersect a 3D segment with the z = 0 plane.

Assumes that there is an intersection (fails if the segment is parallel to the plane), and returns the distance from u to the intersection point. The intersection point is returned in isect.

static float csIntersect3::SegmentZ0Plane	(	const csSegment3 &	uv,
		csVector3 &	isect
	)		`[inline, static]`

Intersect a 3D segment with the z = 0 plane.

Assumes that there is an intersection (fails if the segment is parallel to the plane), and returns the distance from u to the intersection point. The intersection point is returned in isect.

Definition at line 437 of file math3d.h.

static float csIntersect3::SegmentZPlane	(	const csVector3 &	u,
		const csVector3 &	v,
		float	zval,
		csVector3 &	isect
	)		`[static]`

Intersect a 3D segment with the plane z = zval.

Assumes that there is an intersection (fails if the segment is parallel to the plane), and returns the distance from u to the intersection point. The intersection point is returned in isect.

static float csIntersect3::SegmentZPlane	(	const csSegment3 &	uv,
		float	zval,
		csVector3 &	isect
	)		`[inline, static]`

Intersect a 3D segment with the plane z = zval.

Assumes that there is an intersection (fails if the segment is parallel to the plane), and returns the distance from u to the intersection point. The intersection point is returned in isect.

Definition at line 511 of file math3d.h.

static bool csIntersect3::ThreePlanes	(	const csPlane3 &	p1,
		const csPlane3 &	p2,
		const csPlane3 &	p3,
		csVector3 &	isect
	)		`[static]`

Intersect 3 planes to get the point that is part of all three planes.

Returns:: true if there is a single point that fits. If some planes are parallel, then it will return false.

static bool csIntersect3::TriangleTriangle	(	const csVector3	tri1[3],
		const csVector3	tri2[3]
	)		`[static]`

Test intersection between two triangles.

Parameters:

tri1	Vertices of triangle 1
tri2	Vertices of triangle 2

Returns:: true if the triangles intersect, otherwise false

static bool csIntersect3::TriangleTriangle	(	const csVector3	tri1[3],
		const csVector3	tri2[3],
		csSegment3 &	isectline,
		bool &	coplanar
	)		`[static]`

Calculate intersection between two triangles and return it in isectline.

Parameters:

	tri1	Vertices of triangle 1
	tri2	Vertices of triangle 2
[out]	isectline	The line segment where they intersect
[out]	coplanar	Returns whether the triangles are coplanar

Returns:: true if the triangles intersect, otherwise false

The documentation for this class was generated from the following file:

csgeom/math3d.h

	Public API Reference

Public API Reference

Static Public Member Functions

Detailed Description

Member Function Documentation