#include <math.h>
#include <float.h>
#include "MT_Point3.h"
#include "MT_Plane3.h"

Defines
#define	VAR_EPSILON
Functions
const MT_Scalar	BOP_EPSILON (9.3132257461547852e-10)
int	BOP_sign (MT_Scalar x)
MT_Scalar	BOP_abs (MT_Scalar x)
int	BOP_comp (const MT_Scalar A, const MT_Scalar B)
int	BOP_comp (const MT_Tuple3 &A, const MT_Tuple3 &B)
int	BOP_comp0 (const MT_Scalar A)
bool	BOP_fuzzyZero (MT_Scalar x)
int	BOP_exactComp (const MT_Scalar A, const MT_Scalar B)
int	BOP_exactComp (const MT_Tuple3 &A, const MT_Tuple3 &B)
bool	BOP_between (const MT_Point3 &p1, const MT_Point3 &p2, const MT_Point3 &p3)
bool	BOP_collinear (const MT_Point3 &p1, const MT_Point3 &p2, const MT_Point3 &p3)
bool	BOP_convex (const MT_Point3 &p1, const MT_Point3 &p2, const MT_Point3 &p3, const MT_Point3 &p4)
int	BOP_concave (const MT_Point3 &p1, const MT_Point3 &p2, const MT_Point3 &p3, const MT_Point3 &p4)
bool	BOP_intersect (const MT_Vector3 &vL1, const MT_Point3 &pL1, const MT_Vector3 &vL2, const MT_Point3 &pL2, MT_Point3 &intersection)
bool	BOP_getCircleCenter (const MT_Point3 &p1, const MT_Point3 &p2, const MT_Point3 &p3, const MT_Point3 &center)
bool	BOP_isInsideCircle (const MT_Point3 &p1, const MT_Point3 &p2, const MT_Point3 &p3, const MT_Point3 &p4, const MT_Point3 &p5)
bool	BOP_isInsideCircle (const MT_Point3 &p1, const MT_Point3 &p2, const MT_Point3 &p3, const MT_Point3 &q)
MT_Scalar	BOP_orientation (const MT_Plane3 &p1, const MT_Plane3 &p2)
int	BOP_classify (const MT_Point3 &p, const MT_Plane3 &plane)
MT_Point3	BOP_intersectPlane (const MT_Plane3 &plane, const MT_Point3 &p1, const MT_Point3 &p2)
bool	BOP_containsPoint (const MT_Plane3 &plane, const MT_Point3 &point)
MT_Point3	BOP_4PointIntersect (const MT_Point3 &p0, const MT_Point3 &p1, const MT_Point3 &p2, const MT_Point3 &q)
MT_Scalar	BOP_EpsilonDistance (const MT_Point3 &p0, const MT_Point3 &p1, const MT_Point3 &q)

Detailed Description

Definition in file BOP_MathUtils.h.

Define Documentation

#define VAR_EPSILON

Definition at line 44 of file BOP_MathUtils.h.

Function Documentation

MT_Point3 BOP_4PointIntersect	(	const MT_Point3 &	p0,
		const MT_Point3 &	p1,
		const MT_Point3 &	p2,
		const MT_Point3 &	q
	)

Pre: p0, p1 and p2 is a triangle and q is an interior point.

Parameters:

p0	point
p1	point
p2	point
q	point

Returns:: intersection point I v (p0)-----(I)----->(p1) \ ^ / \ |w / \ | / \ (q) / \ | / \ | / \ | / (p2)

v = P1-P2 w = P3-Q r0(t) = v*t+P1 r1(t) = w*t+P3 I = r0^r1

Definition at line 438 of file BOP_MathUtils.cpp.

References BOP_intersect(), I, simple_enum_gen::w, MT_Tuple3::x(), MT_Tuple3::y(), and MT_Tuple3::z().

MT_Scalar BOP_abs ( MT_Scalar x ) [inline]

Definition at line 55 of file BOP_MathUtils.h.

References fabs().

bool BOP_between	(	const MT_Point3 &	p1,
		const MT_Point3 &	p2,
		const MT_Point3 &	p3
	)

Returns if p1 is between p2 and p3 and lay on the same line (are collinears).

Parameters:

p1	point
p2	point
p3	point

Returns:: true if p1 is between p2 and p3 and lay on the same line, false otherwise

Definition at line 141 of file BOP_MathUtils.cpp.

References BOP_collinear(), distance(), and MT_Point3::distance().

int BOP_classify	(	const MT_Point3 &	p,
		const MT_Plane3 &	plane
	)

Classifies a point according to the specified plane with EPSILON accuracy.

Parameters:

p	point
plane	plane

Returns:: >0 if the point is above (OUT), =0 if the point is on (ON), <0 if the point is below (IN)

Definition at line 366 of file BOP_MathUtils.cpp.

References BOP_comp0(), and MT_Plane3::signedDistance().

Referenced by BOP_concave(), BOP_convex(), BOP_overlap(), BOP_splitFace(), and BOP_BSPNode::testPoint().

bool BOP_collinear	(	const MT_Point3 &	p1,
		const MT_Point3 &	p2,
		const MT_Point3 &	p3
	)

Returns if three points lay on the same line (are collinears).

Parameters:

p1	point
p2	point
p3	point

Returns:: true if the three points lay on the same line, false otherwise

Definition at line 154 of file BOP_MathUtils.cpp.

References BOP_comp(), BOP_fuzzyZero(), MT_Vector3::cross(), MT_Vector3::normalize(), simple_enum_gen::w, MT_Tuple3::x(), MT_Tuple3::y(), and MT_Tuple3::z().

Referenced by BOP_between(), BOP_mergeVertexs(), and clean_nonmanifold().

int BOP_comp	(	const MT_Tuple3 &	A,
		const MT_Tuple3 &	B
	)

Compares two scalar triplets with EPSILON accuracy.

Parameters:

A	scalar triplet
B	scalar triplet

Returns:: 1 if A > B, -1 if A < B, 0 otherwise

Definition at line 86 of file BOP_MathUtils.cpp.

References BOP_comp(), BOP_EPSILON(), MT_Tuple3::x(), MT_Tuple3::y(), and MT_Tuple3::z().

int BOP_comp	(	const MT_Scalar	A,
		const MT_Scalar	B
	)

Compares two scalars with EPSILON accuracy.

Parameters:

A	scalar
B	scalar

Returns:: 1 if A > B, -1 if A < B, 0 otherwise

Definition at line 44 of file BOP_MathUtils.cpp.

References BOP_EPSILON().

Referenced by BOP_collinear(), BOP_comp(), BOP_getNearestVertex(), BOP_isInsideCircle(), and BOP_BBox::intersect().

int BOP_comp0 ( const MT_Scalar A )

Compares a scalar with EPSILON accuracy.

Parameters:

A scalar

Returns:: 1 if A > 0, -1 if A < 0, 0 otherwise

Definition at line 73 of file BOP_MathUtils.cpp.

References BOP_EPSILON().

Referenced by BOP_classify(), and BOP_fuzzyZero().

int BOP_concave	(	const MT_Point3 &	p1,
		const MT_Point3 &	p2,
		const MT_Point3 &	p3,
		const MT_Point3 &	p4
	)

Returns if a quad (coplanar) is concave and where is the split edge.

Returns:: 0 if is convex, 1 if is concave and split edge is p1-p3 and -1 if is cancave and split edge is p2-p4.

Definition at line 198 of file BOP_MathUtils.cpp.

References BOP_classify(), and MT_Vector3::cross().

Referenced by BOP_splitQuad().

bool BOP_containsPoint	(	const MT_Plane3 &	plane,
		const MT_Point3 &	point
	)

Returns if a plane contains a point with EPSILON accuracy.

Parameters:

plane	plane
point	point

Returns:: true if the point is on the plane, false otherwise

Definition at line 409 of file BOP_MathUtils.cpp.

References BOP_fuzzyZero(), and MT_Plane3::signedDistance().

Referenced by BOP_Face2Face(), BOP_removeOverlappedFaces(), and BOP_sew().

bool BOP_convex	(	const MT_Point3 &	p1,
		const MT_Point3 &	p2,
		const MT_Point3 &	p3,
		const MT_Point3 &	p4
	)

Returns if a quad (coplanar) is convex.

Returns:: true if the quad is convex, false otherwise

Definition at line 176 of file BOP_MathUtils.cpp.

References BOP_classify(), and MT_Vector3::cross().

const MT_Scalar BOP_EPSILON ( 9.3132257461547852e- 10 )

Referenced by BOP_comp(), and BOP_comp0().

MT_Scalar BOP_EpsilonDistance	(	const MT_Point3 &	p0,
		const MT_Point3 &	p1,
		const MT_Point3 &	q
	)

Pre: p0, p1 and q are collinears.

Parameters:

p0	point
p1	point
q	point

Returns:: 0 if q == p0, 1 if q == p1, or a value between 0 and 1 otherwise

(p0)-----(q)------------(p1) |<-d1-->| | |<---------d0---------->|

Definition at line 461 of file BOP_MathUtils.cpp.

References BOP_fuzzyZero(), simple_enum_gen::d, and MT_Point3::distance().

int BOP_exactComp	(	const MT_Scalar	A,
		const MT_Scalar	B
	)

Compares two scalars strictly.

Parameters:

A	scalar
B	scalar

Returns:: 1 if A > B, -1 if A < B, 0 otherwise

Definition at line 111 of file BOP_MathUtils.cpp.

int BOP_exactComp	(	const MT_Tuple3 &	A,
		const MT_Tuple3 &	B
	)

Compares two scalar strictly.

Parameters:

A	scalar triplet
B	scalar triplet

Returns:: 1 if A > B, -1 if A < B, 0 otherwise

Definition at line 123 of file BOP_MathUtils.cpp.

References MT_Tuple3::x(), MT_Tuple3::y(), and MT_Tuple3::z().

bool BOP_fuzzyZero ( MT_Scalar x ) [inline]

Definition at line 59 of file BOP_MathUtils.h.

References BOP_comp0().

Referenced by BOP_collinear(), BOP_containsPoint(), BOP_EpsilonDistance(), BOP_intersect(), and BOP_mergeSort().

bool BOP_getCircleCenter	(	const MT_Point3 &	p1,
		const MT_Point3 &	p2,
		const MT_Point3 &	p3,
		const MT_Point3 &	center
	)

bool BOP_intersect	(	const MT_Vector3 &	vL1,
		const MT_Point3 &	pL1,
		const MT_Vector3 &	vL2,
		const MT_Point3 &	pL2,
		MT_Point3 &	intersection
	)

Computes the intersection between two lines (on the same plane).

Parameters:

vL1	first line vector
pL1	first line point
vL2	second line vector
pL2	second line point
intersection	intersection point (if exists)

Returns:: false if lines are parallels, true otherwise

Definition at line 225 of file BOP_MathUtils.cpp.

References BOP_fuzzyZero(), MT_Tuple3::setValue(), MT_Tuple3::x(), MT_Tuple3::y(), and MT_Tuple3::z().

Referenced by BOP_4PointIntersect(), and BOP_getCircleCenter().

MT_Point3 BOP_intersectPlane	(	const MT_Plane3 &	plane,
		const MT_Point3 &	p1,
		const MT_Point3 &	p2
	)

Intersects a plane with the line that contains the specified points.

Parameters:

plane	split plane
p1	first line point
p2	second line point

Returns:: intersection between plane and line that contains p1 and p2

Definition at line 379 of file BOP_MathUtils.cpp.

References MT_Tuple3::setValue(), MT_Tuple4::w(), MT_Tuple3::x(), MT_Tuple4::x(), MT_Tuple3::y(), MT_Tuple4::y(), MT_Tuple3::z(), and MT_Tuple4::z().

Referenced by BOP_BSPNode::addFace(), BOP_splitEdge(), BOP_BSPNode::classifyFace(), and BOP_BSPNode::splitTriangle().

bool BOP_isInsideCircle	(	const MT_Point3 &	p1,
		const MT_Point3 &	p2,
		const MT_Point3 &	p3,
		const MT_Point3 &	p4,
		const MT_Point3 &	p5
	)

Returns if points p4 or p5 is inside the circle defined by p1, p2 and p3.

Parameters:

p1	point
p2	point
p3	point
p4	point
p5	point

Returns:: true if p4 or p5 is inside the circle, false otherwise. If the circle does not exist (p1, p2 and p3 are collinears) returns true

Definition at line 333 of file BOP_MathUtils.cpp.

References BOP_comp(), BOP_getCircleCenter(), and MT_Point3::distance().

bool BOP_isInsideCircle	(	const MT_Point3 &	p1,
		const MT_Point3 &	p2,
		const MT_Point3 &	p3,
		const MT_Point3 &	q
	)

Returns if points q is inside the circle defined by p1, p2 and p3.

Parameters:

p1	point
p2	point
p3	point
q	point

Returns:: true if p4 or p5 are inside the circle, false otherwise. If the circle does not exist (p1, p2 and p3 are collinears) returns true

Definition at line 307 of file BOP_MathUtils.cpp.

References BOP_comp(), BOP_getCircleCenter(), simple_enum_gen::d, and MT_Point3::distance().

Referenced by BOP_getTriangleVertex(), BOP_isInsideCircle(), BOP_splitQuad(), BOP_triangulateC(), and BOP_BSPNode::classifyFace().

MT_Scalar BOP_orientation	(	const MT_Plane3 &	p1,
		const MT_Plane3 &	p2
	)

Returns if two planes share the same orientation.

Returns:: >0 if planes share the same orientation

Definition at line 352 of file BOP_MathUtils.cpp.

References MT_Tuple4::x(), MT_Tuple4::y(), and MT_Tuple4::z().

Referenced by BOP_Face2Face(), BOP_sew(), BOP_splitQuad(), and BOP_BSPNode::hasSameOrientation().

int BOP_sign ( MT_Scalar x ) [inline]

Definition at line 52 of file BOP_MathUtils.h.

BOP_MathUtils.h File Reference

Defines

Functions

Detailed Description

Define Documentation

Function Documentation