D:/CHAI3D/build-2-0-0/2.0.0/win32/src/math/CMaths.h File Reference

Math
General Utility Functions. More...

#include "math/CMatrix3d.h"
#include <math.h>

Go to the source code of this file.

Functions

bool cZero (const double &a_value)

bool cPositiveBound (const double &a_value, const double &a_boundMax)

template<class T >

T cAbs (const T a_value)

template<class T >

T cMax (const T a_value1, const T a_value2)

template<class T >

T cMin (const T a_value1, const T a_value2)

template<class T >

T cMax3 (const T &a_value1, const T &a_value2, const T &a_value3)

template<class T >

T cMin3 (const T &a_value1, const T &a_value2, const T &a_value3)

template<class T >

T cMaxAbs (const T a_value1, const T a_value2)

template<class T >

T cMinAbs (const T a_value1, const T a_value2)

template<class T >

T cMax3Abs (const T &a_value1, const T &a_value2, const T &a_value3)

template<class T >

T cMin3Abs (const T &a_value1, const T &a_value2, const T &a_value3)

template<class T >

void cSwap (T &a_value1, T &a_value2)

template<class T >

T cLerp (const double &a_level, const T &a_value1, const T &a_value2)

template<class T >

T cClamp (const T a_value, const T a_low, const T a_high)

template<class T >

T cClamp0 (T &a_value)

double cClamp01 (double &a_value)

template<class T , class V >

bool cContains (const T &a_value, const V &a_low, const V &a_high)

double cSqr (const double &a_value)

double cCosDeg (const double &a_angleDeg)

double cSinDeg (const double &a_angleDeg)

double cTanDeg (const double &a_angleDeg)

double cCosRad (const double &a_angleRad)

double cSinRad (const double &a_value)

double cTanRad (const double &a_value)

double cDegToRad (const double &a_angleDeg)

double cRadToDeg (const double &a_angleRad)

cVector3d cAdd (const cVector3d &a_vector1, const cVector3d &a_vector2)

cVector3d cAdd (const cVector3d &a_vector1, const cVector3d &a_vector2, const cVector3d &a_vector3)

cVector3d cSub (const cVector3d &a_vector1, const cVector3d &a_vector2)

cVector3d cNegate (const cVector3d &a_vector)

cVector3d cMul (const double &a_value, const cVector3d &a_vector)

cVector3d cDiv (const double &a_value, const cVector3d &a_vector)

cVector3d cDivVect (const double &a_value, const cVector3d &a_vector)

cVector3d cCross (const cVector3d &a_vector1, const cVector3d &a_vector2)

double cDot (const cVector3d &a_vector1, const cVector3d &a_vector2)

cVector3d cNormalize (const cVector3d &a_vector)

double cDistance (const cVector3d &a_point1, const cVector3d &a_point2)

double cDistanceSq (const cVector3d &a_point1, const cVector3d &a_point2)

bool cEqualPoints (const cVector3d &v1, const cVector3d &v2, const double epsilon=CHAI_SMALL)

cMatrix3d cIdentity3d (void)

cMatrix3d cMul (const cMatrix3d &a_matrix1, const cMatrix3d &a_matrix2)

cVector3d cMul (const cMatrix3d &a_matrix, const cVector3d &a_vector)

cMatrix3d cTrans (const cMatrix3d &a_matrix)

cMatrix3d cInv (const cMatrix3d &a_matrix)

double cAngle (const cVector3d &a_vector0, const cVector3d &a_vector1)

double cCosAngle (const cVector3d &a_vector0, const cVector3d &a_vector1)

cMatrix3d cRotMatrix (const cVector3d &a_axis, const double &a_angleRad)

cMatrix3d cRotate (const cMatrix3d &a_matrix, const cVector3d &a_axis, const double &a_angleRad)

cVector3d cProjectPointOnPlane (const cVector3d &a_point, const cVector3d &a_planePoint, const cVector3d &n)

cVector3d cProjectPointOnPlane (const cVector3d &a_point, const cVector3d &a_planePoint0, const cVector3d &a_planePoint1, const cVector3d &a_planePoint2)

void cProjectPointOnPlane (const cVector3d &a_point, const cVector3d &a_planePoint0, const cVector3d &a_planePoint1, const cVector3d &a_planePoint2, double &a_v01, double a_v02)

cVector3d cProjectPointOnLine (const cVector3d &a_point, const cVector3d &a_pointOnLine, const cVector3d &a_directionOfLine)

cVector3d cProjectPointOnSegment (const cVector3d &a_point, const cVector3d &a_segmentPointA, const cVector3d &a_segmentPointB)

cVector3d cProject (const cVector3d &a_vector0, const cVector3d &a_vector1)

cVector3d cComputeSurfaceNormal (const cVector3d &a_surfacePoint0, const cVector3d &a_surfacePoint1, const cVector3d &a_surfacePoint2)

bool cBoxContains (const cVector3d &a_point, const cVector3d &box_min, const cVector3d &box_max)

int cIntersectionSegmentSphere (cVector3d &a_segmentPointA, cVector3d &a_segmentPointB, cVector3d &a_spherePos, double &a_sphereRadius, cVector3d &a_collisionPoint0, cVector3d &a_collisionNormal0, cVector3d &a_collisionPoint1, cVector3d &a_collisionNormal1)

int cIntersectionSegmentToplessCylinder (cVector3d &a_segmentPointA, cVector3d &a_segmentPointB, cVector3d &a_cylinderPointA, cVector3d &a_cylinderPointB, double &a_cylinderRadius, cVector3d &a_collisionPoint0, cVector3d &a_collisionNormal0, cVector3d &a_collisionPoint1, cVector3d &a_collisionNormal1)

bool cIntersectionSegmentTriangle (cVector3d &a_segmentPointA, cVector3d &a_segmentPointB, cVector3d &a_triangleVertex0, cVector3d &a_triangleVertex1, cVector3d &a_triangleVertex2, cVector3d &a_collisionPoint, cVector3d &a_collisionNormal)

Detailed Description

Math
General Utility Functions.

Function Documentation

template<class T >

T cAbs ( const T a_value ) [inline]

Compute absolute value.

Parameters:

a_value

Input value.

Returns:: Return the absolute value of value.

cVector3d cAdd	(	const cVector3d &	a_vector1,
		const cVector3d &	a_vector2,
		const cVector3d &	a_vector3
	)			`[inline]`

Compute the addition between three vectors.
Result = Vector1 + Vector2 + Vector3

Parameters:

	a_vector1	First vector.
	a_vector2	Second vector.
	a_vector3	Third vector.

Returns:: Return the addition of all three vectors.

cVector3d cAdd	(	const cVector3d &	a_vector1,
		const cVector3d &	a_vector2
	)			`[inline]`

Compute the addition between two vectors.
Result = Vector1 + Vector2

Parameters:

	a_vector1	First vector.
	a_vector2	Second vector.

Returns:: Return the addition of both vectors.

double cAngle	(	const cVector3d &	a_vector0,
		const cVector3d &	a_vector1
	)			`[inline]`

Compute the angle in radians between two vectors.

Parameters:

	a_vector0	Input vector.
	a_vector1	Input vector.

Returns:: Returns the angle in radians between the input vectors.

bool cBoxContains	(	const cVector3d &	a_point,
		const cVector3d &	box_min,
		const cVector3d &	box_max
	)			`[inline]`

Returns true if point is contained in the bounding box defined by min and max

Parameters:

	a_point	Test point
	box_min	Minimum coordinate in the boundary box
	box_max	Maximum coordinate in the boundary box

Returns:: Returns true if p is in [box_min,box_max], inclusive

template<class T >

T cClamp	(	const T	a_value,
		const T	a_low,
		const T	a_high
	)			`[inline]`

Clamp the input to the specified range.

Parameters:

	a_value	Input value.
	a_low	Low boundary.
	a_high	High boundary.

Returns:: Return clamped value.

Note that this function should not be modified to take inputs by reference.

template<class T >

T cClamp0 ( T & a_value ) [inline]

Clamp the input to the range 0 - infinity.

Parameters:

a_value

Input value.

Returns:: Return clamped value.

double cClamp01 ( double & a_value ) [inline]

Clamp the input to the range [0,1].

Parameters:

a_value

Input value of type double.

Returns:: Return clamped value.

cVector3d cComputeSurfaceNormal	(	const cVector3d &	a_surfacePoint0,
		const cVector3d &	a_surfacePoint1,
		const cVector3d &	a_surfacePoint2
	)			`[inline]`

Compute the normal of a surface defined by three point passed as parameters.

Parameters:

	a_surfacePoint0	Point 0 of surface.
	a_surfacePoint1	Point 1 of surface.
	a_surfacePoint2	Point 2 of surface.

Returns:: Return surface normal.

template<class T , class V >

bool cContains	(	const T &	a_value,
		const V &	a_low,
		const V &	a_high
	)			`[inline]`

Check whether value is in the range of [low, high].

Parameters:

	a_value	Input value.
	a_low	Low boundary.
	a_high	High boundary.

Returns:: Return true if value is in the rage of [low, high] and false otherwise.

double cCosAngle	(	const cVector3d &	a_vector0,
		const cVector3d &	a_vector1
	)			`[inline]`

Compute the cosine of the angle between two vectors.

Parameters:

	a_vector0	Input vector.
	a_vector1	Input vector.

Returns:: Returns the cosine of the angle between the input vectors.

double cCosDeg ( const double & a_angleDeg ) [inline]

Compute the cosine of an angle defined in degrees.

Parameters:

a_angleDeg

Angle in degrees.

Returns:: Return the cosine of angle.

double cCosRad ( const double & a_angleRad ) [inline]

Return the cosine of an angle defined in radians.

Parameters:

a_angleRad

Angle in radians.

Returns:: Return the cosine of angle.

cVector3d cCross	(	const cVector3d &	a_vector1,
		const cVector3d &	a_vector2
	)			`[inline]`

Compute the cross product between two 3D vectors.

Parameters:

	a_vector1	Vector1.
	a_vector2	Vector2.

Returns:: Returns the cross product between Vector1 and Vector2.

double cDegToRad ( const double & a_angleDeg ) [inline]

Convert an angle from degrees to radians.

Parameters:

a_angleDeg

Angle in degrees.

Returns:: Return angle in radians.

double cDistance	(	const cVector3d &	a_point1,
		const cVector3d &	a_point2
	)			`[inline]`

Compute the distance between two points.

Parameters:

	a_point1	First point.
	a_point2	Second point.

Returns:: Return distance between points

double cDistanceSq	(	const cVector3d &	a_point1,
		const cVector3d &	a_point2
	)			`[inline]`

Compute the squared distance between two points.

Parameters:

	a_point1	First point.
	a_point2	Second point.

Returns:: Return squared distance between points.

cVector3d cDiv	(	const double &	a_value,
		const cVector3d &	a_vector
	)			`[inline]`

Divide a vector by a scalar.

Parameters:

	a_value	Scalar.
	a_vector	Input vector.

Returns:: Returns result of division.

cVector3d cDivVect	(	const double &	a_value,
		const cVector3d &	a_vector
	)			`[inline]`

Divide a scalar by components of a 3D vector and return vector

Parameters:

	a_value	Scalar.
	a_vector	Input vector.

Returns:: Returns a vector. result = value / vector.

double cDot	(	const cVector3d &	a_vector1,
		const cVector3d &	a_vector2
	)			`[inline]`

Compute the dot product between two vectors.

Parameters:

	a_vector1	Vector1.
	a_vector2	Vector2.

Returns:: Returns the dot product between between both vectors.

bool inline cEqualPoints	(	const cVector3d &	v1,
		const cVector3d &	v2,
		const double	epsilon = `CHAI_SMALL`
	)			`[inline]`

Determine whether two vectors represent the same point.

Parameters:

	v1	First point.
	v2	Second point.
	epsilon	Two points will be considered equal if each component is within epsilon units. Defaults to CHAI_SMALL.

Returns:: Return whether the two vectors represent the same point.

cMatrix3d cIdentity3d ( void ) [inline]

Return the Identity Matrix .

Returns:: Return the identity matrix.

int cIntersectionSegmentSphere	(	cVector3d &	a_segmentPointA,
		cVector3d &	a_segmentPointB,
		cVector3d &	a_spherePos,
		double &	a_sphereRadius,
		cVector3d &	a_collisionPoint0,
		cVector3d &	a_collisionNormal0,
		cVector3d &	a_collisionPoint1,
		cVector3d &	a_collisionNormal1
	)			`[inline]`

Returns the number of intersection points between a segment AB and a sphere of radius R.
The number of points can be 0, 1 or 2.
If two intersection points are detected, collisionPoint0 will be the closest one to segmentPointA of segment AB.

Parameters:

	a_segmentPointA	First point of segment AB.
	a_segmentPointB	Second point of segment AB.
	a_spherePos	Position of sphere center.
	a_sphereRadius	Radius of sphere.
	a_collisionPoint0	Intersection point 0 if detected.
	a_collisionNormal0	Surface normal at intersection point 0
	a_collisionPoint1	Intersection point 1 if detected.
	a_collisionNormal1	Surface normal at intersection point 1

Returns:: Returns the number of intersection points found.

int cIntersectionSegmentToplessCylinder	(	cVector3d &	a_segmentPointA,
		cVector3d &	a_segmentPointB,
		cVector3d &	a_cylinderPointA,
		cVector3d &	a_cylinderPointB,
		double &	a_cylinderRadius,
		cVector3d &	a_collisionPoint0,
		cVector3d &	a_collisionNormal0,
		cVector3d &	a_collisionPoint1,
		cVector3d &	a_collisionNormal1
	)			`[inline]`

Returns the number of intersection points between a segment AB and a open topless cylinder of radius R.
The number of intersection points can be 0, 1 or 2.
If two intersection points are detected, collisionPoint0 will correspond to the point nearest to segmentPointA of segment AB.

Parameters:

	a_segmentPointA	First point of segment AB
	a_segmentPointB	Second point of segment AB
	a_cylinderPointA	Extremity point A of cylinder.
	a_cylinderPointB	Extremity point B of cylinder.
	a_cylinderRadius	Radius of cylinder.
	a_collisionPoint0	Intersection point 0 if detected
	a_collisionNormal0	Surface normal at intersection point 0
	a_collisionPoint1	Intersection point 1 if detected
	a_collisionNormal1	Surface normal at intersection point 1

Returns:: Returns the number of intersection points found

bool cIntersectionSegmentTriangle	(	cVector3d &	a_segmentPointA,
		cVector3d &	a_segmentPointB,
		cVector3d &	a_triangleVertex0,
		cVector3d &	a_triangleVertex1,
		cVector3d &	a_triangleVertex2,
		cVector3d &	a_collisionPoint,
		cVector3d &	a_collisionNormal
	)			`[inline]`

Returns true if segment AB intersects triangle defined by its three vertices (V0, V1, V2).

Parameters:

	a_segmentPointA	First point of segment AB
	a_segmentPointB	Second point of segment AB
	a_triangleVertex0	Vertex 0 of triangle
	a_triangleVertex1	Vertex 1 of triangle
	a_triangleVertex2	Vertex 2 of triangle
	a_collisionPoint	If a collision occurs, collision point is returned here
	a_collisionNormal	Surface normal at the point where the collision occurred

Returns:: Return true id collision occurs, otherwise return false

cMatrix3d cInv ( const cMatrix3d & a_matrix ) [inline]

Compute the inverse of a matrix.

Parameters:

a_matrix

Input matrix.

Returns:: Returns the inverse of the input matrix.

template<class T >

T cLerp	(	const double &	a_level,
		const T &	a_value1,
		const T &	a_value2
	)			`[inline]`

Linear interpolation from value0 (when a=0) to value1 (when a=1).

Parameters:

	a_level	Interpolation parameter.
	a_value1	First value.
	a_value2	Second value.

Returns:: Return an interpolated result: (1-a_level) * a_value1 + a_level * a_value2

template<class T >

T cMax	(	const T	a_value1,
		const T	a_value2
	)			`[inline]`

Compute maximum between two values.

Parameters:

	a_value1	First value.
	a_value2	Second value.

Returns:: Return maximum of a_value1 and a_value2.

Note that this function should not be modified to take inputs by reference.

template<class T >

T cMax3	(	const T &	a_value1,
		const T &	a_value2,
		const T &	a_value3
	)			`[inline]`

Compute maximum of 3 values.

Parameters:

	a_value1	First value.
	a_value2	Second value.
	a_value3	Third value.

Returns:: Return maximum of a_value1, a_value2 and a_value3.

template<class T >

T cMax3Abs	(	const T &	a_value1,
		const T &	a_value2,
		const T &	a_value3
	)			`[inline]`

Compute maximum of absolute values of 3 values.

Parameters:

	a_value1	First value.
	a_value2	Second value.
	a_value3	Third value.

Returns:: Return max(abs(p), abs(q), abs(r)).

template<class T >

T cMaxAbs	(	const T	a_value1,
		const T	a_value2
	)			`[inline]`

Compute maximum of absolute values of 2 numbers.

Parameters:

	a_value1	First value.
	a_value2	Second value.

Returns:: Return max(abs(p), abs(q)).

Note that this function should not be modified to take inputs by reference.

template<class T >

T cMin	(	const T	a_value1,
		const T	a_value2
	)			`[inline]`

Compute minimum between two values.

Parameters:

	a_value1	First value.
	a_value2	Second value.

Returns:: Return minimum of a_value1 and a_value2.

Note that this function should not be modified to take inputs by reference.

template<class T >

T cMin3	(	const T &	a_value1,
		const T &	a_value2,
		const T &	a_value3
	)			`[inline]`

Return minimum of 3 values.

Parameters:

	a_value1	First value.
	a_value2	Second value.
	a_value3	Third value.

Returns:: Return minimum of a_value1, a_value2 and a_value3.

template<class T >

T cMin3Abs	(	const T &	a_value1,
		const T &	a_value2,
		const T &	a_value3
	)			`[inline]`

Compute minimum of absolute values of 3 values.

Parameters:

	a_value1	First value.
	a_value2	Second value.
	a_value3	Third value.

Returns:: Return min(abs(p), abs(q), abs(r)).

template<class T >

T cMinAbs	(	const T	a_value1,
		const T	a_value2
	)			`[inline]`

Compute minimum of absolute values of 2 values.

Parameters:

	a_value1	First value.
	a_value2	Second value.

Returns:: Return min(abs(p), abs(q)).

Note that this function should not be modified to take inputs by reference.

cVector3d cMul	(	const cMatrix3d &	a_matrix,
		const cVector3d &	a_vector
	)			`[inline]`

Compute the multiplication of a matrix and a vector.

Parameters:

	a_matrix	Input matrix.
	a_vector	Input vector.

Returns:: Returns the multiplication of the matrix and vector.

cMatrix3d cMul	(	const cMatrix3d &	a_matrix1,
		const cMatrix3d &	a_matrix2
	)			`[inline]`

Compute the multiplication between two matrices.

Parameters:

	a_matrix1	First matrix.
	a_matrix2	Second matrix.

Returns:: Returns multiplication of /e matrix1 * /e matrix2.

cVector3d cMul	(	const double &	a_value,
		const cVector3d &	a_vector
	)			`[inline]`

Multiply a vector by a scalar.

Parameters:

	a_value	Scalar.
	a_vector	Input vector.

Returns:: Returns result of multiplication.

cVector3d cNegate ( const cVector3d & a_vector ) [inline]

Compute the negated vector of a input vector.

Parameters:

a_vector

Input vector.

Returns:: Return (-a_vector).

cVector3d cNormalize ( const cVector3d & a_vector ) [inline]

Compute the normalized vector (length = 1) of an input vector.

Parameters:

a_vector

Input vector.

Returns:: Returns the normalized vector.

bool cPositiveBound	(	const double &	a_value,
		const double &	a_boundMax
	)			`[inline]`

Check if value is strictly positive and less than maxBound in case maxBound is positive.

Parameters:

	a_value	Value to be checked.
	a_boundMax	Positive bound.

Returns:: Return true if value is greater than 0 and either maxBound is negative, or value is less thanmaxBound. Otherwise return false.

cVector3d cProject	(	const cVector3d &	a_vector0,
		const cVector3d &	a_vector1
	)			`[inline]`

Project a vector V0 onto a second vector V1.

Parameters:

	a_vector0	Vector 0.
	a_vector1	Vector 1.

Returns:: Returns the projection of V0 onto V1.

cVector3d cProjectPointOnLine	(	const cVector3d &	a_point,
		const cVector3d &	a_pointOnLine,
		const cVector3d &	a_directionOfLine
	)			`[inline]`

Compute the projection of a point on a line. the line is expressed by a point located on the line and a direction vector.

Parameters:

	a_point	Point to project on the line.
	a_pointOnLine	Point located on the line
	a_directionOfLine	Vector expressing the direction of the line

Returns:: Returns the projection of a_point on the line.

void cProjectPointOnPlane	(	const cVector3d &	a_point,
		const cVector3d &	a_planePoint0,
		const cVector3d &	a_planePoint1,
		const cVector3d &	a_planePoint2,
		double &	a_v01,
		double	a_v02
	)			`[inline]`

Projects a 3D point on a plane composed of three points.
This function returns two parameters v01 and v02 which correspond to the factord which express the following relation: projectedPoint = planePoint0 + v01 * V01 + v02 * V02
where:
V01 = planePoint1 - planePoint0, and
V02 = planePoint2 - planePoint0

Parameters:

	a_point	Point to project on plane.
	a_planePoint0	Point 0 on plane.
	a_planePoint1	Point 1 on plane.
	a_planePoint2	Point 2 on plane.
	a_v01	returned factor.
	a_v02	returned factor.

cVector3d cProjectPointOnPlane	(	const cVector3d &	a_point,
		const cVector3d &	a_planePoint0,
		const cVector3d &	a_planePoint1,
		const cVector3d &	a_planePoint2
	)			`[inline]`

Compute the projection of a point on a plane. the plane is expressed by a set of three points.

Parameters:

	a_point	Point to project on plane.
	a_planePoint0	Point 0 on plane.
	a_planePoint1	Point 1 on plane.
	a_planePoint2	Point 2 on plane.

Returns:: Returns the projection of point on plane.

cVector3d cProjectPointOnPlane	(	const cVector3d &	a_point,
		const cVector3d &	a_planePoint,
		const cVector3d &	n
	)			`[inline]`

Compute the projection of a point on a plane. the plane is expressed by a point and a surface normal.

Parameters:

	a_point	Point to project on plane.
	a_planePoint	Point on plane.
	n	Plane normal.

Returns:: Returns the projection of point on plane.

cVector3d cProjectPointOnSegment	(	const cVector3d &	a_point,
		const cVector3d &	a_segmentPointA,
		const cVector3d &	a_segmentPointB
	)			`[inline]`

Compute the projection of a point on a segment. the segment is described by its two extremity points.

Parameters:

	a_point	Point that is projected.
	a_segmentPointA	Point A of segment.
	a_segmentPointB	Point B of segment.

Returns:: Returns the projection of a_point on the segment.

double cRadToDeg ( const double & a_angleRad ) [inline]

Convert an angle from radians to degrees

Parameters:

a_angleRad

Angle in radians.

Returns:: Return angle in degrees.

cMatrix3d cRotate	(	const cMatrix3d &	a_matrix,
		const cVector3d &	a_axis,
		const double &	a_angleRad
	)			`[inline]`

Compute the rotation of a matrix around an axis and an angle.

Parameters:

	a_matrix	Input matrix.
	a_axis	Axis of rotation.
	a_angleRad	Rotation angle in Radian.

Returns:: Returns input matrix after rotation.

cMatrix3d cRotMatrix	(	const cVector3d &	a_axis,
		const double &	a_angleRad
	)			`[inline]`

Compute a rotation matrix given a rotation axis and an angle.

Parameters:

	a_axis	Axis of rotation.
	a_angleRad	Rotation angle in Radian.

Returns:: Returns a rotation matrix.

double cSinDeg ( const double & a_angleDeg ) [inline]

Compute the sine of an angle defined in degrees.

Parameters:

a_angleDeg

Angle in degrees.

Returns:: Return the sine of angle.

double cSinRad ( const double & a_value ) [inline]

Return the sine of an angle defined in radians.

Parameters:

a_value

Angle in radians.

Returns:: Return the sine of angle a_value.

double cSqr ( const double & a_value ) [inline]

Compute the square of a scalar.

Parameters:

a_value

Input value.

Returns:: Return (/e value * /e value).

cVector3d cSub	(	const cVector3d &	a_vector1,
		const cVector3d &	a_vector2
	)			`[inline]`

Compute the subtraction between two vectors.
Result = Vector1 - Vector2

Parameters:

	a_vector1	First vector.
	a_vector2	Second vector.

Returns:: Return result of subtraction.

template<class T >

void cSwap	(	T &	a_value1,
		T &	a_value2
	)			`[inline]`

Swap two elements.

Parameters:

	a_value1	First value.
	a_value2	Second value.

double cTanDeg ( const double & a_angleDeg ) [inline]

Compute the tangent of an angle defined in degrees.

Parameters:

a_angleDeg

Angle in degrees.

Returns:: Return the tangent of angle.

double cTanRad ( const double & a_value ) [inline]

Return the tangent of an angle defined in radians.

Parameters:

a_value

Angle in radians.

Returns:: Return the tangent of angle a_value.

cMatrix3d cTrans ( const cMatrix3d & a_matrix ) [inline]

Compute the transpose of a matrix

Parameters:

a_matrix

Input matrix.

Returns:: Returns the transpose of the input matrix.

bool cZero ( const double & a_value ) [inline]

Check if value is equal or near zero.

Parameters:

a_value

Value to be checked.

Returns:: Returns true if it's almost zero, otherwise false.


Functions
bool	cZero (const double &a_value)
bool	cPositiveBound (const double &a_value, const double &a_boundMax)
template<class T >
T	cAbs (const T a_value)
template<class T >
T	cMax (const T a_value1, const T a_value2)
template<class T >
T	cMin (const T a_value1, const T a_value2)
template<class T >
T	cMax3 (const T &a_value1, const T &a_value2, const T &a_value3)
template<class T >
T	cMin3 (const T &a_value1, const T &a_value2, const T &a_value3)
template<class T >
T	cMaxAbs (const T a_value1, const T a_value2)
template<class T >
T	cMinAbs (const T a_value1, const T a_value2)
template<class T >
T	cMax3Abs (const T &a_value1, const T &a_value2, const T &a_value3)
template<class T >
T	cMin3Abs (const T &a_value1, const T &a_value2, const T &a_value3)
template<class T >
void	cSwap (T &a_value1, T &a_value2)
template<class T >
T	cLerp (const double &a_level, const T &a_value1, const T &a_value2)
template<class T >
T	cClamp (const T a_value, const T a_low, const T a_high)
template<class T >
T	cClamp0 (T &a_value)
double	cClamp01 (double &a_value)
template<class T , class V >
bool	cContains (const T &a_value, const V &a_low, const V &a_high)
double	cSqr (const double &a_value)
double	cCosDeg (const double &a_angleDeg)
double	cSinDeg (const double &a_angleDeg)
double	cTanDeg (const double &a_angleDeg)
double	cCosRad (const double &a_angleRad)
double	cSinRad (const double &a_value)
double	cTanRad (const double &a_value)
double	cDegToRad (const double &a_angleDeg)
double	cRadToDeg (const double &a_angleRad)
cVector3d	cAdd (const cVector3d &a_vector1, const cVector3d &a_vector2)
cVector3d	cAdd (const cVector3d &a_vector1, const cVector3d &a_vector2, const cVector3d &a_vector3)
cVector3d	cSub (const cVector3d &a_vector1, const cVector3d &a_vector2)
cVector3d	cNegate (const cVector3d &a_vector)
cVector3d	cMul (const double &a_value, const cVector3d &a_vector)
cVector3d	cDiv (const double &a_value, const cVector3d &a_vector)
cVector3d	cDivVect (const double &a_value, const cVector3d &a_vector)
cVector3d	cCross (const cVector3d &a_vector1, const cVector3d &a_vector2)
double	cDot (const cVector3d &a_vector1, const cVector3d &a_vector2)
cVector3d	cNormalize (const cVector3d &a_vector)
double	cDistance (const cVector3d &a_point1, const cVector3d &a_point2)
double	cDistanceSq (const cVector3d &a_point1, const cVector3d &a_point2)
bool	cEqualPoints (const cVector3d &v1, const cVector3d &v2, const double epsilon=CHAI_SMALL)
cMatrix3d	cIdentity3d (void)
cMatrix3d	cMul (const cMatrix3d &a_matrix1, const cMatrix3d &a_matrix2)
cVector3d	cMul (const cMatrix3d &a_matrix, const cVector3d &a_vector)
cMatrix3d	cTrans (const cMatrix3d &a_matrix)
cMatrix3d	cInv (const cMatrix3d &a_matrix)
double	cAngle (const cVector3d &a_vector0, const cVector3d &a_vector1)
double	cCosAngle (const cVector3d &a_vector0, const cVector3d &a_vector1)
cMatrix3d	cRotMatrix (const cVector3d &a_axis, const double &a_angleRad)
cMatrix3d	cRotate (const cMatrix3d &a_matrix, const cVector3d &a_axis, const double &a_angleRad)
cVector3d	cProjectPointOnPlane (const cVector3d &a_point, const cVector3d &a_planePoint, const cVector3d &n)
cVector3d	cProjectPointOnPlane (const cVector3d &a_point, const cVector3d &a_planePoint0, const cVector3d &a_planePoint1, const cVector3d &a_planePoint2)
void	cProjectPointOnPlane (const cVector3d &a_point, const cVector3d &a_planePoint0, const cVector3d &a_planePoint1, const cVector3d &a_planePoint2, double &a_v01, double a_v02)
cVector3d	cProjectPointOnLine (const cVector3d &a_point, const cVector3d &a_pointOnLine, const cVector3d &a_directionOfLine)
cVector3d	cProjectPointOnSegment (const cVector3d &a_point, const cVector3d &a_segmentPointA, const cVector3d &a_segmentPointB)
cVector3d	cProject (const cVector3d &a_vector0, const cVector3d &a_vector1)
cVector3d	cComputeSurfaceNormal (const cVector3d &a_surfacePoint0, const cVector3d &a_surfacePoint1, const cVector3d &a_surfacePoint2)
bool	cBoxContains (const cVector3d &a_point, const cVector3d &box_min, const cVector3d &box_max)
int	cIntersectionSegmentSphere (cVector3d &a_segmentPointA, cVector3d &a_segmentPointB, cVector3d &a_spherePos, double &a_sphereRadius, cVector3d &a_collisionPoint0, cVector3d &a_collisionNormal0, cVector3d &a_collisionPoint1, cVector3d &a_collisionNormal1)
int	cIntersectionSegmentToplessCylinder (cVector3d &a_segmentPointA, cVector3d &a_segmentPointB, cVector3d &a_cylinderPointA, cVector3d &a_cylinderPointB, double &a_cylinderRadius, cVector3d &a_collisionPoint0, cVector3d &a_collisionNormal0, cVector3d &a_collisionPoint1, cVector3d &a_collisionNormal1)
bool	cIntersectionSegmentTriangle (cVector3d &a_segmentPointA, cVector3d &a_segmentPointB, cVector3d &a_triangleVertex0, cVector3d &a_triangleVertex1, cVector3d &a_triangleVertex2, cVector3d &a_collisionPoint, cVector3d &a_collisionNormal)