CMaths.h File Reference

Various mathematical utility functions. More...

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

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)
cVector3d	cProjectPointOnLine (const cVector3d &a_point, const cVector3d &a_pointOnLine, const cVector3d &a_directionOfLine)
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 &p, const cVector3d &box_min, const cVector3d &box_max)

---

Detailed Description

Various mathematical utility functions.

---

Function Documentation

template<class T>

T cAbs

(

const T

a_value

)

[inline]

Compute absolute value.

Parameters:

a_value

Input value

Returns:

Return |a_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 between two vectors (in radians).

Parameters:

	a_vector0	Input vector.
	a_vector1	Input vector.

Returns:

Returns the angle (in radians) between the input vectors.

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

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

Parameters:

	p	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 input 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 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	First vector.
	a_vector2	Second vector.

Returns:

Returns the cross product between both vectors.

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	First vector.
	a_vector2	Second vector.

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.

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 maximum 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 a_point on the line.

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.

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 a_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 a_point on plane.

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 double.

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.

---