Implements general math tools. More...

Files
file	CBezier.h
	Implements support for Bezier curves and surface patches.

file	CConstants.h
	Implements mathematical constants.

file	CGeometry.h
	Implements general geometry utility functions.

file	CMarchingCubes.h
	Implementation of the marching cube algorithm.

file	CMaths.h
	Implements general math utility functions.

file	CMatrix3d.h
	Implements a 3D matrix.

file	CPolySolver.h
	Implements polynomial solvers.

file	CQuaternion.h
	Implements a quaternion.

file	CTransform.h
	Implements a transformation matrix.

file	CVector3d.h
	Implements a 3D vector.

Classes
struct	chai3d::cMarchingCubeTriangle

struct	chai3d::cMarchingCubeGridCell

struct	chai3d::cMatrix3d
	This class implements a 3D matrix. More...

struct	chai3d::cQuaternion
	This class implements a quaternion. More...

struct	chai3d::cTransform
	This class implements a 4D transformation matrix encoded as column-major. More...

struct	chai3d::cVector3d
	This class implements a 3D vector. More...

Functions
cVector3d	chai3d::cEvalBezierCurve (const cVector3d *a_controlPoints, double a_t)
	This function determines the position of a point along a Bezier curve. More...

cVector3d	chai3d::cEvalBezierPatch (const cVector3d *a_controlPoints, double a_u, double a_v)
	This function determines the position of a point along a Bezier patch. More...

cVector3d	chai3d::cDerivBezier (const cVector3d *a_controlPoints, double a_t)
	This function determines the derivative of a point along a Bezier curve. More...

cVector3d	chai3d::cDerivUBezier (const cVector3d *a_controlPoints, double a_u, double a_v)
	This function determines the derivative of a point on a Bezier patch along the u parametric direction. More...

cVector3d	chai3d::cDerivVBezier (const cVector3d *a_controlPoints, double a_u, double a_v)
	This function determines the derivative of a point on a Bezier patch along the v parametric direction. More...

cVector3d	chai3d::cSurfaceNormalBezier (const cVector3d *a_controlPoints, double a_u, double a_v)
	This function determines the surface normal at a point on a Bezier patch. More...

double	chai3d::cTriangleArea (const cVector3d &a_vertex0, const cVector3d &a_vertex1, const cVector3d &a_vertex2)
	This function computes the area of a triangle. More...

cVector3d	chai3d::cProjectPointOnPlane (const cVector3d &a_point, const cVector3d &a_planePoint, const cVector3d &a_planeNormal)
	This function computes the projection of a point onto a plane. More...

cVector3d	chai3d::cProjectPointOnPlane (const cVector3d &a_point, const cVector3d &a_planePoint0, const cVector3d &a_planePoint1, const cVector3d &a_planePoint2)
	This function computes the projection of a point onto a plane. More...

void	chai3d::cProjectPointOnPlane (const cVector3d &a_point, const cVector3d &a_planePoint0, const cVector3d &a_planePoint1, const cVector3d &a_planePoint2, double &a_r01, double &a_r02)
	This function computes the projection of a point onto a plane. More...

cVector3d	chai3d::cProjectPointOnLine (const cVector3d &a_point, const cVector3d &a_pointOnLine, const cVector3d &a_directionOfLine)
	This function computes the projection of a point onto a line. More...

cVector3d	chai3d::cProjectPointOnSegment (const cVector3d &a_point, const cVector3d &a_segmentPointA, const cVector3d &a_segmentPointB)
	This function computes the projection of a point onto a segment. More...

cVector3d	chai3d::cProjectPointOnDiskXY (const cVector3d &a_point, const double &a_height, const double &a_radius)
	This function computes the projection of a point onto a disk. More...

cVector3d	chai3d::cProjectPointOnTriangle (const cVector3d &a_point, const cVector3d &a_vertex0, const cVector3d &a_vertex1, const cVector3d &a_vertex2)
	This function computes the projection of a point onto a triangle. More...

cVector3d	chai3d::cProject (const cVector3d &a_vector0, const cVector3d &a_vector1)
	This function computes the projection of a vector V0 onto a vector V1. More...

double	chai3d::cDistanceToLine (const cVector3d &a_point, const cVector3d &a_linePoint1, const cVector3d &a_linePoint2)
	This function computes the distance between a point and a line. More...

cVector3d	chai3d::cComputeSurfaceNormal (const cVector3d &a_surfacePoint0, const cVector3d &a_surfacePoint1, const cVector3d &a_surfacePoint2)
	This function computes the surface normal of a plane. More...

bool	chai3d::cBoxContains (const cVector3d &a_point, const cVector3d &a_boxMin, const cVector3d &a_boxMax)
	This function checks if a point is contained in a box. More...

int	chai3d::cIntersectionSegmentPlane (const cVector3d &a_segmentPointA, const cVector3d &a_segmentPointB, const cVector3d &a_planePos, const cVector3d &a_planeNormal, cVector3d &a_collisionPoint, cVector3d &a_collisionNormal)
	This function computes the intersection between a segment and a plane. More...

int	chai3d::cIntersectionSegmentDisk (const cVector3d &a_segmentPointA, const cVector3d &a_segmentPointB, const cVector3d &a_diskPos, const cVector3d &a_diskNormal, const double &a_diskRadius, cVector3d &a_collisionPoint, cVector3d &a_collisionNormal)
	This function computes the intersection between a segment and a disk. More...

int	chai3d::cIntersectionSegmentSphere (const cVector3d &a_segmentPointA, const cVector3d &a_segmentPointB, const cVector3d &a_spherePos, const double &a_sphereRadius, cVector3d &a_collisionPoint0, cVector3d &a_collisionNormal0, cVector3d &a_collisionPoint1, cVector3d &a_collisionNormal1)
	This function computes the intersection between a segment and a sphere. More...

int	chai3d::cIntersectionSegmentEllipsoid (const cVector3d &a_segmentPointA, const cVector3d &a_segmentPointB, const cVector3d &a_pos, const double &a_radiusX, const double &a_radiusY, const double &a_radiusZ, cVector3d &a_collisionPoint0, cVector3d &a_collisionNormal0, cVector3d &a_collisionPoint1, cVector3d &a_collisionNormal1)
	This function computes the intersection between a segment and a sphere. More...

int	chai3d::cIntersectionSegmentToplessCylinder (const cVector3d &a_segmentPointA, const cVector3d &a_segmentPointB, const cVector3d &a_cylinderPointA, const cVector3d &a_cylinderPointB, const double &a_cylinderRadius, cVector3d &a_collisionPoint0, cVector3d &a_collisionNormal0, double &a_collisionPointRelPosAB0, cVector3d &a_collisionPoint1, cVector3d &a_collisionNormal1, double &a_collisionPointRelPosAB1)
	This function computes the intersection between a segment and a topless cylinder. More...

int	chai3d::cIntersectionSegmentCylinder (const cVector3d &a_segmentPointA, const cVector3d &a_segmentPointB, const double &a_baseRadius, const double &a_topRadius, const double &a_height, cVector3d &a_collisionPoint, cVector3d &a_collisionNormal)
	This function computes the nearest intersection point between a segment and a cylinder. More...

int	chai3d::cIntersectionSegmentBox (const cVector3d &a_segmentPointA, const cVector3d &a_segmentPointB, const cVector3d &a_boxMin, const cVector3d &a_boxMax, cVector3d &a_collisionPoint, cVector3d &a_collisionNormal)
	This function computes the nearest intersection point between a segment and a box. More...

int	chai3d::cIntersectionSegmentTorus (const cVector3d &a_segmentPointA, const cVector3d &a_segmentPointB, const double &a_innerRadius, const double &a_outerRadius, cVector3d &a_collisionPoint, cVector3d &a_collisionNormal)
	This function computes the nearest intersection point between a segment and a torus. More...

bool	chai3d::cIntersectionSegmentTriangle (const cVector3d &a_segmentPointA, const cVector3d &a_segmentPointB, const cVector3d &a_triangleVertex0, const cVector3d &a_triangleVertex1, const cVector3d &a_triangleVertex2, const bool a_reportFrontSideCollision, const bool a_reportBackSideCollision, cVector3d &a_collisionPoint, cVector3d &a_collisionNormal, double &a_collisionPosVertex01, double &a_collisionPosVertex02)
	This function computes the intersection between a segment and a triangle. More...

cVector3d	chai3d::cVertexInterpolation (double a_isolevel, cVector3d a_p1, cVector3d a_p2, double a_valp1, double a_valp2)
	This function linearly interpolate the position where an isosurface cuts an edge between two vertices, each with their own scalar value. More...

int	chai3d::cPolygonize (cMarchingCubeGridCell a_grid, double a_isolevel, cMarchingCubeTriangle *a_triangles)
	This function calculates the triangular facets required to represent the isosurface through the cell. More...

bool	chai3d::cCheckBit (const unsigned int &a_value, const unsigned int &a_bitPosition)
	This function checks if a given bit is enabled. More...

unsigned int	chai3d::cSetBit (const unsigned int &a_data, const unsigned int &a_bitPosition, const bool a_value)
	This function sets the value of a specified bit of an unsigned integer. More...

bool	chai3d::cZero (const double &a_value)
	This function checks if a value is equal to or almost near zero. More...

template<class T >
T	chai3d::cAbs (const T &a_value)
	This function computes an absolute value. More...

template<class T >
double	chai3d::cSign (const T &a_value)
	This function computes the sign of a value. More...

template<class T >
T	chai3d::cMax (const T &a_value1, const T &a_value2)
	This function computes the maximum value between two values. More...

template<class T >
T	chai3d::cMin (const T &a_value1, const T &a_value2)
	This function computes the minimum value between two values. More...

template<class T >
T	chai3d::cMax3 (const T &a_value1, const T &a_value2, const T &a_value3)
	This function computes the maximum value between three values. More...

template<class T >
T	chai3d::cMin3 (const T &a_value1, const T &a_value2, const T &a_value3)
	This function computes the minimum value between three values. More...

template<class T >
void	chai3d::cSwap (T &a_value1, T &a_value2)
	This function swaps two elements. More...

template<class T >
T	chai3d::cLerp (const double &a_level, const T &a_value1, const T &a_value2)
	This function computes a linear interpolation between two values. More...

template<class T >
T	chai3d::cClamp (const T &a_value, const T &a_low, const T &a_high)
	This function clamps a value to a specified range. More...

template<class T >
T	chai3d::cClamp0 (const T &a_value)
	This function clamps a value to a value ranged between 0 and infinity. More...

double	chai3d::cClamp01 (const double &a_value)
	This function clamps a value to a value ranged between 0.0 and 1.0. More...

template<class T , class V >
bool	chai3d::cContains (const T &a_value, const V &a_low, const V &a_high)
	This function checks whether a value is within a specified range. More...

double	chai3d::cSqr (const double &a_value)
	This function computes the square of a scalar. More...

double	chai3d::cSqrt (const double &a_value)
	This function computes the square root of a scalar. More...

double	chai3d::cCbrt (const double &a_value)
	This function computes the cubic root of a scalar. More...

double	chai3d::cCosDeg (const double &a_angleDeg)
	Compute the cosine of an angle defined in degrees. More...

double	chai3d::cSinDeg (const double &a_angleDeg)
	This function computes the sine of an angle defined in degrees. More...

double	chai3d::cTanDeg (const double &a_angleDeg)
	This function computes the tangent of an angle defined in degrees. More...

double	chai3d::cCosRad (const double &a_angleRad)
	This function computes the cosine of an angle defined in radians. More...

double	chai3d::cSinRad (const double &a_angleRad)
	This function computes the sine of an angle defined in radians. More...

double	chai3d::cTanRad (const double &a_angleRad)
	This function computes the tangent of an angle defined in radians. More...

double	chai3d::cDegToRad (const double &a_angleDeg)
	This function converts an angle from degrees to radians. More...

double	chai3d::cRadToDeg (const double &a_angleRad)
	This function converts an angle from radians to degrees. More...

int	chai3d::cNumDigits (int a_value)
	This function computes the number of digits that compose a given integer. More...

cVector3d	chai3d::cAdd (const cVector3d &a_vector1, const cVector3d &a_vector2)
	This function computes the addition of two vectors. More...

cVector3d	chai3d::cAdd (const cVector3d &a_vector1, const cVector3d &a_vector2, const cVector3d &a_vector3)
	This function computes the addition of three vectors. More...

cVector3d	chai3d::cSub (const cVector3d &a_vector1, const cVector3d &a_vector2)
	This function computes the subtraction of two vectors. More...

cVector3d	chai3d::cNegate (const cVector3d &a_vector)
	This function computes the negated vector. More...

cVector3d	chai3d::cMul (const double &a_value, const cVector3d &a_vector)
	This function computes the multiplication of a vector by a scalar. More...

cVector3d	chai3d::cDiv (const double &a_value, const cVector3d &a_vector)
	This function computes the division of a vector by a scalar. More...

cVector3d	chai3d::cCross (const cVector3d &a_vector1, const cVector3d &a_vector2)
	This function computes the cross product between two vectors. More...

double	chai3d::cDot (const cVector3d &a_vector1, const cVector3d &a_vector2)
	This function computes the dot product between two vectors. More...

cVector3d	chai3d::cNormalize (const cVector3d &a_vector)
	This function computes the normalized vector. More...

double	chai3d::cDistance (const cVector3d &a_point1, const cVector3d &a_point2)
	This function computes the Euclidean distance between two points. More...

double	chai3d::cDistanceSq (const cVector3d &a_point1, const cVector3d &a_point2)
	This function computes the squared distance between two points. More...

bool	chai3d::cEqualPoints (const cVector3d &a_point1, const cVector3d &a_point2, const double a_epsilon=C_SMALL)
	This function determines whether two vectors are equal (i.e. represent the same point). More...

cMatrix3d	chai3d::cIdentity3d (void)
	This function return a 3x3 identity matrix. More...

cMatrix3d	chai3d::cAdd (const cMatrix3d &a_matrix1, const cMatrix3d &a_matrix2)
	This function computes the addition between two matrices. More...

cMatrix3d	chai3d::cSub (const cMatrix3d &a_matrix1, const cMatrix3d &a_matrix2)
	This function computes the subtraction between two matrices. More...

cMatrix3d	chai3d::cRotEulerRad (const double &a_angleRad1, const double &a_angleRad2, const double &a_angleRad3, const cEulerOrder a_eulerOrder, const bool a_useIntrinsicEulerModel=true)
	This function builds a rotation matrix from a set of Euler angles defined in radians. More...

cMatrix3d	chai3d::cRotEulerDeg (const double &a_angleDeg1, const double &a_angleDeg2, const double &a_angleDeg3, const cEulerOrder a_eulerOrder, const bool a_useIntrinsicEulerModel=true)
	This function builds a rotation matrix from a set of Euler angles defined in degrees. More...

cMatrix3d	chai3d::cRotAxisAngleRad (const double &a_axisX, const double &a_axisY, const double &a_axisZ, const double &a_angleRad)
	This function builds a rotation matrix from an axis-angle representation. More...

cMatrix3d	chai3d::cRotAxisAngleDeg (const double &a_axisX, const double &a_axisY, const double &a_axisZ, const double &a_angleDeg)
	This function builds a rotation matrix from an axis-angle representation. More...

cMatrix3d	chai3d::cMul (const cMatrix3d &a_matrix1, const cMatrix3d &a_matrix2)
	This function computes the multiplication of two matrices. More...

cVector3d	chai3d::cMul (const cMatrix3d &a_matrix, const cVector3d &a_vector)
	This function computes the multiplication of a matrix and a vector. More...

cMatrix3d	chai3d::cTranspose (const cMatrix3d &a_matrix)
	This function computes the transpose of a matrix. More...

cMatrix3d	chai3d::cInverse (const cMatrix3d &a_matrix)
	This function computes the inverse of a matrix. More...

double	chai3d::cAngle (const cVector3d &a_vector1, const cVector3d &a_vector2)
	This function computes the angle in radians between two vectors. More...

double	chai3d::cCosAngle (const cVector3d &a_vector1, const cVector3d &a_vector2)
	This function computes the cosine of the angle between two vectors. More...

int	chai3d::cSolveLinear (double a_coefficient[2], double a_solution[1])
	This function computes the solution of a linear equation. More...

int	chai3d::cSolveQuadric (double a_coefficient[3], double a_solution[2])
	This function computes the solution of a quadric equation. More...

int	chai3d::cSolveCubic (double a_coefficient[4], double a_solution[3])
	This function computes the solution of a cubic equation. More...

int	chai3d::cSolveQuartic (double a_coefficient[5], double a_solution[4])
	This function computes the solution of a quartic equation. More...

Detailed Description

Function Documentation

cVector3d chai3d::cEvalBezierCurve	(	const cVector3d *	a_controlPoints,
		double	a_t
	)

inline

This function determines the position of a point along a Bezier curve at t [0:1].

Parameters

a_controlPoints	Control points. (4 in total)
a_t	Parameter t between 0 and 1.

Returns: The computed point.

cVector3d chai3d::cEvalBezierPatch	(	const cVector3d *	a_controlPoints,
		double	a_u,
		double	a_v
	)

inline

This function determines the position of a point along a Bezier patch at u [0:1] and v [0:1].

Parameters

a_controlPoints	Control points. (16 in total)
a_u	Parameter u between 0 and 1.
a_v	Parameter v between 0 and 1.

Returns: The computed point.

cVector3d chai3d::cDerivBezier	(	const cVector3d *	a_controlPoints,
		double	a_t
	)

inline

This function determines the derivative of a point along a Bezier curve at t [0:1].

Parameters

a_controlPoints	Control points. (4 in total)
a_t	Parameter t between 0 and 1.

Returns: The computed derivative.

cVector3d chai3d::cDerivUBezier	(	const cVector3d *	a_controlPoints,
		double	a_u,
		double	a_v
	)

inline

This function determines the derivative of a point on a Bezier patch along the u parametric direction.

Parameters

a_controlPoints	Control points. (16 in total)
a_u	Parameter u between 0 and 1.
a_v	Parameter v between 0 and 1.

Returns: The computed derivative.

cVector3d chai3d::cDerivVBezier	(	const cVector3d *	a_controlPoints,
		double	a_u,
		double	a_v
	)

inline

This function determines the derivative of a point on a Bezier patch along the v parametric direction.

Parameters

a_controlPoints	Control points. (16 in total)
a_u	Parameter u between 0 and 1.
a_v	Parameter v between 0 and 1.

Returns: The computed derivative.

cVector3d chai3d::cSurfaceNormalBezier	(	const cVector3d *	a_controlPoints,
		double	a_u,
		double	a_v
	)

inline

This function determines the surface normal at a point on a Bezier patch at u [0:1] and v [0:1].

Parameters

a_controlPoints	Control points. (16 in total)
a_u	Parameter u between 0 and 1.
a_v	Parameter v between 0 and 1.

Returns: The computed surface normal.

double chai3d::cTriangleArea	(	const cVector3d &	a_vertex0,
		const cVector3d &	a_vertex1,
		const cVector3d &	a_vertex2
	)

inline

This function computes the area of a triangle described by the position of its three vertices a_vertex0, a_vertex1, and a_vertex2.

Parameters

a_vertex0	Vertex 0 of triangle.
a_vertex1	Vertex 1 of triangle.
a_vertex2	Vertex 2 of triangle.

Returns: The area of the triangle.

cVector3d chai3d::cProjectPointOnPlane	(	const cVector3d &	a_point,
		const cVector3d &	a_planePoint,
		const cVector3d &	a_planeNormal
	)

inline

This function computes the projection of a point a_point onto a plane. The plane is expressed by a point a_planePoint and a surface normal a_planeNormal.

Parameters

a_point	Point to be projected on the plane.
a_planePoint	Point on the plane.
a_planeNormal	Surface normal of the plane.

Returns: The projection of the point onto the plane.

cVector3d chai3d::cProjectPointOnPlane	(	const cVector3d &	a_point,
		const cVector3d &	a_planePoint0,
		const cVector3d &	a_planePoint1,
		const cVector3d &	a_planePoint2
	)

inline

This function computes the projection of a point onto a plane. The plane is expressed by a set of three points passed by argument.

Parameters

a_point	Point to be projected onto the plane.
a_planePoint0	Point 0 of plane.
a_planePoint1	Point 1 of plane.
a_planePoint2	Point 2 of plane.

Returns: The projection of the point onto the plane.

void chai3d::cProjectPointOnPlane	(	const cVector3d &	a_point,
		const cVector3d &	a_planePoint0,
		const cVector3d &	a_planePoint1,
		const cVector3d &	a_planePoint2,
		double &	a_r01,
		double &	a_r02
	)

inline

This function computes the projection of a point a_point onto a plane described by three points a_planePoint0, a_planePoint1, and a_planePoint2.

The function returns two parameters a_r01 and a_r01 which describe the position of the projected point onto the plane.

projectedPoint = a_planePoint0 + a_r01 * V01 + a_r02 * V02

where:

V01 = a_planePoint1 - a_planePoint0

V02 = a_planePoint2 - a_planePoint0

Parameters

a_point	Point to be projected onto plane.
a_planePoint0	Point 0 of plane.
a_planePoint1	Point 1 of plane.
a_planePoint2	Point 2 of plane.
a_r01	Returned relative position factor v01.
a_r02	Returned relative position factor v02.

cVector3d chai3d::cProjectPointOnLine	(	const cVector3d &	a_point,
		const cVector3d &	a_pointOnLine,
		const cVector3d &	a_directionOfLine
	)

inline

This function computes the projection of a point a_point on a line. The line is expressed by a point a_pointOnLine located on the line and a direction vector a_directionOfLine.

Parameters

a_point	Point to be projected onto the line.
a_pointOnLine	Point located on the line.
a_directionOfLine	Direction vector of the line.

Returns: The projection of the point onto the line.

cVector3d chai3d::cProjectPointOnSegment	(	const cVector3d &	a_point,
		const cVector3d &	a_segmentPointA,
		const cVector3d &	a_segmentPointB
	)

inline

This function computes the projection of a point a_point onto a segment. The segment is described by its two extremity points a_segmentPointA and a_segmentPointB.

Parameters

a_point	Point to be projected.
a_segmentPointA	Point A of segment.
a_segmentPointB	Point B of segment.

Returns: The projection of the point onto the segment.

cVector3d chai3d::cProjectPointOnDiskXY	(	const cVector3d &	a_point,
		const double &	a_height,
		const double &	a_radius
	)

inline

This function computes the projection of a point onto a disk lying in the XY plane.
The position of the disk along the z-axis is expressed by parameter a_height.
The radius of the disk is expressed by parameter a_radius.

Parameters

a_point	Point to be projected.
a_height	Position of the disk along the z-axis.
a_radius	Radius of the disk.

Returns: The projection of the point onto the disk.

cVector3d chai3d::cProjectPointOnTriangle	(	const cVector3d &	a_point,
		const cVector3d &	a_vertex0,
		const cVector3d &	a_vertex1,
		const cVector3d &	a_vertex2
	)

inline

This function computes the projection of a point onto a triangle expressed by its three vertices.

Parameters

a_point	Point to be projected.
a_vertex0	Triangle vertex 0.
a_vertex1	Triangle vertex 1.
a_vertex2	Triangle vertex 2.

Returns: The projection of the point onto the triangle.

cVector3d chai3d::cProject	(	const cVector3d &	a_vector0,
		const cVector3d &	a_vector1
	)

inline

This function computes the projection of a vector V0 onto a vector V1, where V0 and V1 are passed by argument as a_vector0 and a_vector1.

Parameters

a_vector0	Vector V0.
a_vector1	Vector V1.

Returns: The projection of vector V0 onto vector V1.

double chai3d::cDistanceToLine	(	const cVector3d &	a_point,
		const cVector3d &	a_linePoint1,
		const cVector3d &	a_linePoint2
	)

inline

This function computes the distance between a point and a line. The line is described by two points a_linePoint1 and a_linePoint2 located along the line.

Parameters

a_point	Point to be tested.
a_linePoint1	Point 1 on line.
a_linePoint2	Point 2 on line.

Returns: The distance between the point and the line.

cVector3d chai3d::cComputeSurfaceNormal	(	const cVector3d &	a_surfacePoint0,
		const cVector3d &	a_surfacePoint1,
		const cVector3d &	a_surfacePoint2
	)

inline

This function computes the surface normal of a plane defined by three points passed by argument.

Parameters

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

Returns: The surface normal.

bool chai3d::cBoxContains	(	const cVector3d &	a_point,
		const cVector3d &	a_boxMin,
		const cVector3d &	a_boxMax
	)

inline

This function check if a point is contained in a box. The box is described by its minimum and maximum corners a_boxMin and a_boxMax.
If the point is located inside the box, then then function returns true, otherwise it returns false.

Parameters

a_point	Test point.
a_boxMin	Minimum coordinate of the box.
a_boxMax	Maximum coordinate of the box.

Returns: true if the point is contained in the box, false otherwise.

int chai3d::cIntersectionSegmentPlane	(	const cVector3d &	a_segmentPointA,
		const cVector3d &	a_segmentPointB,
		const cVector3d &	a_planePos,
		const cVector3d &	a_planeNormal,
		cVector3d &	a_collisionPoint,
		cVector3d &	a_collisionNormal
	)

inline

This function computes the intersection between a segment and a plane.
The segment is described by two points a_segmentPointA and a_segmentPointB.
The plane is described by a point a_planePos and a surface normal a_planeNormal.
The function returns the number of collision points that were detected (0 or 1).
If a collision occurs, the collision point and collision normal are returned by arguments a_collisionPoint and a_collisionNormal.

Parameters

a_segmentPointA	First point of segment AB.
a_segmentPointB	Second point of segment AB.
a_planePos	Position of a point on the plane.
a_planeNormal	Surface normal of the plane.
a_collisionPoint	Returned intersection point (if detected).
a_collisionNormal	Returned surface normal at intersection point (if detected).

Returns: The number of intersection points found (0 or 1).

int chai3d::cIntersectionSegmentDisk	(	const cVector3d &	a_segmentPointA,
		const cVector3d &	a_segmentPointB,
		const cVector3d &	a_diskPos,
		const cVector3d &	a_diskNormal,
		const double &	a_diskRadius,
		cVector3d &	a_collisionPoint,
		cVector3d &	a_collisionNormal
	)

inline

This function computes the intersection between a segment and a disk.
The segment is described by two points a_segmentPointA and a_segmentPointB.
The disk is described by a point a_diskPos, a surface normal a_diskNormal, and a radius a_diskRadius.
The function returns the number of collision points that were detected (0 or 1).
If a collision occurs, the collision point and collision normal are returned by arguments a_collisionPoint and a_collisionNormal.

Parameters

a_segmentPointA	First point of segment AB.
a_segmentPointB	Second point of segment AB.
a_diskPos	Position of the disk center.
a_diskNormal	Surface normal of the disk.
a_diskRadius	Radius of the disk.
a_collisionPoint	Returned intersection point (if detected).
a_collisionNormal	Returned surface normal at intersection point (if detected).

Returns: The number of intersection points found (0 or 1).

int chai3d::cIntersectionSegmentSphere	(	const cVector3d &	a_segmentPointA,
		const cVector3d &	a_segmentPointB,
		const cVector3d &	a_spherePos,
		const double &	a_sphereRadius,
		cVector3d &	a_collisionPoint0,
		cVector3d &	a_collisionNormal0,
		cVector3d &	a_collisionPoint1,
		cVector3d &	a_collisionNormal1
	)

inline

This function computes the intersection between a segment and a sphere.
The segment is described by two points a_segmentPointA and a_segmentPointB.
The sphere is described by its position a_spherePos and a radius a_sphereRadius.
The function returns the number of collision points that were detected (0, 1, or 2).
If a collision occurs, the collision point(s) and collision normal(s) are returned by arguments a_collisionPoint0, a_collisionNormal0, a_collisionPoint1, and a_collisionNormal1.
If two intersection points are detected, collisionPoint0 is the nearest point to segmentPointA of segment AB.
If the segment begins inside the sphere, then all intersections are ignored.

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	Returned intersection point 0 (if detected).
a_collisionNormal0	Returned surface normal 0 at intersection point (if detected).
a_collisionPoint1	Returned intersection point 1 (if detected).
a_collisionNormal1	Returned surface normal 1 at intersection point (if detected).

Returns: The number of intersection points found (0, 1, or 2).

int chai3d::cIntersectionSegmentEllipsoid	(	const cVector3d &	a_segmentPointA,
		const cVector3d &	a_segmentPointB,
		const cVector3d &	a_pos,
		const double &	a_radiusX,
		const double &	a_radiusY,
		const double &	a_radiusZ,
		cVector3d &	a_collisionPoint0,
		cVector3d &	a_collisionNormal0,
		cVector3d &	a_collisionPoint1,
		cVector3d &	a_collisionNormal1
	)

inline

This function computes the intersection between a segment and a sphere.
The segment is described by two points a_segmentPointA and a_segmentPointB.
The sphere is described by its position a_spherePos and a radius a_sphereRadius.
The function returns the number of collision points that were detected (0, 1, or 2).
If a collision occurs, the collision point(s) and collision normal(s) are returned by arguments a_collisionPoint0, a_collisionNormal0, a_collisionPoint1, and a_collisionNormal1.
If two intersection points are detected, collisionPoint0 is the nearest point to segmentPointA of segment AB.
If the segment begins inside the sphere, then all intersections are ignored.

Parameters

a_segmentPointA	First point of segment AB.
a_segmentPointB	Second point of segment AB.
a_pos	Position of ellipsoid center.
a_radiusX	Ellipsoid radius along x axis.
a_radiusY	Ellipsoid radius along y axis.
a_radiusZ	Ellipsoid radius along z axis.
a_collisionPoint0	Returned intersection point 0 (if detected).
a_collisionNormal0	Returned surface normal 0 at intersection point (if detected).
a_collisionPoint1	Returned intersection point 1 (if detected).
a_collisionNormal1	Returned surface normal 1 at intersection point (if detected).

Returns: The number of intersection points found (0, 1, or 2).

int chai3d::cIntersectionSegmentToplessCylinder	(	const cVector3d &	a_segmentPointA,
		const cVector3d &	a_segmentPointB,
		const cVector3d &	a_cylinderPointA,
		const cVector3d &	a_cylinderPointB,
		const double &	a_cylinderRadius,
		cVector3d &	a_collisionPoint0,
		cVector3d &	a_collisionNormal0,
		double &	a_collisionPointRelPosAB0,
		cVector3d &	a_collisionPoint1,
		cVector3d &	a_collisionNormal1,
		double &	a_collisionPointRelPosAB1
	)

inline

This function computes the intersection between a segment and a topless cylinder.

The segment is described by two points a_segmentPointA and a_segmentPointB.
The cylinder is described by two extremity points a_cylinderPointA and a_cylinderPointB, and a radius a_cylinderRadius.
The function returns the number of collision points that were detected (0, 1, or 2).
If a collision occurs, the collision point(s) and collision normal(s) are returned by arguments a_collisionPoint0, a_collisionPoint1, a_collisionNormal0 and a_collisionNormal1.
If two intersection points occur, collisionPoint0 is the nearest point to segmentPointA of segment AB.
If the segment begins inside the cylinder, then all intersections are ignored.

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	Returned intersection point 0 (if detected).
a_collisionNormal0	Returned surface normal 0 at intersection point (if detected).
a_collisionPointRelPosAB0	Returned relative position of collision point 0 projected on segment `a_segmentPointA` - `a_segmentPointB`
a_collisionPoint1	Returned intersection point 1 (if detected).
a_collisionNormal1	Returned surface normal 1 at intersection point (if detected).
a_collisionPointRelPosAB1	Returned relative position of collision point 1 projected on segment `a_segmentPointA` - `a_segmentPointB`

Returns: The number of intersection points found (0, 1, or 2).

int chai3d::cIntersectionSegmentCylinder	(	const cVector3d &	a_segmentPointA,
		const cVector3d &	a_segmentPointB,
		const double &	a_baseRadius,
		const double &	a_topRadius,
		const double &	a_height,
		cVector3d &	a_collisionPoint,
		cVector3d &	a_collisionNormal
	)

inline

This function computes the nearest intersection point between a segment and a cylinder.
The segment is described by two points a_segmentPointA and a_segmentPointB.
The cylinder is aligned along the z-axis and is described by its height a_height, base radius a_baseRadius, and a top radius a_topRadius.
The function returns the number of collision points that were detected (0 or 1).
If a collision occurs, the collision point and collision normal are returned by arguments a_collisionPoint and a_collisionNormal.
If the segment begins inside the cylinder, then all intersections are ignored.

Parameters

a_segmentPointA	First point of segment AB.
a_segmentPointB	Second point of segment AB.
a_baseRadius	Radius of cylinder a z = 0.0.
a_topRadius	Radius of cylinder a z = a_height.
a_height	Height of cylinder.
a_collisionPoint	Returned intersection point (if detected).
a_collisionNormal	Returned surface normal at intersection point (if detected).

Returns: The number of intersection points found (0 or 1).

int chai3d::cIntersectionSegmentBox	(	const cVector3d &	a_segmentPointA,
		const cVector3d &	a_segmentPointB,
		const cVector3d &	a_boxMin,
		const cVector3d &	a_boxMax,
		cVector3d &	a_collisionPoint,
		cVector3d &	a_collisionNormal
	)

inline

This function computes the nearest intersection point between a segment and a box.
The segment is described by two points a_segmentPointA and a_segmentPointB.
The box is aligned with all axes and is described by its minimum and maximum corners a_boxMin and a_boxMax.

The function returns the number of collision points that were detected (0 or 1).
If a collision occurs, the collision point and collision normal are returned by arguments a_collisionPoint and a_collisionNormal.

Parameters

a_segmentPointA	First point of segment AB.
a_segmentPointB	Second point of segment AB.
a_boxMin	Minimum coordinate of box.
a_boxMax	Maximum coordinate of box.
a_collisionPoint	Returned intersection point (if detected).
a_collisionNormal	Returned surface normal at intersection point (if detected).

Returns: The number of intersection points found (0 or 1).

int chai3d::cIntersectionSegmentTorus	(	const cVector3d &	a_segmentPointA,
		const cVector3d &	a_segmentPointB,
		const double &	a_innerRadius,
		const double &	a_outerRadius,
		cVector3d &	a_collisionPoint,
		cVector3d &	a_collisionNormal
	)

inline

This function computes the nearest intersection point between a segment and a torus centered around the z-axis.
The segment is described by two points a_segmentPointA and a_segmentPointB.
The torus is described by its inner a_innerRadius and outer radius a_outerRadius.
The function returns the number of collision points that were detected (0 or 1).
If a collision occurs, the collision point and collision normal are returned by arguments a_collisionPoint and a_collisionNormal.

Parameters

a_segmentPointA	First point of segment AB.
a_segmentPointB	Second point of segment AB.
a_innerRadius	Inner radius of torus.
a_outerRadius	Outer radius of torus.
a_collisionPoint	Returned intersection point (if detected).
a_collisionNormal	Returned surface normal at intersection point (if detected).

Returns: The number of intersection points found (0 or 1).

bool chai3d::cIntersectionSegmentTriangle	(	const cVector3d &	a_segmentPointA,
		const cVector3d &	a_segmentPointB,
		const cVector3d &	a_triangleVertex0,
		const cVector3d &	a_triangleVertex1,
		const cVector3d &	a_triangleVertex2,
		const bool	a_reportFrontSideCollision,
		const bool	a_reportBackSideCollision,
		cVector3d &	a_collisionPoint,
		cVector3d &	a_collisionNormal,
		double &	a_collisionPosVertex01,
		double &	a_collisionPosVertex02
	)

inline

This function computes the intersection between a segment and a triangle defined by three vertices a_triangleVertex0, a_triangleVertex1, and a_triangleVertex2.
The segment is described by two points a_segmentPointA and a_segmentPointB.
The function returns the number of collision points that were detected (0 or 1).
If a collision occurs, the collision point and collision normal are returned by arguments a_collisionPoint and a_collisionNormal.

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_reportFrontSideCollision	If true, then front side collisions are reported.
a_reportBackSideCollision	If true, then back side collisions are reported.
a_collisionPoint	Returned intersection point (if detected).
a_collisionNormal	Returned surface normal at intersection point (if detected).
a_collisionPosVertex01	Returned relative position of collision point projected on segment `a_triangleVertex0` -`a_triangleVertex1`.
a_collisionPosVertex02	Returned relative position of collision point projected on segment `a_triangleVertex0` -`a_triangleVertex1`

Returns: true if a collision has occurred, otherwise false.

cVector3d chai3d::cVertexInterpolation	(	double	a_isolevel,
		cVector3d	a_p1,
		cVector3d	a_p2,
		double	a_valp1,
		double	a_valp2
	)

inline

This function linearly interpolate the position where an isosurface cuts an edge between two vertices, each with their own scalar value.

Parameters

a_isolevel	Iso value.
a_p1	Point 1.
a_p2	Point 2.
a_valp1	Value at point 1.
a_valp2	Value at point 2.

Returns: The interpolated point.

int chai3d::cPolygonize	(	cMarchingCubeGridCell	a_grid,
		double	a_isolevel,
		cMarchingCubeTriangle *	a_triangles
	)

inline

Given a grid cell and an isolevel, this function calculates the triangular facets required to represent the isosurface through the cell. The function returns the number of triangular facets and at most 5 of them. 0 will be returned if the grid cell is either totally above of totally below the isolevel.

Parameters

a_grid	Grid composed of 8 voxels
a_isolevel	Isovalue.
a_triangles	Returned triangles.

Returns: The number of triangles.

bool chai3d::cCheckBit	(	const unsigned int &	a_value,
		const unsigned int &	a_bitPosition
	)

inline

This function checks if a given bit is enabled. The function takes by argument an unsigned integer a_value and the position of the bit a_bitPosition to be tested.
If the selected bit is enabled, the function returns true, otherwise false.

Parameters

a_value	Unsigned int value.
a_bitPosition	Bit position [0..31].

Returns: true if the selected bit is enabled, false otherwise.

unsigned int chai3d::cSetBit	(	const unsigned int &	a_data,
		const unsigned int &	a_bitPosition,
		const bool	a_value
	)

inline

This function sets the value of a specified bit of an unsigned integer.
The function takes by argument an unsigned integer a_value, the position of the bit to be tested a_bitPosition, and its new value a_value as a boolean.
The function returns the modified unsigned integer as a result.

Parameters

a_data	Input unsigned integer data.
a_bitPosition	Bit position [0..31]
a_value	New state of bit (true = 1, false = 0).

Returns: Input data with modified bit.

bool chai3d::cZero ( const double & a_value )

inline

This function checks if a value passed by argument a_value is equal to or almost near zero.

Parameters

a_value Value to be checked.

Returns: true if the value is equal to zero, false otherwise.

template<class T >

T chai3d::cAbs ( const T & a_value )

inline

This function computes the absolute value of a value a_value passed by argument.

Parameters

a_value Input value.

Returns: Absolute value.

template<class T >

double chai3d::cSign ( const T & a_value )

inline

This function computes the sign of a value passed by argument a_value.

Parameters

a_value Value to be evaluated.

Returns: 1.0 if the value is zero or positive, -1.0 otherwise.

template<class T >

T chai3d::cMax	(	const T &	a_value1,
		const T &	a_value2
	)

inline

This function returns the maximum value between two values a_value1 and a_value2 passed by argument.

Parameters

a_value1	First value.
a_value2	Second value.

Returns: Maximum value between a_value1 and a_value2.

template<class T >

T chai3d::cMin	(	const T &	a_value1,
		const T &	a_value2
	)

inline

This function returns the minimum value between two values a_value1 and a_value2 passed by argument.

Parameters

a_value1	First value.
a_value2	Second value.

Returns: Minimum value between a_value1 and a_value2.

template<class T >

T chai3d::cMax3	(	const T &	a_value1,
		const T &	a_value2,
		const T &	a_value3
	)

inline

This function returns the maximum value between three values a_value1, a_value2, and a_value3 passed by argument.

Parameters

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

Returns: Maximum value between a_value1, a_value2, and a_value3.

template<class T >

T chai3d::cMin3	(	const T &	a_value1,
		const T &	a_value2,
		const T &	a_value3
	)

inline

This function returns the minimum value between three values a_value1, a_value2, and a_value3 passed by argument.

Parameters

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

Returns: Minimum value between a_value1, a_value2, and a_value3.

template<class T >

void chai3d::cSwap	(	T &	a_value1,
		T &	a_value2
	)

inline

This function swaps two elements a_value1 and a_value2 passed by argument.

Parameters

a_value1	First value.
a_value2	Second value.

template<class T >

T chai3d::cLerp	(	const double &	a_level,
		const T &	a_value1,
		const T &	a_value2
	)

inline

This function computes a linear interpolation between values a_value1 (when a_level = 0.0) and a_value2 (when a_level = 1.0).

result = (1.0-a_level) * a_value1 + a_level * a_value2

Parameters

a_level	Interpolation factor ranging from 0.0 to 1.0.
a_value1	First value.
a_value2	Second value.

Returns: Interpolated value.

template<class T >

T chai3d::cClamp	(	const T &	a_value,
		const T &	a_low,
		const T &	a_high
	)

inline

This function clamps an input value a_value to a specified range.
The range is specified by a lower bound a_low and upper bound a_high.

Parameters

a_value	Value to be clamped.
a_low	Lower boundary value.
a_high	Upper boundary value.

Returns: Clamped value.

template<class T >

T chai3d::cClamp0 ( const T & a_value )

inline

This function clamps an input value a_value to a value ranged between 0 and infinity.

Parameters

a_value Value to be clamped.

Returns: Clamped value.

double chai3d::cClamp01 ( const double & a_value )

inline

This function clamps an input value a_value to a value ranged between 0.0 and 1.0.

Parameters

a_value Value to be clamped.

Returns: Clamped value.

template<class T , class V >

bool chai3d::cContains	(	const T &	a_value,
		const V &	a_low,
		const V &	a_high
	)

inline

This function checks whether a value a_value is within a range specified by arguments a_low and a_high.

Parameters

a_value	Value to be tested.
a_low	Lower boundary value.
a_high	Upper boundary value.

Returns: true if the value is within the specified range, false otherwise.

double chai3d::cSqr ( const double & a_value )

inline

This function computes the square of a scalar a_value passed by argument.

result = a_value * a_value

Parameters

a_value Input value.

Returns: Square of a_value.

double chai3d::cSqrt ( const double & a_value )

inline

This function computes the square root of a scalar a_value passed by argument.

Parameters

a_value Input value.

Returns: Square root of a_value.

double chai3d::cCbrt ( const double & a_value )

inline

This function computes the cubic root of a scalar a_value passed by argument.

Parameters

a_value Input value.

Returns: Cubic root of a_value.

double chai3d::cCosDeg ( const double & a_angleDeg )

inline

This function computes the cosine of an angle defined in degrees.
The angle a_angleDeg is passed by argument.

Parameters

a_angleDeg Angle in degrees.

Returns: Cosine of angle a_angleDeg.

double chai3d::cSinDeg ( const double & a_angleDeg )

inline

This function computes the sine of an angle defined in degrees.
The angle a_angleDeg is passed by argument.

Parameters

a_angleDeg Angle in degrees.

Returns: Sine of angle a_angleDeg.

double chai3d::cTanDeg ( const double & a_angleDeg )

inline

This function computes the tangent of an angle defined in degrees.
The angle a_angleDeg is passed by argument.

Parameters

a_angleDeg Angle in degrees.

Returns: Tangent of angle a_angleDeg.

double chai3d::cCosRad ( const double & a_angleRad )

inline

This function computes the cosine of an angle defined in radians.
The angle a_angleRad is passed by argument.

Parameters

a_angleRad Angle in radians.

Returns: Cosine of angle a_angleRad.

double chai3d::cSinRad ( const double & a_angleRad )

inline

This function computes the sine of an angle defined in radians.
The angle a_angleRad is passed by argument.

Parameters

a_angleRad Angle in radians.

Returns: Sine of angle a_angleRad.

double chai3d::cTanRad ( const double & a_angleRad )

inline

This function computes the tangent of an angle defined in radians.
The angle a_angleRad is passed by argument.

Parameters

a_angleRad Angle in radians.

Returns: Tangent of angle a_angleRad.

double chai3d::cDegToRad ( const double & a_angleDeg )

inline

This function converts an angle a_angleDeg expressed in degrees to an angle expressed in radians.

Parameters

a_angleDeg Angle in degrees.

Returns: Converted angle in radians.

double chai3d::cRadToDeg ( const double & a_angleRad )

inline

This function converts an angle a_angleRad expressed in radians to an angle expressed in degrees.

Parameters

a_angleRad Angle in radians.

Returns: Converted angle in degrees.

int chai3d::cNumDigits ( int a_value )

inline

This function returns the number of digits that compose a given integer a_value passed by argument.

Parameters

a_value Value to be evaluated.

Returns: Number of digits.

cVector3d chai3d::cAdd	(	const cVector3d &	a_vector1,
		const cVector3d &	a_vector2
	)

inline

This function computes the addition of two vectors.
The vectors are passed by argument as a_vector1 and a_vector2.

result = a_vector1 + a_vector2

Parameters

a_vector1	First vector.
a_vector2	Second vector.

Returns: Addition of two vectors.

cVector3d chai3d::cAdd	(	const cVector3d &	a_vector1,
		const cVector3d &	a_vector2,
		const cVector3d &	a_vector3
	)

inline

This function computes the addition of three vectors.
The vectors are passed by argument as a_vector1, a_vector2, and a_vector3.

result = a_vector1 + a_vector2 + a_vector3

Parameters

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

Returns: Result of operation.

cVector3d chai3d::cSub	(	const cVector3d &	a_vector1,
		const cVector3d &	a_vector2
	)

inline

This function computes the subtraction of two vectors.
The vectors are passed by argument as a_vector1 and a_vector2.

result = a_vector1 - a_vector2

Parameters

a_vector1	First vector.
a_vector2	Second vector.

Returns: Result of operation.

cVector3d chai3d::cNegate ( const cVector3d & a_vector )

inline

This function computes the negated vector of a vector a_vector passed by argument.

result = -a_vector

Parameters

a_vector Vector to be negated.

Returns: Negated vector.

cVector3d chai3d::cMul	(	const double &	a_value,
		const cVector3d &	a_vector
	)

inline

This function computes the multiplication of a vector by a scalar.
The vector a_vector and scalar a_scalar are passed by argument.

result = a_value * a_vector

Parameters

a_value	Scalar.
a_vector	Vector to be scaled.

Returns: Result of operation.

cVector3d chai3d::cDiv	(	const double &	a_value,
		const cVector3d &	a_vector
	)

inline

This function computes the division of a vector by a scalar.
The vector a_vector and scalar a_scalar are passed by argument.

result = (1.0 / a_value) * a_vector

Parameters

a_value	Scalar.
a_vector	Vector to be scaled.

Returns: Result of operation.

cVector3d chai3d::cCross	(	const cVector3d &	a_vector1,
		const cVector3d &	a_vector2
	)

inline

This function compute the cross product between two vectors.
Both vectors are passed by argument as a_vector1 and a_vector2.

result = a_vector1 x a_vector2

Parameters

a_vector1	Vector1.
a_vector2	Vector2.

Returns: Cross product between both vectors.

double chai3d::cDot	(	const cVector3d &	a_vector1,
		const cVector3d &	a_vector2
	)

inline

This function computes the dot product between two vectors.
Both vectors are passed by argument as a_vector1 and a_vector2.

result = a_vector1 * a_vector2

Parameters

a_vector1	Vector1.
a_vector2	Vector2.

Returns: Dot product between both vectors.

cVector3d chai3d::cNormalize ( const cVector3d & a_vector )

inline

This function computes the normalized vector of a vector a_vector passed by argument.

Parameters

a_vector Vector to be normalized.

Returns: Normalized vector.

double chai3d::cDistance	(	const cVector3d &	a_point1,
		const cVector3d &	a_point2
	)

inline

This function computes the distance between two points a_point1 and a_point2 passed by argument.

Parameters

a_point1	First point.
a_point2	Second point.

Returns: Euclidean Distance between both points.

double chai3d::cDistanceSq	(	const cVector3d &	a_point1,
		const cVector3d &	a_point2
	)

inline

This function computes the squared distance between two points a_point1 and a_point2 passed by argument.

Parameters

a_point1	First point.
a_point2	Second point.

Returns: Squared distance between both points.

bool chai3d::cEqualPoints	(	const cVector3d &	a_point1,
		const cVector3d &	a_point2,
		const double	a_epsilon = `C_SMALL`
	)

inline

This function determine whether two vectors represent the same point.
Both points, a_point1 and a_point2, are passed by argument.
A parameter a_epsilon defines the distance tolerance between both points such that if the computed distance is smaller than a_epsilon, then both points are considered to be equal.
The function returns true if both points are determined equal, or false otherwise.

Parameters

a_point1	First point.
a_point2	Second point.
a_epsilon	Distance tolerance. Defaults value is set to C_SMALL.

Returns: true if both points are determined equal, false otherwise.

cMatrix3d chai3d::cIdentity3d ( void )

inline

The function returns the identity matrix.

Returns: Identity matrix.

cMatrix3d chai3d::cAdd	(	const cMatrix3d &	a_matrix1,
		const cMatrix3d &	a_matrix2
	)

inline

The function computes the addition between two matrices a_matrix1 and a_matrix2 that are passed by argument.

result = a_matrix1 + a_matrix2

Parameters

a_matrix1	First matrix.
a_matrix2	Second matrix.

Returns: Result of operation.

cMatrix3d chai3d::cSub	(	const cMatrix3d &	a_matrix1,
		const cMatrix3d &	a_matrix2
	)

inline

This function computes the subtraction between two matrices a_matrix1 and a_matrix2 that are passed by argument.

result = a_matrix1 - a_matrix2

Parameters

a_matrix1	First matrix.
a_matrix2	Second matrixs.

Returns: Result of operation.

cMatrix3d chai3d::cRotEulerRad	(	const double &	a_angleRad1,
		const double &	a_angleRad2,
		const double &	a_angleRad3,
		const cEulerOrder	a_eulerOrder,
		const bool	a_useIntrinsicEulerModel = `true`
	)

inline

This function creates a rotation matrix from a set of Euler angles defined in radians and co-moving axes of rotations.
The angles are defined in radians and passed by argument as a_angleRad1, a_angleRad2, and a_angleRad3.
The order of the rotations are defined by argument a_eulerOrder. See cEulerOrder for more information.
The argument a_useIntrinsicEulerModel defines if the instrinsic (true) or extrinsic (false) model is used.

Parameters

a_angleRad1	Angle in radians of the first rotation in the sequence.
a_angleRad2	Angle in radians of the second rotation in the sequence.
a_angleRad3	Angle in radians of the third rotation in the sequence.
a_eulerOrder	The order of the axes about which the rotations are to be applied
a_useIntrinsicEulerModel	If true use intrinsic Euler model, if false use extrinsic Euler model.

Returns: Rotation matrix.

cMatrix3d chai3d::cRotEulerDeg	(	const double &	a_angleDeg1,
		const double &	a_angleDeg2,
		const double &	a_angleDeg3,
		const cEulerOrder	a_eulerOrder,
		const bool	a_useIntrinsicEulerModel = `true`
	)

inline

This function creates a rotation matrix from a set of Euler angles defined in degrees and co-moving axes of rotations.
The angles are defined in radian and passed by argument as a_angleDeg1, a_angleDeg2, and a_angleDeg3.
The order of the rotations are defined by argument a_eulerOrder. See cEulerOrder for more information.
The argument a_useIntrinsicEulerModel defines if the instrinsic (true) or extrinsic (false) model is used.

Parameters

a_angleDeg1	Angle in degrees of the first rotation in the sequence.
a_angleDeg2	Angle in degrees of the second rotation in the sequence.
a_angleDeg3	Angle in degrees of the third rotation in the sequence.
a_eulerOrder	The order of the axes about which the rotations are to be applied
a_useIntrinsicEulerModel	If true use intrinsic Euler model, if false use extrinsic Euler model.

Returns: Rotation matrix.

cMatrix3d chai3d::cRotAxisAngleRad	(	const double &	a_axisX,
		const double &	a_axisY,
		const double &	a_axisZ,
		const double &	a_angleRad
	)

inline

This function creates a rotation matrix from an axis-angle representation.
The axis is defined by arguments a_axisX, a_axisY, and a_axisZ. The rotation angle is defined in radians by argument a_angleRad.

Parameters

a_axisX	x component of axis.
a_axisY	y component of axis.
a_axisZ	z component of axis.
a_angleRad	Angle of rotation in radians.

Returns: Rotation matrix.

cMatrix3d chai3d::cRotAxisAngleDeg	(	const double &	a_axisX,
		const double &	a_axisY,
		const double &	a_axisZ,
		const double &	a_angleDeg
	)

inline

This function creates a rotation matrix from an axis-angle representation.
The axis is defined by arguments a_axisX, a_axisY, and a_axisZ. The rotation angle is defined in degrees by argument a_angleDeg.

Parameters

a_axisX	x component of axis.
a_axisY	y component of axis.
a_axisZ	z component of axis.
a_angleDeg	Angle of roation in degrees.

Returns: Rotation matrix.

cMatrix3d chai3d::cMul	(	const cMatrix3d &	a_matrix1,
		const cMatrix3d &	a_matrix2
	)

inline

This function computes the multiplication of two matrices a_matrix1 and a_matrix2 passed by argument.

result = a_matrix1 * a_matrix2

Parameters

a_matrix1	First matrix.
a_matrix2	Second matrix.

Returns: Result of operation.

cVector3d chai3d::cMul	(	const cMatrix3d &	a_matrix,
		const cVector3d &	a_vector
	)

inline

This function computes the multiplication of a matrix a_matrix and a vector a_vector passed by argument.

result = a_matrix * a_vector

Returns: Result of operation.

cMatrix3d chai3d::cTranspose ( const cMatrix3d & a_matrix )

inline

This function computes the transpose of a matrix a_matrix passed by argument.

Parameters

a_matrix Matrix to be transposed.

Returns: Transpose of a_matrix.

cMatrix3d chai3d::cInverse ( const cMatrix3d & a_matrix )

inline

This function computes the the inverse of a matrix a_matrix passed by argument.

Parameters

a_matrix Matrix to be inversed.

Returns: The inverse of the matrix.

double chai3d::cAngle	(	const cVector3d &	a_vector1,
		const cVector3d &	a_vector2
	)

inline

This function computes the angle in radians between two vectors a_vector1 and a_vector2 passed by argument.

Parameters

a_vector1	First vector.
a_vector2	Second vector.

Returns: Angle in radians between both vectors.

double chai3d::cCosAngle	(	const cVector3d &	a_vector1,
		const cVector3d &	a_vector2
	)

inline

This function computes the cosine of the angle between two vectors a_vector1 and a_vector2 passed by argument.

Parameters

a_vector1	First vector.
a_vector2	Second vector.

Returns: Cosine of the angle between both vectors.

int chai3d::cSolveLinear	(	double	a_coefficient[2],
		double	a_solution[1]
	)

inline

This function determines the solution of a linear equation.
It takes as parameters a pointer to the two coefficient of the linear equation (the c[1] is the coefficient of x and so on) and a pointer to the two element array in which the solution is to be placed. It outputs is a solution has been found.

Parameters

a_coefficient	Input coefficient values.
a_solution	Output roots found.

Returns: The number of solutions found.

int chai3d::cSolveQuadric	(	double	a_coefficient[3],
		double	a_solution[2]
	)

inline

This function determines the roots of a quadric equation
It takes as parameters a pointer to the three coefficient of the quadric equation (the c[2] is the coefficient of x2 and so on) and a pointer to the two element array in which the roots are to be placed. It outputs the number of roots found.

Parameters

a_coefficient	Input coefficient values.
a_solution	Output roots found.

Returns: The number of roots found.

int chai3d::cSolveCubic	(	double	a_coefficient[4],
		double	a_solution[3]
	)

inline

This function determines the roots of a cubic equation.
It takes as parameters a pointer to the four coefficient of the cubic equation (the c[3] is the coefficient of x3 and so on) and a pointer to the three element array in which the roots are to be placed. It outputs the number of roots found.

Parameters

a_coefficient	Input coefficient values.
a_solution	Output roots found.

Returns: The number of roots found.

int chai3d::cSolveQuartic	(	double	a_coefficient[5],
		double	a_solution[4]
	)

inline

This function determines the roots of a quartic equation.
It takes as parameters a pointer to the five coefficient of the quartic equation (the c[4] is the coefficient of x^4 and so on) and a pointer to the four element array in which the roots are to be placed. It outputs the number of roots found.

Parameters

a_coefficient	Input coefficient values.
a_solution	Output roots found.

Returns: The number of roots found.

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