#include "DPoint3.h"
#include "Matrix3.h"

Classes
class	DMatrix3
	Class DPoint3, Matrix Representations of 3D Transformations, Class Quat, Class AngAxis, Structure AffineParts, Class BigMatrix. More...

Functions
DMatrix3	RotateXMatrix (double angle)
	Builds a new matrix for use as a X rotation transformation. More...

DMatrix3	RotateYMatrix (double angle)
	Builds a new matrix for use as a Y rotation transformation. More...

DMatrix3	RotateZMatrix (double angle)
	Builds a new matrix for use as a Z rotation transformation. More...

DMatrix3	TransMatrix (const DPoint3 &p)
	Builds a new matrix for use as a translation transformation. More...

DMatrix3	ScaleMatrix (const DPoint3 &s)
	Builds a new matrix for use as a scale transformation. More...

DMatrix3	RotateYPRMatrix (double yaw, double pitch, double roll)
	Builds a new matrix for use as a rotation transformation by specifying yaw, pitch and roll angles. More...

DMatrix3	RotAngleAxisMatrix (DPoint3 &axis, double angle)
	Builds a new matrix for use as a rotation transformation by specifying an angle and axis. More...

DMatrix3	Inverse (const DMatrix3 &m)
	Return the inverse of the matrix. More...

DMatrix3	InverseHighPrecision (const DMatrix3 &m)
	Return the inverse of the matrix using doubles for the intermediary results. More...

DPoint3	operator* (const DMatrix3 &a, const DPoint3 &v)
	These transform a DPoint3 with a Matrix Representations of 3D Transformations, Class Quat, Class AngAxis...">DMatrix3. More...

DPoint3	operator* (const DPoint3 &v, const DMatrix3 &a)
	These transform a DPoint3 with a Matrix Representations of 3D Transformations, Class Quat, Class AngAxis...">DMatrix3. More...

DPoint3	VectorTransform (const DMatrix3 &m, const DPoint3 &v)
	Transform the vector (DPoint3) with the specified matrix. More...

DPoint3	VectorTransform (const DPoint3 &v, const DMatrix3 &m)

Point4	TransformPlane (const DMatrix3 &m, const Point4 &plane)
	transform a plane. More...

DMatrix3	XFormMat (const DMatrix3 &xm, const DMatrix3 &m)
	This method is used to build a matrix that constructs a transformation in a particular space. More...

void	MirrorMatrix (DMatrix3 &tm, Axis axis, bool scaleMatrix=false)
	Mirrors the input matrix against the X, Y, or Z axis. More...

void	MatrixMultiply (DMatrix3 &outMatrix, const DMatrix3 &matrixA, const DMatrix3 &matrixB)
	Same as Maxtrix3::operator[]. More...

void	Inverse (DMatrix3 &outMatrix, const DMatrix3 &m)
	Same as Maxtrix3::Inverse. More...

Function Documentation

DMatrix3 RotateXMatrix ( double angle )

Builds a new matrix for use as a X rotation transformation.

Parameters

angle Specifies the angle of rotation in radians.

Returns: A new X rotation Matrix Representations of 3D Transformations, Class Quat, Class AngAxis...">DMatrix3.

DMatrix3 RotateYMatrix ( double angle )

Builds a new matrix for use as a Y rotation transformation.

Parameters

angle Specifies the angle of rotation in radians.

Returns: A new Y rotation Matrix Representations of 3D Transformations, Class Quat, Class AngAxis...">DMatrix3.

DMatrix3 RotateZMatrix ( double angle )

Builds a new matrix for use as a Z rotation transformation.

Parameters

angle Specifies the angle of rotation in radians.

Returns: A new Z rotation Matrix Representations of 3D Transformations, Class Quat, Class AngAxis...">DMatrix3.

DMatrix3 TransMatrix ( const DPoint3 & p )

Builds a new matrix for use as a translation transformation.

Parameters

p	Specifies the translation values.

Returns: A new translation Matrix Representations of 3D Transformations, Class Quat, Class AngAxis...">DMatrix3.

DMatrix3 ScaleMatrix ( const DPoint3 & s )

Builds a new matrix for use as a scale transformation.

Parameters

s	Specifies the scale values.

Returns: A new scale Matrix Representations of 3D Transformations, Class Quat, Class AngAxis...">DMatrix3.

DMatrix3 RotateYPRMatrix	(	double	yaw,
		double	pitch,
		double	roll
	)

Builds a new matrix for use as a rotation transformation by specifying yaw, pitch and roll angles.

This definition will depend on what our coordinate system is. This one is equivalent to:

 M.IdentityMatrix();
 M.RotateZ(roll);
 M.RotateX(pitch);
 M.RotateY(yaw);

Which presupposes Y is vertical, X is sideways, Z is forward

Parameters

yaw	Specifies the yaw angle in radians.
pitch	Specifies the pitch angle in radians.
roll	Specifies the roll angle in radians.

Returns: A new rotation Matrix Representations of 3D Transformations, Class Quat, Class AngAxis...">DMatrix3.

DMatrix3 RotAngleAxisMatrix	(	DPoint3 &	axis,
		double	angle
	)

Builds a new matrix for use as a rotation transformation by specifying an angle and axis.

Parameters

axis	Specifies the axis of rotation. Note that this angle is expected to be normalized.
angle	Specifies the angle of rotation. Note: The direction of the angle in this method is opposite of that in AngAxisFromQ().

Returns: A new rotation Matrix Representations of 3D Transformations, Class Quat, Class AngAxis...">DMatrix3.

DMatrix3 Inverse ( const DMatrix3 & m )

Return the inverse of the matrix.

Parameters

m	The matrix to compute the inverse of.

DMatrix3 InverseHighPrecision ( const DMatrix3 & m )

Return the inverse of the matrix using doubles for the intermediary results.

Parameters

m	The matrix to compute the inverse of.

DPoint3 operator*	(	const DMatrix3 &	a,
		const DPoint3 &	v
	)

These transform a DPoint3 with a Matrix Representations of 3D Transformations, Class Quat, Class AngAxis...">DMatrix3.

These two versions of transforming a point with a matrix do the same thing, regardless of the order of operands (linear algebra rules notwithstanding).

Parameters

a	The matrix to transform the point with.
v	The point to transform.

Returns: The transformed DPoint3.

DPoint3 operator*	(	const DPoint3 &	v,
		const DMatrix3 &	a
	)

These transform a DPoint3 with a Matrix Representations of 3D Transformations, Class Quat, Class AngAxis...">DMatrix3.

These two versions of transforming a point with a matrix do the same thing, regardless of the order of operands (linear algebra rules notwithstanding).

Parameters

v	The point to transform.
a	The matrix to transform the point with.

Returns: The transformed DPoint3.

DPoint3 VectorTransform	(	const DMatrix3 &	m,
		const DPoint3 &	v
	)

Transform the vector (DPoint3) with the specified matrix.

Parameters

m	The matrix to transform the vector with.
v	The vector to transform.

Returns: The transformed vector (as a DPoint3).

DPoint3 VectorTransform	(	const DPoint3 &	v,
		const DMatrix3 &	m
	)

Point4 TransformPlane	(	const DMatrix3 &	m,
		const Point4 &	plane
	)

transform a plane.

Note: this only works if M is orthogonal

Parameters

m	The transformation to apply to the plain
plane	the plane to be transformed

DMatrix3 XFormMat	(	const DMatrix3 &	xm,
		const DMatrix3 &	m
	)

This method is used to build a matrix that constructs a transformation in a particular space.

For example, say you have a rotation you want to apply, but you want to perform the rotation in another coordinate system. To do this, you typically transform into the space of the coordinate system, then apply the transformation, and then transform out of that coordinate system. This method constructs a matrix that does just this. It transforms matrix m so it is applied in the space of matrix xm. It returns a Matrix Representations of 3D Transformations, Class Quat, Class AngAxis...">DMatrix3 that is xm*m*Inverse(xm).

Parameters

xm	Specifies the coordinate system you want to work in.
m	Specifies the transformation matrix.

Returns: Returns a Matrix Representations of 3D Transformations, Class Quat, Class AngAxis...">DMatrix3 that is xm*m*Inverse(xm).

void MirrorMatrix	(	DMatrix3 &	tm,
		Axis	axis,
		bool	scaleMatrix = `false`
	)

Mirrors the input matrix against the X, Y, or Z axis.

This function mirrors the input matrix such that if it transformed a DPoint3 p, the transform applied by the mirrored transform would place p in an equivalent position relative but with one of it's elements negated.

 DPoint3 p = ...; // Some arbitrary point;
 DMatrix3 tm = ...; // Some matrix
 DMatrix3 tmMirror = tm;
 MirrorMatrix(tm, kXAxis); // Mirror this matrix around the X Axis;
 DPoint3 p3Result = tm.PointTransform(p);            // Apply the original transformation
 DPoint3 p3Mirrored = tmMirror.PointTransform(p);    // Apply the mirrored transformation
 p3Result[kXAxis] == -p3Mirrored[kXAxis];        // The point is mirrored around X
 p3Result[kYAxis] == p3Mirrored[kYAxis];         // The point is unchanged around Y
 p3Result[kZAxis] == p3Mirrored[kZAxis];         // The point is unchanged around Z

Parameters

[in,out]	tm	The Matrix to mirror
	axis	The world plane to mirror around. The axis will be reflected against the plane formed by the point (0, 0, 0) and the normal where normal[axis] = 1;
	scaleMatrix	The matrix can be mirrored either by pure rotation, or by pure scaling. If true, the matrix is mirrored by flipping one of its axis, changing the handedness of the matrix. This had the advantage that the mirroring will be passed onto all it's children. This is preferential when the system can handle it, but can cause issues in systems that do not compensate for scale, eg game pipelines and skinning. if false, the mirroring will be achieved using rotation only and will not affect child local positions. It is better to use non-scaling mirroring when dealing with tools or processes that do not well support scale, or when the matrix will be blended with non-scaled matrices. (eg, Point/Quat based pipelines and skinning)

void MatrixMultiply	(	DMatrix3 &	outMatrix,
		const DMatrix3 &	matrixA,
		const DMatrix3 &	matrixB
	)

Same as Maxtrix3::operator[].

Perform matrix multiplication without additional matrix copy

Parameters

outMatrix	The result of matrixA * matrixB
matrixA	First matrix to multiply
matrixB	Second matrix to multiply

void Inverse	(	DMatrix3 &	outMatrix,
		const DMatrix3 &	m
	)

Same as Maxtrix3::Inverse.

Compute the inverse of the matrix without additional matrix copy

Parameters

outMatrix	The inversed matrix.
m	The matrix to compute the inverse of.

dmatrix3.h File Reference

Classes

Functions

Function Documentation