LTransform.cpp File Reference

Transformation. More...

#include "LTransform.h"
#include "LProjection.h"

Functions
LMatrix4	ComposeTransformation (const LVector3 &Pos, const LMatrix4 &Rot)
LMatrix4	ComposeCameraTransformation (const LVector3 &Pos, const LMatrix4 &Rot)
void	DecomposeTransformation (const LMatrix4 &T, LVector3 &Pos, LMatrix4 &Rot)
void	DecomposeCameraTransformation (const LMatrix4 &T, LVector3 &Pos, LMatrix4 &Rot)
void	GivensRotation (float a, float b, float &c, float &s, float &r)
void	MatrixToAngles (LEulerAngleSystem Sys, const LMatrix3 &M, float &T1, float &T2, float &T3)
void	MakeRotationMatrix (LMatrix4 &R, int axis, float angle)
void	AnglesToMatrix (LEulerAngleSystem Sys, LMatrix4 &M, float T1, float T2, float T3)
Variables
int	EulerAxes [12][3]
	indices of the axes fora given coordinate system
LVector3	EuclideanBasis [3] = { vec3( 1, 0, 0 ), vec3( 0, 1, 0 ), vec3( 0, 0, 1 ) }

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Detailed Description

Transformation.

Version:

0.5.91

Date:

01/03/2010

Author:

Viktor Latypov, 2009-2010

support@linderdaum.com http://www.linderdaum.com

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Function Documentation

void AnglesToMatrix	(	LEulerAngleSystem	Sys,
		LMatrix4 &	M,
		float	T1,
		float	T2,
		float	T3
	)

Calculate orientation from three Euler angles in a given axis system (ZXZ etc.)

LMatrix4 ComposeCameraTransformation	(	const LVector3 &	Pos,
		const LMatrix4 &	Rot
	)

LMatrix4 ComposeTransformation	(	const LVector3 &	Pos,
		const LMatrix4 &	Rot
	)

void DecomposeCameraTransformation	(	const LMatrix4 &	T,
		LVector3 &	Pos,
		LMatrix4 &	Rot
	)

void DecomposeTransformation	(	const LMatrix4 &	T,
		LVector3 &	Pos,
		LMatrix4 &	Rot
	)

void GivensRotation	(	float	a,
		float	b,
		float &	c,
		float &	s,
		float &	r
	)

Find a planar rotation (c=cos, s=sin) which maps (a,b) vector to (r,0)

http://www.cgafaq.info/wiki/Euler_angles_from_matrix

The following method, choosing either t=cot(theta) or t=tan(theta) as route, is a variation of that recommended by Golub and Van Loan, made continuous as suggested by Edward Anderson

void MakeRotationMatrix	(	LMatrix4 &	R,
		int	axis,
		float	angle
	)

void MatrixToAngles	(	LEulerAngleSystem	Sys,
		const LMatrix3 &	M,
		float &	T1,
		float &	T2,
		float &	T3
	)

Calculate three Euler angles from orientation in a given axis system (ZXZ etc.)

[T1,T2,T3] -> [T3,T2,T1]

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Variable Documentation

LVector3 EuclideanBasis[3] = { vec3( 1, 0, 0 ), vec3( 0, 1, 0 ), vec3( 0, 0, 1 ) }

int EulerAxes[12][3]

Initial value:

{
        {0, 2, 0}, {0, 2, 1}, {0, 1, 0}, {0, 1, 2},
        {1, 0, 1}, {1, 0, 2}, {1, 2, 1}, {1, 2, 0},
        {2, 1, 2}, {2, 1, 0}, {2, 0, 2}, {2, 0, 1}
}

indices of the axes fora given coordinate system