Decompose.cpp File Reference

#include "precompiled.h"
#include <math.h>
#include "Decompose.h"

Include dependency graph for Decompose.cpp:

Macros
#define	mat_pad(A)   (A[W][X]=A[X][W]=A[W][Y]=A[Y][W]=A[W][Z]=A[Z][W]=0,A[W][W]=1)
	Fill out 3x3 matrix to 4x4. More...
#define	mat_copy(C, gets, A, n)
	Copy nxn matrix A to C using "gets" for assignment. More...
#define	mat_tpose(AT, gets, A, n)
	Copy transpose of nxn matrix A to C using "gets" for assignment. More...
#define	mat_binop(C, gets, A, op, B, n)
	Assign nxn matrix C the element-wise combination of A and B using "op". More...
#define	caseMacro(i, j, k, I, J, K)
#define	TOL   1.0e-6
#define	SQRTHALF   (0.7071067811865475244)
#define	sgn(n, v)   ((n)?-(v):(v))
#define	swap(a, i, j)   {a[3]=a[i]; a[i]=a[j]; a[j]=a[3];}
#define	cycle(a, p)

Functions
void	mat_mult (HMatrix A, HMatrix B, HMatrix AB)
	Multiply the upper left 3x3 parts of A and B to get AB. More...
float	vdot (float *va, float *vb)
	Return dot product of length 3 vectors va and vb. More...
void	vcross (float *va, float *vb, float *v)
	Set v to cross product of length 3 vectors va and vb. More...
void	adjoint_transpose (HMatrix M, HMatrix MadjT)
	Set MadjT to transpose of inverse of M times determinant of M. More...
Quat	Qt_ (float x, float y, float z, float w)
Quat	Qt_Conj (Quat q)
Quat	Qt_Mul (Quat qL, Quat qR)
Quat	Qt_Scale (Quat q, float w)
Quat	Qt_FromMatrix (HMatrix mat)
float	mat_norm (HMatrix M, int tpose)
	Compute either the 1 or infinity norm of M, depending on tpose. More...
float	norm_inf (HMatrix M)
float	norm_one (HMatrix M)
int	find_max_col (HMatrix M)
	Return index of column of M containing maximum abs entry, or -1 if M=0. More...
void	make_reflector (float *v, float *u)
	Setup u for Household reflection to zero all v components but first. More...
void	reflect_cols (HMatrix M, float *u)
	Apply Householder reflection represented by u to column vectors of M. More...
void	reflect_rows (HMatrix M, float *u)
	Apply Householder reflection represented by u to row vectors of M. More...
void	do_rank1 (HMatrix M, HMatrix Q)
	Find orthogonal factor Q of rank 1 (or less) M. More...
void	do_rank2 (HMatrix M, HMatrix MadjT, HMatrix Q)
	Find orthogonal factor Q of rank 2 (or less) M using adjoint transpose. More...
float	polar_decomp (HMatrix M, HMatrix Q, HMatrix S)
HVect	spect_decomp (HMatrix S, HMatrix U)
Quat	snuggle (Quat q, HVect *k)
void	decomp_affine (HMatrix A, AffineParts *parts)
void	invert_affine (AffineParts *parts, AffineParts *inverse)

Variables
static HMatrix	mat_id = {{1,0,0,0},{0,1,0,0},{0,0,1,0},{0,0,0,1}}

Macro Definition Documentation

caseMacro

#define caseMacro	(		i,
			j,
			k,
			I,
			J,
			K
	)

Value:

        case I:\
        s = sqrt( (mat[I][I] - (mat[J][J]+mat[K][K])) + mat[W][W] );\
        qu.i = s*0.5;\
        s = 0.5 / s;\
        qu.j = (mat[I][J] + mat[J][I]) * s;\
        qu.k = (mat[K][I] + mat[I][K]) * s;\
        qu.w = (mat[K][J] - mat[J][K]) * s;\
        break

cycle

#define cycle	(		a,
			p
	)

Value:

            if (p) {a[3]=a[0]; a[0]=a[1]; a[1]=a[2]; a[2]=a[3];}\
            else   {a[3]=a[2]; a[2]=a[1]; a[1]=a[0]; a[0]=a[3];}

mat_binop

#define mat_binop	(		C,
			gets,
			A,
			op,
			B,
			n
	)

Value:

    {for (int i = 0; i < n; ++i) for (int j = 0; j < n; ++j)\
    C[i][j] gets (A[i][j]) op (B[i][j]);}

Assign nxn matrix C the element-wise combination of A and B using "op".

mat_copy

#define mat_copy	(		C,
			gets,
			A,
			n
	)

Value:

    {for (int i = 0; i < n; ++i) for (int j = 0; j < n; ++j)\
    C[i][j] gets (A[i][j]);}

Copy nxn matrix A to C using "gets" for assignment.

mat_pad

#define mat_pad

(

A

)

(A[W][X]=A[X][W]=A[W][Y]=A[Y][W]=A[W][Z]=A[Z][W]=0,A[W][W]=1)

Fill out 3x3 matrix to 4x4.

mat_tpose

#define mat_tpose	(		AT,
			gets,
			A,
			n
	)

Value:

    {for (int i = 0; i < n; ++i) for (int j = 0; j < n; ++j)\
    AT[i][j] gets (A[j][i]);}

Copy transpose of nxn matrix A to C using "gets" for assignment.

sgn

#define sgn	(		n,
			v
	)		((n)?-(v):(v))

SQRTHALF

#define SQRTHALF   (0.7071067811865475244)

swap

#define swap	(		a,
			i,
			j
	)		{a[3]=a[i]; a[i]=a[j]; a[j]=a[3];}

TOL

#define TOL   1.0e-6

Function Documentation

adjoint_transpose()

void adjoint_transpose	(	HMatrix	M,
		HMatrix	MadjT
	)

Set MadjT to transpose of inverse of M times determinant of M.

decomp_affine()

void decomp_affine	(	HMatrix	A,
		AffineParts *	parts
	)

do_rank1()

void do_rank1	(	HMatrix	M,
		HMatrix	Q
	)

Find orthogonal factor Q of rank 1 (or less) M.

do_rank2()

void do_rank2	(	HMatrix	M,
		HMatrix	MadjT,
		HMatrix	Q
	)

Find orthogonal factor Q of rank 2 (or less) M using adjoint transpose.

find_max_col()

int find_max_col

(

HMatrix

M

)

Return index of column of M containing maximum abs entry, or -1 if M=0.

invert_affine()

void invert_affine	(	AffineParts *	parts,
		AffineParts *	inverse
	)

make_reflector()

void make_reflector	(	float *	v,
		float *	u
	)

Setup u for Household reflection to zero all v components but first.

mat_mult()

void mat_mult	(	HMatrix	A,
		HMatrix	B,
		HMatrix	AB
	)

Multiply the upper left 3x3 parts of A and B to get AB.

mat_norm()

float mat_norm	(	HMatrix	M,
		int	tpose
	)

Compute either the 1 or infinity norm of M, depending on tpose.

norm_inf()

float norm_inf

(

HMatrix

M

)

norm_one()

float norm_one

(

HMatrix

M

)

polar_decomp()

float polar_decomp	(	HMatrix	M,
		HMatrix	Q,
		HMatrix	S
	)

Qt_()

Quat Qt_	(	float	x,
		float	y,
		float	z,
		float	w
	)

Qt_Conj()

Quat Qt_Conj

(

Quat

q

)

Qt_FromMatrix()

Quat Qt_FromMatrix

(

HMatrix

mat

)

Qt_Mul()

Quat Qt_Mul	(	Quat	qL,
		Quat	qR
	)

Qt_Scale()

Quat Qt_Scale	(	Quat	q,
		float	w
	)

reflect_cols()

void reflect_cols	(	HMatrix	M,
		float *	u
	)

Apply Householder reflection represented by u to column vectors of M.

reflect_rows()

void reflect_rows	(	HMatrix	M,
		float *	u
	)

Apply Householder reflection represented by u to row vectors of M.

snuggle()

Quat snuggle	(	Quat	q,
		HVect *	k
	)

spect_decomp()

HVect spect_decomp	(	HMatrix	S,
		HMatrix	U
	)

vcross()

void vcross	(	float *	va,
		float *	vb,
		float *	v
	)

Set v to cross product of length 3 vectors va and vb.

vdot()

float vdot	(	float *	va,
		float *	vb
	)

Return dot product of length 3 vectors va and vb.

Variable Documentation

mat_id

HMatrix mat_id = {{1,0,0,0},{0,1,0,0},{0,0,1,0},{0,0,0,1}}

static