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

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

#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

#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];}

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

Value:

{int i,j; for(i=0;i<n;i++) for(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".

Definition at line 43 of file Decompose.cpp.

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

Value:

{int i,j; for(i=0;i<n;i++) for(j=0;j<n;j++)\

C[i][j] gets (A[i][j]);}

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

Definition at line 35 of file Decompose.cpp.

#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.

Definition at line 32 of file Decompose.cpp.

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

Value:

{int i,j; for(i=0;i<n;i++) for(j=0;j<n;j++)\

AT[i][j] gets (A[j][i]);}

AT

#define AT(x)

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

Definition at line 39 of file Decompose.cpp.

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

#define SQRTHALF (0.7071067811865475244)

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

#define TOL 1.0e-6

Function Documentation

void adjoint_transpose	(	HMatrix	M,
		HMatrix	MadjT
	)

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

Definition at line 69 of file Decompose.cpp.

void decomp_affine	(	HMatrix	A,
		AffineParts *	parts
	)

Definition at line 486 of file Decompose.cpp.

void do_rank1	(	HMatrix	M,
		HMatrix	Q
	)

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

Definition at line 223 of file Decompose.cpp.

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

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

Definition at line 241 of file Decompose.cpp.

int find_max_col ( HMatrix M )

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

Definition at line 181 of file Decompose.cpp.

void invert_affine	(	AffineParts *	parts,
		AffineParts *	inverse
	)

Definition at line 508 of file Decompose.cpp.

void make_reflector	(	float *	v,
		float *	u
	)

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

Definition at line 194 of file Decompose.cpp.

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

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

Definition at line 47 of file Decompose.cpp.

float mat_norm	(	HMatrix	M,
		int	tpose
	)

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

Definition at line 164 of file Decompose.cpp.

float norm_inf ( HMatrix M )

Definition at line 177 of file Decompose.cpp.

float norm_one ( HMatrix M )

Definition at line 178 of file Decompose.cpp.

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

Definition at line 274 of file Decompose.cpp.

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

Definition at line 79 of file Decompose.cpp.

Quat Qt_Conj ( Quat q )

Definition at line 87 of file Decompose.cpp.

Quat Qt_FromMatrix ( HMatrix mat )

Definition at line 119 of file Decompose.cpp.

Quat Qt_Mul	(	Quat	qL,
		Quat	qR
	)

Definition at line 97 of file Decompose.cpp.

Quat Qt_Scale	(	Quat	q,
		float	w
	)

Definition at line 108 of file Decompose.cpp.

void reflect_cols	(	HMatrix	M,
		float *	u
	)

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

Definition at line 204 of file Decompose.cpp.

void reflect_rows	(	HMatrix	M,
		float *	u
	)

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

Definition at line 213 of file Decompose.cpp.

Quat snuggle	(	Quat	q,
		HVect *	k
	)

Definition at line 381 of file Decompose.cpp.

HVect spect_decomp	(	HMatrix	S,
		HMatrix	U
	)

Definition at line 326 of file Decompose.cpp.

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

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

Definition at line 61 of file Decompose.cpp.

float vdot	(	float *	va,
		float *	vb
	)

Return dot product of length 3 vectors va and vb.

Definition at line 55 of file Decompose.cpp.

Variable Documentation

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

static

Definition at line 161 of file Decompose.cpp.

Macros

Functions

Variables

Macro Definition Documentation

Function Documentation

Variable Documentation