Merge pull request #45 from mwturvey/AddingPosers

Tori Tracking is getting VERY close

3 files changed, 473 insertions, 0 deletions

diff --git a/redist/linmath.c b/redist/linmath.c
index 1724a13..caff1de 100644
--- a/redist/linmath.c
+++ b/redist/linmath.c
@@ -82,6 +82,28 @@ FLT anglebetween3d( FLT * a, FLT * b )
 	return FLT_ACOS(dot);
 }
 
+// algorithm found here: http://inside.mines.edu/fs_home/gmurray/ArbitraryAxisRotation/
+void rotatearoundaxis(FLT *outvec3, FLT *invec3, FLT *axis, FLT angle)
+{
+	// TODO: this really should be external.
+	normalize3d(axis, axis);
+
+	FLT s = FLT_SIN(angle);
+	FLT c = FLT_COS(angle);
+
+	FLT u=axis[0];
+	FLT v=axis[1];
+	FLT w=axis[2];
+
+	FLT x=invec3[0];
+	FLT y=invec3[1];
+	FLT z=invec3[2];
+
+	outvec3[0] = u*(u*x + v*y + w*z)*(1-c)   +   x*c   +   (-w*y + v*z)*s;
+	outvec3[1] = v*(u*x + v*y + w*z)*(1-c)   +   y*c   +   ( w*x - u*z)*s;
+	outvec3[2] = w*(u*x + v*y + w*z)*(1-c)   +   z*c   +   (-v*x + u*y)*s;
+}
+
 /////////////////////////////////////QUATERNIONS//////////////////////////////////////////
 //Originally from Mercury (Copyright (C) 2009 by Joshua Allen, Charles Lohr, Adam Lowman)
 //Under the mit/X11 license.
diff --git a/redist/linmath.h b/redist/linmath.h
index 4e0cb77..6f0bf60 100644
--- a/redist/linmath.h
+++ b/redist/linmath.h
@@ -70,6 +70,7 @@ FLT magnitude3d(const FLT * a );
 
 FLT anglebetween3d( FLT * a, FLT * b );
 
+void rotatearoundaxis(FLT *outvec3, FLT *invec3, FLT *axis, FLT angle);
 //Quaternion things...
 
 void quatsetnone( FLT * q );
diff --git a/redist/svd.h b/redist/svd.h
new file mode 100644
index 0000000..41708da
--- /dev/null
+++ b/redist/svd.h
@@ -0,0 +1,450 @@
+/**************************************************************************
+**
+**  svd3
+**
+** Quick singular value decomposition as described by:
+** A. McAdams, A. Selle, R. Tamstorf, J. Teran and E. Sifakis,
+** "Computing the Singular Value Decomposition of 3x3 matrices
+** with minimal branching and elementary floating point operations",
+**  University of Wisconsin - Madison technical report TR1690, May 2011
+**
+**	OPTIMIZED CPU VERSION
+** 	Implementation by: Eric Jang
+**
+**  13 Apr 2014
+**
+** This file originally retrieved from:
+** https://github.com/ericjang/svd3/blob/master/svd3.h  3/26/2017
+**
+** Original licesnse is MIT per:
+** https://github.com/ericjang/svd3/blob/master/LICENSE.md
+**
+** Ported from C++ to C by Mike Turvey.  All modifications also released 
+** under an MIT license.
+**************************************************************************/
+
+
+#ifndef SVD3_H
+#define SVD3_H
+
+#define _gamma 5.828427124 // FOUR_GAMMA_SQUARED = sqrt(8)+3;
+#define _cstar 0.923879532 // cos(pi/8)
+#define _sstar 0.3826834323 // sin(p/8)
+#define EPSILON 1e-6
+
+#include <math.h>
+
+/* This is a novel and fast routine for the reciprocal square root of an
+IEEE float (single precision).
+http://www.lomont.org/Math/Papers/2003/InvSqrt.pdf
+http://playstation2-linux.com/download/p2lsd/fastrsqrt.pdf
+http://www.beyond3d.com/content/articles/8/
+*/
+inline float rsqrt(float x) {
+	// int ihalf = *(int *)&x - 0x00800000; // Alternative to next line,
+	// float xhalf = *(float *)&ihalf;      // for sufficiently large nos.
+	float xhalf = 0.5f*x;
+	int i = *(int *)&x;          // View x as an int.
+								 // i = 0x5f3759df - (i >> 1);   // Initial guess (traditional).
+	i = 0x5f375a82 - (i >> 1);   // Initial guess (slightly better).
+	x = *(float *)&i;            // View i as float.
+	x = x*(1.5f - xhalf*x*x);    // Newton step.
+								 // x = x*(1.5008908 - xhalf*x*x);  // Newton step for a balanced error.
+	return x;
+}
+
+/* This is rsqrt with an additional step of the Newton iteration, for
+increased accuracy. The constant 0x5f37599e makes the relative error
+range from 0 to -0.00000463.
+You can't balance the error by adjusting the constant. */
+inline float rsqrt1(float x) {
+	float xhalf = 0.5f*x;
+	int i = *(int *)&x;          // View x as an int.
+	i = 0x5f37599e - (i >> 1);   // Initial guess.
+	x = *(float *)&i;            // View i as float.
+	x = x*(1.5f - xhalf*x*x);    // Newton step.
+	x = x*(1.5f - xhalf*x*x);    // Newton step again.
+	return x;
+}
+
+inline float accurateSqrt(float x)
+{
+	return x * rsqrt1(x);
+}
+
+inline void condSwap(bool c, float *X, float *Y)
+{
+	// used in step 2
+	float Z = *X;
+	*X = c ? *Y : *X;
+	*Y = c ? Z : *Y;
+}
+
+inline void condNegSwap(bool c, float *X, float *Y)
+{
+	// used in step 2 and 3
+	float Z = -*X;
+	*X = c ? *Y : *X;
+	*Y = c ? Z : *Y;
+}
+
+// matrix multiplication M = A * B
+inline void multAB(float a11, float a12, float a13,
+	float a21, float a22, float a23,
+	float a31, float a32, float a33,
+	//
+	float b11, float b12, float b13,
+	float b21, float b22, float b23,
+	float b31, float b32, float b33,
+	//
+	float *m11, float *m12, float *m13,
+	float *m21, float *m22, float *m23,
+	float *m31, float *m32, float *m33)
+{
+
+	*m11 = a11*b11 + a12*b21 + a13*b31; *m12 = a11*b12 + a12*b22 + a13*b32; *m13 = a11*b13 + a12*b23 + a13*b33;
+	*m21 = a21*b11 + a22*b21 + a23*b31; *m22 = a21*b12 + a22*b22 + a23*b32; *m23 = a21*b13 + a22*b23 + a23*b33;
+	*m31 = a31*b11 + a32*b21 + a33*b31; *m32 = a31*b12 + a32*b22 + a33*b32; *m33 = a31*b13 + a32*b23 + a33*b33;
+}
+
+// matrix multiplication M = Transpose[A] * B
+inline void multAtB(float a11, float a12, float a13,
+	float a21, float a22, float a23,
+	float a31, float a32, float a33,
+	//
+	float b11, float b12, float b13,
+	float b21, float b22, float b23,
+	float b31, float b32, float b33,
+	//
+	float *m11, float *m12, float *m13,
+	float *m21, float *m22, float *m23,
+	float *m31, float *m32, float *m33)
+{
+	*m11 = a11*b11 + a21*b21 + a31*b31; *m12 = a11*b12 + a21*b22 + a31*b32; *m13 = a11*b13 + a21*b23 + a31*b33;
+	*m21 = a12*b11 + a22*b21 + a32*b31; *m22 = a12*b12 + a22*b22 + a32*b32; *m23 = a12*b13 + a22*b23 + a32*b33;
+	*m31 = a13*b11 + a23*b21 + a33*b31; *m32 = a13*b12 + a23*b22 + a33*b32; *m33 = a13*b13 + a23*b23 + a33*b33;
+}
+
+inline void quatToMat3(const float * qV,
+	float *m11, float *m12, float *m13,
+	float *m21, float *m22, float *m23,
+	float *m31, float *m32, float *m33
+)
+{
+	float w = qV[3];
+	float x = qV[0];
+	float y = qV[1];
+	float z = qV[2];
+
+	float qxx = x*x;
+	float qyy = y*y;
+	float qzz = z*z;
+	float qxz = x*z;
+	float qxy = x*y;
+	float qyz = y*z;
+	float qwx = w*x;
+	float qwy = w*y;
+	float qwz = w*z;
+
+	*m11 = 1 - 2 * (qyy + qzz); *m12 = 2 * (qxy - qwz); *m13 = 2 * (qxz + qwy);
+	*m21 = 2 * (qxy + qwz); *m22 = 1 - 2 * (qxx + qzz); *m23 = 2 * (qyz - qwx);
+	*m31 = 2 * (qxz - qwy); *m32 = 2 * (qyz + qwx); *m33 = 1 - 2 * (qxx + qyy);
+}
+
+inline void approximateGivensQuaternion(float a11, float a12, float a22, float *ch, float *sh)
+{
+	/*
+	* Given givens angle computed by approximateGivensAngles,
+	* compute the corresponding rotation quaternion.
+	*/
+	*ch = 2 * (a11 - a22);
+	*sh = a12;
+	bool b = _gamma* (*sh)*(*sh) < (*ch)*(*ch);
+	// fast rsqrt function suffices
+	// rsqrt2 (https://code.google.com/p/lppython/source/browse/algorithm/HDcode/newCode/rsqrt.c?r=26)
+	// is even faster but results in too much error
+	float w = rsqrt((*ch)*(*ch) + (*sh)*(*sh));
+	*ch = b ? w*(*ch) : (float)_cstar;
+	*sh = b ? w*(*sh) : (float)_sstar;
+}
+
+inline void jacobiConjugation(const int x, const int y, const int z,
+	float *s11,
+	float *s21, float *s22,
+	float *s31, float *s32, float *s33,
+	float * qV)
+{
+	float ch, sh;
+	approximateGivensQuaternion(*s11, *s21, *s22, &ch, &sh);
+
+	float scale = ch*ch + sh*sh;
+	float a = (ch*ch - sh*sh) / scale;
+	float b = (2 * sh*ch) / scale;
+
+	// make temp copy of S
+	float _s11 = *s11;
+	float _s21 = *s21; float _s22 = *s22;
+	float _s31 = *s31; float _s32 = *s32; float _s33 = *s33;
+
+	// perform conjugation S = Q'*S*Q
+	// Q already implicitly solved from a, b
+	*s11 = a*(a*_s11 + b*_s21) + b*(a*_s21 + b*_s22);
+	*s21 = a*(-b*_s11 + a*_s21) + b*(-b*_s21 + a*_s22);	*s22 = -b*(-b*_s11 + a*_s21) + a*(-b*_s21 + a*_s22);
+	*s31 = a*_s31 + b*_s32;								*s32 = -b*_s31 + a*_s32; *s33 = _s33;
+
+	// update cumulative rotation qV
+	float tmp[3];
+	tmp[0] = qV[0] * sh;
+	tmp[1] = qV[1] * sh;
+	tmp[2] = qV[2] * sh;
+	sh *= qV[3];
+
+	qV[0] *= ch;
+	qV[1] *= ch;
+	qV[2] *= ch;
+	qV[3] *= ch;
+
+	// (x,y,z) corresponds to ((0,1,2),(1,2,0),(2,0,1))
+	// for (p,q) = ((0,1),(1,2),(0,2))
+	qV[z] += sh;
+	qV[3] -= tmp[z]; // w
+	qV[x] += tmp[y];
+	qV[y] -= tmp[x];
+
+	// re-arrange matrix for next iteration
+	_s11 = *s22;
+	_s21 = *s32; _s22 = *s33;
+	_s31 = *s21; _s32 = *s31; _s33 = *s11;
+	*s11 = _s11;
+	*s21 = _s21; *s22 = _s22;
+	*s31 = _s31; *s32 = _s32; *s33 = _s33;
+
+}
+
+inline float dist2(float x, float y, float z)
+{
+	return x*x + y*y + z*z;
+}
+
+// finds transformation that diagonalizes a symmetric matrix
+inline void jacobiEigenanlysis( // symmetric matrix
+	float *s11,
+	float *s21, float *s22,
+	float *s31, float *s32, float *s33,
+	// quaternion representation of V
+	float * qV)
+{
+	qV[3] = 1; qV[0] = 0; qV[1] = 0; qV[2] = 0; // follow same indexing convention as GLM
+	for (int i = 0; i<4; i++)
+	{
+		// we wish to eliminate the maximum off-diagonal element
+		// on every iteration, but cycling over all 3 possible rotations
+		// in fixed order (p,q) = (1,2) , (2,3), (1,3) still retains
+		//  asymptotic convergence
+		jacobiConjugation(0, 1, 2, s11, s21, s22, s31, s32, s33, qV); // p,q = 0,1
+		jacobiConjugation(1, 2, 0, s11, s21, s22, s31, s32, s33, qV); // p,q = 1,2
+		jacobiConjugation(2, 0, 1, s11, s21, s22, s31, s32, s33, qV); // p,q = 0,2
+	}
+}
+
+
+inline void sortSingularValues(// matrix that we want to decompose
+	float *b11, float *b12, float *b13,
+	float *b21, float *b22, float *b23,
+	float *b31, float *b32, float *b33,
+	// sort V simultaneously
+	float *v11, float *v12, float *v13,
+	float *v21, float *v22, float *v23,
+	float *v31, float *v32, float *v33)
+{
+	float rho1 = dist2(*b11, *b21, *b31);
+	float rho2 = dist2(*b12, *b22, *b32);
+	float rho3 = dist2(*b13, *b23, *b33);
+	bool c;
+	c = rho1 < rho2;
+	condNegSwap(c, b11, b12); condNegSwap(c, v11, v12);
+	condNegSwap(c, b21, b22); condNegSwap(c, v21, v22);
+	condNegSwap(c, b31, b32); condNegSwap(c, v31, v32);
+	condSwap(c, &rho1, &rho2);
+	c = rho1 < rho3;
+	condNegSwap(c, b11, b13); condNegSwap(c, v11, v13);
+	condNegSwap(c, b21, b23); condNegSwap(c, v21, v23);
+	condNegSwap(c, b31, b33); condNegSwap(c, v31, v33);
+	condSwap(c, &rho1, &rho3);
+	c = rho2 < rho3;
+	condNegSwap(c, b12, b13); condNegSwap(c, v12, v13);
+	condNegSwap(c, b22, b23); condNegSwap(c, v22, v23);
+	condNegSwap(c, b32, b33); condNegSwap(c, v32, v33);
+}
+
+
+void QRGivensQuaternion(float a1, float a2, float *ch, float *sh)
+{
+	// a1 = pivot point on diagonal
+	// a2 = lower triangular entry we want to annihilate
+	float epsilon = (float)EPSILON;
+	float rho = accurateSqrt(a1*a1 + a2*a2);
+
+	*sh = rho > epsilon ? a2 : 0;
+	*ch = fabsf(a1) + fmaxf(rho, epsilon);
+	bool b = a1 < 0;
+	condSwap(b, sh, ch);
+	float w = rsqrt((*ch)*(*ch) + (*sh)*(*sh));
+	*ch *= w;
+	*sh *= w;
+}
+
+
+inline void QRDecomposition(// matrix that we want to decompose
+	float b11, float b12, float b13,
+	float b21, float b22, float b23,
+	float b31, float b32, float b33,
+	// output Q
+	float *q11, float *q12, float *q13,
+	float *q21, float *q22, float *q23,
+	float *q31, float *q32, float *q33,
+	// output R
+	float *r11, float *r12, float *r13,
+	float *r21, float *r22, float *r23,
+	float *r31, float *r32, float *r33)
+{
+	float ch1, sh1, ch2, sh2, ch3, sh3;
+	float a, b;
+
+	// first givens rotation (ch,0,0,sh)
+	QRGivensQuaternion(b11, b21, &ch1, &sh1);
+	a = 1 - 2 * sh1*sh1;
+	b = 2 * ch1*sh1;
+	// apply B = Q' * B
+	*r11 = a*b11 + b*b21;  *r12 = a*b12 + b*b22;  *r13 = a*b13 + b*b23;
+	*r21 = -b*b11 + a*b21; *r22 = -b*b12 + a*b22; *r23 = -b*b13 + a*b23;
+	*r31 = b31;          *r32 = b32;          *r33 = b33;
+
+	// second givens rotation (ch,0,-sh,0)
+	QRGivensQuaternion(*r11, *r31, &ch2, &sh2);
+	a = 1 - 2 * sh2*sh2;
+	b = 2 * ch2*sh2;
+	// apply B = Q' * B;
+	b11 = a*(*r11) + b*(*r31);  b12 = a*(*r12) + b*(*r32);  b13 = a*(*r13) + b*(*r33);
+	b21 = *r21;           b22 = *r22;           b23 = *r23;
+	b31 = -b*(*r11) + a*(*r31); b32 = -b*(*r12) + a*(*r32); b33 = -b*(*r13) + a*(*r33);
+
+	// third givens rotation (ch,sh,0,0)
+	QRGivensQuaternion(b22, b32, &ch3, &sh3);
+	a = 1 - 2 * sh3*sh3;
+	b = 2 * ch3*sh3;
+	// R is now set to desired value
+	*r11 = b11;               *r12 = b12;             *r13 = b13;
+	*r21 = a*b21 + b*b31;     *r22 = a*b22 + b*b32;   *r23 = a*b23 + b*b33;
+	*r31 = -b*b21 + a*b31;    *r32 = -b*b22 + a*b32;  *r33 = -b*b23 + a*b33;
+
+	// construct the cumulative rotation Q=Q1 * Q2 * Q3
+	// the number of floating point operations for three quaternion multiplications
+	// is more or less comparable to the explicit form of the joined matrix.
+	// certainly more memory-efficient!
+	float sh12 = sh1*sh1;
+	float sh22 = sh2*sh2;
+	float sh32 = sh3*sh3;
+
+	*q11 = (-1 + 2 * sh12)*(-1 + 2 * sh22);
+	*q12 = 4 * ch2*ch3*(-1 + 2 * sh12)*sh2*sh3 + 2 * ch1*sh1*(-1 + 2 * sh32);
+	*q13 = 4 * ch1*ch3*sh1*sh3 - 2 * ch2*(-1 + 2 * sh12)*sh2*(-1 + 2 * sh32);
+
+	*q21 = 2 * ch1*sh1*(1 - 2 * sh22);
+	*q22 = -8 * ch1*ch2*ch3*sh1*sh2*sh3 + (-1 + 2 * sh12)*(-1 + 2 * sh32);
+	*q23 = -2 * ch3*sh3 + 4 * sh1*(ch3*sh1*sh3 + ch1*ch2*sh2*(-1 + 2 * sh32));
+
+	*q31 = 2 * ch2*sh2;
+	*q32 = 2 * ch3*(1 - 2 * sh22)*sh3;
+	*q33 = (-1 + 2 * sh22)*(-1 + 2 * sh32);
+}
+
+void svd(// input A
+	float a11, float a12, float a13,
+	float a21, float a22, float a23,
+	float a31, float a32, float a33,
+	// output U
+	float *u11, float *u12, float *u13,
+	float *u21, float *u22, float *u23,
+	float *u31, float *u32, float *u33,
+	// output S
+	float *s11, float *s12, float *s13,
+	float *s21, float *s22, float *s23,
+	float *s31, float *s32, float *s33,
+	// output V
+	float *v11, float *v12, float *v13,
+	float *v21, float *v22, float *v23,
+	float *v31, float *v32, float *v33)
+{
+	// normal equations matrix
+	float ATA11, ATA12, ATA13;
+	float ATA21, ATA22, ATA23;
+	float ATA31, ATA32, ATA33;
+
+	multAtB(a11, a12, a13, a21, a22, a23, a31, a32, a33,
+		a11, a12, a13, a21, a22, a23, a31, a32, a33,
+		&ATA11, &ATA12, &ATA13, &ATA21, &ATA22, &ATA23, &ATA31, &ATA32, &ATA33);
+
+	// symmetric eigenalysis
+	float qV[4];
+	jacobiEigenanlysis(&ATA11, &ATA21, &ATA22, &ATA31, &ATA32, &ATA33, qV);
+	quatToMat3(qV, v11, v12, v13, v21, v22, v23, v31, v32, v33);
+
+	float b11, b12, b13;
+	float b21, b22, b23;
+	float b31, b32, b33;
+	multAB(a11, a12, a13, a21, a22, a23, a31, a32, a33,
+		*v11, *v12, *v13, *v21, *v22, *v23, *v31, *v32, *v33,
+		&b11, &b12, &b13, &b21, &b22, &b23, &b31, &b32, &b33);
+
+	// sort singular values and find V
+	sortSingularValues(&b11, &b12, &b13, &b21, &b22, &b23, &b31, &b32, &b33,
+		v11, v12, v13, v21, v22, v23, v31, v32, v33);
+
+	// QR decomposition
+	QRDecomposition(b11, b12, b13, b21, b22, b23, b31, b32, b33,
+		u11, u12, u13, u21, u22, u23, u31, u32, u33,
+		s11, s12, s13, s21, s22, s23, s31, s32, s33
+	);
+}
+
+/// polar decomposition can be reconstructed trivially from SVD result
+// A = UP
+void pd(float a11, float a12, float a13,
+	float a21, float a22, float a23,
+	float a31, float a32, float a33,
+	// output U
+	float *u11, float *u12, float *u13,
+	float *u21, float *u22, float *u23,
+	float *u31, float *u32, float *u33,
+	// output P
+	float *p11, float *p12, float *p13,
+	float *p21, float *p22, float *p23,
+	float *p31, float *p32, float *p33)
+{
+	float w11, w12, w13, w21, w22, w23, w31, w32, w33;
+	float s11, s12, s13, s21, s22, s23, s31, s32, s33;
+	float v11, v12, v13, v21, v22, v23, v31, v32, v33;
+
+	svd(a11, a12, a13, a21, a22, a23, a31, a32, a33,
+		&w11, &w12, &w13, &w21, &w22, &w23, &w31, &w32, &w33,
+		&s11, &s12, &s13, &s21, &s22, &s23, &s31, &s32, &s33,
+		&v11, &v12, &v13, &v21, &v22, &v23, &v31, &v32, &v33);
+
+	// P = VSV'
+	float t11, t12, t13, t21, t22, t23, t31, t32, t33;
+	multAB(v11, v12, v13, v21, v22, v23, v31, v32, v33,
+		s11, s12, s13, s21, s22, s23, s31, s32, s33,
+		&t11, &t12, &t13, &t21, &t22, &t23, &t31, &t32, &t33);
+
+	multAB(t11, t12, t13, t21, t22, t23, t31, t32, t33,
+		v11, v21, v31, v12, v22, v32, v13, v23, v33,
+		p11, p12, p13, p21, p22, p23, p31, p32, p33);
+
+	// U = WV'
+	multAB(w11, w12, w13, w21, w22, w23, w31, w32, w33,
+		v11, v21, v31, v12, v22, v32, v13, v23, v33,
+		u11, u12, u13, u21, u22, u23, u31, u32, u33);
+}
+
+#endif
\ No newline at end of file