/*
** unlike the thing above, this one assumes that the quaternions in qq
** have already been normalized, and, that the sum of wght[] is 1.0
*/
int
ell_q_avgN_d(double mm[4], unsigned int *iterP,
const double *qq, double *qlog,
const double *wght, const unsigned int NN,
const double eps, const unsigned int maxIter) {
static const char me[]="ell_q_avgN_d";
double tmp, qdiv[4], elen;
unsigned int ii, iter;
/* iterP optional */
/* wght optional, to signify equal 1/NN weighting for all */
if (!( mm && qq )) {
biffAddf(ELL, "%s: got NULL pointer", me);
return 1;
}
if (!( eps >= 0 )) {
biffAddf(ELL, "%s: need eps >= 0 (not %g)", me, eps);
return 1;
}
/* initialize with euclidean mean */
ELL_4V_SET(mm, 0, 0, 0, 0);
for (ii=0; ii<NN; ii++) {
double ww;
ww = wght ? wght[ii] : 1.0/NN;
ELL_4V_SCALE_INCR(mm, ww, qq + 4*ii);
}
ELL_4V_NORM(mm, mm, tmp);
iter = 0;
do {
double logavg[4], qexp[4];
/* take log of everyone */
for (ii=0; ii<NN; ii++) {
ell_q_div_d(qdiv, mm, qq + 4*ii); /* div = mm^1 * qq[ii] */
ell_q_log_d(qlog + 4*ii, qdiv);
}
/* average, and find length */
ELL_4V_SET(logavg, 0, 0, 0, 0);
for (ii=0; ii<NN; ii++) {
double ww;
ww = wght ? wght[ii] : 1.0/NN;
ELL_4V_SCALE_INCR(logavg, ww, qlog + 4*ii);
}
elen = ELL_4V_LEN(logavg);
/* use exp to put it back on S^3 */
ell_q_exp_d(qexp, logavg);
ell_q_mul_d(mm, mm, qexp);
iter++;
} while ((!maxIter || iter < maxIter) && elen > eps);
if (elen > eps) {
biffAddf(ELL, "%s: still have error %g (> eps %g) after max %d iters", me,
elen, eps, maxIter);
return 1;
}
if (iterP) {
*iterP = iter;
}
return 0;
}
void
ell_3m_to_q_d(double q[4], const double m[9]) {
_ELL_M_TO_Q(double, 0, 1, 2, 3, 4, 5, 6, 7, 8);
ELL_4V_NORM(q, q, len);
}
void
ell_q_to_4m_d(double m[16], const double q[4]) {
double u[4], w=0.0, x=0.0, y=0.0, z=0.0;
ELL_4V_NORM(u, q, w);
_ELL_Q_TO_4M(double);
}
int
ell_q_avg4_d(double m[4], unsigned int *iterP,
const double _q1[4], const double _q2[4],
const double _q3[4], const double _q4[4],
const double _wght[4],
const double eps, const unsigned int maxIter) {
static const char me[]="ell_q_avg4_d";
double N, elen, a[4], b[4], c[4], d[4],
tmp[4], la[4], lb[4], lc[4], ld[4], u[4], wght[4];
unsigned int iter;
/* *iterP optional */
if (!( m && _q1 && _q2 && _q3 && _q4 && _wght )) {
biffAddf(ELL, "%s: got NULL pointer", me);
return 1;
}
if (!( eps >= 0 )) {
biffAddf(ELL, "%s: need eps >= 0 (not %g)", me, eps);
return 1;
}
/* normalize (wrt L2) all given quaternions */
ELL_4V_NORM(a, _q1, N);
ELL_4V_NORM(b, _q2, N);
ELL_4V_NORM(c, _q3, N);
ELL_4V_NORM(d, _q4, N);
/* normalize (wrt L1) the given weights */
ELL_4V_COPY(wght, _wght);
N = wght[0] + wght[1] + wght[2] + wght[3];
ELL_4V_SCALE(wght, 1.0/N, wght);
/* initialize mean to normalized euclidean mean */
ELL_4V_SCALE_ADD4(m, wght[0], a, wght[1], b, wght[2], c, wght[3], d);
ELL_4V_NORM(m, m, N);
iter = 0;
do {
/* take log of everyone */
ell_q_div_d(tmp, m, a); ell_q_log_d(la, tmp);
ell_q_div_d(tmp, m, b); ell_q_log_d(lb, tmp);
ell_q_div_d(tmp, m, c); ell_q_log_d(lc, tmp);
ell_q_div_d(tmp, m, d); ell_q_log_d(ld, tmp);
/* average, and find length */
ELL_4V_SCALE_ADD4(u, wght[0], la, wght[1], lb, wght[2], lc, wght[3], ld);
elen = ELL_4V_LEN(u);
/* use exp to put it back on S^3 */
ell_q_exp_d(tmp, u); ell_q_mul_d(m, m, tmp);
iter++;
} while ((!maxIter || iter < maxIter) && elen > eps);
if (elen > eps) {
biffAddf(ELL, "%s: still have error %g after max %d iters", me,
elen, maxIter);
return 1;
}
if (iterP) {
*iterP = iter;
}
return 0;
}
/*
** This does (non-optionally) use biff, to report convergence failures
**
** we do in fact require non-NULL tip, because it holds the buffers we need
*/
int
_tenQGLInterpNEvec(double evecOut[9],
const double *evecIn, /* size 9 -by- NN */
const double *wght, /* size NN */
unsigned int NN,
tenInterpParm *tip) {
static const char me[]="_tenQGLInterpNEvec";
double qOut[4], maxWght, len, /* odsum, */ dsum, rot[9];
unsigned int ii, centerIdx=0, fix, qiter;
if (!( evecOut && evecIn && tip )) {
biffAddf(TEN, "%s: got NULL pointer", me);
return 1;
}
/* convert to quaternions */
for (ii=0; ii<NN; ii++) {
ELL_3M_TRANSPOSE(rot, evecIn + 9*ii);
ell_3m_to_q_d(tip->qIn + 4*ii, rot);
}
/* HEY: what should this be used for? variable odsum set but not used */
/* odsum = _tenQGL_q_interdot(¢erIdx, tip->qIn, tip->qInter, NN); */
/* find quaternion with maximal weight, use it as is (decree that
its the right representative), and then align rest with that.
This is actually principled; symmetry allows it */
centerIdx = 0;
if (wght) {
maxWght = wght[centerIdx];
for (ii=1; ii<NN; ii++) {
if (wght[ii] > maxWght) {
centerIdx = ii;
maxWght = wght[centerIdx];
}
}
}
for (ii=0; ii<NN; ii++) {
if (ii == centerIdx) {
continue;
}
_tenQGL_q_align(tip->qIn + 4*ii, tip->qIn + 4*centerIdx, tip->qIn + 4*ii);
}
dsum = _tenQGL_q_interdot(¢erIdx, tip->qIn, tip->qInter, NN);
/* try to settle on tightest set of representatives */
qiter = 0;
do {
fix = 0;
for (ii=0; ii<NN; ii++) {
unsigned int ff;
if (ii == centerIdx) {
continue;
}
ff = _tenQGL_q_align(tip->qIn + 4*ii, tip->qIn + 4*centerIdx,
tip->qIn + 4*ii);
fix = AIR_MAX(fix, ff);
}
dsum = _tenQGL_q_interdot(¢erIdx, tip->qIn, tip->qInter, NN);
if (tip->maxIter && qiter > tip->maxIter) {
biffAddf(TEN, "%s: q tightening unconverged after %u iters; "
"interdot = %g -> maxfix = %u; center = %u\n",
me, tip->maxIter, dsum, fix, centerIdx);
return 1;
}
qiter++;
} while (fix);
/*
fprintf(stderr, "!%s: dsum %g --%u--> %g\n", me, odsum, qiter, dsum);
*/
/* make sure they're normalized */
for (ii=0; ii<NN; ii++) {
ELL_4V_NORM(tip->qIn + 4*ii, tip->qIn + 4*ii, len);
}
/* compute iterated weighted mean, stored in qOut */
if (ell_q_avgN_d(qOut, &qiter, tip->qIn, tip->qBuff, wght,
NN, tip->convEps, tip->maxIter)) {
biffMovef(TEN, ELL, "%s: problem doing quaternion mean", me);
return 1;
}
/*
fprintf(stderr, "!%s: q avg converged in %u\n", me, qiter);
*/
/* finish, convert back to evec */
ell_q_to_3m_d(rot, qOut);
ELL_3M_TRANSPOSE(evecOut, rot);
return 0;
}
void
ell_4m_to_q_d(double q[4], const double m[16]) {
_ELL_M_TO_Q(double, 0, 1, 2, 4, 5, 6, 8, 9, 10);
ELL_4V_NORM(q, q, len);
}
int
main(int argc, const char *argv[]) {
const char *me;
char *err, *outS;
float p[3], q[4], mR[9], eval[3]={0,0,0}, scale[3], len, sh, cl, cp, qA, qB;
float matA[16], matB[16], os, rad, AB[2];
hestOpt *hopt=NULL;
airArray *mop;
limnObject *obj;
limnLook *look; int lookRod, lookSoid;
int partIdx=-1; /* sssh */
int res, axis, sphere;
FILE *file;
me = argv[0];
hestOptAdd(&hopt, "sc", "scalings", airTypeFloat, 3, 3, scale, "1 1 1",
"axis-aligned scaling to do on ellipsoid");
hestOptAdd(&hopt, "AB", "A, B exponents", airTypeFloat, 2, 2, AB, "nan nan",
"Directly set the A, B parameters to the superquadric surface, "
"over-riding the default behavior of determining them from the "
"scalings \"-sc\" as superquadric tensor glyphs");
hestOptAdd(&hopt, "os", "over-all scaling", airTypeFloat, 1, 1, &os, "1",
"over-all scaling (multiplied by scalings)");
hestOptAdd(&hopt, "sh", "superquad sharpness", airTypeFloat, 1, 1, &sh, "0",
"how much to sharpen edges as a "
"function of differences between eigenvalues");
hestOptAdd(&hopt, "sphere", NULL, airTypeInt, 0, 0, &sphere, NULL,
"use a sphere instead of a superquadric");
hestOptAdd(&hopt, "p", "x y z", airTypeFloat, 3, 3, p, "0 0 0",
"location in quaternion quotient space");
hestOptAdd(&hopt, "r", "radius", airTypeFloat, 1, 1, &rad, "0.015",
"black axis cylinder radius (or 0.0 to not drawn these)");
hestOptAdd(&hopt, "res", "resolution", airTypeInt, 1, 1, &res, "25",
"tesselation resolution for both glyph and axis cylinders");
hestOptAdd(&hopt, "o", "output OFF", airTypeString, 1, 1, &outS, "out.off",
"output file to save OFF into");
hestParseOrDie(hopt, argc-1, argv+1, NULL,
me, info, AIR_TRUE, AIR_TRUE, AIR_TRUE);
mop = airMopNew();
airMopAdd(mop, hopt, (airMopper)hestOptFree, airMopAlways);
airMopAdd(mop, hopt, (airMopper)hestParseFree, airMopAlways);
obj = limnObjectNew(100, AIR_FALSE);
airMopAdd(mop, obj, (airMopper)limnObjectNix, airMopAlways);
/* create limnLooks for ellipsoid and for rods */
lookSoid = limnObjectLookAdd(obj);
look = obj->look + lookSoid;
ELL_4V_SET(look->rgba, 1, 1, 1, 1);
ELL_3V_SET(look->kads, 0.2, 0.8, 0);
look->spow = 0;
lookRod = limnObjectLookAdd(obj);
look = obj->look + lookRod;
ELL_4V_SET(look->rgba, 0, 0, 0, 1);
ELL_3V_SET(look->kads, 1, 0, 0);
look->spow = 0;
ELL_4V_SET(q, 1, p[0], p[1], p[2]);
ELL_4V_NORM(q, q, len);
ell_q_to_3m_f(mR, q);
if (AIR_EXISTS(AB[0]) && AIR_EXISTS(AB[1])) {
qA = AB[0];
qB = AB[1];
axis = 2;
} else {
ELL_3V_SCALE(scale, os, scale);
ELL_3V_COPY(eval, scale);
ELL_SORT3(eval[0], eval[1], eval[2], cl);
cl = (eval[0] - eval[1])/(eval[0] + eval[1] + eval[2]);
cp = 2*(eval[1] - eval[2])/(eval[0] + eval[1] + eval[2]);
if (cl > cp) {
axis = ELL_MAX3_IDX(scale[0], scale[1], scale[2]);
qA = pow(1-cp, sh);
qB = pow(1-cl, sh);
} else {
axis = ELL_MIN3_IDX(scale[0], scale[1], scale[2]);
qA = pow(1-cl, sh);
qB = pow(1-cp, sh);
}
/*
fprintf(stderr, "eval = %g %g %g -> cl=%g %s cp=%g -> axis = %d\n",
eval[0], eval[1], eval[2], cl, cl > cp ? ">" : "<", cp, axis);
*/
}
if (sphere) {
partIdx = limnObjectPolarSphereAdd(obj, lookSoid,
0, 2*res, res);
} else {
partIdx = limnObjectPolarSuperquadAdd(obj, lookSoid,
axis, qA, qB, 2*res, res);
}
ELL_4M_IDENTITY_SET(matA);
ELL_4M_SCALE_SET(matB, scale[0], scale[1], scale[2]);
ell_4m_post_mul_f(matA, matB);
ELL_43M_INSET(matB, mR);
ell_4m_post_mul_f(matA, matB);
limnObjectPartTransform(obj, partIdx, matA);
if (rad) {
partIdx = limnObjectCylinderAdd(obj, lookRod, 0, res);
ELL_4M_IDENTITY_SET(matA);
ELL_4M_SCALE_SET(matB, (1-eval[0])/2, rad, rad);
ell_4m_post_mul_f(matA, matB);
ELL_4M_TRANSLATE_SET(matB, (1+eval[0])/2, 0.0, 0.0);
ell_4m_post_mul_f(matA, matB);
limnObjectPartTransform(obj, partIdx, matA);
partIdx = limnObjectCylinderAdd(obj, lookRod, 0, res);
ELL_4M_IDENTITY_SET(matA);
ELL_4M_SCALE_SET(matB, (1-eval[0])/2, rad, rad);
ell_4m_post_mul_f(matA, matB);
ELL_4M_TRANSLATE_SET(matB, -(1+eval[0])/2, 0.0, 0.0);
ell_4m_post_mul_f(matA, matB);
limnObjectPartTransform(obj, partIdx, matA);
partIdx = limnObjectCylinderAdd(obj, lookRod, 1, res);
ELL_4M_IDENTITY_SET(matA);
ELL_4M_SCALE_SET(matB, rad, (1-eval[1])/2, rad);
ell_4m_post_mul_f(matA, matB);
ELL_4M_TRANSLATE_SET(matB, 0.0, (1+eval[1])/2, 0.0);
ell_4m_post_mul_f(matA, matB);
limnObjectPartTransform(obj, partIdx, matA);
partIdx = limnObjectCylinderAdd(obj, lookRod, 1, res);
ELL_4M_IDENTITY_SET(matA);
ELL_4M_SCALE_SET(matB, rad, (1-eval[1])/2, rad);
ell_4m_post_mul_f(matA, matB);
ELL_4M_TRANSLATE_SET(matB, 0.0, -(1+eval[1])/2, 0.0);
ell_4m_post_mul_f(matA, matB);
limnObjectPartTransform(obj, partIdx, matA);
partIdx = limnObjectCylinderAdd(obj, lookRod, 2, res);
ELL_4M_IDENTITY_SET(matA);
ELL_4M_SCALE_SET(matB, rad, rad, (1-eval[2])/2);
ell_4m_post_mul_f(matA, matB);
ELL_4M_TRANSLATE_SET(matB, 0.0, 0.0, (1+eval[2])/2);
ell_4m_post_mul_f(matA, matB);
limnObjectPartTransform(obj, partIdx, matA);
partIdx = limnObjectCylinderAdd(obj, lookRod, 2, res);
ELL_4M_IDENTITY_SET(matA);
ELL_4M_SCALE_SET(matB, rad, rad, (1-eval[2])/2);
ell_4m_post_mul_f(matA, matB);
ELL_4M_TRANSLATE_SET(matB, 0.0, 0.0, -(1+eval[2])/2);
ell_4m_post_mul_f(matA, matB);
limnObjectPartTransform(obj, partIdx, matA);
}
file = airFopen(outS, stdout, "w");
airMopAdd(mop, file, (airMopper)airFclose, airMopAlways);
if (limnObjectWriteOFF(file, obj)) {
airMopAdd(mop, err = biffGetDone(LIMN), airFree, airMopAlways);
fprintf(stderr, "%s: trouble:\n%s\n", me, err);
airMopError(mop); return 1;
}
airMopOkay(mop);
return 0;
}
int
main(int argc, const char *argv[]) {
const char *me;
char *err, *outS;
double eval[3], matA[9], matB[9], sval[3], uu[9], vv[9], escl[5],
view[3];
float matAf[9], matBf[16];
float pp[3], qq[4], mR[9], len, gamma;
float os, vs, rad, AB[2], ten[7];
hestOpt *hopt=NULL;
airArray *mop;
limnObject *obj;
limnLook *look; int lookRod, lookSoid;
float kadsRod[3], kadsSoid[3];
int gtype, partIdx=-1; /* sssh */
int res;
FILE *file;
me = argv[0];
hestOptAdd(&hopt, "sc", "evals", airTypeDouble, 3, 3, eval, "1 1 1",
"original eigenvalues of tensor to be visualized");
hestOptAdd(&hopt, "AB", "A, B exponents", airTypeFloat, 2, 2, AB, "nan nan",
"Directly set the A, B parameters to the superquadric surface, "
"over-riding the default behavior of determining them from the "
"scalings \"-sc\" as superquadric tensor glyphs");
hestOptAdd(&hopt, "os", "over-all scaling", airTypeFloat, 1, 1, &os, "1",
"over-all scaling (multiplied by scalings)");
hestOptAdd(&hopt, "vs", "view-dir scaling", airTypeFloat, 1, 1, &vs, "1",
"scaling along view-direction (to show off bas-relief "
"ambibuity of ellipsoids versus superquads)");
hestOptAdd(&hopt, "es", "extra scaling", airTypeDouble, 5, 5, escl,
"2 1 0 0 1", "extra scaling specified with five values "
"0:tensor|1:geometry|2:none vx vy vz scaling");
hestOptAdd(&hopt, "fr", "from (eye) point", airTypeDouble, 3, 3, &view,
"4 4 4", "eye point, needed for non-unity \"-vs\"");
hestOptAdd(&hopt, "gamma", "superquad sharpness", airTypeFloat, 1, 1,
&gamma, "0",
"how much to sharpen edges as a "
"function of differences between eigenvalues");
hestOptAdd(&hopt, "g", "glyph shape", airTypeEnum, 1, 1, >ype, "sqd",
"glyph to use; not all are implemented here",
NULL, tenGlyphType);
hestOptAdd(&hopt, "pp", "x y z", airTypeFloat, 3, 3, pp, "0 0 0",
"transform: rotation identified by"
"location in quaternion quotient space");
hestOptAdd(&hopt, "r", "radius", airTypeFloat, 1, 1, &rad, "0.015",
"black axis cylinder radius (or 0.0 to not drawn these)");
hestOptAdd(&hopt, "res", "resolution", airTypeInt, 1, 1, &res, "25",
"tesselation resolution for both glyph and axis cylinders");
hestOptAdd(&hopt, "pg", "ka kd ks", airTypeFloat, 3, 3, kadsSoid,
"0.2 0.8 0.0",
"phong coefficients for glyph");
hestOptAdd(&hopt, "pr", "ka kd ks", airTypeFloat, 3, 3, kadsRod, "1 0 0",
"phong coefficients for black rods (if being drawn)");
hestOptAdd(&hopt, "o", "output OFF", airTypeString, 1, 1, &outS, "out.off",
"output file to save OFF into");
hestParseOrDie(hopt, argc-1, argv+1, NULL,
me, info, AIR_TRUE, AIR_TRUE, AIR_TRUE);
mop = airMopNew();
airMopAdd(mop, hopt, (airMopper)hestOptFree, airMopAlways);
airMopAdd(mop, hopt, (airMopper)hestParseFree, airMopAlways);
obj = limnObjectNew(1000, AIR_TRUE);
airMopAdd(mop, obj, (airMopper)limnObjectNix, airMopAlways);
if (!( 0 == escl[0] || 1 == escl[0] || 2 == escl[0] )) {
fprintf(stderr, "%s: escl[0] %g not 0, 1 or 2\n", me, escl[0]);
airMopError(mop); return 1;
}
if (!(tenGlyphTypeBox == gtype ||
tenGlyphTypeSphere == gtype ||
tenGlyphTypeSuperquad == gtype)) {
fprintf(stderr, "%s: got %s %s, but here only do %s, %s, or %s\n", me,
tenGlyphType->name,
airEnumStr(tenGlyphType, gtype),
airEnumStr(tenGlyphType, tenGlyphTypeBox),
airEnumStr(tenGlyphType, tenGlyphTypeSphere),
airEnumStr(tenGlyphType, tenGlyphTypeSuperquad));
airMopError(mop); return 1;
}
/* create limnLooks for glyph and for rods */
lookSoid = limnObjectLookAdd(obj);
look = obj->look + lookSoid;
ELL_4V_SET(look->rgba, 1, 1, 1, 1);
ELL_3V_COPY(look->kads, kadsSoid);
look->spow = 0;
lookRod = limnObjectLookAdd(obj);
look = obj->look + lookRod;
ELL_4V_SET(look->rgba, 0, 0, 0, 1);
ELL_3V_COPY(look->kads, kadsRod);
look->spow = 0;
ELL_3M_IDENTITY_SET(matA); /* A = I */
ELL_3V_SCALE(eval, os, eval);
ELL_3M_SCALE_SET(matB, eval[0], eval[1], eval[2]); /* B = diag(eval) */
ell_3m_post_mul_d(matA, matB); /* A = B*A = diag(eval) */
if (0 == escl[0]) {
scalingMatrix(matB, escl + 1, escl[4]);
ell_3m_post_mul_d(matA, matB);
}
if (1 != vs) {
if (!ELL_3V_LEN(view)) {
fprintf(stderr, "%s: need non-zero view for vs %g != 1\n", me, vs);
airMopError(mop); return 1;
}
scalingMatrix(matB, view, vs);
/* the scaling along the view direction is a symmetric matrix,
but applying that scaling to the symmetric input tensor
is not necessarily symmetric */
ell_3m_post_mul_d(matA, matB); /* A = B*A */
}
/* so we do an SVD to get rotation U and the scalings sval[] */
/* U * diag(sval) * V */
ell_3m_svd_d(uu, sval, vv, matA, AIR_TRUE);
/*
fprintf(stderr, "%s: ____________________________________\n", me);
fprintf(stderr, "%s: mat = \n", me);
ell_3m_print_d(stderr, matA);
fprintf(stderr, "%s: uu = \n", me);
ell_3m_print_d(stderr, uu);
ELL_3M_TRANSPOSE(matC, uu);
ELL_3M_MUL(matB, uu, matC);
fprintf(stderr, "%s: uu * uu^T = \n", me);
ell_3m_print_d(stderr, matB);
fprintf(stderr, "%s: sval = %g %g %g\n", me, sval[0], sval[1], sval[2]);
fprintf(stderr, "%s: vv = \n", me);
ell_3m_print_d(stderr, vv);
ELL_3M_MUL(matB, vv, vv);
fprintf(stderr, "%s: vv * vv^T = \n", me);
ELL_3M_TRANSPOSE(matC, vv);
ELL_3M_MUL(matB, vv, matC);
ell_3m_print_d(stderr, matB);
ELL_3M_IDENTITY_SET(matA);
ell_3m_pre_mul_d(matA, uu);
ELL_3M_SCALE_SET(matB, sval[0], sval[1], sval[2]);
ell_3m_pre_mul_d(matA, matB);
ell_3m_pre_mul_d(matA, vv);
fprintf(stderr, "%s: uu * diag(sval) * vv = \n", me);
ell_3m_print_d(stderr, matA);
fprintf(stderr, "%s: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n", me);
*/
/* now create symmetric matrix out of U and sval */
/* A = I */
ELL_3M_IDENTITY_SET(matA);
ell_3m_pre_mul_d(matA, uu); /* A = A*U = I*U = U */
ELL_3M_SCALE_SET(matB, sval[0], sval[1], sval[2]); /* B = diag(sval) */
ell_3m_pre_mul_d(matA, matB); /* A = U*diag(sval) */
ELL_3M_TRANSPOSE(matB, uu);
ell_3m_pre_mul_d(matA, matB); /* A = U*diag(sval)*U^T */
TEN_M2T(ten, matA);
partIdx = soidDoit(obj, lookSoid,
gtype, gamma, res,
(AIR_EXISTS(AB[0]) && AIR_EXISTS(AB[1])) ? AB : NULL,
ten);
if (1 == escl[0]) {
scalingMatrix(matB, escl + 1, escl[4]);
ELL_43M_INSET(matBf, matB);
limnObjectPartTransform(obj, partIdx, matBf);
}
/* this is a rotate on the geomtry; nothing to do with the tensor */
ELL_4V_SET(qq, 1, pp[0], pp[1], pp[2]);
ELL_4V_NORM(qq, qq, len);
ell_q_to_3m_f(mR, qq);
ELL_43M_INSET(matBf, mR);
limnObjectPartTransform(obj, partIdx, matBf);
if (rad) {
partIdx = limnObjectCylinderAdd(obj, lookRod, 0, res);
ELL_4M_IDENTITY_SET(matAf);
ELL_4M_SCALE_SET(matBf, (1-eval[0])/2, rad, rad);
ell_4m_post_mul_f(matAf, matBf);
ELL_4M_TRANSLATE_SET(matBf, (1+eval[0])/2, 0.0, 0.0);
ell_4m_post_mul_f(matAf, matBf);
limnObjectPartTransform(obj, partIdx, matAf);
partIdx = limnObjectCylinderAdd(obj, lookRod, 0, res);
ELL_4M_IDENTITY_SET(matAf);
ELL_4M_SCALE_SET(matBf, (1-eval[0])/2, rad, rad);
ell_4m_post_mul_f(matAf, matBf);
ELL_4M_TRANSLATE_SET(matBf, -(1+eval[0])/2, 0.0, 0.0);
ell_4m_post_mul_f(matAf, matBf);
limnObjectPartTransform(obj, partIdx, matAf);
partIdx = limnObjectCylinderAdd(obj, lookRod, 1, res);
ELL_4M_IDENTITY_SET(matAf);
ELL_4M_SCALE_SET(matBf, rad, (1-eval[1])/2, rad);
ell_4m_post_mul_f(matAf, matBf);
ELL_4M_TRANSLATE_SET(matBf, 0.0, (1+eval[1])/2, 0.0);
ell_4m_post_mul_f(matAf, matBf);
limnObjectPartTransform(obj, partIdx, matAf);
partIdx = limnObjectCylinderAdd(obj, lookRod, 1, res);
ELL_4M_IDENTITY_SET(matAf);
ELL_4M_SCALE_SET(matBf, rad, (1-eval[1])/2, rad);
ell_4m_post_mul_f(matAf, matBf);
ELL_4M_TRANSLATE_SET(matBf, 0.0, -(1+eval[1])/2, 0.0);
ell_4m_post_mul_f(matAf, matBf);
limnObjectPartTransform(obj, partIdx, matAf);
partIdx = limnObjectCylinderAdd(obj, lookRod, 2, res);
ELL_4M_IDENTITY_SET(matAf);
ELL_4M_SCALE_SET(matBf, rad, rad, (1-eval[2])/2);
ell_4m_post_mul_f(matAf, matBf);
ELL_4M_TRANSLATE_SET(matBf, 0.0, 0.0, (1+eval[2])/2);
ell_4m_post_mul_f(matAf, matBf);
limnObjectPartTransform(obj, partIdx, matAf);
partIdx = limnObjectCylinderAdd(obj, lookRod, 2, res);
ELL_4M_IDENTITY_SET(matAf);
ELL_4M_SCALE_SET(matBf, rad, rad, (1-eval[2])/2);
ell_4m_post_mul_f(matAf, matBf);
ELL_4M_TRANSLATE_SET(matBf, 0.0, 0.0, -(1+eval[2])/2);
ell_4m_post_mul_f(matAf, matBf);
limnObjectPartTransform(obj, partIdx, matAf);
}
file = airFopen(outS, stdout, "w");
airMopAdd(mop, file, (airMopper)airFclose, airMopAlways);
if (limnObjectWriteOFF(file, obj)) {
airMopAdd(mop, err = biffGetDone(LIMN), airFree, airMopAlways);
fprintf(stderr, "%s: trouble:\n%s\n", me, err);
airMopError(mop); return 1;
}
airMopOkay(mop);
return 0;
}
int
main(int argc, const char *argv[]) {
const char *me;
char *err, *outS;
double scale[3], matA[9], matB[9], matC[9], sval[3], uu[9], vv[9];
float matAf[9], matBf[16];
float p[3], q[4], mR[9], len, gamma;
float os, vs, rad, AB[2], ten[7], view[3];
hestOpt *hopt=NULL;
airArray *mop;
limnObject *obj;
limnLook *look; int lookRod, lookSoid;
int partIdx=-1; /* sssh */
int res, sphere;
FILE *file;
me = argv[0];
hestOptAdd(&hopt, "sc", "scalings", airTypeDouble, 3, 3, scale, "1 1 1",
"axis-aligned scaling to do on ellipsoid");
hestOptAdd(&hopt, "AB", "A, B exponents", airTypeFloat, 2, 2, AB, "nan nan",
"Directly set the A, B parameters to the superquadric surface, "
"over-riding the default behavior of determining them from the "
"scalings \"-sc\" as superquadric tensor glyphs");
hestOptAdd(&hopt, "os", "over-all scaling", airTypeFloat, 1, 1, &os, "1",
"over-all scaling (multiplied by scalings)");
hestOptAdd(&hopt, "vs", "over-all scaling", airTypeFloat, 1, 1, &vs, "1",
"scaling along view-direction (to show off bas-relief "
"ambibuity of ellipsoids versus superquads)");
hestOptAdd(&hopt, "fr", "from (eye) point", airTypeFloat, 3, 3, &view,
"4 4 4", "eye point, needed for non-unity \"-vs\"");
hestOptAdd(&hopt, "gamma", "superquad sharpness", airTypeFloat, 1, 1,
&gamma, "0",
"how much to sharpen edges as a "
"function of differences between eigenvalues");
hestOptAdd(&hopt, "sphere", NULL, airTypeInt, 0, 0, &sphere, NULL,
"use a sphere instead of a superquadric");
hestOptAdd(&hopt, "p", "x y z", airTypeFloat, 3, 3, p, "0 0 0",
"location in quaternion quotient space");
hestOptAdd(&hopt, "r", "radius", airTypeFloat, 1, 1, &rad, "0.015",
"black axis cylinder radius (or 0.0 to not drawn these)");
hestOptAdd(&hopt, "res", "resolution", airTypeInt, 1, 1, &res, "25",
"tesselation resolution for both glyph and axis cylinders");
hestOptAdd(&hopt, "o", "output OFF", airTypeString, 1, 1, &outS, "out.off",
"output file to save OFF into");
hestParseOrDie(hopt, argc-1, argv+1, NULL,
me, info, AIR_TRUE, AIR_TRUE, AIR_TRUE);
mop = airMopNew();
airMopAdd(mop, hopt, (airMopper)hestOptFree, airMopAlways);
airMopAdd(mop, hopt, (airMopper)hestParseFree, airMopAlways);
obj = limnObjectNew(1000, AIR_TRUE);
airMopAdd(mop, obj, (airMopper)limnObjectNix, airMopAlways);
/* create limnLooks for ellipsoid and for rods */
lookSoid = limnObjectLookAdd(obj);
look = obj->look + lookSoid;
ELL_4V_SET(look->rgba, 1, 1, 1, 1);
ELL_3V_SET(look->kads, 0.2, 0.8, 0);
look->spow = 0;
lookRod = limnObjectLookAdd(obj);
look = obj->look + lookRod;
ELL_4V_SET(look->rgba, 0, 0, 0, 1);
ELL_3V_SET(look->kads, 1, 0, 0);
look->spow = 0;
ELL_3M_IDENTITY_SET(matA);
ELL_3V_SCALE(scale, os, scale);
ELL_3M_SCALE_SET(matB, scale[0], scale[1], scale[2]);
ell_3m_post_mul_d(matA, matB);
if (1 != vs) {
ELL_3V_NORM(view, view, len);
if (!len) {
/* HEY: perhaps do more diplomatic error message here */
fprintf(stderr, "%s: stupido!\n", me);
exit(1);
}
ELL_3MV_OUTER(matB, view, view);
ELL_3M_SCALE(matB, vs-1, matB);
ELL_3M_IDENTITY_SET(matC);
ELL_3M_ADD2(matB, matC, matB);
ell_3m_post_mul_d(matA, matB);
}
ell_3m_svd_d(uu, sval, vv, matA, AIR_TRUE);
/*
fprintf(stderr, "%s: ____________________________________\n", me);
fprintf(stderr, "%s: mat = \n", me);
ell_3m_print_d(stderr, matA);
fprintf(stderr, "%s: uu = \n", me);
ell_3m_print_d(stderr, uu);
ELL_3M_TRANSPOSE(matC, uu);
ELL_3M_MUL(matB, uu, matC);
fprintf(stderr, "%s: uu * uu^T = \n", me);
ell_3m_print_d(stderr, matB);
fprintf(stderr, "%s: sval = %g %g %g\n", me, sval[0], sval[1], sval[2]);
fprintf(stderr, "%s: vv = \n", me);
ell_3m_print_d(stderr, vv);
ELL_3M_MUL(matB, vv, vv);
fprintf(stderr, "%s: vv * vv^T = \n", me);
ELL_3M_TRANSPOSE(matC, vv);
ELL_3M_MUL(matB, vv, matC);
ell_3m_print_d(stderr, matB);
ELL_3M_IDENTITY_SET(matA);
ell_3m_pre_mul_d(matA, uu);
ELL_3M_SCALE_SET(matB, sval[0], sval[1], sval[2]);
ell_3m_pre_mul_d(matA, matB);
ell_3m_pre_mul_d(matA, vv);
fprintf(stderr, "%s: uu * diag(sval) * vv = \n", me);
ell_3m_print_d(stderr, matA);
fprintf(stderr, "%s: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n", me);
*/
ELL_3M_IDENTITY_SET(matA);
ell_3m_pre_mul_d(matA, uu);
ELL_3M_SCALE_SET(matB, sval[0], sval[1], sval[2]);
ell_3m_pre_mul_d(matA, matB);
ELL_3M_TRANSPOSE(matB, uu);
ell_3m_pre_mul_d(matA, matB);
TEN_M2T(ten, matA);
partIdx = soidDoit(obj, lookSoid,
sphere, gamma, res,
(AIR_EXISTS(AB[0]) && AIR_EXISTS(AB[1])) ? AB : NULL,
ten);
ELL_4V_SET(q, 1, p[0], p[1], p[2]);
ELL_4V_NORM(q, q, len);
ell_q_to_3m_f(mR, q);
ELL_43M_INSET(matBf, mR);
limnObjectPartTransform(obj, partIdx, matBf);
if (rad) {
partIdx = limnObjectCylinderAdd(obj, lookRod, 0, res);
ELL_4M_IDENTITY_SET(matAf);
ELL_4M_SCALE_SET(matBf, (1-scale[0])/2, rad, rad);
ell_4m_post_mul_f(matAf, matBf);
ELL_4M_TRANSLATE_SET(matBf, (1+scale[0])/2, 0.0, 0.0);
ell_4m_post_mul_f(matAf, matBf);
limnObjectPartTransform(obj, partIdx, matAf);
partIdx = limnObjectCylinderAdd(obj, lookRod, 0, res);
ELL_4M_IDENTITY_SET(matAf);
ELL_4M_SCALE_SET(matBf, (1-scale[0])/2, rad, rad);
ell_4m_post_mul_f(matAf, matBf);
ELL_4M_TRANSLATE_SET(matBf, -(1+scale[0])/2, 0.0, 0.0);
ell_4m_post_mul_f(matAf, matBf);
limnObjectPartTransform(obj, partIdx, matAf);
partIdx = limnObjectCylinderAdd(obj, lookRod, 1, res);
ELL_4M_IDENTITY_SET(matAf);
ELL_4M_SCALE_SET(matBf, rad, (1-scale[1])/2, rad);
ell_4m_post_mul_f(matAf, matBf);
ELL_4M_TRANSLATE_SET(matBf, 0.0, (1+scale[1])/2, 0.0);
ell_4m_post_mul_f(matAf, matBf);
limnObjectPartTransform(obj, partIdx, matAf);
partIdx = limnObjectCylinderAdd(obj, lookRod, 1, res);
ELL_4M_IDENTITY_SET(matAf);
ELL_4M_SCALE_SET(matBf, rad, (1-scale[1])/2, rad);
ell_4m_post_mul_f(matAf, matBf);
ELL_4M_TRANSLATE_SET(matBf, 0.0, -(1+scale[1])/2, 0.0);
ell_4m_post_mul_f(matAf, matBf);
limnObjectPartTransform(obj, partIdx, matAf);
partIdx = limnObjectCylinderAdd(obj, lookRod, 2, res);
ELL_4M_IDENTITY_SET(matAf);
ELL_4M_SCALE_SET(matBf, rad, rad, (1-scale[2])/2);
ell_4m_post_mul_f(matAf, matBf);
ELL_4M_TRANSLATE_SET(matBf, 0.0, 0.0, (1+scale[2])/2);
ell_4m_post_mul_f(matAf, matBf);
limnObjectPartTransform(obj, partIdx, matAf);
partIdx = limnObjectCylinderAdd(obj, lookRod, 2, res);
ELL_4M_IDENTITY_SET(matAf);
ELL_4M_SCALE_SET(matBf, rad, rad, (1-scale[2])/2);
ell_4m_post_mul_f(matAf, matBf);
ELL_4M_TRANSLATE_SET(matBf, 0.0, 0.0, -(1+scale[2])/2);
ell_4m_post_mul_f(matAf, matBf);
limnObjectPartTransform(obj, partIdx, matAf);
}
file = airFopen(outS, stdout, "w");
airMopAdd(mop, file, (airMopper)airFclose, airMopAlways);
if (limnObjectWriteOFF(file, obj)) {
airMopAdd(mop, err = biffGetDone(LIMN), airFree, airMopAlways);
fprintf(stderr, "%s: trouble:\n%s\n", me, err);
airMopError(mop); return 1;
}
airMopOkay(mop);
return 0;
}
int
main(int argc, const char *argv[]) {
const char *me;
hestOpt *hopt=NULL;
airArray *mop;
double _tt[6], tt[7], ss, pp[3], qq[4], rot[9], mat1[9], mat2[9], tmp,
evalA[3], evecA[9], evalB[3], evecB[9];
int roots;
mop = airMopNew();
me = argv[0];
hestOptAdd(&hopt, NULL, "m00 m01 m02 m11 m12 m22",
airTypeDouble, 6, 6, _tt, NULL, "symmtric matrix coeffs");
hestOptAdd(&hopt, "p", "vec", airTypeDouble, 3, 3, pp, "0 0 0",
"rotation as P vector");
hestOptAdd(&hopt, "s", "scl", airTypeDouble, 1, 1, &ss, "1.0",
"scaling");
hestParseOrDie(hopt, argc-1, argv+1, NULL,
me, info, AIR_TRUE, AIR_TRUE, AIR_TRUE);
airMopAdd(mop, hopt, (airMopper)hestOptFree, airMopAlways);
airMopAdd(mop, hopt, (airMopper)hestParseFree, airMopAlways);
ELL_6V_COPY(tt + 1, _tt);
tt[0] = 1.0;
TEN_T_SCALE(tt, ss, tt);
ELL_4V_SET(qq, 1, pp[0], pp[1], pp[2]);
ELL_4V_NORM(qq, qq, tmp);
ell_q_to_3m_d(rot, qq);
printf("%s: rot\n", me);
printf(" %g %g %g\n", rot[0], rot[1], rot[2]);
printf(" %g %g %g\n", rot[3], rot[4], rot[5]);
printf(" %g %g %g\n", rot[6], rot[7], rot[8]);
TEN_T2M(mat1, tt);
ell_3m_mul_d(mat2, rot, mat1);
ELL_3M_TRANSPOSE_IP(rot, tmp);
ell_3m_mul_d(mat1, mat2, rot);
TEN_M2T(tt, mat1);
printf("input matrix = \n %g %g %g\n %g %g\n %g\n",
tt[1], tt[2], tt[3], tt[4], tt[5], tt[6]);
printf("================== tenEigensolve_d ==================\n");
roots = tenEigensolve_d(evalA, evecA, tt);
printf("%s roots\n", airEnumStr(ell_cubic_root, roots));
testeigen(tt, evalA, evecA);
printf("================== new eigensolve ==================\n");
roots = evals(evalB, tt[1], tt[2], tt[3], tt[4], tt[5], tt[6]);
printf("%s roots: %g %g %g\n", airEnumStr(ell_cubic_root, roots),
evalB[0], evalB[1], evalB[2]);
roots = evals_evecs(evalB, evecB,
tt[1], tt[2], tt[3], tt[4], tt[5], tt[6]);
printf("%s roots\n", airEnumStr(ell_cubic_root, roots));
testeigen(tt, evalB, evecB);
airMopOkay(mop);
return 0;
}
static int
csimDo(double tm[7], double tcov[21], double rm[3], double rv[3],
Nrrd *ntbuff, tenEstimateContext *tec, double *dwibuff, double sigma,
double bvalue, double B0, unsigned int NN, int randrot,
double _tenOrig[7]) {
char me[]="csimDo", err[BIFF_STRLEN];
double *tbuff;
unsigned int II, taa, tbb, cc;
if (!(ntbuff
&& ntbuff->data
&& 2 == ntbuff->dim
&& 7 == ntbuff->axis[0].size
&& NN == ntbuff->axis[1].size)) {
sprintf(err, "%s: ntbuff not allocated for 2-by-%u array of %s", me,
NN, airEnumStr(nrrdType, nrrdTypeDouble));
biffAdd(TEN, err); return 1;
}
/* find all tensors from simulated DWIs */
tbuff = AIR_CAST(double *, ntbuff->data);
for (II=0; II<NN; II++) {
double tenOrig[7], rotf[9], rotb[9], matA[9], matB[9], qq[4], tmp;
ELL_3M_IDENTITY_SET(rotf); /* sssh warnings */
ELL_3M_IDENTITY_SET(rotb); /* sssh warnings */
if (randrot) {
if (1) {
double eval[3], evec[9], eps, ma[9], mb[9], rf[9], rb[9];
tenEigensolve_d(eval, evec, _tenOrig);
airNormalRand(&eps, NULL);
ell_aa_to_3m_d(rf, 0*eps/20, evec + 0);
TEN_T_SCALE_INCR(_tenOrig, 0*eps/30, _tenOrig);
TEN_T2M(ma, _tenOrig);
ELL_3M_TRANSPOSE(rb, rf);
ELL_3M_MUL(mb, ma, rf);
ELL_3M_MUL(ma, rb, mb);
TEN_M2T(_tenOrig, ma);
}
TEN_T2M(matA, _tenOrig);
airNormalRand(qq+0, qq+1);
airNormalRand(qq+2, qq+3);
ELL_4V_NORM(qq, qq, tmp);
ell_q_to_3m_d(rotf, qq);
ELL_3M_TRANSPOSE(rotb, rotf);
ELL_3M_MUL(matB, matA, rotf);
ELL_3M_MUL(matA, rotb, matB);
TEN_M2T(tenOrig, matA);
} else {
TEN_T_COPY(tenOrig, _tenOrig);
}
if (tenEstimate1TensorSimulateSingle_d(tec, dwibuff, sigma,
bvalue, B0, tenOrig)
|| tenEstimate1TensorSingle_d(tec, tbuff, dwibuff)) {
sprintf(err, "%s: trouble on exp %u/%u", me, II, NN);
biffAdd(TEN, err); return 1;
}
if (randrot) {
TEN_T2M(matA, tbuff);
ELL_3M_MUL(matB, matA, rotb);
ELL_3M_MUL(matA, rotf, matB);
TEN_M2T(tbuff, matA);
} /* else we leave tbuff as it is */
/*
if (_tenOrig[0] > 0.5) {
double tdiff[7];
TEN_T_SUB(tdiff, _tenOrig, tbuff);
fprintf(stderr, "!%s: %g\n"
" (%g) %g,%g,%g %g,%g %g\n"
" (%g) %g,%g,%g %g,%g %g\n",
me, TEN_T_NORM(tdiff),
_tenOrig[0], _tenOrig[1], _tenOrig[2], _tenOrig[3], _tenOrig[4],
_tenOrig[5], _tenOrig[6],
tbuff[0], tbuff[1], tbuff[2], tbuff[3], tbuff[4],
tbuff[5], tbuff[6]);
}
*/
tbuff += 7;
}
/* find mean tensor, and mean R_i */
tbuff = AIR_CAST(double *, ntbuff->data);
TEN_T_SET(tm, 0, 0, 0, 0, 0, 0, 0);
ELL_3V_SET(rm, 0, 0, 0);
for (II=0; II<NN; II++) {
TEN_T_INCR(tm, tbuff);
rm[0] += sqrt(_tenAnisoTen_d[tenAniso_S](tbuff));
rm[1] += _tenAnisoTen_d[tenAniso_FA](tbuff);
rm[2] += _tenAnisoTen_d[tenAniso_Mode](tbuff);
tbuff += 7;
}
rm[0] /= NN;
rm[1] /= NN;
rm[2] /= NN;
TEN_T_SCALE(tm, 1.0/NN, tm);
/* accumulate covariance tensor, and R_i variances */
for (cc=0; cc<21; cc++) {
tcov[cc] = 0;
}
ELL_3V_SET(rv, 0, 0, 0);
tbuff = AIR_CAST(double *, ntbuff->data);
for (II=0; II<NN; II++) {
double r[3];
r[0] = sqrt(_tenAnisoTen_d[tenAniso_S](tbuff));
r[1] = _tenAnisoTen_d[tenAniso_FA](tbuff);
r[2] = _tenAnisoTen_d[tenAniso_Mode](tbuff);
cc = 0;
rv[0] += (r[0] - rm[0])*(r[0] - rm[0])/(NN-1);
rv[1] += (r[1] - rm[1])*(r[1] - rm[1])/(NN-1);
rv[2] += (r[2] - rm[2])*(r[2] - rm[2])/(NN-1);
for (taa=0; taa<6; taa++) {
for (tbb=taa; tbb<6; tbb++) {
tcov[cc] += (10000*(tbuff[taa+1]-tm[taa+1])
*10000*(tbuff[tbb+1]-tm[tbb+1])/(NN-1));
cc++;
}
}
tbuff += 7;
}
return 0;
}