/*
** creaseProj
**
** eigenvectors (with non-zero eigenvalues) of output posproj are
** tangents to the directions along which particle is allowed to move
** *downward* (in height) for constraint satisfaction (according to
** tangent 1 or tangents 1&2)
**
** negproj is the same, but for points moving upwards (according to
** negativetangent1 or negativetangent 1&2)
*/
static void
creaseProj(pullTask *task, pullPoint *point,
int tang1Use, int tang2Use,
int negtang1Use, int negtang2Use,
/* output */
double posproj[9], double negproj[9]) {
#if PRAYING
static const char me[]="creaseProj";
#endif
double pp[9];
double *tng;
ELL_3M_ZERO_SET(posproj);
if (tang1Use) {
tng = point->info + task->pctx->infoIdx[pullInfoTangent1];
#if PRAYING
fprintf(stderr, "!%s: tng1 = %g %g %g\n", me, tng[0], tng[1], tng[2]);
#endif
ELL_3MV_OUTER(pp, tng, tng);
ELL_3M_ADD2(posproj, posproj, pp);
}
if (tang2Use) {
tng = point->info + task->pctx->infoIdx[pullInfoTangent2];
ELL_3MV_OUTER(pp, tng, tng);
ELL_3M_ADD2(posproj, posproj, pp);
}
ELL_3M_ZERO_SET(negproj);
if (negtang1Use) {
tng = point->info + task->pctx->infoIdx[pullInfoNegativeTangent1];
ELL_3MV_OUTER(pp, tng, tng);
ELL_3M_ADD2(negproj, negproj, pp);
}
if (negtang2Use) {
tng = point->info + task->pctx->infoIdx[pullInfoNegativeTangent2];
ELL_3MV_OUTER(pp, tng, tng);
ELL_3M_ADD2(negproj, negproj, pp);
}
if (!tang1Use && !tang2Use && !negtang1Use && !negtang2Use) {
/* we must be after points, and so need freedom to go after them */
/* for now we do this via posproj not negproj; see haveNada below */
ELL_3M_IDENTITY_SET(posproj);
}
return;
}
static void
scalingMatrix(double mat[9], double vec[3], double scl) {
double dir[3], tmp[9], len;
ELL_3V_NORM(dir, vec, len);
ELL_3MV_OUTER(tmp, dir, dir);
ELL_3M_SCALE(tmp, scl-1, tmp);
ELL_3M_IDENTITY_SET(mat);
ELL_3M_ADD2(mat, mat, tmp);
return;
}
/*
** _pullConstraintTangent
**
** eigenvectors (with non-zero eigenvalues) of output proj are
** (hopefully) approximate tangents to the manifold to which particles
** are constrained. It is *not* the local tangent of the directions
** along which particles are allowed to move during constraint
** satisfaction (that is given by creaseProj for creases)
**
** this can assume that probe() has just been called
*/
void
_pullConstraintTangent(pullTask *task, pullPoint *point,
/* output */
double proj[9]) {
double vec[4], nvec[3], outer[9], len, posproj[9], negproj[9];
ELL_3M_IDENTITY_SET(proj); /* NOTE: we are starting with identity . . . */
switch (task->pctx->constraint) {
case pullInfoHeight:
creaseProj(task, point,
!!task->pctx->ispec[pullInfoTangent1],
!!task->pctx->ispec[pullInfoTangent2],
!!task->pctx->ispec[pullInfoNegativeTangent1],
!!task->pctx->ispec[pullInfoNegativeTangent2],
posproj, negproj);
/* .. and subracting out output from creaseProj */
ELL_3M_SUB(proj, proj, posproj);
ELL_3M_SUB(proj, proj, negproj);
break;
case pullInfoHeightLaplacian:
case pullInfoIsovalue:
if (pullInfoHeightLaplacian == task->pctx->constraint) {
/* using gradient of height as approx normal to laplacian 0-crossing */
pullPointScalar(task->pctx, point, pullInfoHeight, vec, NULL);
} else {
pullPointScalar(task->pctx, point, pullInfoIsovalue, vec, NULL);
}
ELL_3V_NORM(nvec, vec, len);
if (len) {
/* .. or and subracting out tensor product of normal with itself */
ELL_3MV_OUTER(outer, nvec, nvec);
ELL_3M_SUB(proj, proj, outer);
}
break;
}
return;
}
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;
}
/* Calculates 2 new centroids (and a new segmentation) from distances
between Q-balls and centroids, returns true if segmentation changed
*/
int
_tenCalccent2(const int gradcount, const double qpoints[],
const double dists[], double centroid[6], unsigned int seg[]) {
#if 0
/* HEY: Attempt to implement better line-adding by adding
outerproducts of points and estimating major eigenvector
afterwards */
int i,changed=AIR_FALSE;
double sum0[9],sum1[9],mat[9], eval[3],evec[9];
ELL_3M_ZERO_SET( sum0 );
ELL_3M_ZERO_SET( sum1 );
for( i = 0; i < gradcount; i++ ) {
if( dists[i] < dists[gradcount+i] ) {
ELL_3MV_OUTER( mat, qpoints +3*i, qpoints +3*i );
ELL_3M_ADD2( sum0, sum0, mat );
changed = changed || (seg[i] != 0);
seg[i] = 0;
} else {
ELL_3MV_OUTER( mat, qpoints +3*i +gradcount, qpoints +3*i +gradcount );
ELL_3M_ADD2( sum1, sum1, mat );
changed = changed || (seg[i] != 1);
seg[i] = 1;
}
}
ell_3m_eigensolve_d( eval, evec, sum0, 0 );
ELL_3V_COPY( centroid, evec + 3*ELL_MAX3_IDX( eval[0], eval[1], eval[2] ) );
/* ELL_3V_SCALE( centroid, ELL_3V_LEN( centroid ), centroid ); */
ell_3m_eigensolve_d( eval, evec, sum1, 0 );
ELL_3V_COPY( centroid +3, evec + 3*ELL_MAX3_IDX( eval[0], eval[1], eval[2] ) );
/* ELL_3V_SCALE( centroid +3, ELL_3V_LEN( centroid ), centroid +3); Normalize */
return changed;
#endif
int i, sign, seg0count=0, seg1count=0, changed=AIR_FALSE;
double oldcentroid[6], diff[3], sum[3];
memcpy( oldcentroid, centroid, 6 * sizeof( double ));
for( i = 0; i < gradcount; i++ ) {
if( dists[ 0*gradcount +i] < dists[1*gradcount +i] ) {
/* Try to resolve sign so that centroid do not end up as all 0 */
/* Choose signs so that the point lies "on the same side" as */
/* the previous centroid. */
diff[0] = oldcentroid[0] - qpoints[3*i +0];
diff[1] = oldcentroid[1] - qpoints[3*i +1];
diff[2] = oldcentroid[2] - qpoints[3*i +2];
sum[0] = oldcentroid[0] + qpoints[3*i +0];
sum[1] = oldcentroid[1] + qpoints[3*i +1];
sum[2] = oldcentroid[2] + qpoints[3*i +2];
sign = (diff[0]*diff[0] + diff[1]*diff[1] + diff[2]*diff[2]) <
(sum[0]*sum[0] + sum[1]*sum[1] + sum[2]*sum[2]) ? -1 : +1;
changed = changed || (seg[i] != 0);
seg[i] = 0;
centroid[0] += sign * qpoints[3*i +0];
centroid[1] += sign * qpoints[3*i +1];
centroid[2] += sign * qpoints[3*i +2];
seg0count++;
} else {
diff[0] = oldcentroid[3+0] - qpoints[3*i +0];
diff[1] = oldcentroid[3+1] - qpoints[3*i +1];
diff[2] = oldcentroid[3+2] - qpoints[3*i +2];
sum[0] = oldcentroid[3+0] + qpoints[3*i +0];
sum[1] = oldcentroid[3+1] + qpoints[3*i +1];
sum[2] = oldcentroid[3+2] + qpoints[3*i +2];
sign = (diff[0]*diff[0] + diff[1]*diff[1] + diff[2]*diff[2]) <
(sum[0]*sum[0] + sum[1]*sum[1] + sum[2]*sum[2]) ? -1 : +1;
changed = changed || (seg[i] != 1);
seg[i] = 1;
centroid[3+0] += sign * qpoints[3*i +0];
centroid[3+1] += sign * qpoints[3*i +1];
centroid[3+2] += sign * qpoints[3*i +2];
seg1count++;
}
}
centroid[0] /= seg0count;
centroid[1] /= seg0count;
centroid[2] /= seg0count;
centroid[3+0] /= seg1count;
centroid[3+1] /= seg1count;
centroid[3+2] /= seg1count;
/* printf("cent = %f %f %f %f %f %f\n", centroid[0],centroid[1],centroid[2],centroid[3],centroid[4],centroid[5] ); */
/*
Should give error if any segment contains less than 6 elements,
i.e. if( seg0count < 6 || seg1count < 6 ), since that would
imply that a tensor cannot be computed for that segment.
*/
return changed;
}
void
_gageSclAnswer (gageContext *ctx, gagePerVolume *pvl) {
char me[]="_gageSclAnswer";
double gmag=0, *hess, *norm, *gvec, *gten, *k1, *k2, curv=0,
sHess[9]={0,0,0,0,0,0,0,0,0};
double tmpMat[9], tmpVec[3], hevec[9], heval[3];
double len, gp1[3], gp2[3], *nPerp, ncTen[9], nProj[9]={0,0,0,0,0,0,0,0,0};
double alpha = 0.5;
double beta = 0.5;
double gamma = 5;
double cc = 1e-6;
#define FD_MEDIAN_MAX 16
int fd, nidx, xi, yi, zi;
double *fw, iv3wght[2*FD_MEDIAN_MAX*FD_MEDIAN_MAX*FD_MEDIAN_MAX],
wghtSum, wght;
/* convenience pointers for work below */
hess = pvl->directAnswer[gageSclHessian];
gvec = pvl->directAnswer[gageSclGradVec];
norm = pvl->directAnswer[gageSclNormal];
nPerp = pvl->directAnswer[gageSclNPerp];
gten = pvl->directAnswer[gageSclGeomTens];
k1 = pvl->directAnswer[gageSclK1];
k2 = pvl->directAnswer[gageSclK2];
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageSclValue)) {
/* done if doV */
if (ctx->verbose) {
fprintf(stderr, "%s: val = % 15.7f\n", me,
(double)(pvl->directAnswer[gageSclValue][0]));
}
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageSclGradVec)) {
/* done if doD1 */
if (ctx->verbose) {
fprintf(stderr, "%s: gvec = ", me);
ell_3v_print_d(stderr, gvec);
}
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageSclGradMag)) {
/* this is the true value of gradient magnitude */
gmag = pvl->directAnswer[gageSclGradMag][0] = sqrt(ELL_3V_DOT(gvec, gvec));
}
/* NB: it would seem that gageParmGradMagMin is completely ignored ... */
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageSclNormal)) {
if (gmag) {
ELL_3V_SCALE(norm, 1/gmag, gvec);
/* polishing ...
len = sqrt(ELL_3V_DOT(norm, norm));
ELL_3V_SCALE(norm, 1/len, norm);
*/
} else {
ELL_3V_COPY(norm, gageZeroNormal);
}
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageSclNPerp)) {
/* nPerp = I - outer(norm, norm) */
/* NB: this sets both nPerp and nProj */
ELL_3MV_OUTER(nProj, norm, norm);
ELL_3M_SCALE(nPerp, -1, nProj);
nPerp[0] += 1;
nPerp[4] += 1;
nPerp[8] += 1;
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageSclHessian)) {
/* done if doD2 */
if (ctx->verbose) {
fprintf(stderr, "%s: hess = \n", me);
ell_3m_print_d(stderr, hess);
}
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageSclLaplacian)) {
pvl->directAnswer[gageSclLaplacian][0] = hess[0] + hess[4] + hess[8];
if (ctx->verbose) {
fprintf(stderr, "%s: lapl = %g + %g + %g = %g\n", me,
hess[0], hess[4], hess[8],
pvl->directAnswer[gageSclLaplacian][0]);
}
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageSclHessFrob)) {
pvl->directAnswer[gageSclHessFrob][0] = ELL_3M_FROB(hess);
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageSclHessEval)) {
/* HEY: look at the return value for root multiplicity? */
ell_3m_eigensolve_d(heval, hevec, hess, AIR_TRUE);
ELL_3V_COPY(pvl->directAnswer[gageSclHessEval], heval);
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageSclHessEvec)) {
ELL_3M_COPY(pvl->directAnswer[gageSclHessEvec], hevec);
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageSclHessRidgeness)) {
double A, B, S;
if (heval[1] >0 || heval[2]>0) {
pvl->directAnswer[gageSclHessRidgeness][0] = 0;
}
else if (AIR_ABS(heval[1])<1e-10 || AIR_ABS(heval[2])<1e-10) {
pvl->directAnswer[gageSclHessRidgeness][0] = 0;
}
else {
double *ans;
A = AIR_ABS(heval[1])/AIR_ABS(heval[2]);
B = AIR_ABS(heval[0])/sqrt(AIR_ABS(heval[1]*heval[2]));
S = sqrt(heval[0]*heval[0] + heval[1]*heval[1] + heval[2]*heval[2]);
ans = pvl->directAnswer[gageSclHessRidgeness];
ans[0] = (1-exp(-A*A/(2*alpha*alpha))) *
exp(-B*B/(2*beta*beta)) *
(1-exp(-S*S/(2*gamma*gamma))) *
exp(-2*cc*cc/(AIR_ABS(heval[1])*heval[2]*heval[2]));
}
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageSclHessValleyness)) {
double A, B, S;
if (heval[0] <0 || heval[1]<0) {
pvl->directAnswer[gageSclHessValleyness][0] = 0;
}
else if (AIR_ABS(heval[0])<1e-10 || AIR_ABS(heval[1])<1e-10) {
pvl->directAnswer[gageSclHessValleyness][0] = 0;
}
else {
double *ans;
A = AIR_ABS(heval[1])/AIR_ABS(heval[0]);
B = AIR_ABS(heval[2])/sqrt(AIR_ABS(heval[1]*heval[0]));
S = sqrt(heval[0]*heval[0] + heval[1]*heval[1] + heval[2]*heval[2]);
ans = pvl->directAnswer[gageSclHessValleyness];
ans[0] = (1-exp(-A*A/(2*alpha*alpha))) *
exp(-B*B/(2*beta*beta)) *
(1-exp(-S*S/(2*gamma*gamma))) *
exp(-2*cc*cc/(AIR_ABS(heval[1])*heval[0]*heval[0]));
}
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageSclHessMode)) {
pvl->directAnswer[gageSclHessMode][0] = airMode3_d(heval);
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageScl2ndDD)) {
ELL_3MV_MUL(tmpVec, hess, norm);
pvl->directAnswer[gageScl2ndDD][0] = ELL_3V_DOT(norm, tmpVec);
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageSclGeomTens)) {
if (gmag > ctx->parm.gradMagCurvMin) {
/* parm.curvNormalSide applied here to determine the sense of the
normal when doing all curvature calculations */
ELL_3M_SCALE(sHess, -(ctx->parm.curvNormalSide)/gmag, hess);
/* gten = nPerp * sHess * nPerp */
ELL_3M_MUL(tmpMat, sHess, nPerp);
ELL_3M_MUL(gten, nPerp, tmpMat);
if (ctx->verbose) {
fprintf(stderr, "%s: gten: \n", me);
ell_3m_print_d(stderr, gten);
ELL_3MV_MUL(tmpVec, gten, norm);
len = ELL_3V_LEN(tmpVec);
fprintf(stderr, "%s: should be small: %30.15f\n", me, (double)len);
ell_3v_perp_d(gp1, norm);
ELL_3MV_MUL(tmpVec, gten, gp1);
len = ELL_3V_LEN(tmpVec);
fprintf(stderr, "%s: should be bigger: %30.15f\n", me, (double)len);
ELL_3V_CROSS(gp2, gp1, norm);
ELL_3MV_MUL(tmpVec, gten, gp2);
len = ELL_3V_LEN(tmpVec);
fprintf(stderr, "%s: should (also) be bigger: %30.15f\n",
me, (double)len);
}
} else {
ELL_3M_ZERO_SET(gten);
}
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageSclTotalCurv)) {
curv = pvl->directAnswer[gageSclTotalCurv][0] = ELL_3M_FROB(gten);
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageSclShapeTrace)) {
pvl->directAnswer[gageSclShapeTrace][0] = (curv
? ELL_3M_TRACE(gten)/curv
: 0);
}
if ( (GAGE_QUERY_ITEM_TEST(pvl->query, gageSclK1)) ||
(GAGE_QUERY_ITEM_TEST(pvl->query, gageSclK2)) ){
double T, N, D;
T = ELL_3M_TRACE(gten);
N = curv;
D = 2*N*N - T*T;
/*
if (D < -0.0000001) {
fprintf(stderr, "%s: %g %g\n", me, T, N);
fprintf(stderr, "%s: !!! D curv determinant % 22.10f < 0.0\n", me, D);
fprintf(stderr, "%s: gten: \n", me);
ell_3m_print_d(stderr, gten);
}
*/
D = AIR_MAX(D, 0);
D = sqrt(D);
k1[0] = 0.5*(T + D);
k2[0] = 0.5*(T - D);
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageSclMeanCurv)) {
pvl->directAnswer[gageSclMeanCurv][0] = (*k1 + *k2)/2;
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageSclGaussCurv)) {
pvl->directAnswer[gageSclGaussCurv][0] = (*k1)*(*k2);
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageSclShapeIndex)) {
pvl->directAnswer[gageSclShapeIndex][0] =
-(2/AIR_PI)*atan2(*k1 + *k2, *k1 - *k2);
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageSclCurvDir1)) {
/* HEY: this only works when K1, K2, 0 are all well mutually distinct,
since these are the eigenvalues of the geometry tensor, and this
code assumes that the eigenspaces are all one-dimensional */
ELL_3M_COPY(tmpMat, gten);
ELL_3M_DIAG_SET(tmpMat, gten[0] - *k1, gten[4]- *k1, gten[8] - *k1);
ell_3m_1d_nullspace_d(tmpVec, tmpMat);
ELL_3V_COPY(pvl->directAnswer[gageSclCurvDir1], tmpVec);
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageSclCurvDir2)) {
/* HEY: this only works when K1, K2, 0 are all well mutually distinct,
since these are the eigenvalues of the geometry tensor, and this
code assumes that the eigenspaces are all one-dimensional */
ELL_3M_COPY(tmpMat, gten);
ELL_3M_DIAG_SET(tmpMat, gten[0] - *k2, gten[4] - *k2, gten[8] - *k2);
ell_3m_1d_nullspace_d(tmpVec, tmpMat);
ELL_3V_COPY(pvl->directAnswer[gageSclCurvDir2], tmpVec);
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageSclFlowlineCurv)) {
if (gmag >= ctx->parm.gradMagCurvMin) {
/* because of the gageSclGeomTens prerequisite, sHess, nPerp, and
nProj are all already set */
/* ncTen = nPerp * sHess * nProj */
ELL_3M_MUL(tmpMat, sHess, nProj);
ELL_3M_MUL(ncTen, nPerp, tmpMat);
} else {
ELL_3M_ZERO_SET(ncTen);
}
/* there used to be a wrong extra sqrt() here */
pvl->directAnswer[gageSclFlowlineCurv][0] = ELL_3M_FROB(ncTen);
}
if (GAGE_QUERY_ITEM_TEST(pvl->query, gageSclMedian)) {
/* this item is currently a complete oddball in that it does not
benefit from anything done in the "filter" stage, which is in
fact a waste of time if the query consists only of this item */
fd = 2*ctx->radius;
if (fd > FD_MEDIAN_MAX) {
fprintf(stderr, "%s: PANIC: current filter diameter = %d "
"> FD_MEDIAN_MAX = %d\n", me, fd, FD_MEDIAN_MAX);
exit(1);
}
fw = ctx->fw + fd*3*gageKernel00;
/* HEY: this needs some optimization help */
wghtSum = 0;
nidx = 0;
for (xi=0; xi<fd; xi++) {
for (yi=0; yi<fd; yi++) {
for (zi=0; zi<fd; zi++) {
iv3wght[0 + 2*nidx] = pvl->iv3[nidx];
iv3wght[1 + 2*nidx] = fw[xi + 0*fd]*fw[yi + 1*fd]*fw[zi + 2*fd];
wghtSum += iv3wght[1 + 2*nidx];
nidx++;
}
}
}
qsort(iv3wght, fd*fd*fd, 2*sizeof(double), nrrdValCompare[nrrdTypeDouble]);
wght = 0;
for (nidx=0; nidx<fd*fd*fd; nidx++) {
wght += iv3wght[1 + 2*nidx];
if (wght > wghtSum/2) {
break;
}
}
pvl->directAnswer[gageSclMedian][0] = iv3wght[0 + 2*nidx];
}
return;
}
