void
_coilKind7TensorFilterFinish(coil_t *delta, coil_t **iv3,
double spacing[3],
double parm[COIL_PARMS_NUM]) {
coil_t rspX, rspY, rspZ,
rspsqX, rspsqY, rspsqZ;
double eval[3], evec[9], tens[7], tengrad[21], grad[3], LL, KK,
cnd,
dmu1[7], dmu2[7], dskw[7], phi3[7];
rspX = AIR_CAST(coil_t, 1.0/spacing[0]); rspsqX = rspX*rspX;
rspY = AIR_CAST(coil_t, 1.0/spacing[1]); rspsqY = rspY*rspY;
rspZ = AIR_CAST(coil_t, 1.0/spacing[2]); rspsqZ = rspZ*rspZ;
TENS(tens, iv3);
TENGRAD(tengrad, iv3, rspX, rspY, rspZ);
tenEigensolve_d(eval, evec, tens);
tenInvariantGradientsK_d(dmu1, dmu2, dskw, tens, 0.000001);
tenRotationTangents_d(NULL, NULL, phi3, evec);
/* \midhat{\nabla} \mu_1 ----------------- */
ELL_3V_SET(grad,
TEN_T_DOT(dmu1, tengrad + 0*7),
TEN_T_DOT(dmu1, tengrad + 1*7),
TEN_T_DOT(dmu1, tengrad + 2*7));
LL = ELL_3V_DOT(grad,grad);
KK = parm[1]*parm[1];
cnd = _COIL_CONDUCT(LL, KK);
/* \midhat{\nabla} \mu_2 ----------------- */
ELL_3V_SET(grad,
TEN_T_DOT(dmu2, tengrad + 0*7),
TEN_T_DOT(dmu2, tengrad + 1*7),
TEN_T_DOT(dmu2, tengrad + 2*7));
LL = ELL_3V_DOT(grad,grad);
KK = parm[2]*parm[2];
cnd *= _COIL_CONDUCT(LL, KK);
/* \midhat{\nabla} \skw and twist! ----------------- */
ELL_3V_SET(grad,
TEN_T_DOT(dskw, tengrad + 0*7),
TEN_T_DOT(dskw, tengrad + 1*7),
TEN_T_DOT(dskw, tengrad + 2*7));
LL = ELL_3V_DOT(grad,grad);
ELL_3V_SET(grad,
TEN_T_DOT(phi3, tengrad + 0*7),
TEN_T_DOT(phi3, tengrad + 1*7),
TEN_T_DOT(phi3, tengrad + 2*7));
LL += ELL_3V_DOT(grad,grad);
KK = AIR_CAST(coil_t, parm[3]*parm[3]);
cnd *= _COIL_CONDUCT(LL, KK);
delta[0]= 0.0f;
delta[1]= AIR_CAST(coil_t, parm[0]*cnd*LAPL(iv3, 1, rspsqX, rspsqY, rspsqZ));
delta[2]= AIR_CAST(coil_t, parm[0]*cnd*LAPL(iv3, 2, rspsqX, rspsqY, rspsqZ));
delta[3]= AIR_CAST(coil_t, parm[0]*cnd*LAPL(iv3, 3, rspsqX, rspsqY, rspsqZ));
delta[4]= AIR_CAST(coil_t, parm[0]*cnd*LAPL(iv3, 4, rspsqX, rspsqY, rspsqZ));
delta[5]= AIR_CAST(coil_t, parm[0]*cnd*LAPL(iv3, 5, rspsqX, rspsqY, rspsqZ));
delta[6]= AIR_CAST(coil_t, parm[0]*cnd*LAPL(iv3, 6, rspsqX, rspsqY, rspsqZ));
}
void
_coilKindScalarFilterPeronaMalik(coil_t *delta, coil_t **iv3,
double spacing[3],
double parm[COIL_PARMS_NUM]) {
coil_t forwX[3], backX[3], forwY[3], backY[3], forwZ[3], backZ[3],
KK, rspX, rspY, rspZ;
/* reciprocals of spacings in X, Y, and Z */
rspX = AIR_CAST(coil_t, 1.0/spacing[0]);
rspY = AIR_CAST(coil_t, 1.0/spacing[1]);
rspZ = AIR_CAST(coil_t, 1.0/spacing[2]);
_coilKindScalar3x3x3Gradients(forwX, backX,
forwY, backY,
forwZ, backZ,
iv3,
rspX, rspY, rspZ);
/* compute fluxes */
KK = AIR_CAST(coil_t, parm[1]*parm[1]);
forwX[0] *= _COIL_CONDUCT(ELL_3V_DOT(forwX, forwX), KK);
forwY[1] *= _COIL_CONDUCT(ELL_3V_DOT(forwY, forwY), KK);
forwZ[2] *= _COIL_CONDUCT(ELL_3V_DOT(forwZ, forwZ), KK);
backX[0] *= _COIL_CONDUCT(ELL_3V_DOT(backX, backX), KK);
backY[1] *= _COIL_CONDUCT(ELL_3V_DOT(backY, backY), KK);
backZ[2] *= _COIL_CONDUCT(ELL_3V_DOT(backZ, backZ), KK);
delta[0] = AIR_CAST(coil_t, parm[0])*(rspX*(forwX[0] - backX[0])
+ rspY*(forwY[1] - backY[1])
+ rspZ*(forwZ[2] - backZ[2]));
}
void
_coilKindScalarFilterModifiedCurvature(coil_t *delta, coil_t **iv3,
double spacing[3],
double parm[COIL_PARMS_NUM]) {
coil_t forwX[3], backX[3], forwY[3], backY[3], forwZ[3], backZ[3],
grad[3], gm, eps, KK, LL, denom, rspX, rspY, rspZ, lerp;
/* reciprocals of spacings in X, Y, and Z */
rspX = AIR_CAST(coil_t, 1.0/spacing[0]);
rspY = AIR_CAST(coil_t, 1.0/spacing[1]);
rspZ = AIR_CAST(coil_t, 1.0/spacing[2]);
_coilKindScalar3x3x3Gradients(forwX, backX,
forwY, backY,
forwZ, backZ,
iv3,
rspX, rspY, rspZ);
grad[0] = rspX*(iv3[2][4] - iv3[0][4]);
grad[1] = rspY*(iv3[1][5] - iv3[1][3]);
grad[2] = rspZ*(iv3[1][7] - iv3[1][1]);
gm = AIR_CAST(coil_t, ELL_3V_LEN(grad));
/* compute fluxes */
eps = 0.000001f;
KK = AIR_CAST(coil_t, parm[1]*parm[1]);
LL = ELL_3V_DOT(forwX, forwX);
denom = AIR_CAST(coil_t, 1.0/(eps + sqrt(LL)));
forwX[0] *= _COIL_CONDUCT(LL, KK)*denom;
LL = ELL_3V_DOT(forwY, forwY);
forwY[1] *= _COIL_CONDUCT(LL, KK)*denom;
LL = ELL_3V_DOT(forwZ, forwZ);
forwZ[2] *= _COIL_CONDUCT(LL, KK)*denom;
LL = ELL_3V_DOT(backX, backX);
backX[0] *= _COIL_CONDUCT(LL, KK)*denom;
LL = ELL_3V_DOT(backY, backY);
backY[1] *= _COIL_CONDUCT(LL, KK)*denom;
LL = ELL_3V_DOT(backZ, backZ);
backZ[2] *= _COIL_CONDUCT(LL, KK)*denom;
lerp = AIR_CAST(coil_t, parm[2]);
delta[0] = (lerp*_coilLaplacian3(iv3, spacing)
+ (1-lerp)*gm*(rspX*(forwX[0] - backX[0])
+ rspY*(forwY[1] - backY[1])
+ rspZ*(forwZ[2] - backZ[2])));
delta[0] *= AIR_CAST(coil_t, parm[0]);
}
/*
** parm vector:
** 0 1 2 3 4 5 (6)
** step K_perp K_tan lerp X_ring Y_ring
*/
void
_coilKindScalarFilterModifiedCurvatureRings(coil_t *delta,
int xi, int yi, int zi,
coil_t **iv3, double spacing[3],
double parm[COIL_PARMS_NUM]) {
coil_t forwX[3], backX[3], forwY[3], backY[3], forwZ[3], backZ[3],
grad[3], gm, eps, KK, LL, denom, rspX, rspY, rspZ, lerp;
double bas0[3], bas1[3], bas2[3], len, norm[3], sk;
AIR_UNUSED(zi);
ELL_3V_SET(bas0, 0, 0, 1);
ELL_3V_SET(bas1, xi - parm[4], yi - parm[5], 0);
ELL_3V_NORM(bas1, bas1, len);
ELL_3V_CROSS(bas2, bas0, bas1);
rspX = AIR_CAST(coil_t, 1.0/spacing[0]);
rspY = AIR_CAST(coil_t, 1.0/spacing[1]);
rspZ = AIR_CAST(coil_t, 1.0/spacing[2]);
_coilKindScalar3x3x3Gradients(forwX, backX,
forwY, backY,
forwZ, backZ,
iv3,
rspX, rspY, rspZ);
grad[0] = rspX*(iv3[2][4] - iv3[0][4]);
grad[1] = rspY*(iv3[1][5] - iv3[1][3]);
grad[2] = rspZ*(iv3[1][7] - iv3[1][1]);
gm = AIR_CAST(coil_t, ELL_3V_LEN(grad));
if (gm) {
double tc, rcsq;
ELL_3V_SCALE(norm, 1.0/gm, grad);
tc = ELL_3V_DOT(norm, bas2);
rcsq = 1 - tc*tc;
sk = AIR_LERP(rcsq, parm[1], parm[2]);
} else {
sk = parm[1];
}
/* compute fluxes */
eps = 0.0000000001f;
KK = AIR_CAST(coil_t, sk*sk);
LL = ELL_3V_DOT(forwX, forwX);
denom = AIR_CAST(coil_t, 1.0/(eps + sqrt(LL)));
forwX[0] *= _COIL_CONDUCT(LL, KK)*denom;
LL = ELL_3V_DOT(forwY, forwY);
denom = AIR_CAST(coil_t, 1.0/(eps + sqrt(LL)));
forwY[1] *= _COIL_CONDUCT(LL, KK)*denom;
LL = ELL_3V_DOT(forwZ, forwZ);
denom = AIR_CAST(coil_t, 1.0/(eps + sqrt(LL)));
forwZ[2] *= _COIL_CONDUCT(LL, KK)*denom;
LL = ELL_3V_DOT(backX, backX);
denom = AIR_CAST(coil_t, 1.0/(eps + sqrt(LL)));
backX[0] *= _COIL_CONDUCT(LL, KK)*denom;
LL = ELL_3V_DOT(backY, backY);
denom = AIR_CAST(coil_t, 1.0/(eps + sqrt(LL)));
backY[1] *= _COIL_CONDUCT(LL, KK)*denom;
LL = ELL_3V_DOT(backZ, backZ);
denom = AIR_CAST(coil_t, 1.0/(eps + sqrt(LL)));
backZ[2] *= _COIL_CONDUCT(LL, KK)*denom;
lerp = AIR_CAST(coil_t, parm[2]);
delta[0] = (lerp*_coilLaplacian3(iv3, spacing)
+ (1-lerp)*gm*(rspX*(forwX[0] - backX[0])
+ rspY*(forwY[1] - backY[1])
+ rspZ*(forwZ[2] - backZ[2])));
delta[0] *= AIR_CAST(coil_t, parm[0]);
}
/*
** (mcde)
** parm vector:
** 0 1 2 (3)
** step K lerp (lerp=1: all laplacian)
*/
void
_coilKindScalarFilterModifiedCurvature(coil_t *delta,
int xi, int yi, int zi,
coil_t **iv3, double spacing[3],
double parm[COIL_PARMS_NUM]) {
/* char me[]="_coilKindScalarFilterModifiedCurvature"; */
coil_t forwX[3], backX[3], forwY[3], backY[3], forwZ[3], backZ[3],
grad[3], gm, eps, KK, LL, denom, rspX, rspY, rspZ, lerp;
AIR_UNUSED(xi);
AIR_UNUSED(yi);
AIR_UNUSED(zi);
/*
if (coilVerbose) {
fprintf(stderr, "!%s: --------- hello --------\n", me);
}
*/
/* reciprocals of spacings in X, Y, and Z */
rspX = AIR_CAST(coil_t, 1.0/spacing[0]);
rspY = AIR_CAST(coil_t, 1.0/spacing[1]);
rspZ = AIR_CAST(coil_t, 1.0/spacing[2]);
_coilKindScalar3x3x3Gradients(forwX, backX,
forwY, backY,
forwZ, backZ,
iv3,
rspX, rspY, rspZ);
grad[0] = rspX*(iv3[2][4] - iv3[0][4]);
grad[1] = rspY*(iv3[1][5] - iv3[1][3]);
grad[2] = rspZ*(iv3[1][7] - iv3[1][1]);
gm = AIR_CAST(coil_t, ELL_3V_LEN(grad));
/*
if (coilVerbose) {
fprintf(stderr, "forwX = %g %g %g backX = %g %g %g\n",
forwX[0], forwX[1], forwX[2],
backX[0], backX[1], backX[2]);
fprintf(stderr, "forwY = %g %g %g backY = %g %g %g\n",
forwY[0], forwY[1], forwY[2],
backY[0], backY[1], backY[2]);
fprintf(stderr, "forwZ = %g %g %g backZ = %g %g %g\n",
forwZ[0], forwZ[1], forwZ[2],
backZ[0], backZ[1], backZ[2]);
fprintf(stderr, "grad = %g %g %g --> gm = %g\n",
grad[0], grad[1], grad[2], gm);
}
*/
/* compute fluxes */
eps = 0.0000000001f;
KK = AIR_CAST(coil_t, parm[1]*parm[1]);
LL = ELL_3V_DOT(forwX, forwX);
denom = AIR_CAST(coil_t, 1.0/(eps + sqrt(LL)));
forwX[0] *= _COIL_CONDUCT(LL, KK)*denom;
LL = ELL_3V_DOT(forwY, forwY);
denom = AIR_CAST(coil_t, 1.0/(eps + sqrt(LL)));
forwY[1] *= _COIL_CONDUCT(LL, KK)*denom;
LL = ELL_3V_DOT(forwZ, forwZ);
denom = AIR_CAST(coil_t, 1.0/(eps + sqrt(LL)));
forwZ[2] *= _COIL_CONDUCT(LL, KK)*denom;
LL = ELL_3V_DOT(backX, backX);
denom = AIR_CAST(coil_t, 1.0/(eps + sqrt(LL)));
backX[0] *= _COIL_CONDUCT(LL, KK)*denom;
LL = ELL_3V_DOT(backY, backY);
denom = AIR_CAST(coil_t, 1.0/(eps + sqrt(LL)));
backY[1] *= _COIL_CONDUCT(LL, KK)*denom;
LL = ELL_3V_DOT(backZ, backZ);
denom = AIR_CAST(coil_t, 1.0/(eps + sqrt(LL)));
backZ[2] *= _COIL_CONDUCT(LL, KK)*denom;
lerp = AIR_CAST(coil_t, parm[2]);
delta[0] = (lerp*_coilLaplacian3(iv3, spacing)
+ (1-lerp)*gm*(rspX*(forwX[0] - backX[0])
+ rspY*(forwY[1] - backY[1])
+ rspZ*(forwZ[2] - backZ[2])));
delta[0] *= AIR_CAST(coil_t, parm[0]);
/*
if (coilVerbose) {
fprintf(stderr, "!%s: delta = %g\n", me, delta[0]);
}
*/
}
