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// Gmsh - Copyright (C) 1997-2021 C. Geuzaine, J.-F. Remacle
//
// See the LICENSE.txt file for license information. Please report all
// issues on https://gitlab.onelab.info/gmsh/gmsh/issues.
#include "Numeric.h"
static void affect(double *xi, double *yi, double *zi, int i, double *xp,
double *yp, double *zp, int j)
{
xi[i] = xp[j];
yi[i] = yp[j];
zi[i] = zp[j];
}
double InterpolateIso(double *X, double *Y, double *Z, double *Val, double V,
int I1, int I2, double *XI, double *YI, double *ZI)
{
if(Val[I1] == Val[I2]) {
*XI = X[I1];
*YI = Y[I1];
*ZI = Z[I1];
return 0;
}
else {
double coef = (V - Val[I1]) / (Val[I2] - Val[I1]);
*XI = coef * (X[I2] - X[I1]) + X[I1];
*YI = coef * (Y[I2] - Y[I1]) + Y[I1];
*ZI = coef * (Z[I2] - Z[I1]) + Z[I1];
return coef;
}
}
// Compute an iso-point in a line
int IsoLine(double *X, double *Y, double *Z, double *Val, double V, double *Xp,
double *Yp, double *Zp)
{
if(Val[0] == Val[1]) return 0;
if((Val[0] >= V && Val[1] <= V) || (Val[1] >= V && Val[0] <= V)) {
InterpolateIso(X, Y, Z, Val, V, 0, 1, Xp, Yp, Zp);
return 1;
}
return 0;
}
// Compute an iso-line inside a triangle
int IsoTriangle(double *X, double *Y, double *Z, double *Val, double V,
double *Xp, double *Yp, double *Zp)
{
if(Val[0] == Val[1] && Val[0] == Val[2]) return 0;
int nb = 0;
if((Val[0] >= V && Val[1] <= V) || (Val[1] >= V && Val[0] <= V)) {
InterpolateIso(X, Y, Z, Val, V, 0, 1, &Xp[nb], &Yp[nb], &Zp[nb]);
nb++;
}
if((Val[0] >= V && Val[2] <= V) || (Val[2] >= V && Val[0] <= V)) {
InterpolateIso(X, Y, Z, Val, V, 0, 2, &Xp[nb], &Yp[nb], &Zp[nb]);
nb++;
}
if((Val[1] >= V && Val[2] <= V) || (Val[2] >= V && Val[1] <= V)) {
InterpolateIso(X, Y, Z, Val, V, 1, 2, &Xp[nb], &Yp[nb], &Zp[nb]);
nb++;
}
if(nb == 2) return 2;
return 0;
}
// Compute an iso-polygon inside a tetrahedron
int IsoSimplex(double *X, double *Y, double *Z, double *Val, double V,
double *Xp, double *Yp, double *Zp, double n[3])
{
if(Val[0] == Val[1] && Val[0] == Val[2] && Val[0] == Val[3]) return 0;
int nb = 0;
if((Val[0] >= V && Val[1] <= V) || (Val[1] >= V && Val[0] <= V)) {
InterpolateIso(X, Y, Z, Val, V, 0, 1, &Xp[nb], &Yp[nb], &Zp[nb]);
nb++;
}
if((Val[0] >= V && Val[2] <= V) || (Val[2] >= V && Val[0] <= V)) {
InterpolateIso(X, Y, Z, Val, V, 0, 2, &Xp[nb], &Yp[nb], &Zp[nb]);
nb++;
}
if((Val[0] >= V && Val[3] <= V) || (Val[3] >= V && Val[0] <= V)) {
InterpolateIso(X, Y, Z, Val, V, 0, 3, &Xp[nb], &Yp[nb], &Zp[nb]);
nb++;
}
if((Val[1] >= V && Val[2] <= V) || (Val[2] >= V && Val[1] <= V)) {
InterpolateIso(X, Y, Z, Val, V, 1, 2, &Xp[nb], &Yp[nb], &Zp[nb]);
nb++;
}
if((Val[1] >= V && Val[3] <= V) || (Val[3] >= V && Val[1] <= V)) {
InterpolateIso(X, Y, Z, Val, V, 1, 3, &Xp[nb], &Yp[nb], &Zp[nb]);
nb++;
}
if((Val[2] >= V && Val[3] <= V) || (Val[3] >= V && Val[2] <= V)) {
InterpolateIso(X, Y, Z, Val, V, 2, 3, &Xp[nb], &Yp[nb], &Zp[nb]);
nb++;
}
// Remove identical nodes (this can happen if an edge belongs to the
// zero levelset). We should be doing this even for nb < 4, but it
// would slow us down even more (and we don't really care if some
// nodes in a postprocessing element are identical)
if(nb > 4) {
double xi[6], yi[6], zi[6];
affect(xi, yi, zi, 0, Xp, Yp, Zp, 0);
int ni = 1;
for(int j = 1; j < nb; j++) {
for(int i = 0; i < ni; i++) {
if(fabs(Xp[j] - xi[i]) < 1.e-12 && fabs(Yp[j] - yi[i]) < 1.e-12 &&
fabs(Zp[j] - zi[i]) < 1.e-12) {
break;
}
if(i == ni - 1) {
affect(xi, yi, zi, i + 1, Xp, Yp, Zp, j);
ni++;
}
}
}
for(int i = 0; i < ni; i++) affect(Xp, Yp, Zp, i, xi, yi, zi, i);
nb = ni;
}
if(nb < 3 || nb > 4) return 0;
// 3 possible quads at this point: (0,2,5,3), (0,1,5,4) or
// (1,2,4,3), so simply invert the 2 last vertices for having the
// quad ordered
if(nb == 4) {
double x = Xp[3], y = Yp[3], z = Zp[3];
Xp[3] = Xp[2];
Yp[3] = Yp[2];
Zp[3] = Zp[2];
Xp[2] = x;
Yp[2] = y;
Zp[2] = z;
}
// to get a nice isosurface, we should have n . grad v > 0, where n
// is the normal to the polygon and v is the unknown field we want
// to draw
double v1[3] = {Xp[2] - Xp[0], Yp[2] - Yp[0], Zp[2] - Zp[0]};
double v2[3] = {Xp[1] - Xp[0], Yp[1] - Yp[0], Zp[1] - Zp[0]};
prodve(v1, v2, n);
norme(n);
double g[3];
gradSimplex(X, Y, Z, Val, g);
if(prosca(g, n) > 0.0) {
double Xpi[6], Ypi[6], Zpi[6];
for(int i = 0; i < nb; i++) {
Xpi[i] = Xp[i];
Ypi[i] = Yp[i];
Zpi[i] = Zp[i];
}
for(int i = 0; i < nb; i++) {
Xp[i] = Xpi[nb - i - 1];
Yp[i] = Ypi[nb - i - 1];
Zp[i] = Zpi[nb - i - 1];
}
}
else {
n[0] = -n[0];
n[1] = -n[1];
n[2] = -n[2];
}
return nb;
}
// Compute the line between the two iso-points V1 and V2 in a line
int CutLine(double *X, double *Y, double *Z, double *Val, double V1, double V2,
double *Xp2, double *Yp2, double *Zp2, double *Vp2)
{
int io[2];
if(Val[0] < Val[1]) {
io[0] = 0;
io[1] = 1;
}
else {
io[0] = 1;
io[1] = 0;
}
if(Val[io[0]] > V2 || Val[io[1]] < V1) return 0;
if(V1 <= Val[io[0]] && Val[io[1]] <= V2) {
for(int i = 0; i < 2; i++) {
Vp2[i] = Val[i];
Xp2[i] = X[i];
Yp2[i] = Y[i];
Zp2[i] = Z[i];
}
return 2;
}
if(V1 <= Val[io[0]]) {
Vp2[0] = Val[io[0]];
Xp2[0] = X[io[0]];
Yp2[0] = Y[io[0]];
Zp2[0] = Z[io[0]];
}
else {
Vp2[0] = V1;
InterpolateIso(X, Y, Z, Val, V1, io[0], io[1], &Xp2[0], &Yp2[0], &Zp2[0]);
}
if(V2 >= Val[io[1]]) {
Vp2[1] = Val[io[1]];
Xp2[1] = X[io[1]];
Yp2[1] = Y[io[1]];
Zp2[1] = Z[io[1]];
}
else {
Vp2[1] = V2;
InterpolateIso(X, Y, Z, Val, V2, io[0], io[1], &Xp2[1], &Yp2[1], &Zp2[1]);
}
return 2;
}
// Compute the polygon between the two iso-lines V1 and V2 in a
// triangle
int CutTriangle(double *X, double *Y, double *Z, double *Val, double V1,
double V2, double *Xp2, double *Yp2, double *Zp2, double *Vp2)
{
// fill io so that it contains an indexing of the nodes such that
// Val[io[i]] > Val[io[j]] if i > j
int io[3] = {0, 1, 2};
for(int i = 0; i < 2; i++) {
for(int j = i + 1; j < 3; j++) {
if(Val[io[i]] > Val[io[j]]) {
int iot = io[i];
io[i] = io[j];
io[j] = iot;
}
}
}
if(Val[io[0]] > V2 || Val[io[2]] < V1) return 0;
if(V1 <= Val[io[0]] && Val[io[2]] <= V2) {
for(int i = 0; i < 3; i++) {
Vp2[i] = Val[i];
Xp2[i] = X[i];
Yp2[i] = Y[i];
Zp2[i] = Z[i];
}
return 3;
}
int Np = 0, Fl = 0;
double Xp[10], Yp[10], Zp[10], Vp[10];
if(V1 <= Val[io[0]]) {
Vp[Np] = Val[io[0]];
Xp[Np] = X[io[0]];
Yp[Np] = Y[io[0]];
Zp[Np] = Z[io[0]];
Np++;
Fl = 1;
}
else if(Val[io[0]] < V1 && V1 <= Val[io[1]]) {
Vp[Np] = V1;
InterpolateIso(X, Y, Z, Val, V1, io[0], io[2], &Xp[Np], &Yp[Np], &Zp[Np]);
Np++;
Vp[Np] = V1;
InterpolateIso(X, Y, Z, Val, V1, io[0], io[1], &Xp[Np], &Yp[Np], &Zp[Np]);
Np++;
Fl = 1;
}
else {
Vp[Np] = V1;
InterpolateIso(X, Y, Z, Val, V1, io[0], io[2], &Xp[Np], &Yp[Np], &Zp[Np]);
Np++;
Vp[Np] = V1;
InterpolateIso(X, Y, Z, Val, V1, io[1], io[2], &Xp[Np], &Yp[Np], &Zp[Np]);
Np++;
Fl = 0;
}
if(V2 == Val[io[0]]) { return 0; }
else if((Val[io[0]] < V2) && (V2 < Val[io[1]])) {
Vp[Np] = V2;
InterpolateIso(X, Y, Z, Val, V2, io[0], io[1], &Xp[Np], &Yp[Np], &Zp[Np]);
Np++;
Vp[Np] = V2;
InterpolateIso(X, Y, Z, Val, V2, io[0], io[2], &Xp[Np], &Yp[Np], &Zp[Np]);
Np++;
}
else if(V2 < Val[io[2]]) {
if(Fl) {
Vp[Np] = Val[io[1]];
Xp[Np] = X[io[1]];
Yp[Np] = Y[io[1]];
Zp[Np] = Z[io[1]];
Np++;
}
Vp[Np] = V2;
InterpolateIso(X, Y, Z, Val, V2, io[1], io[2], &Xp[Np], &Yp[Np], &Zp[Np]);
Np++;
Vp[Np] = V2;
InterpolateIso(X, Y, Z, Val, V2, io[0], io[2], &Xp[Np], &Yp[Np], &Zp[Np]);
Np++;
}
else {
if(Fl) {
Vp[Np] = Val[io[1]];
Xp[Np] = X[io[1]];
Yp[Np] = Y[io[1]];
Zp[Np] = Z[io[1]];
Np++;
}
Vp[Np] = Val[io[2]];
Xp[Np] = X[io[2]];
Yp[Np] = Y[io[2]];
Zp[Np] = Z[io[2]];
Np++;
}
Vp2[0] = Vp[0];
Xp2[0] = Xp[0];
Yp2[0] = Yp[0];
Zp2[0] = Zp[0];
int Np2 = 1;
for(int i = 1; i < Np; i++) {
if((Xp[i] != Xp2[Np2 - 1]) || (Yp[i] != Yp2[Np2 - 1]) ||
(Zp[i] != Zp2[Np2 - 1])) {
Vp2[Np2] = Vp[i];
Xp2[Np2] = Xp[i];
Yp2[Np2] = Yp[i];
Zp2[Np2] = Zp[i];
Np2++;
}
}
if(Xp2[0] == Xp2[Np2 - 1] && Yp2[0] == Yp2[Np2 - 1] &&
Zp2[0] == Zp2[Np2 - 1]) {
Np2--;
}
// check and fix orientation
double in1[3] = {X[1] - X[0], Y[1] - Y[0], Z[1] - Z[0]};
double in2[3] = {X[2] - X[0], Y[2] - Y[0], Z[2] - Z[0]};
double inn[3];
prodve(in1, in2, inn);
double out1[3] = {Xp2[1] - Xp2[0], Yp2[1] - Yp2[0], Zp2[1] - Zp2[0]};
double out2[3] = {Xp2[2] - Xp2[0], Yp2[2] - Yp2[0], Zp2[2] - Zp2[0]};
double outn[3];
prodve(out1, out2, outn);
if(prosca(inn, outn) < 0.0) {
for(int i = 0; i < Np2; i++) {
Vp[i] = Vp2[Np2 - i - 1];
Xp[i] = Xp2[Np2 - i - 1];
Yp[i] = Yp2[Np2 - i - 1];
Zp[i] = Zp2[Np2 - i - 1];
}
for(int i = 0; i < Np2; i++) {
Vp2[i] = Vp[i];
Xp2[i] = Xp[i];
Yp2[i] = Yp[i];
Zp2[i] = Zp[i];
}
}
return Np2;
}
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