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rug:: Clifford torus factored out for other uses

This commit is contained in:
Zeno Rogue 2021-02-04 15:02:47 +01:00
parent c1555c3ffa
commit e8aa080536
1 changed files with 66 additions and 32 deletions
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98
rug.cpp
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@ -356,62 +356,96 @@ EX void calcparam_rug() {
cd->radius = cd->scrsize * pconf.scale;
}
EX void buildTorusRug() {
#if HDR
struct clifford_torus {
transmatrix T;
transmatrix iT;
ld xfactor, yfactor;
bool flipped;
hyperpoint xh, yh;
hyperpoint torus_to_s4(hyperpoint t);
hyperpoint actual_to_torus(const hyperpoint& a) {
return iT * a;
}
hyperpoint torus_to_actual(const hyperpoint& t) {
return T * t;
}
clifford_torus();
ld get_modelscale() {
return hypot_d(2, xh) * xfactor * 2 * M_PI;
}
ld compute_mx();
};
#endif
calcparam_rug();
models::configure();
struct hyperpoint clifford_torus::torus_to_s4(hyperpoint t) {
double alpha = -t[0] * 2 * M_PI;
double beta = t[1] * 2 * M_PI;
ld ax = alpha + 1.124651, bx = beta + 1.214893;
return hyperpoint(
xfactor * sin(ax),
xfactor * cos(ax),
yfactor * sin(bx),
yfactor * cos(bx)
);
}
clifford_torus::clifford_torus() {
auto p1 = to_loc(euc::eu.user_axes[0]);
auto p2 = to_loc(euc::eu.user_axes[1]);
hyperpoint xh = euc::eumove(p1)*C0-C0;
hyperpoint yh = euc::eumove(p2)*C0-C0;
xh = euc::eumove(p1)*C0-C0;
yh = euc::eumove(p2)*C0-C0;
if(nonorientable) yh *= 2;
bool flipped = false; // sqhypot_d(2, xh) < sqhypot_d(2, yh);
flipped = false; // sqhypot_d(2, xh) < sqhypot_d(2, yh);
if(flipped) swap(xh, yh);
cell *gs = currentmap->gamestart();
ld xfactor, yfactor;
ld factor2 = sqhypot_d(2, xh) / sqhypot_d(2, yh);
ld factor = sqrt(factor2);
yfactor = sqrt(1/(1+factor2));
xfactor = factor * yfactor;
transmatrix T = build_matrix(xh, yh, C0, C03);
transmatrix iT = inverse(T);
T = build_matrix(xh, yh, C0, C03);
iT = inverse(T);
}
if(gwhere == gSphere)
modelscale = hypot_d(2, xh) * xfactor * 2 * M_PI;
map<pair<int, int>, rugpoint*> glues;
ld clifford_torus::compute_mx() {
ld mx = 0;
for(int i=0; i<1000; i++)
mx = max(mx, hypot(xfactor, yfactor * sin(i)) / (1-yfactor * cos(i)));
mx = max(mx, hypot(xfactor, yfactor * sin(i)) / (1-yfactor * cos(i)));
println(hlog, "mx = ", mx);
return mx;
}
EX void buildTorusRug() {
calcparam_rug();
models::configure();
clifford_torus ct;
if(gwhere == gSphere)
modelscale = ct.get_modelscale();
cell *gs = currentmap->gamestart();
map<pair<int, int>, rugpoint*> glues;
ld mx = ct.compute_mx();
auto addToruspoint = [&] (hyperpoint h) {
auto r = addRugpoint(shiftless(C0), 0);
hyperpoint onscreen;
shiftpoint h1 = gmatrix[gs] * T * h;
shiftpoint h1 = gmatrix[gs] * ct.torus_to_actual(h);
applymodel(h1, onscreen);
r->x1 = onscreen[0];
r->y1 = onscreen[1];
double alpha = -h[0] * 2 * M_PI;
double beta = h[1] * 2 * M_PI;
ld ax = alpha + 1.124651, bx = beta + 1.214893;
ld x = xfactor * sin(ax), y = xfactor * cos(ax), z = yfactor * sin(bx), t = yfactor * cos(bx);
if(1) {
hyperpoint hp = hyperpoint(x, y, z, t);
hyperpoint hp = ct.torus_to_s4(h);
USING_NATIVE_GEOMETRY;
@ -419,7 +453,7 @@ EX void buildTorusRug() {
if(!sphere) {
/* stereographic projection to get Euclidean conformal torus */
hp /= (t+1);
hp /= (hp[3]+1);
hp /= mx;
#if MAXMDIM >= 4
hp[3] = 1;
@ -448,15 +482,15 @@ EX void buildTorusRug() {
ld rmd = rugmax;
hyperpoint sx = iT * (currentmap->adj(gs, 0)*C0-C0)/rmd;
hyperpoint sy = iT * (currentmap->adj(gs, 1)*C0-C0)/rmd;
hyperpoint sx = ct.iT * (currentmap->adj(gs, 0)*C0-C0)/rmd;
hyperpoint sy = ct.iT * (currentmap->adj(gs, 1)*C0-C0)/rmd;
for(int leaf=0; leaf<(nonorientable ? 2 : 1); leaf++)
for(cell *c: currentmap->allcells()) {
hyperpoint h = iT * calc_relative_matrix(c, gs, C0) * C0;
hyperpoint h = ct.iT * calc_relative_matrix(c, gs, C0) * C0;
if(leaf) h[flipped ? 0 : 1] += .5;
if(leaf) h[ct.flipped ? 0 : 1] += .5;
rugpoint *rugarr[32][32];
for(int yy=0; yy<=rugmax; yy++)