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Clifford torus embedding (needs to be configured manually and on a straight square for now)

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Zeno Rogue
2023-01-04 23:30:36 +01:00
parent bc96b7fba9
commit 32546cee4a
4 changed files with 59 additions and 6 deletions
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38
hyperpoint.cpp
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@@ -572,6 +572,15 @@ EX hyperpoint normalize_flat(hyperpoint h) {
if(geom3::euc_in_nil()) h[1] = 0;
if(geom3::euc_in_solnih()) h[2] = 0;
if(geom3::hyp_in_solnih()) h[0] = 0;
if(geom3::euc_in_sph()) {
ld tx = hypot(h[0], h[2]);
ld ty = hypot(h[1], h[3]);
h[0] = h[0] / tx * sin(1);
h[1] = h[1] / ty * cos(1);
h[2] = h[2] / tx * sin(1);
h[3] = h[3] / ty * cos(1);
return h;
}
if(geom3::euc_in_hyp()) {
h = normalize(h);
auto h1 = deparabolic13(h);
@@ -837,6 +846,19 @@ EX hyperpoint orthogonal_move(const hyperpoint& h, ld z) {
hf[3] = cosh(z0 + z);
return hf;
}
if(geom3::euc_in_sph()) {
// cspin(0,2,x) * cspin(1,3,y) * cspin0(2, 3, z)
ld tx = hypot(h[0], h[2]);
ld ty = hypot(h[1], h[3]);
ld z0 = atan2(ty, tx);
z0 -= z;
hyperpoint hf;
hf[0] = h[0] / tx * cos(z0);
hf[1] = h[1] / ty * sin(z0);
hf[2] = h[2] / tx * cos(z0);
hf[3] = h[3] / ty * sin(z0);
return hf;
}
if(GDIM == 2) return scale_point(h, geom3::scale_at_lev(z));
if(gproduct) return scale_point(h, exp(z));
if(sl2) return slr::translate(h) * cpush0(2, z);
@@ -874,6 +896,11 @@ EX transmatrix matrix4(ld a, ld b, ld c, ld d, ld e, ld f, ld g, ld h, ld i, ld
#endif
}
EX void euc_in_sph_rescale(hyperpoint& h) {
h[0] *= TAU * geom3::euclid_embed_scale;
h[1] *= TAU * geom3::euclid_embed_scale;
}
#if MAXMDIM >= 4
/** Transform a matrix between the 'embedded_plane' and underlying representation. Switches to the current variant. */
EX void swapmatrix(transmatrix& T) {
@@ -916,6 +943,11 @@ EX void swapmatrix(transmatrix& T) {
else if(geom3::in_product()) {
/* just do nothing */
}
else if(geom3::euc_in_sph()) {
hyperpoint h1 = get_column(T, 2);
euc_in_sph_rescale(h1);
T = cspin(0, 2, h1[0]) * cspin(1, 3, h1[1]);
}
else {
for(int i=0; i<4; i++) swap(T[i][2], T[i][3]);
for(int i=0; i<4; i++) swap(T[2][i], T[3][i]);
@@ -934,6 +966,10 @@ EX void swapmatrix(hyperpoint& h) {
if(geom3::sph_in_euc()) { h[3] = 1; return; }
if(geom3::sph_in_hyp()) { h[0] *= sinh(1); h[1] *= sinh(1); h[2] *= sinh(1); h[3] = cosh(1); return; }
if(geom3::euc_in_nil()) { h[3] = 1; h[2] = h[1] * geom3::euclid_embed_scale; h[1] = 0; h[0] *= geom3::euclid_embed_scale; return; }
if(geom3::euc_in_sph()) {
euc_in_sph_rescale(h); h = cspin(0, 2, h[0]) * cspin(1, 3, h[1]) * lzpush(1) * C0;
return;
}
if(geom3::euc_in_solnih()) { h[3] = 1; h[1] = h[1] * geom3::euclid_embed_scale; h[2] = 0; h[0] *= geom3::euclid_embed_scale; return; }
if(geom3::hyp_in_solnih()) {
// copied from deparabolic13
@@ -1524,12 +1560,14 @@ EX hyperpoint scale_point(const hyperpoint& h, ld scale_factor) {
EX bool moved_center() {
if(geom3::sph_in_euc()) return true;
if(geom3::sph_in_hyp()) return true;
if(geom3::euc_in_sph()) return true;
return false;
}
/** Returns the intended center of the tile, relative to its local matrix. Usually C0 but may be different, e.g. when embedding a sphere in E3 or H3. */
EX hyperpoint tile_center() {
if(geom3::sph_in_euc()) return C02 + C03;
if(geom3::euc_in_sph()) return zpush0(1);
if(geom3::sph_in_hyp()) return zpush0(1);
return C0;
}