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

This commit is contained in:
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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14
geometry.cpp
View File

@ -1080,7 +1080,7 @@ EX namespace geom3 {
seProduct,
seNil,
seSol, seNIH, seSolN,
seNIH_inv
seCliffordTorus
};
#endif
@ -1094,6 +1094,7 @@ EX namespace geom3 {
{"Sol", "Embed into Sol. Works only with Euclidean. You need to set the variation to Pure."},
{"stretched hyperbolic", "Embed into stretched hyperbolic geometry. Works only with Euclidean. You need to set the variation to Pure."},
{"stretched Sol", "Embed into stretched Sol geometry. Works only with Euclidean. You need to set the variation to Pure."},
{"Clifford Torus", "Embed Euclidean torus into S3. You need to set the variation to Pure."},
};
EX eSpatialEmbedding spatial_embedding = seDefault;
@ -1132,13 +1133,17 @@ EX namespace geom3 {
}
EX bool euc_in_noniso() {
return among(ggclass(), gcNil, gcSol, gcNIH, gcSolN) && mgclass() == gcEuclid;
return among(ggclass(), gcNil, gcSol, gcNIH, gcSolN, gcSphere) && mgclass() == gcEuclid;
}
EX bool sph_in_euc() {
return ggclass() == gcEuclid && mgclass() == gcSphere;
}
EX bool euc_in_sph() {
return ggclass() == gcSphere && mgclass() == gcEuclid;
}
EX bool sph_in_hyp() {
return ggclass() == gcHyperbolic && mgclass() == gcSphere;
}
@ -1220,6 +1225,11 @@ EX namespace geom3 {
g.gameplay_dimension = 2;
}
if(spatial_embedding == seCliffordTorus && ieuclid) {
g = ginf[gCell120].g;
g.gameplay_dimension = 2;
}
bool ieuc_or_binary = ieuclid || (gi.flags & qBINARY);
if(spatial_embedding == seSol && ieuc_or_binary) {

2
geometry2.cpp
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@ -442,7 +442,7 @@ EX bool no_easy_spin() {
return NONSTDVAR || arcm::in() || WDIM == 3 || bt::in() || kite::in();
}
EX bool dont_inverse() { return geometry == 1 && PURE && geom3::euc_in_noniso(); }
EX bool dont_inverse() { return meuclid && PURE && geom3::euc_in_noniso(); }
ld hrmap_standard::spin_angle(cell *c, int d) {
if(WDIM == 3) return SPIN_NOT_AVAILABLE;

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;
}

11
hypgraph.cpp
View File

@ -2028,7 +2028,7 @@ EX void adjust_eye(transmatrix& T, cell *c, ld sign) {
geom3::do_auto_eye();
int sl = snakelevel(c);
if(isWorm(c->monst) && sl < 3) sl++;
int i = geom3::sph_in_low() ? 1 : 0;
int i = moved_center() ? 1 : 0;
if(sl || vid.eye || i)
T = T * lzpush(sign * (cgi.SLEV[sl] - cgi.FLOOR - vid.eye + i));
}
@ -2917,7 +2917,7 @@ EX namespace dq {
EX set<unsigned> visited_by_matrix;
EX void enqueue_by_matrix(heptagon *h, const shiftmatrix& T) {
if(!h) return;
unsigned b = bucketer(tC0(T));
unsigned b = bucketer(T * tile_center());
if(visited_by_matrix.count(b)) { return; }
visited_by_matrix.insert(b);
drawqueue.emplace(h, T);
@ -2934,7 +2934,7 @@ EX namespace dq {
EX void enqueue_by_matrix_c(cell *c, const shiftmatrix& T) {
if(!c) return;
unsigned b = bucketer(tC0(T));
unsigned b = bucketer(T * tile_center());
if(visited_by_matrix.count(b)) { return; }
visited_by_matrix.insert(b);
drawqueue_c.emplace(c, T);
@ -3368,6 +3368,11 @@ EX transmatrix map_relative_push(hyperpoint h) {
geom3::light_flip(false);
return T * zpush(z);
}
if(geom3::euc_in_sph()) {
ld tx = hypot(h[0], h[2]);
ld ty = hypot(h[1], h[3]);
return cspin(0, 2, atan2(h[0], h[2])) * cspin(1, 3, atan2(h[1], h[3])) * cspin(2, 3, atan2(tx, ty));
}
return rgpushxto0(h);
}