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extra two-point projections

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Zeno Rogue
2019-07-12 23:10:01 +02:00
parent e5e0dfbac1
commit ec82e5695b
4 changed files with 124 additions and 7 deletions
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110
hypgraph.cpp
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@@ -257,6 +257,52 @@ hyperpoint mobius(hyperpoint h, ld angle, ld scale = 1) {
return space_to_perspective(h, 1) / scale;
}
hyperpoint compute_hybrid(hyperpoint H, int rootid) {
auto& t = vid.twopoint_param;
hyperpoint Hl = xpush(+t) * H;
hyperpoint Hr = xpush(-t) * H;
ld g = (Hl[0] + 1e-7) / (Hl[1] + 1e-8);
ld d = hdist0(Hr);
hyperpoint spinned = spintox(Hl) * xpush0(2*t);
if(Hl[0] < 0) spinned = pispin * spinned;
ld y = asin_auto(spinned[1]);
ld x = asin_auto_clamp(spinned[0] / cos_auto(y));
int sign = (Hl[0] > 0 ? 1 : -1) * hdist0(Hl) < x ? -1 : 1;
switch(rootid & 3) {
case 1: sign = -sign; break;
case 2: sign = 1; break;
case 3: sign = -1; break;
}
// (x + t) / g = y
// yy + (x-t)(x-t) = dd
// (x+t)*(x+t)/g*g + x*x + t*t - 2*x*t = dd
// x*x*(1+1/g*g) + t*t*(1+1/g*g) + 2xt (1/gg-1) = dd
// xx + 2xt (1/gg-1) / (1+1/gg) = dd / (1+1/gg) - tt
ld b = t*(1/g/g - 1) / (1+1/g/g);
ld c = d*d / (1+1/g/g) - t*t;
// xx + 2bx = c
// xx + 2bx + bb = c + bb
// (x+b)^2 = c+bb
// x = +/- sqrt(c+bb) - b
ld a = c+b*b;
hyperpoint ret;
ret[0] = (a > 0 ? sign * sqrt(a) : 0) - b;
ret[1] = (ret[0] + t) / g;
ret[2] = 0;
return ret;
}
void applymodel(hyperpoint H, hyperpoint& ret) {
using namespace hyperpoint_vec;
@@ -436,6 +482,43 @@ void applymodel(hyperpoint H, hyperpoint& ret) {
break;
}
case mdSimulatedPerspective: {
conformal::apply_orientation_yz(H[1], H[2]);
conformal::apply_orientation(H[0], H[1]);
auto yz = move_z_to_y(H);
hyperpoint Hl = xpush(-vid.twopoint_param) * H;
hyperpoint Hr = xpush(+vid.twopoint_param) * H;
ld lyx = (Hl[1] + 1e-7) / (Hl[0] + 1e-8);
ld ryx = (Hr[1] + 1e-7) / (Hr[0] + 1e-8);
// (r.x + t) * lyx = (r.x - t) * ryx = r.y
// r.x * lyx + t * lyx = r.x * ryx - t * ryx
// r.x * (lyx-ryx) = - t * (ryx + lyx)
// r.x = -t * (ryx+lyx) / (lyx-ryx)
// r.x = - 2 * t * lyx * ryx / lyx / ryx
ret[0] = -vid.twopoint_param * (ryx + lyx) / (lyx - ryx);
ret[1] = (ret[0] + vid.twopoint_param) * lyx;
ret[2] = 0;
move_y_to_z(ret, yz);
conformal::apply_orientation(ret[0], ret[1]);
conformal::apply_orientation_yz(ret[2], ret[1]);
break;
}
case mdTwoHybrid: {
conformal::apply_orientation_yz(H[1], H[2]);
conformal::apply_orientation(H[0], H[1]);
auto yz = move_z_to_y(H);
ret = compute_hybrid(H, whateveri[0]);
move_y_to_z(ret, yz);
conformal::apply_orientation(ret[0], ret[1]);
conformal::apply_orientation_yz(ret[2], ret[1]);
break;
}
case mdJoukowsky:
case mdJoukowskyInverted: {
conformal::apply_orientation_yz(H[1], H[2]);
@@ -1394,8 +1477,33 @@ void draw_model_elements() {
queuechr(current_display->xcenter, current_display->ycenter + current_display->radius * vid.alpha, 0, vid.fsize, 'X', ringcolor, 1, 8);
return;
}
case mdTwoHybrid: {
queuereset(mdUnchanged, PPR::CIRCLE);
for(int mode=0; mode<4; mode++) {
for(int s=-199; s<=199; s += 2) {
ld p = s / 200.;
ld a = vid.twopoint_param * (1+p);
ld b = vid.twopoint_param * (1-p);
ld h = ((mode & 2) ? -1 : 1) * sqrt(asin_auto(tan_auto(a) * tan_auto(b)));
hyperpoint H = xpush(p * vid.twopoint_param) * ypush0(h);
hyperpoint res = compute_hybrid(H, 2 | mode);
conformal::apply_orientation(res[0], res[1]);
conformal::apply_orientation_yz(res[2], res[1]);
using namespace hyperpoint_vec;
curvepoint(res * current_display->radius);
}
queuecurve(ringcolor, 0, PPR::CIRCLE);
}
case mdTwoPoint: {
queuereset(pmodel, PPR::CIRCLE);
/* fallthrough */
}
case mdTwoPoint: case mdSimulatedPerspective: {
ld a = -conformal::model_orientation * degree;
queuechr(xspinpush0(a, +vid.twopoint_param), vid.xres / 100, 'X', ringcolor >> 8);
queuechr(xspinpush0(a, -vid.twopoint_param), vid.xres / 100, 'X', ringcolor >> 8);