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hyperrogue/rogueviz/triangle.cpp
2020-02-17 10:33:56 +01:00

300 lines
8.4 KiB
C++

#include "../hyper.h"
// Impossible Triangle visualization
// used in: https://www.youtube.com/watch?v=YmFDd49WsrY
// settings:
// ./mymake -O3 rogueviz/triangle
// ./hyper -geo Nil -canvas x -tstep 8 -nilperiod 3 3 3
// also used in: https://youtu.be/RPL4-Ydviug
// ./hyper -geo Nil -nilwidth .9 -canvas x -tstep 1 -nilperiod 1 10 1 -triset 32 31 992
namespace hr {
// each color group (i.e., each face direction) is a different hpcshape
hpcshape ptriangle[6];
EX hyperpoint lerp(hyperpoint a0, hyperpoint a1, ld x) {
return a0 + (a1-a0) * x;
}
hyperpoint operator+(hyperpoint x) { return x; }
// do not change this
int shape = 1;
// how many cubes to subdivide edges to
int how = 8;
// how many cubes to draw (should be smaller than how because they are not really cubes and thus they get into each other)
int how1 = how - 1;
// precision: number of substeps to simulate (best if divisible by how and how1)
int isteps = 4 * 1024;
/* make the impossible triangle shape */
void make_shape() {
static bool done = false;
if(done) return;
done = true;
// four main axes of the regular tetrahedron, rotated so that ds[3] points to (0,0,1)
ld rest = sqrt(8/9.);
ld rex = sqrt(1 - 1/9. - pow(rest/2., 2));
hyperpoint ds[4];
ds[0] = point3(rex, -rest/2, -1/3.);
ds[1] = point3(0, rest, -1/3.);
ds[2] = point3(-rex, -rest/2, -1/3.);
ds[3] = point3(0, 0, +1);
hyperpoint start = point31(0, 0, 0);
double lastz;
double lasta;
double ca;
// compute how to scale this in Nil so that everything fits
for(ld a = 1e-5;; a+=1e-5) {
hyperpoint at = start;
for(int d=0; d<3; d++) {
for(int i=0; i<isteps; i++) {
at = nisot::translate(at) * (start + ds[d] * a);
}
}
println(hlog, "at = ", at, " for a = ", a, " sq = ", at[2] / a / a);
if(at[2] > 0) {
ld z = at[2];
ca = lerp(lasta, a, ilerp(lastz, z, 0));
break;
}
lastz = at[2]; lasta =a;
}
println(hlog, "ca = ", ca);
ld scale = .2;
// compute the shift between the cubes
array<hyperpoint, 4> uds;
for(int d=0; d<3; d++) {
hyperpoint at = start;
for(int i=0; i<isteps/how; i++) {
at = nisot::translate(at) * (start + ds[d] * ca);
}
uds[d] = (at - start) / 2.;
}
println(hlog, "uds = ", uds);
for(int a=0; a<3; a++) println(hlog, sqhypot_d(3, inverse_exp(start + ds[a] * ca, iTable, false)));
for(int a=0; a<3; a++) println(hlog, sqhypot_d(3, inverse_exp(uds[a], iTable, false)));
// compute cube vertices
hyperpoint verts[8];
for(int a=0; a<8; a++) {
verts[a] = start;
for(int k=0; k<3; k++)
verts[a] += (a&(1<<k)) ? uds[k] : -uds[k];
}
// since Nil does not really have cubes, we need to move the vertices a bit so that it looks nicer
// ugliness of the current vertices
auto errf = [&] {
ld res = 0;
for(int s=0; s<8; s++)
for(int t=0; t<3; t++) {
if((s & (1<<t)) == 0) {
int s1 = s | (1<<t);
ld dix = sqhypot_d(3, inverse(nisot::translate(nisot::translate(start + 2*uds[t]) * verts[s])) * verts[s1]);
// println(hlog, tie(s, t), "di = ", dix);
res += dix * dix;
}
}
return res;
};
// minimize the ugliness
ld curerr = errf();
println(hlog, "curerr = ", curerr);
int att = 0;
if(1) while(true) {
int id = rand() % 8;
int j = rand() % 3;
ld eps = (rand() % 100 - rand() % 100) / 100000.;
verts[id][j] += eps;
ld nerr = errf();
if(nerr < curerr) {
curerr = nerr;
println(hlog, "curerr = ", curerr, " # ", att);
att = 0;
}
else {
verts[id][j] -= eps;
}
att++;
if(att > 50000) break;
}
for(int s=0; s<8; s++)
for(int t=0; t<3; t++) {
if((s & (1<<t)) == 0) {
int s1 = s | (1<<t);
ld dix = sqhypot_d(3, inverse(nisot::translate(nisot::translate(start + 2*uds[t]) * verts[s])) * verts[s1]);
println(hlog, tie(s, t), "di = ", dix);
}
}
scale = 1.;
// build all the faces
for(int si=0; si<6; si++) {
cgi.bshape(ptriangle[si], PPR::WALL);
hyperpoint at = start;
for(int d=0; d<3; d++) {
int d1 = (d+1) % 3;
int d2 = (d+2) % 3;
hyperpoint path[isteps+1];
for(int i=0; i<isteps; i++) {
path[i] = at;
at = nisot::translate(at) * (start + ds[d] * ca);
}
path[isteps] = at;
auto &u = uds[d];
auto &v = uds[d1];
auto &w = uds[d2];
auto textured_square = [&] (auto f) {
texture_order([&] (ld ix, ld iy) { f(.5 + ix/2 + iy/2, .5 + ix/2 - iy/2); });
texture_order([&] (ld ix, ld iy) { f(.5 - ix/2 - iy/2, .5 - ix/2 + iy/2); });
texture_order([&] (ld ix, ld iy) { f(.5 + ix/2 - iy/2, .5 - ix/2 - iy/2); });
texture_order([&] (ld ix, ld iy) { f(.5 - ix/2 + iy/2, .5 + ix/2 + iy/2); });
};
auto sidewall = [&] (hyperpoint wide, hyperpoint shift) {
textured_square( [&] (ld ix, ld iy) {
hyperpoint online = path[int(ix * isteps + .1)];
hyperpoint shf = lerp(u, -u, ix) + lerp(-wide, wide, iy) + shift;
shf *= scale;
cgi.hpcpush(nisot::translate(online) * (start + shf));
});
};
auto sidesquare = [&] (hyperpoint wx, hyperpoint wy, hyperpoint shift, ld p) {
textured_square( [&] (ld ix, ld iy) {
hyperpoint online = path[int(p * isteps + .1)];
hyperpoint shf = lerp(wx, -wx, ix) + lerp(wy, -wy, iy) + shift;
shf *= scale;
cgi.hpcpush(nisot::translate(online) * (start + shf));
});
};
auto sidesquare1 = [&] (hyperpoint a00, hyperpoint a01, hyperpoint a10, hyperpoint a11, ld p) {
hyperpoint online = path[int(p * isteps + .1)];
textured_square( [&] (ld ix, ld iy) {
hyperpoint shf = lerp(lerp(a00, a01, ix), lerp(a10, a11, ix), iy);
shf *= scale;
cgi.hpcpush(nisot::translate(online) * (shf));
});
};
if(shape == 0) {
if(si == d2*2) sidewall(v, w);
if(si == d1*2) sidewall(w, v);
if(si == d2*2+1) sidewall(v, -w);
if(si == d1*2+1) sidewall(w, -v);
if(si == d2*2) sidesquare(u, v, w, 0);
if(si == d1*2) sidesquare(w, u, v, 0);
if(si == d1*2+1) sidesquare(u, w, -v, 0);
if(si == d*2+1) sidesquare(w, v, -u, 0);
}
if(shape == 1) for(int a=0; a<how1; a++) {
ld c = a * 1. / how1;
/*
if(si == d*2) sidesquare(v, w, u, c);
if(si == d*2+1) sidesquare(w, v, -u, c);
if(si == d1*2) sidesquare(w, u, v, c);
if(si == d1*2+1) sidesquare(u, w, -v, c);
if(si == d2*2) sidesquare(u, v, w, c);
if(si == d2*2+1) sidesquare(v, u, -w, c);
*/
if(si == 0) sidesquare1(verts[0], verts[2], verts[4], verts[6], c);
if(si == 1) sidesquare1(verts[1], verts[3], verts[5], verts[7], c);
if(si == 2) sidesquare1(verts[0], verts[1], verts[4], verts[5], c);
if(si == 3) sidesquare1(verts[2], verts[3], verts[6], verts[7], c);
if(si == 4) sidesquare1(verts[0], verts[1], verts[2], verts[3], c);
if(si == 5) sidesquare1(verts[4], verts[5], verts[6], verts[7], c);
}
}
cgi.last->flags |= POLY_TRIANGLES;
cgi.last->tinf = &floor_texture_vertices[0];
cgi.last->texture_offset = 0;
cgi.finishshape();
cgi.extra_vertices();
}
}
// Magic Cube (aka Rubik Cube) colors
color_t magiccolors[6] = { 0xFFFF00FF, 0xFFFFFFFF, 0x0000FFFF, 0x00FF00FF, 0xFF0000FF, 0xFF8000FF};
bool draw_ptriangle(cell *c, const transmatrix& V) {
make_shape();
if(c == cwt.at) {
for(int side=0; side<6; side++) {
auto &s = queuepoly(V, ptriangle[side], magiccolors[side]);
ensure_vertex_number(*s.tinf, s.cnt);
}
}
return false;
}
auto hchook = addHook(hooks_drawcell, 100, draw_ptriangle)
+ addHook(hooks_args, 100, [] {
using namespace arg;
if(0) ;
else if(argis("-triset")) {
shift(); how = argi();
shift(); how1 = argi();
shift(); isteps = argi();
}
else return 1;
return 0;
});
}