143 lines
3.7 KiB
C++
143 lines
3.7 KiB
C++
// Hyperbolic Rogue
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// geometrical constants
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// Copyright (C) 2011-2012 Zeno Rogue, see 'hyper.cpp' for details
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ld tessf, crossf, hexf, hcrossf;
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// tessf: distance from heptagon center to another heptagon center
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// hexf: distance from heptagon center to heptagon vertex
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// crossf: distance from heptagon center to adjacent hexagon center
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#define ALPHA (M_PI*2/7)
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hyperpoint Crad[42];
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transmatrix heptmove[7], hexmove[7];
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transmatrix invheptmove[7], invhexmove[7];
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// the results are:
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// hexf = 0.378077 hcrossf = 0.620672 tessf = 1.090550
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void precalc() {
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DEBB(DF_INIT, (debugfile,"precalc\n"));
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if(euclid) return;
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ld fmin = 1, fmax = 2;
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for(int p=0; p<100; p++) {
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ld f = (fmin+fmax) / 2;
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hyperpoint H = xpush(f) * C0;
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ld v1 = intval(H, C0), v2 = intval(H, spin(2*M_PI/7)*H);
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if(v1 > v2) fmin = f; else fmax = f;
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}
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tessf = fmin;
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fmin = 0, fmax = 2;
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for(int p=0; p<100; p++) {
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ld f = (fmin+fmax) / 2;
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hyperpoint H = spin(M_PI/7) * xpush(f) * C0;
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ld v1 = intval(H, C0), v2 = intval(H, xpush(tessf) * C0);
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if(v1 < v2) fmin = f; else fmax = f;
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}
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hcrossf = fmin;
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crossf = purehepta ? tessf : hcrossf;
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fmin = 0, fmax = tessf;
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for(int p=0; p<100; p++) {
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ld f = (fmin+fmax) / 2;
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hyperpoint H = xpush(f) * C0;
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hyperpoint H1 = spin(2*M_PI/7) * H;
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hyperpoint H2 = xpush(tessf-f) * C0;
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ld v1 = intval(H, H1), v2 = intval(H, H2);
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if(v1 < v2) fmin = f; else fmax = f;
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}
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hexf = fmin;
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// printf("hexf = %.6Lf cross = %.6Lf tessf = %.6Lf\n", hexf, crossf, tessf);
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for(int i=0; i<42; i++)
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Crad[i] = spin(2*M_PI*i/42) * xpush(.4) * C0;
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for(int d=0; d<7; d++)
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heptmove[d] = spin(-d * ALPHA) * xpush(tessf) * spin(M_PI);
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for(int d=0; d<7; d++)
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hexmove[d] = spin(-d * ALPHA) * xpush(-crossf)* spin(M_PI);
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for(int d=0; d<7; d++) invheptmove[d] = inverse(heptmove[d]);
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for(int d=0; d<7; d++) invhexmove[d] = inverse(hexmove[d]);
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}
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transmatrix ddi(ld dir, ld dist) {
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// EUCLIDEAN
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if(euclid)
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return eupush(cos(M_PI*dir/42) * dist, -sin(M_PI*dir/42) * dist);
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else
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return spin(M_PI*dir/42) * xpush(dist) * spin(-M_PI*dir/42);
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}
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// tesselation drawing
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#define NUMFACE 500
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transmatrix tess[NUMFACE];
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void genTesselation() {
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int N = 1;
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tess[0] = Id;
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for(int i=0; i<N; i++) {
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for(int t=0; t<7; t++) {
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ld trot = (t % 8) * M_PI * 2 / 7.0;
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transmatrix T = spin(trot) * xpush(tessf) * /*spin(-trot) */ spin(M_PI) * tess[i];
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for(int j=0; j<N; j++) if(intval(T*C0, tess[j]*C0) < 0.1) goto nextt;
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// printf("%d:%d -> %d\n", i,t, N);
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tess[N] = T; N++;
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if(N == NUMFACE) return;
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nextt: ;
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}
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}
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}
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struct ltd {
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hyperpoint P1;
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hyperpoint P2;
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int col;
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};
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vector<ltd> lines;
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void addline(hyperpoint P1, hyperpoint P2, int col) {
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ltd L;
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L.P1 = P1; L.P2 = P2; L.col = col;
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lines.push_back(L);
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}
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void addlines() {
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// change the if(0) conditions to see the underlying structure
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if(0) for(int t =0; t<NUMFACE; t++) for(int u=1; u<8; u++) {
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addline(View * tess[t] * C0, View * tess[t] * tess[u] * C0, u==1 ? 0xA000 : 0x4000);
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}
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if(0) for(int t =0; t<NUMFACE; t++) for(int r=0; r<7; r++) {
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addline(
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View * tess[t] * spin((2*r+1)*M_PI/7) * xpush(crossf) * C0,
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View * tess[t] * spin((2*r+3)*M_PI/7) * xpush(crossf) * C0,
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0x808080);
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}
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if(1) for(int t =0; t<NUMFACE; t++) for(int r=0; r<7; r++) {
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addline(tess[t] * spin(M_PI*2*(r+1)/7) * xpush(hexf) * C0, tess[t] * spin(M_PI*2*r/7) * xpush(hexf) * C0, 0x404040);
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addline(tess[t] * spin(M_PI*2*r/7) * xpush(hexf) * C0, tess[t] * spin(M_PI*2*r/7) * xpush(tessf/2) * C0, 0x404040);
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}
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}
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void initgeo() {
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precalc();
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genTesselation();
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addlines();
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}
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