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new Conformal Square projection (with transition and shader and Euclidean form)
This commit is contained in:
Zeno Rogue
parent
02f0b1e714
commit
1b7f4b869e
@ -1014,9 +1014,9 @@ enum eModel : int {
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mdWerner, mdAitoff, mdHammer, mdLoximuthal, mdMiller, mdGallStereographic, mdWinkelTripel,
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// 39..48
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mdPoorMan, mdPanini, mdRetroCraig, mdRetroLittrow, mdRetroHammer, mdThreePoint, mdLiePerspective, mdLieOrthogonal, mdRelPerspective, mdRelOrthogonal,
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// 49
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mdHorocyclicEqa,
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// 50..
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// 49..50
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mdHorocyclicEqa, mdConformalSquare,
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// 51..
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mdGUARD, mdPixel, mdHyperboloidFlat, mdPolynomial, mdManual
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};
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#endif
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@ -1078,6 +1078,7 @@ EX vector<modelinfo> mdinf = {
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{X3("relativistic perspective"), mf::euc_boring | mf::perspective},
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{X3("relativistic orthogonal"), mf::euc_boring},
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{X3("horocyclic equal-area"), mf::euc_boring | mf::equiarea | mf::orientation | mf::horocyclic},
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{X3("conformal square"), mf::orientation | mf::broken | mf::transition},
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{X3("guard"), mf::technical},
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{X3("pixel"), mf::technical},
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{X3("hypflat"), mf::technical},
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56
drawing.cpp
56
drawing.cpp
@ -1622,10 +1622,14 @@ EX namespace ods {
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bool broken_projection(dqi_poly& p0) {
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int broken_coord = models::get_broken_coord(pmodel);
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static bool in_broken = false;
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bool both_broken = pmodel == mdConformalSquare;
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if(broken_coord && !in_broken) {
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int zcoord = broken_coord;
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int ycoord = 3 - zcoord;
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int xcoord = 0;
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zcoord = 2;
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vector<hyperpoint> all;
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for(int i=0; i<p0.cnt; i++)
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@ -1634,9 +1638,17 @@ bool broken_projection(dqi_poly& p0) {
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int last_fail;
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for(auto& h: all) models::apply_orientation(h[0], h[1]);
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auto break_in_xz = [&] (hyperpoint a, hyperpoint b, int xcoord, int zcoord) {
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return a[xcoord] * b[xcoord] <= 0 && (a[xcoord] * b[zcoord] - b[xcoord] * a[zcoord]) * (a[xcoord] - b[xcoord]) < 0;
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};
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auto break_in = [&] (hyperpoint a, hyperpoint b) {
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return a[0] * b[0] <= 0 && (a[0] * b[zcoord] - b[0] * a[zcoord]) * (a[0] - b[0]) < 0;
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if(both_broken) {
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for(int xc=0; xc<2; xc++) {if(break_in_xz(a, b, xc, zcoord)) { xcoord = xc; ycoord = 1-xc; return true; } }
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return false;
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}
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return break_in_xz(a, b, xcoord, zcoord);
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};
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for(int i=0; i<p0.cnt-1; i++)
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@ -1655,7 +1667,12 @@ bool broken_projection(dqi_poly& p0) {
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if(fail) {
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if(p0.tinf) return true;
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dynamicval<bool> ib(in_broken, true);
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ld part = ilerp(all[last_fail][0], all[last_fail+1][0], 0);
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ld part = ilerp(all[last_fail][xcoord], all[last_fail+1][xcoord], 0);
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if(both_broken && all[last_fail][ycoord] * all[last_fail+1][ycoord] < 0) {
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ld part2 = ilerp(all[last_fail][ycoord], all[last_fail+1][ycoord], 0);
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if(part2 > part) part = part2, swap(xcoord, ycoord);
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}
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hyperpoint initial = normalize(lerp(all[last_fail], all[last_fail+1], 1 - (1-part) * .99));
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bool have_initial = true;
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v.push_back(glhr::pointtogl(initial));
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@ -1663,19 +1680,46 @@ bool broken_projection(dqi_poly& p0) {
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int at = last_fail;
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do {
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v.push_back(glhr::pointtogl(all[at]));
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if(at == p0.cnt-1 && all[at] != all[0]) {
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if(at == p0.cnt-1 && sqhypot_d(2, all[at] - all[0]) > 1e-6) {
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p.cnt = isize(v); p.draw(); v.clear(); at = 0;
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have_initial = false;
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}
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int next = at+1;
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if(next == p0.cnt) next = 0;
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if(break_in(all[at], all[next])) {
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ld part = ilerp(all[at][0], all[next][0], 0);
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ld part = ilerp(all[at][xcoord], all[next][xcoord], 0);
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if(both_broken && all[at][ycoord] * all[next][ycoord] < 0) {
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ld part2 = ilerp(all[at][ycoord], all[next][ycoord], 0);
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if(part2 < part) part = part2, swap(xcoord, ycoord);
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}
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hyperpoint final = normalize(lerp(all[at], all[next], part * .99));
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v.push_back(glhr::pointtogl(final));
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if(have_initial) {
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int max = 4 << vid.linequality;
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if(final[0] * initial[0] > 0) {
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if(both_broken) {
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auto square_close_corner = [] (hyperpoint h) {
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hyperpoint end = -C0;
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if(abs(h[0]) > abs(h[1]))
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end[0] = 0.01 * signum(h[0]), end[1] = 0.001 * signum(h[1]);
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else
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end[1] = 0.01 * signum(h[1]), end[0] = 0.001 * signum(h[0]);
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return normalize(end);
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};
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hyperpoint endf = square_close_corner(final);
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hyperpoint endi = square_close_corner(initial);
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if(endf != endi) {
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for(int i=1; i<=max; i++)
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v.push_back(glhr::pointtogl(lerp(final, endf, i * 1. / max)));
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for(int i=0; i<=max; i++)
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v.push_back(glhr::pointtogl(lerp(endi, initial, i * 1. / max)));
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}
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else {
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for(int i=1; i<=max; i++)
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v.push_back(glhr::pointtogl(lerp(final, initial, i * 1. / max)));
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}
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}
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else if(final[xcoord] * initial[xcoord] > 0) {
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for(int i=1; i<=max; i++)
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v.push_back(glhr::pointtogl(lerp(final, initial, i * 1. / max)));
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}
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85
hypgraph.cpp
85
hypgraph.cpp
@ -528,6 +528,81 @@ EX void make_axial(hyperpoint H, hyperpoint& ret, const hr::function<ld(hyperpoi
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models::apply_orientation_yz(ret[2], ret[1]);
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}
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// according to https://github.com/cspersonal/peirce-quincuncial-projection/blob/master/peirceQuincuncialProjection.R
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ld ellRF(ld x, ld y, ld z) {
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ld delx = 1, dely = 1, delz = 1;
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const ld eps = 0.0025;
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ld mean;
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while(abs(delx) > eps || abs(dely) > eps || abs(delz) > eps) {
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ld sx = sqrt(x);
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ld sy = sqrt(y);
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ld sz = sqrt(z);
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ld len = sx * (sy+sz) + sy * sz;
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x = .25 * (x+len);
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y = .25 * (y+len);
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z = .25 * (z+len);
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mean = (x+y+z)/3;
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delx = (mean-x) / mean;
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dely = (mean-y) / mean;
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delz = (mean-z) / mean;
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}
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ld e2 = delx * dely - delz * delz;
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ld e3 = delx * dely * delz;
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return ((1.0 + (e2 / 24.0 - 0.1 - 3.0 * e3 / 44.0) * e2+ e3 / 14) / sqrt(mean));
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}
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ld ellFaux(ld cos_phi, ld sin_phi, ld k) {
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ld x = cos_phi * cos_phi;
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ld y = 1 - k * k * sin_phi * sin_phi;
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return sin_phi * ellRF(x, y, 1);
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}
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ld sqrt_clamp(ld x) { if(x<0) return 0; return sqrt(x); }
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hyperpoint to_square(hyperpoint H) {
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ld d = hypot_d(2, H);
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ld x = d / (H[2] + 1);
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x *= pconf.model_transition;
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ld cos_phiosqrt2 = sqrt(2) / (x + 1/x);
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ld cos_lambda = -H[1] / d;
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ld sin_lambda = H[0] / d;
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ld cos_a = cos_phiosqrt2 * (sin_lambda + cos_lambda);
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ld cos_b = cos_phiosqrt2 * (sin_lambda - cos_lambda);
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ld sin_a = sqrt(1 - cos_a * cos_a);
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ld sin_b = sqrt(1 - cos_b * cos_b);
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ld cos_a_cos_b = cos_a * cos_b;
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ld sin_a_sin_b = sin_a * sin_b;
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ld sin2_m = 1.0 + cos_a_cos_b - sin_a_sin_b;
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ld sin2_n = 1.0 - cos_a_cos_b - sin_a_sin_b;
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ld sin_m = sqrt_clamp(sin2_m);
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ld cos_m = sqrt_clamp(1 - sin2_m);
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if(sin_lambda < 0) sin_m = -sin_m;
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ld sin_n = sqrt_clamp(sin2_n);
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ld cos_n = sqrt_clamp(1.0 - sin2_n);
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if(cos_lambda > 0.0) sin_n = -sin_n;
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hyperpoint res;
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ld divby = 0.53935260118837935472;
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res[0] = ellFaux(cos_m,sin_m,sqrt(2)/2.) * divby;
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res[1] = ellFaux(cos_n,sin_n,sqrt(2)/2.) * divby;
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res[2] = 0; res[3] = 1;
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if(x > 1) {
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if(abs(res[0]) > abs(res[1])) {
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if(res[0] > 0) res[0] = 2 - res[0]; else res[0] = -2 - res[0];
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}
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else {
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if(res[1] > 0) res[1] = 2 - res[1]; else res[1] = -2 - res[1];
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}
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}
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res /= pconf.model_transition;
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return res;
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}
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EX void apply_other_model(shiftpoint H_orig, hyperpoint& ret, eModel md) {
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hyperpoint H = H_orig.h;
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@ -810,6 +885,16 @@ EX void apply_other_model(shiftpoint H_orig, hyperpoint& ret, eModel md) {
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break;
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}
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case mdConformalSquare: {
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find_zlev(H);
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models::apply_orientation_yz(H[1], H[2]);
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models::apply_orientation(H[0], H[1]);
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ret = to_square(H);
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models::apply_orientation(ret[1], ret[0]);
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models::apply_orientation_yz(ret[2], ret[1]);
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break;
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}
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case mdLieOrthogonal: {
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ret = lie_log_correct(H_orig, H);
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68
shaders.cpp
68
shaders.cpp
@ -276,10 +276,15 @@ shared_ptr<glhr::GLprogram> write_shader(flagtype shader_flags) {
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}
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else if(pmodel == mdDisk && GDIM == 3 && !spherespecial && !nonisotropic && !gproduct) {
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coordinator += "t /= (t[3] + uAlpha);\n";
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vsh += "uniform mediump float uAlpha;";
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vsh += "uniform mediump float uAlpha;\n";
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shader_flags |= SF_DIRECT | SF_BOX | SF_ZFOG;
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treset = true;
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}
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else if(pmodel == mdConformalSquare && pconf.model_transition == 1) {
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shader_flags |= SF_ORIENT | SF_DIRECT;
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coordinator += "t = uPP * t;", vsh += "uniform mediump mat4 uPP;";
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coordinator += "t = to_square(t);";
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}
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else if(pmodel == mdBand && hyperbolic) {
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shader_flags |= SF_BAND | SF_ORIENT | SF_BOX | SF_DIRECT;
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coordinator += "t = uPP * t;", vsh += "uniform mediump mat4 uPP;";
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@ -848,6 +853,67 @@ EX void add_if(string& shader, const string& seek, const string& function) {
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EX void add_fixed_functions(string& shader) {
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/* from the most complex to the simplest */
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add_if(shader, "to_square",
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"mediump vec4 to_square(mediump vec4 h) {\n"
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"float d = length(h.xy);\n"
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"float x = d / (h.z + 1.);\n"
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"float cos_phiosqrt2 = sqrt(2.) / (x + 1./x);\n"
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"float cos_lambda = -h.y / d;\n"
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"float sin_lambda = h.x / d;\n"
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"float cos_a = cos_phiosqrt2 * (sin_lambda + cos_lambda);\n"
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"float cos_b = cos_phiosqrt2 * (sin_lambda - cos_lambda);\n"
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"float sin_a = sqrt(1. - cos_a * cos_a);\n"
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"float sin_b = sqrt(1. - cos_b * cos_b);\n"
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"float cos_a_cos_b = cos_a * cos_b;\n"
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"float sin_a_sin_b = sin_a * sin_b;\n"
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"float sin2_m = 1.0 + cos_a_cos_b - sin_a_sin_b;\n"
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"float sin2_n = 1.0 - cos_a_cos_b - sin_a_sin_b;\n"
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"float sin_m = sqrt_clamp(sin2_m);\n"
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"float cos_m = sqrt_clamp(1. - sin2_m);\n"
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"if(sin_lambda < 0.) sin_m = -sin_m;\n"
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"float sin_n = sqrt_clamp(sin2_n);\n"
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"float cos_n = sqrt_clamp(1.0 - sin2_n);\n"
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"if(cos_lambda > 0.0) sin_n = -sin_n;\n"
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"#define divby 0.53935260118837935472\n"
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"vec4 res = vec4(ellFaux(cos_m,sin_m,sqrt(2.)/2.) * divby, ellFaux(cos_n,sin_n,sqrt(2.)/2.) * divby, 0, 1);\n"
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"if(x > 1.) {\n"
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" if(abs(res[0]) > abs(res[1])) {\n"
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" if(res[0] > 0.) res[0] = 2. - res[0]; else res[0] = -2. - res[0];\n"
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" }\n"
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" else {\n"
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" if(res[1] > 0.) res[1] = 2. - res[1]; else res[1] = -2. - res[1];\n"
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" }\n"
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" }\n"
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"return res;\n"
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"}\n");
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add_if(shader, "sqrt_clamp", "mediump float sqrt_clamp(mediump float x) { return x >= 0. ? sqrt(x) : 0.; }\n");
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add_if(shader, "ellFaux", "mediump float ellFaux(mediump float cos_phi, mediump float sin_phi, mediump float k) {\n"
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"return sin_phi * ellRF(cos_phi * cos_phi, 1. - k * k * sin_phi * sin_phi, 1.);\n"
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"}\n");
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add_if(shader, "ellRF", "mediump float ellRF(mediump float x, mediump float y, mediump float z) {\n"
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"float delx = 1., dely = 1., delz = 1.;\n"
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"const float eps = 0.0025;\n"
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"float mean;\n"
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"while(abs(delx) > eps || abs(dely) > eps || abs(delz) > eps) {\n"
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" float sx = sqrt(x);\n"
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" float sy = sqrt(y);\n"
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" float sz = sqrt(z);\n"
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" float len = sx * (sy+sz) + sy * sz;\n"
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" float x = .25 * (x+len);\n"
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" float y = .25 * (y+len);\n"
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" float z = .25 * (z+len);\n"
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" mean = (x+y+z)/3.;\n"
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" delx = (mean-x) / mean;\n"
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" dely = (mean-y) / mean;\n"
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" delz = (mean-z) / mean;\n"
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" }\n"
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"float e2 = delx * dely - delz * delz;\n"
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"float e3 = delx * dely * delz;\n"
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"return ((1.0 + (e2 / 24.0 - 0.1 - 3.0 * e3 / 44.0) * e2+ e3 / 14.) / sqrt(mean));\n"
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"}\n");
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add_if(shader, "tanh", "mediump float tanh(mediump float x) { return sinh(x) / cosh(x); }\n");
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add_if(shader, "sinh", "mediump float sinh(mediump float x) { return (exp(x) - exp(-x)) / 2.0; }\n");
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add_if(shader, "asin_clamp", "mediump float asin_clamp(mediump float x) { return x > 1. ? PI/2. : x < -1. ? -PI/2. : asin(x); }\n");
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