horospherical rug for Euclidean IN Hyperbolic
This commit is contained in:
Zeno Rogue
parent
f6fa051eab
commit
540f0678ee
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@ -69,6 +69,10 @@ const hyperpoint Cx1 = { {1,0,1.41421356237} };
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// through the interior, not on the surface)
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// also used to verify whether a point h1 is on the hyperbolic plane by using Hypc for h2
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bool zero2(hyperpoint h) { return h[0] == 0 && h[1] == 0; }
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bool zero3(hyperpoint h) { return h[0] == 0 && h[1] == 0 && h[2] == 0; }
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ld intval(const hyperpoint &h1, const hyperpoint &h2) {
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if(elliptic) {
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double d1 = squar(h1[0]-h2[0]) + squar(h1[1]-h2[1]) + squar(h1[2]-h2[2]);
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@ -86,10 +90,22 @@ ld intvalxyz(const hyperpoint &h1, const hyperpoint &h2) {
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return squar(h1[0]-h2[0]) + squar(h1[1]-h2[1]) + squar(h1[2]-h2[2]);
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}
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ld hypot2(const hyperpoint& h) {
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return sqrt(h[0]*h[0]+h[1]*h[1]);
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}
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ld hypot3(const hyperpoint& h) {
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return sqrt(h[0]*h[0]+h[1]*h[1]+h[2]*h[2]);
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}
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ld sqhypot2(const hyperpoint& h) {
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return h[0]*h[0]+h[1]*h[1];
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}
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ld sqhypot3(const hyperpoint& h) {
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return h[0]*h[0]+h[1]*h[1]+h[2]*h[2];
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}
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ld zlevel(const hyperpoint &h) {
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if(euclid) return h[2];
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else if(sphere) return sqrt(intval(h, Hypc));
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205
rug.cpp
205
rug.cpp
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@ -34,9 +34,10 @@ GLAPI void APIENTRY glDeleteFramebuffers (GLsizei n, const GLuint *framebuffers)
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namespace rug {
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bool fast_euclidean = true;
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bool keep_torus = false;
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bool keep_shape = true;
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bool good_shape;
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int torus_precision = 2;
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ld modelscale = 1;
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eGeometry gwhere = gEuclid;
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@ -47,15 +48,16 @@ bool rugged = false;
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bool genrug = false;
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bool glew = false;
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int vertex_limit = 20000;
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bool renderonce = false;
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bool rendernogl = false;
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int texturesize = 1024;
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ld scale = 1;
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ld err_zero = 1e-3, err_zero_current;
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ld err_zero = 1e-3, err_zero_current, current_total_error;
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int queueiter, qvalid, dt;
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double err;
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struct edge {
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struct rugpoint *target;
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@ -103,29 +105,21 @@ bool rug_perspective = false;
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// returns a matrix M
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// such that inverse(M) * h1 = ( |h1|, 0, 0) and inverse(M) * h2 = ( .., .., 0)
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bool zero2(hyperpoint h) { using namespace hyperpoint_vec; return !(h|h); }
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transmatrix orthonormalize(hyperpoint h1, hyperpoint h2) {
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using namespace hyperpoint_vec;
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hyperpoint vec[3];
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vec[2] = (h1 ^ h2);
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if(zero2(vec[2])) vec[2] = hpxyz(.519, .4619, .136);
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vec[2] = vec[2] / sqrt(vec[2]|vec[2]);
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vec[0] = h1 - vec[2] * (h1|vec[2]);
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if(zero2(vec[0])) {
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vec[0] = hpxyz(1.641,2,3);
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vec[0] = vec[0] - vec[2] * (vec[0]|vec[2]);
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}
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vec[0] = vec[0] / sqrt(vec[0]|vec[0]);
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vec[1] = h2 - vec[2] * (h2|vec[2]) - vec[0] * (h2|vec[0]);
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if(zero2(vec[1])) {
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vec[1] = hpxyz(1.713,3,5);
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vec[1] = vec[1] - vec[2] * (vec[1]|vec[2]) - vec[0] * (vec[1]|vec[0]);
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}
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vec[1] = vec[1] / sqrt(vec[1]|vec[1]);
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hyperpoint vec[3] = {h1, h2, h1 ^ h2};
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for(int i=0; i<3; i++) {
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for(int j=0; j<i; j++) vec[i] -= vec[j] * (vec[i] | vec[j]);
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if(zero3(vec[i])) {
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// 'random' direction
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vec[i] = hpxyz(1.12, 1.512+i, 1.12904+i);
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for(int j=0; j<i; j++) vec[i] -= vec[j] * (vec[i] | vec[j]);
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}
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vec[i] /= hypot3(vec[i]);
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}
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transmatrix M;
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for(int i=0; i<3; i++) for(int j=0; j<3; j++)
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M[i][j] = vec[j][i];
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@ -145,13 +139,15 @@ hyperpoint azeq_to_hyperboloid(hyperpoint h) {
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return h;
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}
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if(sphere) {
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h[0] = sin(d) * h[0]/d;
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h[1] = sin(d) * h[1]/d;
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ld d0 = d ? d : 1;
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h[0] = sin(d) * h[0]/d0;
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h[1] = sin(d) * h[1]/d0;
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h[2] = cos(d);
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}
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else {
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h[0] = sinh(d) * h[0]/d;
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h[1] = sinh(d) * h[1]/d;
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ld d0 = d ? d : 1;
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h[0] = sinh(d) * h[0]/d0;
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h[1] = sinh(d) * h[1]/d0;
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h[2] = cosh(d);
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}
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return h;
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@ -165,7 +161,7 @@ hyperpoint hyperboloid_to_azeq(hyperpoint h) {
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else {
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ld d = hdist0(h);
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if(d == 0) { h[2] = 0; return h; }
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ld d2 = hypot(h[0], h[1]);
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ld d2 = hypot2(h);
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if(d2 == 0) { h[2] = 0; return h; }
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h[0] = d * h[0] / d2;
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h[1] = d * h[1] / d2;
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@ -174,19 +170,24 @@ hyperpoint hyperboloid_to_azeq(hyperpoint h) {
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}
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}
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void push_point(hyperpoint& h, int coord, ld val) {
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if(fast_euclidean && gwhere == gEuclid)
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h[coord] += val;
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else if(!val) return;
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else {
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// if(zero3(h)) { h[0] = 1e-9; h[1] = 1e-10; h[2] = 1e-11; }
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dynamicval<eGeometry> gw(geometry, gwhere);
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transmatrix M = orthonormalize(hpxyz(coord==0,coord==1,coord==2), h);
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transmatrix Mi = inverse(M);
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hyperpoint f = azeq_to_hyperboloid(Mi * h);
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h = M * hyperboloid_to_azeq(xpush(val) * f);
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}
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}
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void push_all_points(int coord, ld val) {
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if(!val) return;
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else if(fast_euclidean && gwhere == gEuclid) {
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for(int i=0; i<size(points); i++)
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points[i]->flat[coord] += val;
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}
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else for(int i=0; i<size(points); i++) {
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dynamicval<eGeometry> gw(geometry, gwhere);
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transmatrix M = orthonormalize(hpxyz(coord==0,coord==1,coord==2), points[i]->flat);
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transmatrix Mi = inverse(M);
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hyperpoint f = azeq_to_hyperboloid(Mi * points[i]->flat);
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points[i]->flat = M * hyperboloid_to_azeq(xpush(val) * f);
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}
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else for(int i=0; i<size(points); i++)
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push_point(points[i]->flat, coord, val);
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}
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// construct the graph
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@ -208,12 +209,27 @@ rugpoint *addRugpoint(hyperpoint h, double dist) {
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applymodel(m->h, onscreen);
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m->x1 = (1 + onscreen[0] * vid.scale) / 2;
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m->y1 = (1 + onscreen[1] * vid.scale) / 2;
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m->valid = false;
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m->flat = // hpxyz(h[0], h[1], sin(atan2(h[0], h[1]) * 3 + hyprand) * (h[2]-1) / 1000);
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if(euclid && gwhere == gNormal) {
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m->valid = good_shape = true;
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using namespace hyperpoint_vec;
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h *= modelscale;
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ld d = hypot2(h);
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// point on a horocycle going through C0 in distance d along the horocycle
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hyperpoint horocycle_point = hpxy(d*d/2, d);
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ld horodist = hdist0(horocycle_point);
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ld z = hypot2(horocycle_point);
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if(z==0) z = 1;
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if(d==0) d = 1;
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m->flat =
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hpxyz(horodist * h[0]/d * horocycle_point[1] / z, horodist * h[1]/d * horocycle_point[1] / z, -horodist * horocycle_point[0] / z);
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}
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else m->flat = // hpxyz(h[0], h[1], sin(atan2(h[0], h[1]) * 3 + hyprand) * (h[2]-1) / 1000);
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hpxyz(h[0], h[1], (h[2]-1) * (rand() % 1000 - rand() % 1000) / 1000);
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if(rug_perspective && gwhere == gEuclid) m->flat[2] -= 3;
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m->valid = false;
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// if(rug_perspective && gwhere == gEuclid) m->flat[2] -= 3;
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m->inqueue = false;
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m->dist = dist;
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points.push_back(m);
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@ -232,9 +248,9 @@ rugpoint *findOrAddRugpoint(hyperpoint h, double dist) {
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}
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void addNewEdge(rugpoint *e1, rugpoint *e2, ld len = 1) {
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edge e; e.target = e2; e1->edges.push_back(e);
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edge e; e.len = len;
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e.target = e2; e1->edges.push_back(e);
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e.target = e1; e2->edges.push_back(e);
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e.len = len;
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}
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void addEdge(rugpoint *e1, rugpoint *e2, ld len = 1) {
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@ -250,10 +266,17 @@ void addTriangle(rugpoint *t1, rugpoint *t2, rugpoint *t3, ld len = 1) {
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triangles.push_back(triangle(t1,t2,t3));
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}
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map<pair<rugpoint*, rugpoint*>, rugpoint*> halves;
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rugpoint* findhalf(rugpoint *r1, rugpoint *r2) {
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if(r1 > r2) swap(r1, r2);
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return halves[{r1,r2}];
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}
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void addTriangle1(rugpoint *t1, rugpoint *t2, rugpoint *t3) {
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rugpoint *t12 = findOrAddRugpoint(mid(t1->h, t2->h), (t1->dist+ t2->dist)/2);
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rugpoint *t23 = findOrAddRugpoint(mid(t2->h, t3->h), (t1->dist+ t2->dist)/2);
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rugpoint *t31 = findOrAddRugpoint(mid(t3->h, t1->h), (t1->dist+ t2->dist)/2);
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rugpoint *t12 = findhalf(t1, t2);
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rugpoint *t23 = findhalf(t2, t3);
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rugpoint *t31 = findhalf(t3, t1);
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addTriangle(t1, t12, t31);
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addTriangle(t12, t2, t23);
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addTriangle(t23, t3, t31);
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@ -264,8 +287,6 @@ bool psort(rugpoint *a, rugpoint *b) {
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return hdist0(a->h) < hdist0(b->h);
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}
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ld modelscale = 1;
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void calcLengths() {
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for(int i=0; i<size(points); i++) for(int j=0; j<size(points[i]->edges); j++) {
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ld d = hdist(points[i]->h, points[i]->edges[j].target->h);
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@ -356,14 +377,18 @@ void buildTorusRug() {
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double beta = -h2[1] * 2 * M_PI;
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// r->flat = {alpha, beta, 0};
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double sc = (factor+1)/4;
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r->flat = hpxyz((factor+cos(alpha)) * cos(beta) * sc, (factor+cos(alpha)) * sin(beta) * sc, -sin(alpha) * sc);
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r->flat = r->h = hpxyz((factor+cos(alpha)) * cos(beta) * sc, (factor+cos(alpha)) * sin(beta) * sc, -sin(alpha) * sc);
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r->valid = true;
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rugpoint *r2 = findRugpoint(r->flat);
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printf("(%lf %lf) %p .. %p\n", x, y, r, r2);
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if(r2 && r2 != r) r->glueto(r2);
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return r;
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};
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int rugmax = (int) sqrt(vertex_limit / qty);
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if(rugmax < 1) rugmax = 1;
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if(rugmax > 16) rugmax = 16;
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int rugmax = min(torus_precision, 16);
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ld rmd = rugmax;
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for(int i=0; i<qty; i++) {
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@ -375,8 +400,8 @@ void buildTorusRug() {
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for(int yy=0; yy<rugmax; yy++)
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for(int xx=0; xx<rugmax; xx++)
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addTriangle(rugarr[yy][xx], rugarr[yy+1][xx], rugarr[yy+1][xx+1], 1./rugmax),
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addTriangle(rugarr[yy][xx], rugarr[yy][xx+1], rugarr[yy+1][xx+1], 1./rugmax);
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addTriangle(rugarr[yy][xx], rugarr[yy+1][xx], rugarr[yy+1][xx+1], modelscale/rugmax),
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addTriangle(rugarr[yy][xx], rugarr[yy][xx+1], rugarr[yy+1][xx+1], modelscale/rugmax);
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}
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double maxz = 0;
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@ -401,6 +426,7 @@ void buildTorusRug() {
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void buildRug() {
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if(torus) {
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good_shape = true;
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buildTorusRug();
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return;
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}
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@ -443,15 +469,17 @@ void enqueue(rugpoint *m) {
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m->inqueue = true;
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}
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void force_euclidean(rugpoint& m1, rugpoint& m2, double rd, double d1=1, double d2=1) {
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if(!m1.valid || !m2.valid) return;
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bool force_euclidean(rugpoint& m1, rugpoint& m2, double rd, double d1=1, double d2=1) {
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if(!m1.valid || !m2.valid) return false;
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// double rd = hdist(m1.h, m2.h) * xd;
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// if(rd > rdz +1e-6 || rd< rdz-1e-6) printf("%lf %lf\n", rd, rdz);
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double t = 0;
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for(int i=0; i<3; i++) t += (m1.flat[i] - m2.flat[i]) * (m1.flat[i] - m2.flat[i]);
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t = sqrt(t);
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// printf("%lf %lf\n", t, rd);
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err += (t-rd) * (t-rd);
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/* printf("%s ", display(m1.flat));
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printf("%s ", display(m2.flat));
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printf("%lf/%lf\n", t, rd); */
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current_total_error += (t-rd) * (t-rd);
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bool nonzero = abs(t-rd) > err_zero_current;
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double force = (t - rd) / t / 2; // 20.0;
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for(int i=0; i<3; i++) {
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@ -460,13 +488,13 @@ void force_euclidean(rugpoint& m1, rugpoint& m2, double rd, double d1=1, double
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m2.flat[i] -= di * d2;
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if(nonzero && d2>0) enqueue(&m2);
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}
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return nonzero;
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}
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void force(rugpoint& m1, rugpoint& m2, double rd, double d1=1, double d2=1) {
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if(!m1.valid || !m2.valid) return;
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bool force(rugpoint& m1, rugpoint& m2, double rd, double d1=1, double d2=1) {
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if(!m1.valid || !m2.valid) return false;
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if(gwhere == gEuclid && fast_euclidean) {
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force_euclidean(m1, m2, rd, d1, d2);
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return;
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return force_euclidean(m1, m2, rd, d1, d2);
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}
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// double rd = hdist(m1.h, m2.h) * xd;
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// if(rd > rdz +1e-6 || rd< rdz-1e-6) printf("%lf %lf\n", rd, rdz);
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@ -478,7 +506,7 @@ void force(rugpoint& m1, rugpoint& m2, double rd, double d1=1, double d2=1) {
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hyperpoint f2 = azeq_to_hyperboloid(Mi * m2.flat);
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ld t = hdist(f1, f2);
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err += (t-rd) * (t-rd);
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current_total_error += (t-rd) * (t-rd);
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bool nonzero = abs(t-rd) > err_zero_current;
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double forcev = (t - rd) / 2; // 20.0;
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@ -514,6 +542,7 @@ void force(rugpoint& m1, rugpoint& m2, double rd, double d1=1, double d2=1) {
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m2.flat = M * hyperboloid_to_azeq(f2);
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if(nonzero && d2>0) enqueue(&m2);
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return nonzero;
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}
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void preset(rugpoint *m) {
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@ -567,11 +596,17 @@ void preset(rugpoint *m) {
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int divides = 0;
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bool stop = false;
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bool subdivide_further() {
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if(torus) return false;
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return size(points) * 4 < vertex_limit;
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}
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void subdivide() {
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int N = size(points);
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// if(euclid && gwhere == gEuclid) return;
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if(N >= 8000 || torus) {
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err_zero /= 2;
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if(!subdivide_further()) {
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err_zero_current /= 2;
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printf("increasing precision to %lg\n", err_zero_current);
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for(auto p: points) enqueue(p);
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return;
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}
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@ -580,12 +615,16 @@ void subdivide() {
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vector<triangle> otriangles = triangles;
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triangles.clear();
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halves.clear();
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// subdivide edges
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for(int i=0; i<N; i++) {
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rugpoint *m = points[i];
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for(int j=0; j<size(m->edges); j++) {
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||||
rugpoint *m2 = m->edges[j].target;
|
||||
if(m2 < m) continue;
|
||||
rugpoint *mm = addRugpoint(mid(m->h, m2->h), (m->dist+m2->dist)/2);
|
||||
halves[{m, m2}] = mm;
|
||||
using namespace hyperpoint_vec;
|
||||
mm->flat = (m->flat + m2->flat) / 2;
|
||||
mm->valid = true; qvalid++;
|
||||
|
|
@ -621,23 +660,24 @@ void addNewPoints() {
|
|||
qvalid++;
|
||||
if(i > 7) preset(&m);
|
||||
|
||||
for(int it=0; it<50; it++)
|
||||
if(good_shape) ;
|
||||
else for(int it=0; it<50; it++)
|
||||
for(int j=0; j<size(m.edges); j++)
|
||||
force(m, *m.edges[j].target, m.edges[j].len, 1, 0);
|
||||
|
||||
enqueue(&m);
|
||||
}
|
||||
}
|
||||
if(qvalid != oqvalid) { printf("%4d %4d %4d %.9lf %9d %9d\n", oqvalid, qvalid, size(points), dist, dt, queueiter); }
|
||||
if(qvalid != oqvalid) { printf("adding new points %4d %4d %4d %.9lf %9d %9d\n", oqvalid, qvalid, size(points), dist, dt, queueiter); }
|
||||
}
|
||||
|
||||
void physics() {
|
||||
|
||||
if(keep_torus && torus) return;
|
||||
if(keep_shape && good_shape) return;
|
||||
|
||||
auto t = SDL_GetTicks();
|
||||
|
||||
int t = SDL_GetTicks();
|
||||
|
||||
err = 0;
|
||||
current_total_error = 0;
|
||||
|
||||
while(SDL_GetTicks() < t + 5 && !stop)
|
||||
for(int it=0; it<50; it++)
|
||||
|
|
@ -647,11 +687,14 @@ void physics() {
|
|||
rugpoint *m = pqueue.front();
|
||||
pqueue.pop();
|
||||
m->inqueue = false;
|
||||
bool moved = false;
|
||||
for(int j=0; j<size(m->edges); j++)
|
||||
force(*m, *m->edges[j].target, m->edges[j].len);
|
||||
moved = force(*m, *m->edges[j].target, m->edges[j].len) || moved;
|
||||
|
||||
if(moved) enqueue(m);
|
||||
}
|
||||
|
||||
if(!stop) printf("%5d %10.7lf D%d Q%3d Qv%5d\n", queueiter, err, divides, size(pqueue), qvalid);
|
||||
if(!stop) printf("%5d %10.7lf D%d Q%3d Qv%5d\n", queueiter, current_total_error, divides, size(pqueue), qvalid);
|
||||
}
|
||||
|
||||
// drawing the Rug
|
||||
|
|
@ -930,9 +973,10 @@ void init() {
|
|||
genrug = false;
|
||||
|
||||
qvalid = 0; dt = 0; queueiter = 0;
|
||||
err_zero = err_zero_current;
|
||||
err_zero_current = err_zero;
|
||||
|
||||
buildRug();
|
||||
while(good_shape && subdivide_further()) subdivide();
|
||||
if(rug_perspective)
|
||||
push_all_points(2, -1);
|
||||
|
||||
|
|
@ -963,7 +1007,6 @@ void actDraw() {
|
|||
transmatrix t = Id;
|
||||
|
||||
if(rug_perspective) {
|
||||
int qms = 0;
|
||||
if(keystate[SDLK_HOME]) qm++, t = t * rotmatrix(alpha, 0, 1);
|
||||
if(keystate[SDLK_END]) qm++, t = t * rotmatrix(alpha, 1, 0);
|
||||
|
||||
|
|
@ -1079,9 +1122,7 @@ void show() {
|
|||
dialog::addBoolItem(XLAT("render texture without OpenGL"), (rendernogl), 'g');
|
||||
dialog::addSelItem(XLAT("texture size"), its(texturesize)+"x"+its(texturesize), 's');
|
||||
if(torus) {
|
||||
if(torus_precision < 1) torus_precision = 1;
|
||||
if(torus_precision > 16) torus_precision = 16;
|
||||
dialog::addSelItem(XLAT("precision"), its(torus_precision), 'p');
|
||||
dialog::addSelItem(XLAT("vertex_limit"), its(vertex_limit), 'p');
|
||||
}
|
||||
dialog::display();
|
||||
keyhandler = [] (int sym, int uni) {
|
||||
|
|
@ -1109,8 +1150,8 @@ void show() {
|
|||
}
|
||||
else if(uni == 'o')
|
||||
renderonce = !renderonce;
|
||||
else if(uni == 'p' && torus_precision)
|
||||
dialog::editNumber(torus_precision, 0, 16, 1, 2, "precision", "precision");
|
||||
else if(uni == 'p')
|
||||
dialog::editNumber(vertex_limit, 0, 16, 1, 2, "vertex limit", "vertex limit");
|
||||
#if !ISPANDORA
|
||||
else if(uni == 'g')
|
||||
rendernogl = !rendernogl;
|
||||
|
|
@ -1150,7 +1191,11 @@ int rugArgs() {
|
|||
}
|
||||
|
||||
else if(argis("-rugerr")) {
|
||||
err_zero = argf();
|
||||
shift(); err_zero = argf();
|
||||
}
|
||||
|
||||
else if(argis("-rugv")) {
|
||||
shift(); vertex_limit = argi();
|
||||
}
|
||||
|
||||
else return 1;
|
||||
|
|
|
|||
Loading…
Reference in New Issue