2 // Written and (C) by Francois Fleuret
3 // Contact <francois.fleuret@idiap.ch> for comments & bug reports
8 static const scalar_t dl = 20.0;
9 static const scalar_t repulsion_constant = 0.2;
10 static const scalar_t dissipation = 0.5;
12 Polygon::Polygon(scalar_t mass,
13 scalar_t red, scalar_t green, scalar_t blue,
14 scalar_t *x, scalar_t *y,
15 int nv) : _mass(mass),
16 _moment_of_inertia(0), _radius(0),
17 _relative_x(new scalar_t[nv]), _relative_y(new scalar_t[nv]),
19 _nb_dots(new int[nv]),
21 _length(new scalar_t[nv]),
22 _triangles(new Triangle[nv-2]),
23 _initialized(false), _nailed(false),
25 _x(new scalar_t[nv]), _y(new scalar_t[nv]),
26 _red(red), _green(green), _blue(blue) {
31 if(x) for(int i = 0; i < nv; i++) _relative_x[i] = x[i];
32 if(y) for(int i = 0; i < nv; i++) _relative_y[i] = y[i];
43 delete[] _effecting_edge;
46 Polygon *Polygon::clone() {
47 return new Polygon(_mass, _red, _green, _blue, _relative_x, _relative_y, _nb_vertices);
50 void Polygon::print_fig(XFigTracer *tracer) {
51 tracer->draw_polygon(_nb_vertices, _x, _y);
54 void Polygon::draw(SimpleWindow *window) {
55 window->color(_red, _green, _blue);
56 int x[_nb_vertices], y[_nb_vertices];
57 for(int n = 0; n < _nb_vertices; n++) {
61 window->fill_polygon(_nb_vertices, x, y);
64 void Polygon::draw_contours(SimpleWindow *window) {
65 int x[_nb_vertices], y[_nb_vertices];
66 for(int n = 0; n < _nb_vertices; n++) {
70 window->color(0.0, 0.0, 0.0);
71 for(int n = 0; n < _nb_vertices; n++)
72 window->draw_line(x[n], y[n], x[(n+1)%_nb_vertices], y[(n+1)%_nb_vertices]);
75 void Polygon::set_vertex(int k, scalar_t x, scalar_t y) {
80 void Polygon::set_position(scalar_t center_x, scalar_t center_y, scalar_t theta) {
86 void Polygon::set_speed(scalar_t dcenter_x, scalar_t dcenter_y, scalar_t dtheta) {
87 _dcenter_x = dcenter_x;
88 _dcenter_y = dcenter_y;
92 bool Polygon::contain(scalar_t x, scalar_t y) {
93 for(int t = 0; t < _nb_vertices-2; t++) {
94 scalar_t xa = _x[_triangles[t].a], ya = _y[_triangles[t].a];
95 scalar_t xb = _x[_triangles[t].b], yb = _y[_triangles[t].b];
96 scalar_t xc = _x[_triangles[t].c], yc = _y[_triangles[t].c];
97 if(prod_vect(x - xa, y - ya, xb - xa, yb - ya) <= 0 &&
98 prod_vect(x - xb, y - yb, xc - xb, yc - yb) <= 0 &&
99 prod_vect(x - xc, y - yc, xa - xc, ya - yc) <= 0) return true;
104 void Polygon::triangularize(int &nt, int nb, int *index) {
107 if(nt >= _nb_vertices-2) {
108 cerr << "Error type #1 in triangularization." << endl;
112 _triangles[nt].a = index[0];
113 _triangles[nt].b = index[1];
114 _triangles[nt].c = index[2];
118 int best_m = -1, best_n = -1;
119 scalar_t best_split = -1, det, s = -1, t = -1;
121 for(int n = 0; n < nb; n++) for(int m = 0; m < n; m++) if(n > m+1 && m+nb > n+1) {
122 bool no_intersection = true;
123 for(int k = 0; no_intersection & (k < nb); k++)
124 if(k != n && k != m && (k+1)%nb != n && (k+1)%nb != m) {
125 intersection(_relative_x[index[n]], _relative_y[index[n]],
126 _relative_x[index[m]], _relative_y[index[m]],
127 _relative_x[index[k]], _relative_y[index[k]],
128 _relative_x[index[(k+1)%nb]], _relative_y[index[(k+1)%nb]], det, s, t);
129 no_intersection = det == 0 || s < 0 || s > 1 || t < 0 || t > 1;
132 if(no_intersection) {
133 scalar_t a1 = 0, a2 = 0;
134 for(int k = 0; k < nb; k++) if(k >= m && k < n)
135 a1 += prod_vect(_relative_x[index[k]] - _relative_x[index[m]],
136 _relative_y[index[k]] - _relative_y[index[m]],
137 _relative_x[index[k+1]] - _relative_x[index[m]],
138 _relative_y[index[k+1]] - _relative_y[index[m]]);
140 a2 += prod_vect(_relative_x[index[k]] - _relative_x[index[m]],
141 _relative_y[index[k]] - _relative_y[index[m]],
142 _relative_x[index[(k+1)%nb]] - _relative_x[index[m]],
143 _relative_y[index[(k+1)%nb]] - _relative_y[index[m]]);
145 if((a1 * a2 > 0 && best_split < 0) || (abs(a1 - a2) < best_split)) {
146 best_n = n; best_m = m;
147 best_split = abs(a1 - a2);
152 if(best_n >= 0 && best_m >= 0) {
153 int index_neg[nb], index_pos[nb];
154 int neg = 0, pos = 0;
155 for(int k = 0; k < nb; k++) {
156 if(k >= best_m && k <= best_n) index_pos[pos++] = index[k];
157 if(k <= best_m || k >= best_n) index_neg[neg++] = index[k];
159 if(pos < 3 || neg < 3) {
160 cerr << "Error type #2 in triangularization." << endl;
163 triangularize(nt, pos, index_pos);
164 triangularize(nt, neg, index_neg);
166 cerr << "Error type #3 in triangularization." << endl;
172 void Polygon::initialize(int nb_polygons) {
175 _nb_polygons = nb_polygons;
177 a = _relative_x[_nb_vertices - 1] * _relative_y[0] - _relative_x[0] * _relative_y[_nb_vertices - 1];
178 for(int n = 0; n < _nb_vertices - 1; n++)
179 a += _relative_x[n] * _relative_y[n+1] - _relative_x[n+1] * _relative_y[n];
182 // Reorder the vertices
187 for(int n = 0; n < _nb_vertices / 2; n++) {
190 _relative_x[n] = _relative_x[_nb_vertices - 1 - n];
191 _relative_y[n] = _relative_y[_nb_vertices - 1 - n];
192 _relative_x[_nb_vertices - 1 - n] = x;
193 _relative_y[_nb_vertices - 1 - n] = y;
197 // Compute the center of mass and moment of inertia
203 for(int n = 0; n < _nb_vertices; n++) {
204 int np = (n+1)%_nb_vertices;
205 w =_relative_x[n] * _relative_y[np] - _relative_x[np] * _relative_y[n];
206 sx += (_relative_x[n] + _relative_x[np]) * w;
207 sy += (_relative_y[n] + _relative_y[np]) * w;
213 for(int n = 0; n < _nb_vertices; n++) {
214 _relative_x[n] -= sx;
215 _relative_y[n] -= sy;
216 scalar_t r = sqrt(sq(_relative_x[n]) + sq(_relative_y[n]));
217 if(r > _radius) _radius = r;
220 scalar_t num = 0, den = 0;
221 for(int n = 0; n < _nb_vertices; n++) {
222 int np = (n+1)%_nb_vertices;
223 den += abs(prod_vect(_relative_x[np], _relative_y[np], _relative_x[n], _relative_y[n]));
224 num += abs(prod_vect(_relative_x[np], _relative_y[np], _relative_x[n], _relative_y[n])) *
225 (_relative_x[np] * _relative_x[np] + _relative_y[np] * _relative_y[np] +
226 _relative_x[np] * _relative_x[n] + _relative_y[np] * _relative_y[n] +
227 _relative_x[n] * _relative_x[n] + _relative_y[n] * _relative_y[n]);
230 _moment_of_inertia = num / (6 * den);
232 scalar_t vx = cos(_theta), vy = sin(_theta);
234 for(int n = 0; n < _nb_vertices; n++) {
235 _x[n] = _center_x + _relative_x[n] * vx + _relative_y[n] * vy;
236 _y[n] = _center_y - _relative_x[n] * vy + _relative_y[n] * vx;
241 for(int n = 0; n < _nb_vertices; n++) {
242 length = sqrt(sq(_relative_x[n] - _relative_x[(n+1)%_nb_vertices]) +
243 sq(_relative_y[n] - _relative_y[(n+1)%_nb_vertices]));
245 _nb_dots[n] = int(length / dl + 1);
246 _total_nb_dots += _nb_dots[n];
249 delete[] _effecting_edge;
250 _effecting_edge = new int[_nb_polygons * _total_nb_dots];
251 for(int p = 0; p < _nb_polygons * _total_nb_dots; p++) _effecting_edge[p] = -1;
254 int index[_nb_vertices];
255 for(int n = 0; n < _nb_vertices; n++) index[n] = n;
256 triangularize(nt, _nb_vertices, index);
261 bool Polygon::update(scalar_t dt) {
263 _center_x += _dcenter_x * dt;
264 _center_y += _dcenter_y * dt;
265 _theta += _dtheta * dt;
268 scalar_t d = exp(log(dissipation) * dt);
273 scalar_t vx = cos(_theta), vy = sin(_theta);
275 for(int n = 0; n < _nb_vertices; n++) {
276 _x[n] = _center_x + _relative_x[n] * vx + _relative_y[n] * vy;
277 _y[n] = _center_y - _relative_x[n] * vy + _relative_y[n] * vx;
280 if(abs(_center_x - _last_center_x) +
281 abs(_center_y - _last_center_y) +
282 abs(_theta - _last_theta) * _radius > 0.1) {
283 _last_center_x = _center_x;
284 _last_center_y = _center_y;
285 _last_theta = _theta;
290 scalar_t Polygon::relative_x(scalar_t ax, scalar_t ay) {
291 return (ax - _center_x) * cos(_theta) - (ay - _center_y) * sin(_theta);
294 scalar_t Polygon::relative_y(scalar_t ax, scalar_t ay) {
295 return (ax - _center_x) * sin(_theta) + (ay - _center_y) * cos(_theta);
298 scalar_t Polygon::absolute_x(scalar_t rx, scalar_t ry) {
299 return _center_x + rx * cos(_theta) + ry * sin(_theta);
302 scalar_t Polygon::absolute_y(scalar_t rx, scalar_t ry) {
303 return _center_y - rx * sin(_theta) + ry * cos(_theta);
306 void Polygon::apply_force(scalar_t dt, scalar_t x, scalar_t y, scalar_t fx, scalar_t fy) {
307 _dcenter_x += fx / _mass * dt;
308 _dcenter_y += fy / _mass * dt;
309 _dtheta -= prod_vect(x - _center_x, y - _center_y, fx, fy) / (_mass * _moment_of_inertia) * dt;
312 void Polygon::apply_border_forces(scalar_t dt, scalar_t xmax, scalar_t ymax) {
313 for(int v = 0; v < _nb_vertices; v++) {
314 int vp = (v+1)%_nb_vertices;
315 for(int d = 0; d < _nb_dots[v]; d++) {
316 scalar_t s = scalar_t(d * dl)/_length[v];
317 scalar_t x = _x[v] * (1 - s) + _x[vp] * s;
318 scalar_t y = _y[v] * (1 - s) + _y[vp] * s;
319 scalar_t vx = 0, vy = 0;
321 else if(x > xmax) vx = x - xmax;
323 else if(y > ymax) vy = y - ymax;
324 apply_force(dt, x, y, - dl * vx * repulsion_constant, - dl * vy * repulsion_constant);
329 void Polygon::apply_collision_forces(scalar_t dt, int n_polygon, Polygon *p) {
330 scalar_t closest_x[_total_nb_dots], closest_y[_total_nb_dots];
331 bool inside[_total_nb_dots];
332 scalar_t distance[_total_nb_dots];
333 int _new_effecting_edge[_total_nb_dots];
337 for(int v = 0; v < _nb_vertices; v++) {
338 int vp = (v+1)%_nb_vertices;
339 scalar_t x = _x[v], y = _y[v], xp = _x[vp], yp = _y[vp];
341 for(int d = 0; d < _nb_dots[v]; d++) {
343 distance[d] = FLT_MAX;
346 // First, we tag the dots located inside the polygon p
348 for(int t = 0; t < p->_nb_vertices-2; t++) {
349 scalar_t min = 0, max = 1;
350 scalar_t xa = p->_x[p->_triangles[t].a], ya = p->_y[p->_triangles[t].a];
351 scalar_t xb = p->_x[p->_triangles[t].b], yb = p->_y[p->_triangles[t].b];
352 scalar_t xc = p->_x[p->_triangles[t].c], yc = p->_y[p->_triangles[t].c];
355 const scalar_t eps = 1e-6;
357 den = prod_vect(xp - x, yp - y, xb - xa, yb - ya);
358 num = prod_vect(xa - x, ya - y, xb - xa, yb - ya);
360 if(num / den < max) max = num / den;
361 } else if(den < -eps) {
362 if(num / den > min) min = num / den;
364 if(num < 0) { min = 1; max = 0; }
367 den = prod_vect(xp - x, yp - y, xc - xb, yc - yb);
368 num = prod_vect(xb - x, yb - y, xc - xb, yc - yb);
370 if(num / den < max) max = num / den;
371 } else if(den < -eps) {
372 if(num / den > min) min = num / den;
374 if(num < 0) { min = 1; max = 0; }
377 den = prod_vect(xp - x, yp - y, xa - xc, ya - yc);
378 num = prod_vect(xc - x, yc - y, xa - xc, ya - yc);
380 if(num / den < max) max = num / den;
381 } else if(den < -eps) {
382 if(num / den > min) min = num / den;
384 if(num < 0) { min = 1; max = 0; }
387 for(int d = 0; d < _nb_dots[v]; d++) {
388 scalar_t s = scalar_t(d * dl)/_length[v];
389 if(s >= min && s <= max) inside[d] = true;
393 // Then, we compute for each dot what is the closest point on
396 for(int m = 0; m < p->_nb_vertices; m++) {
397 int mp = (m+1)%p->_nb_vertices;
398 scalar_t xa = p->_x[m], ya = p->_y[m];
399 scalar_t xb = p->_x[mp], yb = p->_y[mp];
400 scalar_t gamma0 = ((x - xa) * (xb - xa) + (y - ya) * (yb - ya)) / sq(p->_length[m]);
401 scalar_t gamma1 = ((xp - x) * (xb - xa) + (yp - y) * (yb - ya)) / sq(p->_length[m]);
402 scalar_t delta0 = (prod_vect(xb - xa, yb - ya, x - xa, y - ya)) / p->_length[m];
403 scalar_t delta1 = (prod_vect(xb - xa, yb - ya, xp - x, yp - y)) / p->_length[m];
405 for(int d = 0; d < _nb_dots[v]; d++) if(inside[d]) {
406 int r = _effecting_edge[(first_dot + d) * _nb_polygons + n_polygon];
408 // If there is already a spring, we look only at the
409 // vertices next to the current one
411 if(r < 0 || m == r || m == (r+1)%p->_nb_vertices || (m+1)%p->_nb_vertices == r) {
413 scalar_t s = scalar_t(d * dl)/_length[v];
414 scalar_t delta = abs(s * delta1 + delta0);
415 if(delta < distance[d]) {
416 scalar_t gamma = s * gamma1 + gamma0;
418 scalar_t l = sqrt(sq(x * (1 - s) + xp * s - xa) + sq(y * (1 - s) + yp * s - ya));
419 if(l < distance[d]) {
423 _new_effecting_edge[first_dot + d] = m;
425 } else if(gamma > 1) {
426 scalar_t l = sqrt(sq(x * (1 - s) + xp * s - xb) + sq(y * (1 - s) + yp * s - yb));
427 if(l < distance[d]) {
431 _new_effecting_edge[first_dot + d] = m;
435 closest_x[d] = xa * (1 - gamma) + xb * gamma;
436 closest_y[d] = ya * (1 - gamma) + yb * gamma;
437 _new_effecting_edge[first_dot + d] = m;
441 } else _new_effecting_edge[first_dot + d] = -1;
446 for(int d = 0; d < _nb_dots[v]; d++) if(inside[d]) {
447 scalar_t s = scalar_t(d * dl)/_length[v];
448 scalar_t x = _x[v] * (1 - s) + _x[vp] * s;
449 scalar_t y = _y[v] * (1 - s) + _y[vp] * s;
450 scalar_t vx = x - closest_x[d];
451 scalar_t vy = y - closest_y[d];
454 closest_x[d], closest_y[d],
455 dl * vx * repulsion_constant, dl * vy * repulsion_constant);
459 - dl * vx * repulsion_constant, - dl * vy * repulsion_constant);
462 first_dot += _nb_dots[v];
465 for(int d = 0; d < _total_nb_dots; d++)
466 _effecting_edge[d * _nb_polygons + n_polygon] = _new_effecting_edge[d];
470 bool Polygon::collide(Polygon *p) {
471 for(int n = 0; n < _nb_vertices; n++) {
472 int np = (n+1)%_nb_vertices;
473 for(int m = 0; m < p->_nb_vertices; m++) {
474 int mp = (m+1)%p->_nb_vertices;
475 scalar_t det, s = -1, t = -1;
476 intersection(_x[n], _y[n], _x[np], _y[np],
477 p->_x[m], p->_y[m], p->_x[mp], p->_y[mp], det, s, t);
478 if(det != 0 && s>= 0 && s <= 1&& t >= 0 && t <= 1) return true;
482 for(int n = 0; n < _nb_vertices; n++) if(p->contain(_x[n], _y[n])) return true;
483 for(int n = 0; n < p->_nb_vertices; n++) if(contain(p->_x[n], p->_y[n])) return true;