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(ostream &os) {
51 // os << "2 3 0 1 0 7 50 -1 20 0.000 0 0 -1 0 0 " << _nb_vertices + 1 << endl;
53 do { c = int(drand48() * 32); } while(c == 7);
54 os << "2 3 0 1 0 6 50 -1 20 0.000 0 0 -1 0 0 " << _nb_vertices + 1 << endl;
55 // os << "2 3 0 0 0 " << c << " 50 -1 20 0.000 0 0 -1 0 0 " << _nb_vertices + 1 << endl;
56 // os << "2 3 0 2 7 " << c << " 50 -1 20 0.000 0 0 -1 0 0 " << _nb_vertices + 1 << endl;
58 for(int n = 0; n < _nb_vertices; n++) os << " " << int(_x[n]*10) << " " << int(_y[n]*10);
59 os << " " << int(_x[0]*10) << " " << int(_y[0]*10);
63 void Polygon::draw(SimpleWindow *window) {
64 window->color(_red, _green, _blue);
65 int x[_nb_vertices], y[_nb_vertices];
66 for(int n = 0; n < _nb_vertices; n++) {
70 window->fill_polygon(_nb_vertices, x, y);
73 void Polygon::draw_contours(SimpleWindow *window) {
74 int x[_nb_vertices], y[_nb_vertices];
75 for(int n = 0; n < _nb_vertices; n++) {
79 window->color(0.0, 0.0, 0.0);
80 for(int n = 0; n < _nb_vertices; n++)
81 window->draw_line(x[n], y[n], x[(n+1)%_nb_vertices], y[(n+1)%_nb_vertices]);
84 void Polygon::set_vertex(int k, scalar_t x, scalar_t y) {
89 void Polygon::set_position(scalar_t center_x, scalar_t center_y, scalar_t theta) {
95 void Polygon::set_speed(scalar_t dcenter_x, scalar_t dcenter_y, scalar_t dtheta) {
96 _dcenter_x = dcenter_x;
97 _dcenter_y = dcenter_y;
101 bool Polygon::contain(scalar_t x, scalar_t y) {
102 for(int t = 0; t < _nb_vertices-2; t++) {
103 scalar_t xa = _x[_triangles[t].a], ya = _y[_triangles[t].a];
104 scalar_t xb = _x[_triangles[t].b], yb = _y[_triangles[t].b];
105 scalar_t xc = _x[_triangles[t].c], yc = _y[_triangles[t].c];
106 if(prod_vect(x - xa, y - ya, xb - xa, yb - ya) <= 0 &&
107 prod_vect(x - xb, y - yb, xc - xb, yc - yb) <= 0 &&
108 prod_vect(x - xc, y - yc, xa - xc, ya - yc) <= 0) return true;
113 void Polygon::triangularize(int &nt, int nb, int *index) {
116 if(nt >= _nb_vertices-2) {
117 cerr << "Error type #1 in triangularization." << endl;
121 _triangles[nt].a = index[0];
122 _triangles[nt].b = index[1];
123 _triangles[nt].c = index[2];
127 int best_m = -1, best_n = -1;
128 scalar_t best_split = -1, det, s = -1, t = -1;
130 for(int n = 0; n < nb; n++) for(int m = 0; m < n; m++) if(n > m+1 && m+nb > n+1) {
131 bool no_intersection = true;
132 for(int k = 0; no_intersection & (k < nb); k++)
133 if(k != n && k != m && (k+1)%nb != n && (k+1)%nb != m) {
134 intersection(_relative_x[index[n]], _relative_y[index[n]],
135 _relative_x[index[m]], _relative_y[index[m]],
136 _relative_x[index[k]], _relative_y[index[k]],
137 _relative_x[index[(k+1)%nb]], _relative_y[index[(k+1)%nb]], det, s, t);
138 no_intersection = det == 0 || s < 0 || s > 1 || t < 0 || t > 1;
141 if(no_intersection) {
142 scalar_t a1 = 0, a2 = 0;
143 for(int k = 0; k < nb; k++) if(k >= m && k < n)
144 a1 += prod_vect(_relative_x[index[k]] - _relative_x[index[m]],
145 _relative_y[index[k]] - _relative_y[index[m]],
146 _relative_x[index[k+1]] - _relative_x[index[m]],
147 _relative_y[index[k+1]] - _relative_y[index[m]]);
149 a2 += prod_vect(_relative_x[index[k]] - _relative_x[index[m]],
150 _relative_y[index[k]] - _relative_y[index[m]],
151 _relative_x[index[(k+1)%nb]] - _relative_x[index[m]],
152 _relative_y[index[(k+1)%nb]] - _relative_y[index[m]]);
154 if((a1 * a2 > 0 && best_split < 0) || (abs(a1 - a2) < best_split)) {
155 best_n = n; best_m = m;
156 best_split = abs(a1 - a2);
161 if(best_n >= 0 && best_m >= 0) {
162 int index_neg[nb], index_pos[nb];
163 int neg = 0, pos = 0;
164 for(int k = 0; k < nb; k++) {
165 if(k >= best_m && k <= best_n) index_pos[pos++] = index[k];
166 if(k <= best_m || k >= best_n) index_neg[neg++] = index[k];
168 if(pos < 3 || neg < 3) {
169 cerr << "Error type #2 in triangularization." << endl;
172 triangularize(nt, pos, index_pos);
173 triangularize(nt, neg, index_neg);
175 cerr << "Error type #3 in triangularization." << endl;
181 void Polygon::initialize(int nb_polygons) {
184 _nb_polygons = nb_polygons;
186 a = _relative_x[_nb_vertices - 1] * _relative_y[0] - _relative_x[0] * _relative_y[_nb_vertices - 1];
187 for(int n = 0; n < _nb_vertices - 1; n++)
188 a += _relative_x[n] * _relative_y[n+1] - _relative_x[n+1] * _relative_y[n];
191 // Reorder the vertices
196 for(int n = 0; n < _nb_vertices / 2; n++) {
199 _relative_x[n] = _relative_x[_nb_vertices - 1 - n];
200 _relative_y[n] = _relative_y[_nb_vertices - 1 - n];
201 _relative_x[_nb_vertices - 1 - n] = x;
202 _relative_y[_nb_vertices - 1 - n] = y;
206 // Compute the center of mass and moment of inertia
212 for(int n = 0; n < _nb_vertices; n++) {
213 int np = (n+1)%_nb_vertices;
214 w =_relative_x[n] * _relative_y[np] - _relative_x[np] * _relative_y[n];
215 sx += (_relative_x[n] + _relative_x[np]) * w;
216 sy += (_relative_y[n] + _relative_y[np]) * w;
222 for(int n = 0; n < _nb_vertices; n++) {
223 _relative_x[n] -= sx;
224 _relative_y[n] -= sy;
225 scalar_t r = sqrt(sq(_relative_x[n]) + sq(_relative_y[n]));
226 if(r > _radius) _radius = r;
229 scalar_t num = 0, den = 0;
230 for(int n = 0; n < _nb_vertices; n++) {
231 int np = (n+1)%_nb_vertices;
232 den += abs(prod_vect(_relative_x[np], _relative_y[np], _relative_x[n], _relative_y[n]));
233 num += abs(prod_vect(_relative_x[np], _relative_y[np], _relative_x[n], _relative_y[n])) *
234 (_relative_x[np] * _relative_x[np] + _relative_y[np] * _relative_y[np] +
235 _relative_x[np] * _relative_x[n] + _relative_y[np] * _relative_y[n] +
236 _relative_x[n] * _relative_x[n] + _relative_y[n] * _relative_y[n]);
239 _moment_of_inertia = num / (6 * den);
241 scalar_t vx = cos(_theta), vy = sin(_theta);
243 for(int n = 0; n < _nb_vertices; n++) {
244 _x[n] = _center_x + _relative_x[n] * vx + _relative_y[n] * vy;
245 _y[n] = _center_y - _relative_x[n] * vy + _relative_y[n] * vx;
250 for(int n = 0; n < _nb_vertices; n++) {
251 length = sqrt(sq(_relative_x[n] - _relative_x[(n+1)%_nb_vertices]) +
252 sq(_relative_y[n] - _relative_y[(n+1)%_nb_vertices]));
254 _nb_dots[n] = int(length / dl + 1);
255 _total_nb_dots += _nb_dots[n];
258 delete[] _effecting_edge;
259 _effecting_edge = new int[_nb_polygons * _total_nb_dots];
260 for(int p = 0; p < _nb_polygons * _total_nb_dots; p++) _effecting_edge[p] = -1;
263 int index[_nb_vertices];
264 for(int n = 0; n < _nb_vertices; n++) index[n] = n;
265 triangularize(nt, _nb_vertices, index);
270 bool Polygon::update(scalar_t dt) {
272 _center_x += _dcenter_x * dt;
273 _center_y += _dcenter_y * dt;
274 _theta += _dtheta * dt;
277 scalar_t d = exp(log(dissipation) * dt);
282 scalar_t vx = cos(_theta), vy = sin(_theta);
284 for(int n = 0; n < _nb_vertices; n++) {
285 _x[n] = _center_x + _relative_x[n] * vx + _relative_y[n] * vy;
286 _y[n] = _center_y - _relative_x[n] * vy + _relative_y[n] * vx;
289 if(abs(_center_x - _last_center_x) +
290 abs(_center_y - _last_center_y) +
291 abs(_theta - _last_theta) * _radius > 0.1) {
292 _last_center_x = _center_x;
293 _last_center_y = _center_y;
294 _last_theta = _theta;
299 scalar_t Polygon::relative_x(scalar_t ax, scalar_t ay) {
300 return (ax - _center_x) * cos(_theta) - (ay - _center_y) * sin(_theta);
303 scalar_t Polygon::relative_y(scalar_t ax, scalar_t ay) {
304 return (ax - _center_x) * sin(_theta) + (ay - _center_y) * cos(_theta);
307 scalar_t Polygon::absolute_x(scalar_t rx, scalar_t ry) {
308 return _center_x + rx * cos(_theta) + ry * sin(_theta);
311 scalar_t Polygon::absolute_y(scalar_t rx, scalar_t ry) {
312 return _center_y - rx * sin(_theta) + ry * cos(_theta);
315 void Polygon::apply_force(scalar_t dt, scalar_t x, scalar_t y, scalar_t fx, scalar_t fy) {
316 _dcenter_x += fx / _mass * dt;
317 _dcenter_y += fy / _mass * dt;
318 _dtheta -= prod_vect(x - _center_x, y - _center_y, fx, fy) / (_mass * _moment_of_inertia) * dt;
321 void Polygon::apply_border_forces(scalar_t dt, scalar_t xmax, scalar_t ymax) {
322 for(int v = 0; v < _nb_vertices; v++) {
323 int vp = (v+1)%_nb_vertices;
324 for(int d = 0; d < _nb_dots[v]; d++) {
325 scalar_t s = scalar_t(d * dl)/_length[v];
326 scalar_t x = _x[v] * (1 - s) + _x[vp] * s;
327 scalar_t y = _y[v] * (1 - s) + _y[vp] * s;
328 scalar_t vx = 0, vy = 0;
330 else if(x > xmax) vx = x - xmax;
332 else if(y > ymax) vy = y - ymax;
333 apply_force(dt, x, y, - dl * vx * repulsion_constant, - dl * vy * repulsion_constant);
338 void Polygon::apply_collision_forces(scalar_t dt, int n_polygon, Polygon *p) {
339 scalar_t closest_x[_total_nb_dots], closest_y[_total_nb_dots];
340 bool inside[_total_nb_dots];
341 scalar_t distance[_total_nb_dots];
342 int _new_effecting_edge[_total_nb_dots];
346 for(int v = 0; v < _nb_vertices; v++) {
347 int vp = (v+1)%_nb_vertices;
348 scalar_t x = _x[v], y = _y[v], xp = _x[vp], yp = _y[vp];
350 for(int d = 0; d < _nb_dots[v]; d++) {
352 distance[d] = FLT_MAX;
355 // First, we tag the dots located inside the polygon p
357 for(int t = 0; t < p->_nb_vertices-2; t++) {
358 scalar_t min = 0, max = 1;
359 scalar_t xa = p->_x[p->_triangles[t].a], ya = p->_y[p->_triangles[t].a];
360 scalar_t xb = p->_x[p->_triangles[t].b], yb = p->_y[p->_triangles[t].b];
361 scalar_t xc = p->_x[p->_triangles[t].c], yc = p->_y[p->_triangles[t].c];
364 const scalar_t eps = 1e-6;
366 den = prod_vect(xp - x, yp - y, xb - xa, yb - ya);
367 num = prod_vect(xa - x, ya - y, xb - xa, yb - ya);
369 if(num / den < max) max = num / den;
370 } else if(den < -eps) {
371 if(num / den > min) min = num / den;
373 if(num < 0) { min = 1; max = 0; }
376 den = prod_vect(xp - x, yp - y, xc - xb, yc - yb);
377 num = prod_vect(xb - x, yb - y, xc - xb, yc - yb);
379 if(num / den < max) max = num / den;
380 } else if(den < -eps) {
381 if(num / den > min) min = num / den;
383 if(num < 0) { min = 1; max = 0; }
386 den = prod_vect(xp - x, yp - y, xa - xc, ya - yc);
387 num = prod_vect(xc - x, yc - y, xa - xc, ya - yc);
389 if(num / den < max) max = num / den;
390 } else if(den < -eps) {
391 if(num / den > min) min = num / den;
393 if(num < 0) { min = 1; max = 0; }
396 for(int d = 0; d < _nb_dots[v]; d++) {
397 scalar_t s = scalar_t(d * dl)/_length[v];
398 if(s >= min && s <= max) inside[d] = true;
402 // Then, we compute for each dot what is the closest point on
405 for(int m = 0; m < p->_nb_vertices; m++) {
406 int mp = (m+1)%p->_nb_vertices;
407 scalar_t xa = p->_x[m], ya = p->_y[m];
408 scalar_t xb = p->_x[mp], yb = p->_y[mp];
409 scalar_t gamma0 = ((x - xa) * (xb - xa) + (y - ya) * (yb - ya)) / sq(p->_length[m]);
410 scalar_t gamma1 = ((xp - x) * (xb - xa) + (yp - y) * (yb - ya)) / sq(p->_length[m]);
411 scalar_t delta0 = (prod_vect(xb - xa, yb - ya, x - xa, y - ya)) / p->_length[m];
412 scalar_t delta1 = (prod_vect(xb - xa, yb - ya, xp - x, yp - y)) / p->_length[m];
414 for(int d = 0; d < _nb_dots[v]; d++) if(inside[d]) {
415 int r = _effecting_edge[(first_dot + d) * _nb_polygons + n_polygon];
417 // If there is already a spring, we look only at the
418 // vertices next to the current one
420 if(r < 0 || m == r || m == (r+1)%p->_nb_vertices || (m+1)%p->_nb_vertices == r) {
422 scalar_t s = scalar_t(d * dl)/_length[v];
423 scalar_t delta = abs(s * delta1 + delta0);
424 if(delta < distance[d]) {
425 scalar_t gamma = s * gamma1 + gamma0;
427 scalar_t l = sqrt(sq(x * (1 - s) + xp * s - xa) + sq(y * (1 - s) + yp * s - ya));
428 if(l < distance[d]) {
432 _new_effecting_edge[first_dot + d] = m;
434 } else if(gamma > 1) {
435 scalar_t l = sqrt(sq(x * (1 - s) + xp * s - xb) + sq(y * (1 - s) + yp * s - yb));
436 if(l < distance[d]) {
440 _new_effecting_edge[first_dot + d] = m;
444 closest_x[d] = xa * (1 - gamma) + xb * gamma;
445 closest_y[d] = ya * (1 - gamma) + yb * gamma;
446 _new_effecting_edge[first_dot + d] = m;
450 } else _new_effecting_edge[first_dot + d] = -1;
455 for(int d = 0; d < _nb_dots[v]; d++) if(inside[d]) {
456 scalar_t s = scalar_t(d * dl)/_length[v];
457 scalar_t x = _x[v] * (1 - s) + _x[vp] * s;
458 scalar_t y = _y[v] * (1 - s) + _y[vp] * s;
459 scalar_t vx = x - closest_x[d];
460 scalar_t vy = y - closest_y[d];
463 closest_x[d], closest_y[d],
464 dl * vx * repulsion_constant, dl * vy * repulsion_constant);
468 - dl * vx * repulsion_constant, - dl * vy * repulsion_constant);
471 first_dot += _nb_dots[v];
474 for(int d = 0; d < _total_nb_dots; d++)
475 _effecting_edge[d * _nb_polygons + n_polygon] = _new_effecting_edge[d];
479 bool Polygon::collide(Polygon *p) {
480 for(int n = 0; n < _nb_vertices; n++) {
481 int np = (n+1)%_nb_vertices;
482 for(int m = 0; m < p->_nb_vertices; m++) {
483 int mp = (m+1)%p->_nb_vertices;
484 scalar_t det, s = -1, t = -1;
485 intersection(_x[n], _y[n], _x[np], _y[np],
486 p->_x[m], p->_y[m], p->_x[mp], p->_y[mp], det, s, t);
487 if(det != 0 && s>= 0 && s <= 1&& t >= 0 && t <= 1) return true;
491 for(int n = 0; n < _nb_vertices; n++) if(p->contain(_x[n], _y[n])) return true;
492 for(int n = 0; n < p->_nb_vertices; n++) if(contain(p->_x[n], p->_y[n])) return true;