2 // Written and (C) by Francois Fleuret
3 // Contact <francois.fleuret@idiap.ch> for comments & bug reports
12 static const scalar_t dl = 20.0;
13 static const scalar_t repulsion_constant = 0.2;
14 static const scalar_t dissipation = 0.5;
16 Polygon::Polygon(scalar_t mass,
17 scalar_t red, scalar_t green, scalar_t blue,
18 scalar_t *x, scalar_t *y,
19 int nv) : _mass(mass),
20 _moment_of_inertia(0), _radius(0),
21 _relative_x(new scalar_t[nv]), _relative_y(new scalar_t[nv]),
23 _nb_dots(new int[nv]),
25 _length(new scalar_t[nv]),
26 _triangles(new Triangle[nv-2]),
27 _initialized(false), _nailed(false),
29 _x(new scalar_t[nv]), _y(new scalar_t[nv]),
30 _red(red), _green(green), _blue(blue) {
35 if(x) for(int i = 0; i < nv; i++) _relative_x[i] = x[i];
36 if(y) for(int i = 0; i < nv; i++) _relative_y[i] = y[i];
47 delete[] _effecting_edge;
50 Polygon *Polygon::clone() {
51 return new Polygon(_mass, _red, _green, _blue, _relative_x, _relative_y, _nb_vertices);
55 void Polygon::color_xfig(XFigTracer *tracer) {
56 tracer->add_color(int(255 * _red), int(255 * _green), int(255 * _blue));
59 void Polygon::print_xfig(XFigTracer *tracer) {
60 tracer->draw_polygon(int(255 * _red), int(255 * _green), int(255 * _blue),
61 _nb_vertices, _x, _y);
66 void Polygon::draw(SimpleWindow *window) {
67 window->color(_red, _green, _blue);
68 int x[_nb_vertices], y[_nb_vertices];
69 for(int n = 0; n < _nb_vertices; n++) {
73 window->fill_polygon(_nb_vertices, x, y);
76 void Polygon::draw_contours(SimpleWindow *window) {
77 int x[_nb_vertices], y[_nb_vertices];
78 for(int n = 0; n < _nb_vertices; n++) {
82 window->color(0.0, 0.0, 0.0);
83 // window->color(1.0, 1.0, 1.0);
84 for(int n = 0; n < _nb_vertices; n++) {
85 window->draw_line(x[n], y[n], x[(n+1)%_nb_vertices], y[(n+1)%_nb_vertices]);
90 void Polygon::draw(Canvas *canvas) {
91 canvas->set_drawing_color(_red, _green, _blue);
92 canvas->draw_polygon(1, _nb_vertices, _x, _y);
95 void Polygon::draw_contours(Canvas *canvas) {
96 canvas->set_drawing_color(0.0, 0.0, 0.0);
97 canvas->draw_polygon(0, _nb_vertices, _x, _y);
100 void Polygon::set_vertex(int k, scalar_t x, scalar_t y) {
105 void Polygon::set_position(scalar_t center_x, scalar_t center_y, scalar_t theta) {
106 _center_x = center_x;
107 _center_y = center_y;
111 void Polygon::set_speed(scalar_t dcenter_x, scalar_t dcenter_y, scalar_t dtheta) {
112 _dcenter_x = dcenter_x;
113 _dcenter_y = dcenter_y;
117 bool Polygon::contain(scalar_t x, scalar_t y) {
118 for(int t = 0; t < _nb_vertices-2; t++) {
119 scalar_t xa = _x[_triangles[t].a], ya = _y[_triangles[t].a];
120 scalar_t xb = _x[_triangles[t].b], yb = _y[_triangles[t].b];
121 scalar_t xc = _x[_triangles[t].c], yc = _y[_triangles[t].c];
122 if(prod_vect(x - xa, y - ya, xb - xa, yb - ya) <= 0 &&
123 prod_vect(x - xb, y - yb, xc - xb, yc - yb) <= 0 &&
124 prod_vect(x - xc, y - yc, xa - xc, ya - yc) <= 0) return true;
129 void Polygon::triangularize(int &nt, int nb, int *index) {
132 if(nt >= _nb_vertices-2) {
133 cerr << "Error type #1 in triangularization." << endl;
137 _triangles[nt].a = index[0];
138 _triangles[nt].b = index[1];
139 _triangles[nt].c = index[2];
143 int best_m = -1, best_n = -1;
144 scalar_t best_split = -1, det, s = -1, t = -1;
146 for(int n = 0; n < nb; n++) for(int m = 0; m < n; m++) if(n > m+1 && m+nb > n+1) {
147 bool no_intersection = true;
148 for(int k = 0; no_intersection & (k < nb); k++)
149 if(k != n && k != m && (k+1)%nb != n && (k+1)%nb != m) {
150 intersection(_relative_x[index[n]], _relative_y[index[n]],
151 _relative_x[index[m]], _relative_y[index[m]],
152 _relative_x[index[k]], _relative_y[index[k]],
153 _relative_x[index[(k+1)%nb]], _relative_y[index[(k+1)%nb]], det, s, t);
154 no_intersection = det == 0 || s < 0 || s > 1 || t < 0 || t > 1;
157 if(no_intersection) {
158 scalar_t a1 = 0, a2 = 0;
159 for(int k = 0; k < nb; k++) if(k >= m && k < n)
160 a1 += prod_vect(_relative_x[index[k]] - _relative_x[index[m]],
161 _relative_y[index[k]] - _relative_y[index[m]],
162 _relative_x[index[k+1]] - _relative_x[index[m]],
163 _relative_y[index[k+1]] - _relative_y[index[m]]);
165 a2 += prod_vect(_relative_x[index[k]] - _relative_x[index[m]],
166 _relative_y[index[k]] - _relative_y[index[m]],
167 _relative_x[index[(k+1)%nb]] - _relative_x[index[m]],
168 _relative_y[index[(k+1)%nb]] - _relative_y[index[m]]);
170 if((a1 * a2 > 0 && best_split < 0) || (abs(a1 - a2) < best_split)) {
171 best_n = n; best_m = m;
172 best_split = abs(a1 - a2);
177 if(best_n >= 0 && best_m >= 0) {
178 int index_neg[nb], index_pos[nb];
179 int neg = 0, pos = 0;
180 for(int k = 0; k < nb; k++) {
181 if(k >= best_m && k <= best_n) index_pos[pos++] = index[k];
182 if(k <= best_m || k >= best_n) index_neg[neg++] = index[k];
184 if(pos < 3 || neg < 3) {
185 cerr << "Error type #2 in triangularization." << endl;
188 triangularize(nt, pos, index_pos);
189 triangularize(nt, neg, index_neg);
191 cerr << "Error type #3 in triangularization." << endl;
197 void Polygon::initialize(int nb_polygons) {
200 _nb_polygons = nb_polygons;
202 a = _relative_x[_nb_vertices - 1] * _relative_y[0]
203 - _relative_x[0] * _relative_y[_nb_vertices - 1];
205 for(int n = 0; n < _nb_vertices - 1; n++)
206 a += _relative_x[n] * _relative_y[n+1] - _relative_x[n+1] * _relative_y[n];
209 // Reorder the vertices
214 for(int n = 0; n < _nb_vertices / 2; n++) {
217 _relative_x[n] = _relative_x[_nb_vertices - 1 - n];
218 _relative_y[n] = _relative_y[_nb_vertices - 1 - n];
219 _relative_x[_nb_vertices - 1 - n] = x;
220 _relative_y[_nb_vertices - 1 - n] = y;
224 // Compute the center of mass and moment of inertia
230 for(int n = 0; n < _nb_vertices; n++) {
231 int np = (n+1)%_nb_vertices;
232 w =_relative_x[n] * _relative_y[np] - _relative_x[np] * _relative_y[n];
233 sx += (_relative_x[n] + _relative_x[np]) * w;
234 sy += (_relative_y[n] + _relative_y[np]) * w;
240 for(int n = 0; n < _nb_vertices; n++) {
241 _relative_x[n] -= sx;
242 _relative_y[n] -= sy;
243 scalar_t r = sqrt(sq(_relative_x[n]) + sq(_relative_y[n]));
244 if(r > _radius) _radius = r;
247 scalar_t num = 0, den = 0;
248 for(int n = 0; n < _nb_vertices; n++) {
249 int np = (n+1)%_nb_vertices;
250 den += abs(prod_vect(_relative_x[np], _relative_y[np], _relative_x[n], _relative_y[n]));
251 num += abs(prod_vect(_relative_x[np], _relative_y[np], _relative_x[n], _relative_y[n])) *
252 (_relative_x[np] * _relative_x[np] + _relative_y[np] * _relative_y[np] +
253 _relative_x[np] * _relative_x[n] + _relative_y[np] * _relative_y[n] +
254 _relative_x[n] * _relative_x[n] + _relative_y[n] * _relative_y[n]);
257 _moment_of_inertia = num / (6 * den);
259 scalar_t vx = cos(_theta), vy = sin(_theta);
261 for(int n = 0; n < _nb_vertices; n++) {
262 _x[n] = _center_x + _relative_x[n] * vx + _relative_y[n] * vy;
263 _y[n] = _center_y - _relative_x[n] * vy + _relative_y[n] * vx;
268 for(int n = 0; n < _nb_vertices; n++) {
269 length = sqrt(sq(_relative_x[n] - _relative_x[(n+1)%_nb_vertices]) +
270 sq(_relative_y[n] - _relative_y[(n+1)%_nb_vertices]));
272 _nb_dots[n] = int(length / dl + 1);
273 _total_nb_dots += _nb_dots[n];
276 delete[] _effecting_edge;
277 _effecting_edge = new int[_nb_polygons * _total_nb_dots];
278 for(int p = 0; p < _nb_polygons * _total_nb_dots; p++) _effecting_edge[p] = -1;
281 int index[_nb_vertices];
282 for(int n = 0; n < _nb_vertices; n++) index[n] = n;
283 triangularize(nt, _nb_vertices, index);
288 bool Polygon::update(scalar_t dt) {
290 _center_x += _dcenter_x * dt;
291 _center_y += _dcenter_y * dt;
292 _theta += _dtheta * dt;
295 scalar_t d = exp(log(dissipation) * dt);
300 scalar_t vx = cos(_theta), vy = sin(_theta);
302 for(int n = 0; n < _nb_vertices; n++) {
303 _x[n] = _center_x + _relative_x[n] * vx + _relative_y[n] * vy;
304 _y[n] = _center_y - _relative_x[n] * vy + _relative_y[n] * vx;
307 if(abs(_center_x - _last_center_x) +
308 abs(_center_y - _last_center_y) +
309 abs(_theta - _last_theta) * _radius > 0.1) {
310 _last_center_x = _center_x;
311 _last_center_y = _center_y;
312 _last_theta = _theta;
317 scalar_t Polygon::relative_x(scalar_t ax, scalar_t ay) {
318 return (ax - _center_x) * cos(_theta) - (ay - _center_y) * sin(_theta);
321 scalar_t Polygon::relative_y(scalar_t ax, scalar_t ay) {
322 return (ax - _center_x) * sin(_theta) + (ay - _center_y) * cos(_theta);
325 scalar_t Polygon::absolute_x(scalar_t rx, scalar_t ry) {
326 return _center_x + rx * cos(_theta) + ry * sin(_theta);
329 scalar_t Polygon::absolute_y(scalar_t rx, scalar_t ry) {
330 return _center_y - rx * sin(_theta) + ry * cos(_theta);
333 void Polygon::apply_force(scalar_t dt, scalar_t x, scalar_t y, scalar_t fx, scalar_t fy) {
334 _dcenter_x += fx / _mass * dt;
335 _dcenter_y += fy / _mass * dt;
336 _dtheta -= prod_vect(x - _center_x, y - _center_y, fx, fy) / (_mass * _moment_of_inertia) * dt;
339 void Polygon::apply_border_forces(scalar_t dt, scalar_t xmax, scalar_t ymax) {
340 for(int v = 0; v < _nb_vertices; v++) {
341 int vp = (v+1)%_nb_vertices;
342 for(int d = 0; d < _nb_dots[v]; d++) {
343 scalar_t s = scalar_t(d * dl)/_length[v];
344 scalar_t x = _x[v] * (1 - s) + _x[vp] * s;
345 scalar_t y = _y[v] * (1 - s) + _y[vp] * s;
346 scalar_t vx = 0, vy = 0;
348 else if(x > xmax) vx = x - xmax;
350 else if(y > ymax) vy = y - ymax;
351 apply_force(dt, x, y, - dl * vx * repulsion_constant, - dl * vy * repulsion_constant);
356 void Polygon::apply_collision_forces(scalar_t dt, int n_polygon, Polygon *p) {
357 scalar_t closest_x[_total_nb_dots], closest_y[_total_nb_dots];
358 bool inside[_total_nb_dots];
359 scalar_t distance[_total_nb_dots];
360 int _new_effecting_edge[_total_nb_dots];
364 for(int v = 0; v < _nb_vertices; v++) {
365 int vp = (v+1)%_nb_vertices;
366 scalar_t x = _x[v], y = _y[v], xp = _x[vp], yp = _y[vp];
368 for(int d = 0; d < _nb_dots[v]; d++) {
370 distance[d] = FLT_MAX;
373 // First, we tag the dots located inside the polygon p
375 for(int t = 0; t < p->_nb_vertices-2; t++) {
376 scalar_t min = 0, max = 1;
377 scalar_t xa = p->_x[p->_triangles[t].a], ya = p->_y[p->_triangles[t].a];
378 scalar_t xb = p->_x[p->_triangles[t].b], yb = p->_y[p->_triangles[t].b];
379 scalar_t xc = p->_x[p->_triangles[t].c], yc = p->_y[p->_triangles[t].c];
382 const scalar_t eps = 1e-6;
384 den = prod_vect(xp - x, yp - y, xb - xa, yb - ya);
385 num = prod_vect(xa - x, ya - y, xb - xa, yb - ya);
387 if(num / den < max) max = num / den;
388 } else if(den < -eps) {
389 if(num / den > min) min = num / den;
391 if(num < 0) { min = 1; max = 0; }
394 den = prod_vect(xp - x, yp - y, xc - xb, yc - yb);
395 num = prod_vect(xb - x, yb - y, xc - xb, yc - yb);
397 if(num / den < max) max = num / den;
398 } else if(den < -eps) {
399 if(num / den > min) min = num / den;
401 if(num < 0) { min = 1; max = 0; }
404 den = prod_vect(xp - x, yp - y, xa - xc, ya - yc);
405 num = prod_vect(xc - x, yc - y, xa - xc, ya - yc);
407 if(num / den < max) max = num / den;
408 } else if(den < -eps) {
409 if(num / den > min) min = num / den;
411 if(num < 0) { min = 1; max = 0; }
414 for(int d = 0; d < _nb_dots[v]; d++) {
415 scalar_t s = scalar_t(d * dl)/_length[v];
416 if(s >= min && s <= max) inside[d] = true;
420 // Then, we compute for each dot what is the closest point on
423 for(int m = 0; m < p->_nb_vertices; m++) {
424 int mp = (m+1)%p->_nb_vertices;
425 scalar_t xa = p->_x[m], ya = p->_y[m];
426 scalar_t xb = p->_x[mp], yb = p->_y[mp];
427 scalar_t gamma0 = ((x - xa) * (xb - xa) + (y - ya) * (yb - ya)) / sq(p->_length[m]);
428 scalar_t gamma1 = ((xp - x) * (xb - xa) + (yp - y) * (yb - ya)) / sq(p->_length[m]);
429 scalar_t delta0 = (prod_vect(xb - xa, yb - ya, x - xa, y - ya)) / p->_length[m];
430 scalar_t delta1 = (prod_vect(xb - xa, yb - ya, xp - x, yp - y)) / p->_length[m];
432 for(int d = 0; d < _nb_dots[v]; d++) if(inside[d]) {
433 int r = _effecting_edge[(first_dot + d) * _nb_polygons + n_polygon];
435 // If there is already a spring, we look only at the
436 // vertices next to the current one
438 if(r < 0 || m == r || m == (r+1)%p->_nb_vertices || (m+1)%p->_nb_vertices == r) {
440 scalar_t s = scalar_t(d * dl)/_length[v];
441 scalar_t delta = abs(s * delta1 + delta0);
442 if(delta < distance[d]) {
443 scalar_t gamma = s * gamma1 + gamma0;
445 scalar_t l = sqrt(sq(x * (1 - s) + xp * s - xa) + sq(y * (1 - s) + yp * s - ya));
446 if(l < distance[d]) {
450 _new_effecting_edge[first_dot + d] = m;
452 } else if(gamma > 1) {
453 scalar_t l = sqrt(sq(x * (1 - s) + xp * s - xb) + sq(y * (1 - s) + yp * s - yb));
454 if(l < distance[d]) {
458 _new_effecting_edge[first_dot + d] = m;
462 closest_x[d] = xa * (1 - gamma) + xb * gamma;
463 closest_y[d] = ya * (1 - gamma) + yb * gamma;
464 _new_effecting_edge[first_dot + d] = m;
468 } else _new_effecting_edge[first_dot + d] = -1;
473 for(int d = 0; d < _nb_dots[v]; d++) if(inside[d]) {
474 scalar_t s = scalar_t(d * dl)/_length[v];
475 scalar_t x = _x[v] * (1 - s) + _x[vp] * s;
476 scalar_t y = _y[v] * (1 - s) + _y[vp] * s;
477 scalar_t vx = x - closest_x[d];
478 scalar_t vy = y - closest_y[d];
481 closest_x[d], closest_y[d],
482 dl * vx * repulsion_constant, dl * vy * repulsion_constant);
486 - dl * vx * repulsion_constant, - dl * vy * repulsion_constant);
489 first_dot += _nb_dots[v];
492 for(int d = 0; d < _total_nb_dots; d++)
493 _effecting_edge[d * _nb_polygons + n_polygon] = _new_effecting_edge[d];
497 bool Polygon::collide(Polygon *p) {
498 for(int n = 0; n < _nb_vertices; n++) {
499 int np = (n+1)%_nb_vertices;
500 for(int m = 0; m < p->_nb_vertices; m++) {
501 int mp = (m+1)%p->_nb_vertices;
502 scalar_t det, s = -1, t = -1;
503 intersection(_x[n], _y[n], _x[np], _y[np],
504 p->_x[m], p->_y[m], p->_x[mp], p->_y[mp], det, s, t);
505 if(det != 0 && s>= 0 && s <= 1&& t >= 0 && t <= 1) return true;
509 for(int n = 0; n < _nb_vertices; n++) if(p->contain(_x[n], _y[n])) return true;
510 for(int n = 0; n < p->_nb_vertices; n++) if(contain(p->_x[n], p->_y[n])) return true;