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);
51 void Polygon::color_xfig(XFigTracer *tracer) {
52 tracer->add_color(int(255 * _red), int(255 * _green), int(255 * _blue));
55 void Polygon::print_xfig(XFigTracer *tracer) {
56 tracer->draw_polygon(int(255 * _red), int(255 * _green), int(255 * _blue),
57 _nb_vertices, _x, _y);
62 void Polygon::draw(SimpleWindow *window) {
63 window->color(_red, _green, _blue);
64 int x[_nb_vertices], y[_nb_vertices];
65 for(int n = 0; n < _nb_vertices; n++) {
69 window->fill_polygon(_nb_vertices, x, y);
72 void Polygon::draw_contours(SimpleWindow *window) {
73 int x[_nb_vertices], y[_nb_vertices];
74 for(int n = 0; n < _nb_vertices; n++) {
78 window->color(0.0, 0.0, 0.0);
79 // window->color(1.0, 1.0, 1.0);
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]);
86 void Polygon::draw(Canvas *canvas) {
87 canvas->set_drawing_color(_red, _green, _blue);
88 canvas->draw_polygon(1, _nb_vertices, _x, _y);
91 void Polygon::draw_contours(Canvas *canvas) {
92 canvas->set_drawing_color(0.0, 0.0, 0.0);
93 canvas->draw_polygon(0, _nb_vertices, _x, _y);
96 void Polygon::set_vertex(int k, scalar_t x, scalar_t y) {
101 void Polygon::set_position(scalar_t center_x, scalar_t center_y, scalar_t theta) {
102 _center_x = center_x;
103 _center_y = center_y;
107 void Polygon::set_speed(scalar_t dcenter_x, scalar_t dcenter_y, scalar_t dtheta) {
108 _dcenter_x = dcenter_x;
109 _dcenter_y = dcenter_y;
113 bool Polygon::contain(scalar_t x, scalar_t y) {
114 for(int t = 0; t < _nb_vertices-2; t++) {
115 scalar_t xa = _x[_triangles[t].a], ya = _y[_triangles[t].a];
116 scalar_t xb = _x[_triangles[t].b], yb = _y[_triangles[t].b];
117 scalar_t xc = _x[_triangles[t].c], yc = _y[_triangles[t].c];
118 if(prod_vect(x - xa, y - ya, xb - xa, yb - ya) <= 0 &&
119 prod_vect(x - xb, y - yb, xc - xb, yc - yb) <= 0 &&
120 prod_vect(x - xc, y - yc, xa - xc, ya - yc) <= 0) return true;
125 void Polygon::triangularize(int &nt, int nb, int *index) {
128 if(nt >= _nb_vertices-2) {
129 cerr << "Error type #1 in triangularization." << endl;
133 _triangles[nt].a = index[0];
134 _triangles[nt].b = index[1];
135 _triangles[nt].c = index[2];
139 int best_m = -1, best_n = -1;
140 scalar_t best_split = -1, det, s = -1, t = -1;
142 for(int n = 0; n < nb; n++) for(int m = 0; m < n; m++) if(n > m+1 && m+nb > n+1) {
143 bool no_intersection = true;
144 for(int k = 0; no_intersection & (k < nb); k++)
145 if(k != n && k != m && (k+1)%nb != n && (k+1)%nb != m) {
146 intersection(_relative_x[index[n]], _relative_y[index[n]],
147 _relative_x[index[m]], _relative_y[index[m]],
148 _relative_x[index[k]], _relative_y[index[k]],
149 _relative_x[index[(k+1)%nb]], _relative_y[index[(k+1)%nb]], det, s, t);
150 no_intersection = det == 0 || s < 0 || s > 1 || t < 0 || t > 1;
153 if(no_intersection) {
154 scalar_t a1 = 0, a2 = 0;
155 for(int k = 0; k < nb; k++) if(k >= m && k < n)
156 a1 += prod_vect(_relative_x[index[k]] - _relative_x[index[m]],
157 _relative_y[index[k]] - _relative_y[index[m]],
158 _relative_x[index[k+1]] - _relative_x[index[m]],
159 _relative_y[index[k+1]] - _relative_y[index[m]]);
161 a2 += prod_vect(_relative_x[index[k]] - _relative_x[index[m]],
162 _relative_y[index[k]] - _relative_y[index[m]],
163 _relative_x[index[(k+1)%nb]] - _relative_x[index[m]],
164 _relative_y[index[(k+1)%nb]] - _relative_y[index[m]]);
166 if((a1 * a2 > 0 && best_split < 0) || (abs(a1 - a2) < best_split)) {
167 best_n = n; best_m = m;
168 best_split = abs(a1 - a2);
173 if(best_n >= 0 && best_m >= 0) {
174 int index_neg[nb], index_pos[nb];
175 int neg = 0, pos = 0;
176 for(int k = 0; k < nb; k++) {
177 if(k >= best_m && k <= best_n) index_pos[pos++] = index[k];
178 if(k <= best_m || k >= best_n) index_neg[neg++] = index[k];
180 if(pos < 3 || neg < 3) {
181 cerr << "Error type #2 in triangularization." << endl;
184 triangularize(nt, pos, index_pos);
185 triangularize(nt, neg, index_neg);
187 cerr << "Error type #3 in triangularization." << endl;
193 void Polygon::initialize(int nb_polygons) {
196 _nb_polygons = nb_polygons;
198 a = _relative_x[_nb_vertices - 1] * _relative_y[0]
199 - _relative_x[0] * _relative_y[_nb_vertices - 1];
201 for(int n = 0; n < _nb_vertices - 1; n++)
202 a += _relative_x[n] * _relative_y[n+1] - _relative_x[n+1] * _relative_y[n];
205 // Reorder the vertices
210 for(int n = 0; n < _nb_vertices / 2; n++) {
213 _relative_x[n] = _relative_x[_nb_vertices - 1 - n];
214 _relative_y[n] = _relative_y[_nb_vertices - 1 - n];
215 _relative_x[_nb_vertices - 1 - n] = x;
216 _relative_y[_nb_vertices - 1 - n] = y;
220 // Compute the center of mass and moment of inertia
226 for(int n = 0; n < _nb_vertices; n++) {
227 int np = (n+1)%_nb_vertices;
228 w =_relative_x[n] * _relative_y[np] - _relative_x[np] * _relative_y[n];
229 sx += (_relative_x[n] + _relative_x[np]) * w;
230 sy += (_relative_y[n] + _relative_y[np]) * w;
236 for(int n = 0; n < _nb_vertices; n++) {
237 _relative_x[n] -= sx;
238 _relative_y[n] -= sy;
239 scalar_t r = sqrt(sq(_relative_x[n]) + sq(_relative_y[n]));
240 if(r > _radius) _radius = r;
243 scalar_t num = 0, den = 0;
244 for(int n = 0; n < _nb_vertices; n++) {
245 int np = (n+1)%_nb_vertices;
246 den += abs(prod_vect(_relative_x[np], _relative_y[np], _relative_x[n], _relative_y[n]));
247 num += abs(prod_vect(_relative_x[np], _relative_y[np], _relative_x[n], _relative_y[n])) *
248 (_relative_x[np] * _relative_x[np] + _relative_y[np] * _relative_y[np] +
249 _relative_x[np] * _relative_x[n] + _relative_y[np] * _relative_y[n] +
250 _relative_x[n] * _relative_x[n] + _relative_y[n] * _relative_y[n]);
253 _moment_of_inertia = num / (6 * den);
255 scalar_t vx = cos(_theta), vy = sin(_theta);
257 for(int n = 0; n < _nb_vertices; n++) {
258 _x[n] = _center_x + _relative_x[n] * vx + _relative_y[n] * vy;
259 _y[n] = _center_y - _relative_x[n] * vy + _relative_y[n] * vx;
264 for(int n = 0; n < _nb_vertices; n++) {
265 length = sqrt(sq(_relative_x[n] - _relative_x[(n+1)%_nb_vertices]) +
266 sq(_relative_y[n] - _relative_y[(n+1)%_nb_vertices]));
268 _nb_dots[n] = int(length / dl + 1);
269 _total_nb_dots += _nb_dots[n];
272 delete[] _effecting_edge;
273 _effecting_edge = new int[_nb_polygons * _total_nb_dots];
274 for(int p = 0; p < _nb_polygons * _total_nb_dots; p++) _effecting_edge[p] = -1;
277 int index[_nb_vertices];
278 for(int n = 0; n < _nb_vertices; n++) index[n] = n;
279 triangularize(nt, _nb_vertices, index);
284 bool Polygon::update(scalar_t dt) {
286 _center_x += _dcenter_x * dt;
287 _center_y += _dcenter_y * dt;
288 _theta += _dtheta * dt;
291 scalar_t d = exp(log(dissipation) * dt);
296 scalar_t vx = cos(_theta), vy = sin(_theta);
298 for(int n = 0; n < _nb_vertices; n++) {
299 _x[n] = _center_x + _relative_x[n] * vx + _relative_y[n] * vy;
300 _y[n] = _center_y - _relative_x[n] * vy + _relative_y[n] * vx;
303 if(abs(_center_x - _last_center_x) +
304 abs(_center_y - _last_center_y) +
305 abs(_theta - _last_theta) * _radius > 0.1) {
306 _last_center_x = _center_x;
307 _last_center_y = _center_y;
308 _last_theta = _theta;
313 scalar_t Polygon::relative_x(scalar_t ax, scalar_t ay) {
314 return (ax - _center_x) * cos(_theta) - (ay - _center_y) * sin(_theta);
317 scalar_t Polygon::relative_y(scalar_t ax, scalar_t ay) {
318 return (ax - _center_x) * sin(_theta) + (ay - _center_y) * cos(_theta);
321 scalar_t Polygon::absolute_x(scalar_t rx, scalar_t ry) {
322 return _center_x + rx * cos(_theta) + ry * sin(_theta);
325 scalar_t Polygon::absolute_y(scalar_t rx, scalar_t ry) {
326 return _center_y - rx * sin(_theta) + ry * cos(_theta);
329 void Polygon::apply_force(scalar_t dt, scalar_t x, scalar_t y, scalar_t fx, scalar_t fy) {
330 _dcenter_x += fx / _mass * dt;
331 _dcenter_y += fy / _mass * dt;
332 _dtheta -= prod_vect(x - _center_x, y - _center_y, fx, fy) / (_mass * _moment_of_inertia) * dt;
335 void Polygon::apply_border_forces(scalar_t dt, scalar_t xmax, scalar_t ymax) {
336 for(int v = 0; v < _nb_vertices; v++) {
337 int vp = (v+1)%_nb_vertices;
338 for(int d = 0; d < _nb_dots[v]; d++) {
339 scalar_t s = scalar_t(d * dl)/_length[v];
340 scalar_t x = _x[v] * (1 - s) + _x[vp] * s;
341 scalar_t y = _y[v] * (1 - s) + _y[vp] * s;
342 scalar_t vx = 0, vy = 0;
344 else if(x > xmax) vx = x - xmax;
346 else if(y > ymax) vy = y - ymax;
347 apply_force(dt, x, y, - dl * vx * repulsion_constant, - dl * vy * repulsion_constant);
352 void Polygon::apply_collision_forces(scalar_t dt, int n_polygon, Polygon *p) {
353 scalar_t closest_x[_total_nb_dots], closest_y[_total_nb_dots];
354 bool inside[_total_nb_dots];
355 scalar_t distance[_total_nb_dots];
356 int _new_effecting_edge[_total_nb_dots];
360 for(int v = 0; v < _nb_vertices; v++) {
361 int vp = (v+1)%_nb_vertices;
362 scalar_t x = _x[v], y = _y[v], xp = _x[vp], yp = _y[vp];
364 for(int d = 0; d < _nb_dots[v]; d++) {
366 distance[d] = FLT_MAX;
369 // First, we tag the dots located inside the polygon p
371 for(int t = 0; t < p->_nb_vertices-2; t++) {
372 scalar_t min = 0, max = 1;
373 scalar_t xa = p->_x[p->_triangles[t].a], ya = p->_y[p->_triangles[t].a];
374 scalar_t xb = p->_x[p->_triangles[t].b], yb = p->_y[p->_triangles[t].b];
375 scalar_t xc = p->_x[p->_triangles[t].c], yc = p->_y[p->_triangles[t].c];
378 const scalar_t eps = 1e-6;
380 den = prod_vect(xp - x, yp - y, xb - xa, yb - ya);
381 num = prod_vect(xa - x, ya - y, xb - xa, yb - ya);
383 if(num / den < max) max = num / den;
384 } else if(den < -eps) {
385 if(num / den > min) min = num / den;
387 if(num < 0) { min = 1; max = 0; }
390 den = prod_vect(xp - x, yp - y, xc - xb, yc - yb);
391 num = prod_vect(xb - x, yb - y, xc - xb, yc - yb);
393 if(num / den < max) max = num / den;
394 } else if(den < -eps) {
395 if(num / den > min) min = num / den;
397 if(num < 0) { min = 1; max = 0; }
400 den = prod_vect(xp - x, yp - y, xa - xc, ya - yc);
401 num = prod_vect(xc - x, yc - y, xa - xc, ya - yc);
403 if(num / den < max) max = num / den;
404 } else if(den < -eps) {
405 if(num / den > min) min = num / den;
407 if(num < 0) { min = 1; max = 0; }
410 for(int d = 0; d < _nb_dots[v]; d++) {
411 scalar_t s = scalar_t(d * dl)/_length[v];
412 if(s >= min && s <= max) inside[d] = true;
416 // Then, we compute for each dot what is the closest point on
419 for(int m = 0; m < p->_nb_vertices; m++) {
420 int mp = (m+1)%p->_nb_vertices;
421 scalar_t xa = p->_x[m], ya = p->_y[m];
422 scalar_t xb = p->_x[mp], yb = p->_y[mp];
423 scalar_t gamma0 = ((x - xa) * (xb - xa) + (y - ya) * (yb - ya)) / sq(p->_length[m]);
424 scalar_t gamma1 = ((xp - x) * (xb - xa) + (yp - y) * (yb - ya)) / sq(p->_length[m]);
425 scalar_t delta0 = (prod_vect(xb - xa, yb - ya, x - xa, y - ya)) / p->_length[m];
426 scalar_t delta1 = (prod_vect(xb - xa, yb - ya, xp - x, yp - y)) / p->_length[m];
428 for(int d = 0; d < _nb_dots[v]; d++) if(inside[d]) {
429 int r = _effecting_edge[(first_dot + d) * _nb_polygons + n_polygon];
431 // If there is already a spring, we look only at the
432 // vertices next to the current one
434 if(r < 0 || m == r || m == (r+1)%p->_nb_vertices || (m+1)%p->_nb_vertices == r) {
436 scalar_t s = scalar_t(d * dl)/_length[v];
437 scalar_t delta = abs(s * delta1 + delta0);
438 if(delta < distance[d]) {
439 scalar_t gamma = s * gamma1 + gamma0;
441 scalar_t l = sqrt(sq(x * (1 - s) + xp * s - xa) + sq(y * (1 - s) + yp * s - ya));
442 if(l < distance[d]) {
446 _new_effecting_edge[first_dot + d] = m;
448 } else if(gamma > 1) {
449 scalar_t l = sqrt(sq(x * (1 - s) + xp * s - xb) + sq(y * (1 - s) + yp * s - yb));
450 if(l < distance[d]) {
454 _new_effecting_edge[first_dot + d] = m;
458 closest_x[d] = xa * (1 - gamma) + xb * gamma;
459 closest_y[d] = ya * (1 - gamma) + yb * gamma;
460 _new_effecting_edge[first_dot + d] = m;
464 } else _new_effecting_edge[first_dot + d] = -1;
469 for(int d = 0; d < _nb_dots[v]; d++) if(inside[d]) {
470 scalar_t s = scalar_t(d * dl)/_length[v];
471 scalar_t x = _x[v] * (1 - s) + _x[vp] * s;
472 scalar_t y = _y[v] * (1 - s) + _y[vp] * s;
473 scalar_t vx = x - closest_x[d];
474 scalar_t vy = y - closest_y[d];
477 closest_x[d], closest_y[d],
478 dl * vx * repulsion_constant, dl * vy * repulsion_constant);
482 - dl * vx * repulsion_constant, - dl * vy * repulsion_constant);
485 first_dot += _nb_dots[v];
488 for(int d = 0; d < _total_nb_dots; d++)
489 _effecting_edge[d * _nb_polygons + n_polygon] = _new_effecting_edge[d];
493 bool Polygon::collide(Polygon *p) {
494 for(int n = 0; n < _nb_vertices; n++) {
495 int np = (n+1)%_nb_vertices;
496 for(int m = 0; m < p->_nb_vertices; m++) {
497 int mp = (m+1)%p->_nb_vertices;
498 scalar_t det, s = -1, t = -1;
499 intersection(_x[n], _y[n], _x[np], _y[np],
500 p->_x[m], p->_y[m], p->_x[mp], p->_y[mp], det, s, t);
501 if(det != 0 && s>= 0 && s <= 1&& t >= 0 && t <= 1) return true;
505 for(int n = 0; n < _nb_vertices; n++) if(p->contain(_x[n], _y[n])) return true;
506 for(int n = 0; n < p->_nb_vertices; n++) if(contain(p->_x[n], p->_y[n])) return true;