1 /* -*- mode: c; c-basic-offset: 2 -*-
4 * http://en.wikipedia.org/wiki/Verlet_integration
5 * http://www.teknikus.dk/tj/gdc2001.htm
9 * - Add code to add boxes
11 * - Try out this idea: make constraint solver take mean of all
12 * corrections at the end instead of meaning as it goes.
23 const double elasticity = 0.7;
24 const double friction = 1;
25 const double gravity = 20;
28 polygon_init (Polygon *p, int num_points, ...)
30 double dx, dy, length;
34 /* Polygons are defined counter-clock-wise in a coordinate system
35 * with the y-axis pointing down. */
37 va_start (ap, num_points);
38 p->num_points = num_points;
39 p->points = g_new (Point, num_points);
41 for (i = 0; i < num_points; i++) {
42 p->points[i].x = va_arg (ap, double);
43 p->points[i].y = va_arg (ap, double);
47 p->normals = g_new (Vector, p->num_points);
48 /* Compute outward pointing normals. p->normals[i] is the normal
49 * for the edged between p->points[i] and p->points[i + 1]. */
50 for (i = 0; i < p->num_points; i++) {
51 j = (i + 1) % p->num_points;
52 dx = p->points[j].x - p->points[i].x;
53 dy = p->points[j].y - p->points[i].y;
54 length = sqrt (dx * dx + dy * dy);
55 p->normals[i].x = -dy / length;
56 p->normals[i].y = dx / length;
61 polygon_init_diamond (Polygon *polygon, double x, double y)
63 return polygon_init (polygon, 5,
72 polygon_init_rectangle (Polygon *polygon, double x0, double y0,
75 return polygon_init (polygon, 4, x0, y0, x0, y1, x1, y1, x1, y0);
79 model_fini (Model *model)
83 g_free (model->objects);
84 g_free (model->sticks);
85 g_free (model->strings);
86 for (i = 0; i < model->num_offsets; i++)
87 g_free (model->offsets[i].objects);
88 g_free (model->springs);
89 g_free (model->offset_springs);
90 for (i = 0; i < model->num_polygons; i++)
91 g_free (model->polygons[i].points);
92 g_free (model->polygons);
94 memset (model, 0, sizeof *model);
98 model_accumulate_forces (Model *model)
101 double x, y, dx, dy, distance, displacement;
105 for (i = 0; i < model->num_objects; i++) {
107 model->objects[i].force.x = 0;
108 model->objects[i].force.y = gravity * model->objects[i].mass;
111 v.x = model->objects[i].position.x - model->objects[i].previous_position.x;
112 v.y = model->objects[i].position.y - model->objects[i].previous_position.y;
113 model->objects[i].force.x -= v.x * friction;
114 model->objects[i].force.y -= v.y * friction;
117 for (i = 0; i < model->num_springs; i++) {
118 x = model->springs[i].a->position.x;
119 y = model->springs[i].a->position.y;
120 dx = model->springs[i].b->position.x - x;
121 dy = model->springs[i].b->position.y - y;
122 distance = sqrt (dx * dx + dy * dy);
125 displacement = distance - model->springs[i].length;
126 model->springs[i].a->force.x += u.x * model->k * displacement;
127 model->springs[i].a->force.y += u.y * model->k * displacement;
128 model->springs[i].b->force.x -= u.x * model->k * displacement;
129 model->springs[i].b->force.y -= u.y * model->k * displacement;
132 for (i = 0; i < model->num_offset_springs; i++) {
134 (model->offset_springs[i].a->position.x +
135 model->offset_springs[i].b->position.x) / 2;
137 (model->offset_springs[i].a->position.y +
138 model->offset_springs[i].b->position.y) / 2;
140 x = middle.x - model->offset_springs[i].dx / 2;
141 y = middle.y - model->offset_springs[i].dy / 2;
143 dx = x - model->offset_springs[i].a->position.x;
144 dy = y - model->offset_springs[i].a->position.y;
146 model->offset_springs[i].a->force.x += dx * model->k;
147 model->offset_springs[i].a->force.y += dy * model->k;
148 model->offset_springs[i].b->force.x -= dx * model->k;
149 model->offset_springs[i].b->force.y -= dy * model->k;
152 for (i = 0; i < model->num_objects; i++) {
154 model->objects[i].force.x * model->objects[i].force.x +
155 model->objects[i].force.y * model->objects[i].force.y;
163 model_integrate (Model *model, double step)
169 for (i = 0; i < model->num_objects; i++) {
170 o = &model->objects[i];
175 x + (x - o->previous_position.x) + o->force.x * step * step;
177 y + (y - o->previous_position.y) + o->force.y * step * step;
179 o->previous_position.x = x;
180 o->previous_position.y = y;
184 /* The square root in the distance computation for the string and
185 * stick constraints can be aproximated using Newton:
188 * (model->sticks[i].length +
189 * (dx * dx + dy * dy) / model->sticks[i].length) / 2;
191 * This works really well, since the constraints aren't typically
192 * violated much. Thus, the distance is really close to the stick
193 * length, which then makes a good initial guess. However, the
194 * approximation seems to be slower that just calling sqrt()...
198 estimate_distance (double dx, double dy, double r)
200 #ifdef APPROXIMATE_SQUARE_ROOTS
201 return (r + (dx * dx + dy * dy) / r) / 2;
203 return sqrt (dx * dx + dy * dy);
208 polygon_contains_point (Polygon *polygon, Point *point)
213 for (i = 0; i < polygon->num_points; i++) {
214 dx = point->x - polygon->points[i].x;
215 dy = point->y - polygon->points[i].y;
217 if (polygon->normals[i].x * dx + polygon->normals[i].y * dy >= 0)
225 polygon_reflect_object (Polygon *polygon, Object *object)
232 for (i = 0; i < polygon->num_points; i++) {
233 d = polygon->normals[i].x * (object->position.x - polygon->points[i].x) +
234 polygon->normals[i].y * (object->position.y - polygon->points[i].y);
240 n = &polygon->normals[i];
244 object->position.x -= (1 + elasticity) * distance * n->x;
245 object->position.y -= (1 + elasticity) * distance * n->y;
248 n->x * (object->previous_position.x - polygon->points[edge].x) +
249 n->y * (object->previous_position.y - polygon->points[edge].y);
251 object->previous_position.x -= (1 + elasticity) * distance * n->x;
252 object->previous_position.y -= (1 + elasticity) * distance * n->y;
256 model_constrain_polygon (Model *model, Polygon *polygon)
260 for (i = 0; i < model->num_objects; i++) {
261 if (polygon_contains_point (polygon, &model->objects[i].position))
262 polygon_reflect_object (polygon, &model->objects[i]);
267 model_constrain_offset (Model *model, Offset *offset)
274 for (i = 0; i < offset->num_objects; i++) {
275 x += offset->objects[i]->position.x;
276 y += offset->objects[i]->position.y;
279 x = x / offset->num_objects - offset->dx * (offset->num_objects - 1) / 2;
280 y = y / offset->num_objects - offset->dy * (offset->num_objects - 1) / 2;
282 for (i = 0; i < offset->num_objects; i++) {
283 offset->objects[i]->position.x = x + offset->dx * i;
284 offset->objects[i]->position.y = y + offset->dy * i;
289 model_constrain (Model *model)
291 double dx, dy, x, y, distance, fraction;
294 /* Anchor object constraint. */
295 if (model->anchor_object != NULL) {
296 model->anchor_object->position.x = model->anchor_position.x;
297 model->anchor_object->position.y = model->anchor_position.y;
298 model->anchor_object->previous_position.x = model->anchor_position.x;
299 model->anchor_object->previous_position.y = model->anchor_position.y;
302 /* String constraints. */
303 for (i = 0; i < model->num_strings; i++) {
304 x = model->strings[i].a->position.x;
305 y = model->strings[i].a->position.y;
306 dx = model->strings[i].b->position.x - x;
307 dy = model->strings[i].b->position.y - y;
308 distance = estimate_distance (dx, dy, model->strings[i].length);
309 if (distance < model->strings[i].length)
311 fraction = (distance - model->strings[i].length) / distance / 2;
312 model->strings[i].a->position.x = x + dx * fraction;
313 model->strings[i].a->position.y = y + dy * fraction;
314 model->strings[i].b->position.x = x + dx * (1 - fraction);
315 model->strings[i].b->position.y = y + dy * (1 - fraction);
318 /* Stick constraints. */
319 for (i = 0; i < model->num_sticks; i++) {
320 x = model->sticks[i].a->position.x;
321 y = model->sticks[i].a->position.y;
322 dx = model->sticks[i].b->position.x - x;
323 dy = model->sticks[i].b->position.y - y;
324 distance = estimate_distance (dx, dy, model->sticks[i].length);
325 fraction = (distance - model->sticks[i].length) / distance / 2;
326 model->sticks[i].a->position.x = x + dx * fraction;
327 model->sticks[i].a->position.y = y + dy * fraction;
328 model->sticks[i].b->position.x = x + dx * (1 - fraction);
329 model->sticks[i].b->position.y = y + dy * (1 - fraction);
332 /* Offset constraints. */
333 for (i = 0; i < model->num_offsets; i++)
334 model_constrain_offset (model, &model->offsets[i]);
336 /* Polygon constraints. */
337 for (i = 0; i < model->num_polygons; i++)
338 model_constrain_polygon (model, &model->polygons[i]);
342 model_step (Model *model, double delta_t)
346 model_accumulate_forces (model);
347 model_integrate (model, delta_t);
348 for (i = 0; i < 50; i++)
349 model_constrain (model);
351 model->theta += delta_t;
355 object_distance (Object *object, double x, double y)
359 dx = object->position.x - x;
360 dy = object->position.y - y;
362 return sqrt (dx*dx + dy*dy);
366 model_find_nearest (Model *model, double x, double y)
369 double distance, min_distance;
372 for (i = 0; i < model->num_objects; i++) {
373 distance = object_distance (&model->objects[i], x, y);
374 if (i == 0 || distance < min_distance) {
375 min_distance = distance;
376 object = &model->objects[i];