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 object_init (Object *object, double x, double y, double mass)
30 object->position.x = x;
31 object->position.y = y;
32 object->previous_position.x = x;
33 object->previous_position.y = y;
38 spring_init (Spring *spring, Object *a, Object *b, double length)
42 spring->length = length;
46 offset_spring_init (OffsetSpring *spring, Object *a, Object *b,
56 polygon_init (Polygon *p, int num_points, ...)
58 double dx, dy, length;
62 /* Polygons are defined counter-clock-wise in a coordinate system
63 * with the y-axis pointing down. */
65 va_start (ap, num_points);
66 p->num_points = num_points;
67 p->points = g_new (Point, num_points);
69 for (i = 0; i < num_points; i++) {
70 p->points[i].x = va_arg (ap, double);
71 p->points[i].y = va_arg (ap, double);
75 p->normals = g_new (Vector, p->num_points);
76 /* Compute outward pointing normals. p->normals[i] is the normal
77 * for the edged between p->points[i] and p->points[i + 1]. */
78 for (i = 0; i < p->num_points; i++) {
79 j = (i + 1) % p->num_points;
80 dx = p->points[j].x - p->points[i].x;
81 dy = p->points[j].y - p->points[i].y;
82 length = sqrt (dx * dx + dy * dy);
83 p->normals[i].x = -dy / length;
84 p->normals[i].y = dx / length;
89 polygon_init_diamond (Polygon *polygon, double x, double y)
91 return polygon_init (polygon, 5,
100 polygon_init_rectangle (Polygon *polygon, double x0, double y0,
101 double x1, double y1)
103 return polygon_init (polygon, 4, x0, y0, x0, y1, x1, y1, x1, y0);
107 model_fini (Model *model)
111 g_free (model->objects);
112 g_free (model->sticks);
113 g_free (model->strings);
114 for (i = 0; i < model->num_offsets; i++)
115 g_free (model->offsets[i].objects);
116 g_free (model->springs);
117 g_free (model->offset_springs);
118 for (i = 0; i < model->num_polygons; i++)
119 g_free (model->polygons[i].points);
120 g_free (model->polygons);
122 memset (model, 0, sizeof *model);
126 model_accumulate_forces (Model *model)
129 double x, y, dx, dy, distance, displacement;
133 for (i = 0; i < model->num_objects; i++) {
135 model->objects[i].force.x = 0;
136 model->objects[i].force.y = gravity * model->objects[i].mass;
139 v.x = model->objects[i].position.x - model->objects[i].previous_position.x;
140 v.y = model->objects[i].position.y - model->objects[i].previous_position.y;
141 model->objects[i].force.x -= v.x * friction;
142 model->objects[i].force.y -= v.y * friction;
145 for (i = 0; i < model->num_springs; i++) {
146 x = model->springs[i].a->position.x;
147 y = model->springs[i].a->position.y;
148 dx = model->springs[i].b->position.x - x;
149 dy = model->springs[i].b->position.y - y;
150 distance = sqrt (dx * dx + dy * dy);
153 displacement = distance - model->springs[i].length;
154 model->springs[i].a->force.x += u.x * model->k * displacement;
155 model->springs[i].a->force.y += u.y * model->k * displacement;
156 model->springs[i].b->force.x -= u.x * model->k * displacement;
157 model->springs[i].b->force.y -= u.y * model->k * displacement;
160 for (i = 0; i < model->num_offset_springs; i++) {
162 (model->offset_springs[i].a->position.x +
163 model->offset_springs[i].b->position.x) / 2;
165 (model->offset_springs[i].a->position.y +
166 model->offset_springs[i].b->position.y) / 2;
168 x = middle.x - model->offset_springs[i].dx / 2;
169 y = middle.y - model->offset_springs[i].dy / 2;
171 dx = x - model->offset_springs[i].a->position.x;
172 dy = y - model->offset_springs[i].a->position.y;
174 model->offset_springs[i].a->force.x += dx * model->k;
175 model->offset_springs[i].a->force.y += dy * model->k;
176 model->offset_springs[i].b->force.x -= dx * model->k;
177 model->offset_springs[i].b->force.y -= dy * model->k;
180 for (i = 0; i < model->num_objects; i++) {
182 model->objects[i].force.x * model->objects[i].force.x +
183 model->objects[i].force.y * model->objects[i].force.y;
191 model_integrate (Model *model, double step)
197 for (i = 0; i < model->num_objects; i++) {
198 o = &model->objects[i];
203 x + (x - o->previous_position.x) + o->force.x * step * step;
205 y + (y - o->previous_position.y) + o->force.y * step * step;
207 o->previous_position.x = x;
208 o->previous_position.y = y;
212 /* The square root in the distance computation for the string and
213 * stick constraints can be aproximated using Newton:
216 * (model->sticks[i].length +
217 * (dx * dx + dy * dy) / model->sticks[i].length) / 2;
219 * This works really well, since the constraints aren't typically
220 * violated much. Thus, the distance is really close to the stick
221 * length, which then makes a good initial guess. However, the
222 * approximation seems to be slower that just calling sqrt()...
226 estimate_distance (double dx, double dy, double r)
228 #ifdef APPROXIMATE_SQUARE_ROOTS
229 return (r + (dx * dx + dy * dy) / r) / 2;
231 return sqrt (dx * dx + dy * dy);
236 polygon_contains_point (Polygon *polygon, Point *point)
241 for (i = 0; i < polygon->num_points; i++) {
242 dx = point->x - polygon->points[i].x;
243 dy = point->y - polygon->points[i].y;
245 if (polygon->normals[i].x * dx + polygon->normals[i].y * dy >= 0)
253 polygon_reflect_object (Polygon *polygon, Object *object)
260 for (i = 0; i < polygon->num_points; i++) {
261 d = polygon->normals[i].x * (object->position.x - polygon->points[i].x) +
262 polygon->normals[i].y * (object->position.y - polygon->points[i].y);
268 n = &polygon->normals[i];
272 object->position.x -= (1 + elasticity) * distance * n->x;
273 object->position.y -= (1 + elasticity) * distance * n->y;
276 n->x * (object->previous_position.x - polygon->points[edge].x) +
277 n->y * (object->previous_position.y - polygon->points[edge].y);
279 object->previous_position.x -= (1 + elasticity) * distance * n->x;
280 object->previous_position.y -= (1 + elasticity) * distance * n->y;
284 model_constrain_polygon (Model *model, Polygon *polygon)
288 for (i = 0; i < model->num_objects; i++) {
289 if (polygon_contains_point (polygon, &model->objects[i].position))
290 polygon_reflect_object (polygon, &model->objects[i]);
295 model_constrain_offset (Model *model, Offset *offset)
302 for (i = 0; i < offset->num_objects; i++) {
303 x += offset->objects[i]->position.x;
304 y += offset->objects[i]->position.y;
307 x = x / offset->num_objects - offset->dx * (offset->num_objects - 1) / 2;
308 y = y / offset->num_objects - offset->dy * (offset->num_objects - 1) / 2;
310 for (i = 0; i < offset->num_objects; i++) {
311 offset->objects[i]->position.x = x + offset->dx * i;
312 offset->objects[i]->position.y = y + offset->dy * i;
317 model_constrain (Model *model)
319 double dx, dy, x, y, distance, fraction;
322 /* Anchor object constraint. */
323 if (model->anchor_object != NULL) {
324 model->anchor_object->position.x = model->anchor_position.x;
325 model->anchor_object->position.y = model->anchor_position.y;
326 model->anchor_object->previous_position.x = model->anchor_position.x;
327 model->anchor_object->previous_position.y = model->anchor_position.y;
330 /* String constraints. */
331 for (i = 0; i < model->num_strings; i++) {
332 x = model->strings[i].a->position.x;
333 y = model->strings[i].a->position.y;
334 dx = model->strings[i].b->position.x - x;
335 dy = model->strings[i].b->position.y - y;
336 distance = estimate_distance (dx, dy, model->strings[i].length);
337 if (distance < model->strings[i].length)
339 fraction = (distance - model->strings[i].length) / distance / 2;
340 model->strings[i].a->position.x = x + dx * fraction;
341 model->strings[i].a->position.y = y + dy * fraction;
342 model->strings[i].b->position.x = x + dx * (1 - fraction);
343 model->strings[i].b->position.y = y + dy * (1 - fraction);
346 /* Stick constraints. */
347 for (i = 0; i < model->num_sticks; i++) {
348 x = model->sticks[i].a->position.x;
349 y = model->sticks[i].a->position.y;
350 dx = model->sticks[i].b->position.x - x;
351 dy = model->sticks[i].b->position.y - y;
352 distance = estimate_distance (dx, dy, model->sticks[i].length);
353 fraction = (distance - model->sticks[i].length) / distance / 2;
354 model->sticks[i].a->position.x = x + dx * fraction;
355 model->sticks[i].a->position.y = y + dy * fraction;
356 model->sticks[i].b->position.x = x + dx * (1 - fraction);
357 model->sticks[i].b->position.y = y + dy * (1 - fraction);
360 /* Offset constraints. */
361 for (i = 0; i < model->num_offsets; i++)
362 model_constrain_offset (model, &model->offsets[i]);
364 /* Polygon constraints. */
365 for (i = 0; i < model->num_polygons; i++)
366 model_constrain_polygon (model, &model->polygons[i]);
370 model_step (Model *model, double delta_t)
374 model_accumulate_forces (model);
375 model_integrate (model, delta_t);
376 for (i = 0; i < 50; i++)
377 model_constrain (model);
379 model->theta += delta_t;
383 object_distance (Object *object, double x, double y)
387 dx = object->position.x - x;
388 dy = object->position.y - y;
390 return sqrt (dx*dx + dy*dy);
394 model_find_nearest (Model *model, double x, double y)
397 double distance, min_distance;
400 for (i = 0; i < model->num_objects; i++) {
401 distance = object_distance (&model->objects[i], x, y);
402 if (i == 0 || distance < min_distance) {
403 min_distance = distance;
404 object = &model->objects[i];