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 stick_init (Stick *stick, Object *a, Object *b, double length)
50 stick->length = length;
54 string_init (String *string, Object *a, Object *b, double length)
58 string->length = length;
62 offset_spring_init (OffsetSpring *spring, Object *a, Object *b,
72 polygon_init (Polygon *p, int num_points, ...)
74 double dx, dy, length;
78 /* Polygons are defined counter-clock-wise in a coordinate system
79 * with the y-axis pointing down. */
81 va_start (ap, num_points);
82 p->num_points = num_points;
83 p->points = g_new (Point, num_points);
85 for (i = 0; i < num_points; i++) {
86 p->points[i].x = va_arg (ap, double);
87 p->points[i].y = va_arg (ap, double);
91 p->normals = g_new (Vector, p->num_points);
92 /* Compute outward pointing normals. p->normals[i] is the normal
93 * for the edged between p->points[i] and p->points[i + 1]. */
94 for (i = 0; i < p->num_points; i++) {
95 j = (i + 1) % p->num_points;
96 dx = p->points[j].x - p->points[i].x;
97 dy = p->points[j].y - p->points[i].y;
98 length = sqrt (dx * dx + dy * dy);
99 p->normals[i].x = -dy / length;
100 p->normals[i].y = dx / length;
105 polygon_init_diamond (Polygon *polygon, double x, double y)
107 return polygon_init (polygon, 5,
116 polygon_init_rectangle (Polygon *polygon, double x0, double y0,
117 double x1, double y1)
119 return polygon_init (polygon, 4, x0, y0, x0, y1, x1, y1, x1, y0);
123 model_fini (Model *model)
127 g_free (model->objects);
128 g_free (model->sticks);
129 g_free (model->strings);
130 for (i = 0; i < model->num_offsets; i++)
131 g_free (model->offsets[i].objects);
132 g_free (model->springs);
133 g_free (model->offset_springs);
134 for (i = 0; i < model->num_polygons; i++)
135 g_free (model->polygons[i].points);
136 g_free (model->polygons);
138 memset (model, 0, sizeof *model);
142 model_accumulate_forces (Model *model)
145 double x, y, dx, dy, distance, displacement;
149 for (i = 0; i < model->num_objects; i++) {
151 model->objects[i].force.x = 0;
152 model->objects[i].force.y = gravity * model->objects[i].mass;
155 v.x = model->objects[i].position.x - model->objects[i].previous_position.x;
156 v.y = model->objects[i].position.y - model->objects[i].previous_position.y;
157 model->objects[i].force.x -= v.x * friction;
158 model->objects[i].force.y -= v.y * friction;
161 for (i = 0; i < model->num_springs; i++) {
162 x = model->springs[i].a->position.x;
163 y = model->springs[i].a->position.y;
164 dx = model->springs[i].b->position.x - x;
165 dy = model->springs[i].b->position.y - y;
166 distance = sqrt (dx * dx + dy * dy);
169 displacement = distance - model->springs[i].length;
170 model->springs[i].a->force.x += u.x * model->k * displacement;
171 model->springs[i].a->force.y += u.y * model->k * displacement;
172 model->springs[i].b->force.x -= u.x * model->k * displacement;
173 model->springs[i].b->force.y -= u.y * model->k * displacement;
176 for (i = 0; i < model->num_offset_springs; i++) {
178 (model->offset_springs[i].a->position.x +
179 model->offset_springs[i].b->position.x) / 2;
181 (model->offset_springs[i].a->position.y +
182 model->offset_springs[i].b->position.y) / 2;
184 x = middle.x - model->offset_springs[i].dx / 2;
185 y = middle.y - model->offset_springs[i].dy / 2;
187 dx = x - model->offset_springs[i].a->position.x;
188 dy = y - model->offset_springs[i].a->position.y;
190 model->offset_springs[i].a->force.x += dx * model->k;
191 model->offset_springs[i].a->force.y += dy * model->k;
192 model->offset_springs[i].b->force.x -= dx * model->k;
193 model->offset_springs[i].b->force.y -= dy * model->k;
196 for (i = 0; i < model->num_objects; i++) {
198 model->objects[i].force.x * model->objects[i].force.x +
199 model->objects[i].force.y * model->objects[i].force.y;
207 model_integrate (Model *model, double step)
213 for (i = 0; i < model->num_objects; i++) {
214 o = &model->objects[i];
219 x + (x - o->previous_position.x) + o->force.x * step * step;
221 y + (y - o->previous_position.y) + o->force.y * step * step;
223 o->previous_position.x = x;
224 o->previous_position.y = y;
228 /* The square root in the distance computation for the string and
229 * stick constraints can be aproximated using Newton:
232 * (model->sticks[i].length +
233 * (dx * dx + dy * dy) / model->sticks[i].length) / 2;
235 * This works really well, since the constraints aren't typically
236 * violated much. Thus, the distance is really close to the stick
237 * length, which then makes a good initial guess. However, the
238 * approximation seems to be slower that just calling sqrt()...
242 estimate_distance (double dx, double dy, double r)
244 #ifdef APPROXIMATE_SQUARE_ROOTS
245 return (r + (dx * dx + dy * dy) / r) / 2;
247 return sqrt (dx * dx + dy * dy);
252 polygon_contains_point (Polygon *polygon, Point *point)
257 for (i = 0; i < polygon->num_points; i++) {
258 dx = point->x - polygon->points[i].x;
259 dy = point->y - polygon->points[i].y;
261 if (polygon->normals[i].x * dx + polygon->normals[i].y * dy >= 0)
269 polygon_reflect_object (Polygon *polygon, Object *object)
276 for (i = 0; i < polygon->num_points; i++) {
277 d = polygon->normals[i].x * (object->position.x - polygon->points[i].x) +
278 polygon->normals[i].y * (object->position.y - polygon->points[i].y);
284 n = &polygon->normals[i];
288 object->position.x -= (1 + elasticity) * distance * n->x;
289 object->position.y -= (1 + elasticity) * distance * n->y;
292 n->x * (object->previous_position.x - polygon->points[edge].x) +
293 n->y * (object->previous_position.y - polygon->points[edge].y);
295 object->previous_position.x -= (1 + elasticity) * distance * n->x;
296 object->previous_position.y -= (1 + elasticity) * distance * n->y;
300 model_constrain_polygon (Model *model, Polygon *polygon)
304 for (i = 0; i < model->num_objects; i++) {
305 if (polygon_contains_point (polygon, &model->objects[i].position))
306 polygon_reflect_object (polygon, &model->objects[i]);
311 model_constrain_offset (Model *model, Offset *offset)
318 for (i = 0; i < offset->num_objects; i++) {
319 x += offset->objects[i]->position.x;
320 y += offset->objects[i]->position.y;
323 x = x / offset->num_objects - offset->dx * (offset->num_objects - 1) / 2;
324 y = y / offset->num_objects - offset->dy * (offset->num_objects - 1) / 2;
326 for (i = 0; i < offset->num_objects; i++) {
327 offset->objects[i]->position.x = x + offset->dx * i;
328 offset->objects[i]->position.y = y + offset->dy * i;
333 model_constrain (Model *model)
335 double dx, dy, x, y, distance, fraction;
338 /* Anchor object constraint. */
339 if (model->anchor_object != NULL) {
340 model->anchor_object->position.x = model->anchor_position.x;
341 model->anchor_object->position.y = model->anchor_position.y;
342 model->anchor_object->previous_position.x = model->anchor_position.x;
343 model->anchor_object->previous_position.y = model->anchor_position.y;
346 /* String constraints. */
347 for (i = 0; i < model->num_strings; i++) {
348 x = model->strings[i].a->position.x;
349 y = model->strings[i].a->position.y;
350 dx = model->strings[i].b->position.x - x;
351 dy = model->strings[i].b->position.y - y;
352 distance = estimate_distance (dx, dy, model->strings[i].length);
353 if (distance < model->strings[i].length)
355 fraction = (distance - model->strings[i].length) / distance / 2;
356 model->strings[i].a->position.x = x + dx * fraction;
357 model->strings[i].a->position.y = y + dy * fraction;
358 model->strings[i].b->position.x = x + dx * (1 - fraction);
359 model->strings[i].b->position.y = y + dy * (1 - fraction);
362 /* Stick constraints. */
363 for (i = 0; i < model->num_sticks; i++) {
364 x = model->sticks[i].a->position.x;
365 y = model->sticks[i].a->position.y;
366 dx = model->sticks[i].b->position.x - x;
367 dy = model->sticks[i].b->position.y - y;
368 distance = estimate_distance (dx, dy, model->sticks[i].length);
369 fraction = (distance - model->sticks[i].length) / distance / 2;
370 model->sticks[i].a->position.x = x + dx * fraction;
371 model->sticks[i].a->position.y = y + dy * fraction;
372 model->sticks[i].b->position.x = x + dx * (1 - fraction);
373 model->sticks[i].b->position.y = y + dy * (1 - fraction);
376 /* Offset constraints. */
377 for (i = 0; i < model->num_offsets; i++)
378 model_constrain_offset (model, &model->offsets[i]);
380 /* Polygon constraints. */
381 for (i = 0; i < model->num_polygons; i++)
382 model_constrain_polygon (model, &model->polygons[i]);
386 model_step (Model *model, double delta_t)
390 model_accumulate_forces (model);
391 model_integrate (model, delta_t);
392 for (i = 0; i < 50; i++)
393 model_constrain (model);
395 model->theta += delta_t;
399 object_distance (Object *object, double x, double y)
403 dx = object->position.x - x;
404 dy = object->position.y - y;
406 return sqrt (dx*dx + dy*dy);
410 model_find_nearest (Model *model, double x, double y)
413 double distance, min_distance;
416 for (i = 0; i < model->num_objects; i++) {
417 distance = object_distance (&model->objects[i], x, y);
418 if (i == 0 || distance < min_distance) {
419 min_distance = distance;
420 object = &model->objects[i];