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 spacer_init (Spacer *spacer, Object *a, Object *b, double length)
76 spacer->length = length;
80 polygon_init (Polygon *p, int num_points, ...)
82 double dx, dy, length;
86 /* Polygons are defined counter-clock-wise in a coordinate system
87 * with the y-axis pointing down. */
89 va_start (ap, num_points);
90 p->num_points = num_points;
91 p->points = g_new (Point, num_points);
93 for (i = 0; i < num_points; i++) {
94 p->points[i].x = va_arg (ap, double);
95 p->points[i].y = va_arg (ap, double);
99 p->normals = g_new (Vector, p->num_points);
100 /* Compute outward pointing normals. p->normals[i] is the normal
101 * for the edged between p->points[i] and p->points[i + 1]. */
102 for (i = 0; i < p->num_points; i++) {
103 j = (i + 1) % p->num_points;
104 dx = p->points[j].x - p->points[i].x;
105 dy = p->points[j].y - p->points[i].y;
106 length = sqrt (dx * dx + dy * dy);
107 p->normals[i].x = -dy / length;
108 p->normals[i].y = dx / length;
113 polygon_init_diamond (Polygon *polygon, double x, double y)
115 return polygon_init (polygon, 5,
124 polygon_init_rectangle (Polygon *polygon, double x0, double y0,
125 double x1, double y1)
127 return polygon_init (polygon, 4, x0, y0, x0, y1, x1, y1, x1, y0);
131 model_fini (Model *model)
135 g_free (model->objects);
136 g_free (model->sticks);
137 g_free (model->strings);
138 for (i = 0; i < model->num_offsets; i++)
139 g_free (model->offsets[i].objects);
140 g_free (model->springs);
141 g_free (model->offset_springs);
142 g_free (model->spacers);
143 for (i = 0; i < model->num_polygons; i++)
144 g_free (model->polygons[i].points);
145 g_free (model->polygons);
147 memset (model, 0, sizeof *model);
151 model_accumulate_forces (Model *model)
154 double x, y, dx, dy, distance, displacement;
158 for (i = 0; i < model->num_objects; i++) {
160 model->objects[i].force.x = 0;
161 model->objects[i].force.y = gravity * model->objects[i].mass;
164 v.x = model->objects[i].position.x - model->objects[i].previous_position.x;
165 v.y = model->objects[i].position.y - model->objects[i].previous_position.y;
166 model->objects[i].force.x -= v.x * friction;
167 model->objects[i].force.y -= v.y * friction;
170 for (i = 0; i < model->num_springs; i++) {
171 x = model->springs[i].a->position.x;
172 y = model->springs[i].a->position.y;
173 dx = model->springs[i].b->position.x - x;
174 dy = model->springs[i].b->position.y - y;
175 distance = sqrt (dx * dx + dy * dy);
178 displacement = distance - model->springs[i].length;
179 model->springs[i].a->force.x += u.x * model->k * displacement;
180 model->springs[i].a->force.y += u.y * model->k * displacement;
181 model->springs[i].b->force.x -= u.x * model->k * displacement;
182 model->springs[i].b->force.y -= u.y * model->k * displacement;
185 for (i = 0; i < model->num_offset_springs; i++) {
187 (model->offset_springs[i].a->position.x +
188 model->offset_springs[i].b->position.x) / 2;
190 (model->offset_springs[i].a->position.y +
191 model->offset_springs[i].b->position.y) / 2;
193 x = middle.x - model->offset_springs[i].dx / 2;
194 y = middle.y - model->offset_springs[i].dy / 2;
196 dx = x - model->offset_springs[i].a->position.x;
197 dy = y - model->offset_springs[i].a->position.y;
199 model->offset_springs[i].a->force.x += dx * model->k;
200 model->offset_springs[i].a->force.y += dy * model->k;
201 model->offset_springs[i].b->force.x -= dx * model->k;
202 model->offset_springs[i].b->force.y -= dy * model->k;
205 for (i = 0; i < model->num_objects; i++) {
207 model->objects[i].force.x * model->objects[i].force.x +
208 model->objects[i].force.y * model->objects[i].force.y;
216 model_integrate (Model *model, double step)
222 for (i = 0; i < model->num_objects; i++) {
223 o = &model->objects[i];
228 x + (x - o->previous_position.x) + o->force.x * step * step;
230 y + (y - o->previous_position.y) + o->force.y * step * step;
232 o->previous_position.x = x;
233 o->previous_position.y = y;
237 /* The square root in the distance computation for the string and
238 * stick constraints can be aproximated using Newton:
241 * (model->sticks[i].length +
242 * (dx * dx + dy * dy) / model->sticks[i].length) / 2;
244 * This works really well, since the constraints aren't typically
245 * violated much. Thus, the distance is really close to the stick
246 * length, which then makes a good initial guess. However, the
247 * approximation seems to be slower that just calling sqrt()...
251 estimate_distance (double dx, double dy, double r)
253 #ifdef APPROXIMATE_SQUARE_ROOTS
254 return (r + (dx * dx + dy * dy) / r) / 2;
256 return sqrt (dx * dx + dy * dy);
261 polygon_contains_point (Polygon *polygon, Point *point)
266 for (i = 0; i < polygon->num_points; i++) {
267 dx = point->x - polygon->points[i].x;
268 dy = point->y - polygon->points[i].y;
270 if (polygon->normals[i].x * dx + polygon->normals[i].y * dy >= 0)
278 polygon_reflect_object (Polygon *polygon, Object *object)
285 for (i = 0; i < polygon->num_points; i++) {
286 d = polygon->normals[i].x * (object->position.x - polygon->points[i].x) +
287 polygon->normals[i].y * (object->position.y - polygon->points[i].y);
293 n = &polygon->normals[i];
297 object->position.x -= (1 + elasticity) * distance * n->x;
298 object->position.y -= (1 + elasticity) * distance * n->y;
301 n->x * (object->previous_position.x - polygon->points[edge].x) +
302 n->y * (object->previous_position.y - polygon->points[edge].y);
304 object->previous_position.x -= (1 + elasticity) * distance * n->x;
305 object->previous_position.y -= (1 + elasticity) * distance * n->y;
309 model_constrain_polygon (Model *model, Polygon *polygon)
313 for (i = 0; i < model->num_objects; i++) {
314 if (polygon_contains_point (polygon, &model->objects[i].position))
315 polygon_reflect_object (polygon, &model->objects[i]);
320 model_constrain_offset (Model *model, Offset *offset)
327 for (i = 0; i < offset->num_objects; i++) {
328 x += offset->objects[i]->position.x;
329 y += offset->objects[i]->position.y;
332 x = x / offset->num_objects - offset->dx * (offset->num_objects - 1) / 2;
333 y = y / offset->num_objects - offset->dy * (offset->num_objects - 1) / 2;
335 for (i = 0; i < offset->num_objects; i++) {
336 offset->objects[i]->position.x = x + offset->dx * i;
337 offset->objects[i]->position.y = y + offset->dy * i;
342 model_constrain (Model *model)
344 double dx, dy, x, y, distance, fraction;
347 /* Anchor object constraint. */
348 if (model->anchor_object != NULL) {
349 model->anchor_object->position.x = model->anchor_position.x;
350 model->anchor_object->position.y = model->anchor_position.y;
351 model->anchor_object->previous_position.x = model->anchor_position.x;
352 model->anchor_object->previous_position.y = model->anchor_position.y;
355 /* String constraints. */
356 for (i = 0; i < model->num_strings; i++) {
357 x = model->strings[i].a->position.x;
358 y = model->strings[i].a->position.y;
359 dx = model->strings[i].b->position.x - x;
360 dy = model->strings[i].b->position.y - y;
361 distance = estimate_distance (dx, dy, model->strings[i].length);
362 if (distance < model->strings[i].length)
364 fraction = (distance - model->strings[i].length) / distance / 2;
365 model->strings[i].a->position.x = x + dx * fraction;
366 model->strings[i].a->position.y = y + dy * fraction;
367 model->strings[i].b->position.x = x + dx * (1 - fraction);
368 model->strings[i].b->position.y = y + dy * (1 - fraction);
371 /* Spacer constraints. */
372 for (i = 0; i < model->num_spacers; i++) {
373 x = model->spacers[i].a->position.x;
374 y = model->spacers[i].a->position.y;
375 dx = model->spacers[i].b->position.x - x;
376 dy = model->spacers[i].b->position.y - y;
377 distance = estimate_distance (dx, dy, model->spacers[i].length);
378 if (distance > model->spacers[i].length)
380 fraction = (distance - model->spacers[i].length) / distance / 2;
381 model->spacers[i].a->position.x = x + dx * fraction;
382 model->spacers[i].a->position.y = y + dy * fraction;
383 model->spacers[i].b->position.x = x + dx * (1 - fraction);
384 model->spacers[i].b->position.y = y + dy * (1 - fraction);
387 /* Stick constraints. */
388 for (i = 0; i < model->num_sticks; i++) {
389 x = model->sticks[i].a->position.x;
390 y = model->sticks[i].a->position.y;
391 dx = model->sticks[i].b->position.x - x;
392 dy = model->sticks[i].b->position.y - y;
393 distance = estimate_distance (dx, dy, model->sticks[i].length);
394 fraction = (distance - model->sticks[i].length) / distance / 2;
395 model->sticks[i].a->position.x = x + dx * fraction;
396 model->sticks[i].a->position.y = y + dy * fraction;
397 model->sticks[i].b->position.x = x + dx * (1 - fraction);
398 model->sticks[i].b->position.y = y + dy * (1 - fraction);
401 /* Offset constraints. */
402 for (i = 0; i < model->num_offsets; i++)
403 model_constrain_offset (model, &model->offsets[i]);
405 /* Polygon constraints. */
406 for (i = 0; i < model->num_polygons; i++)
407 model_constrain_polygon (model, &model->polygons[i]);
411 model_step (Model *model, double delta_t)
415 model_accumulate_forces (model);
416 model_integrate (model, delta_t);
417 for (i = 0; i < 2; i++)
418 model_constrain (model);
420 model->theta += delta_t;
424 object_distance (Object *object, double x, double y)
428 dx = object->position.x - x;
429 dy = object->position.y - y;
431 return sqrt (dx*dx + dy*dy);
435 model_find_nearest (Model *model, double x, double y)
438 double distance, min_distance;
441 for (i = 0; i < model->num_objects; i++) {
442 distance = object_distance (&model->objects[i], x, y);
443 if (i == 0 || distance < min_distance) {
444 min_distance = distance;
445 object = &model->objects[i];