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.
17 #include <cairo-xlib.h>
26 const double elasticity = 0.7;
27 const double friction = 1;
28 const double gravity = 20;
31 polygon_init (Polygon *p, int num_points, ...)
33 double dx, dy, length;
37 /* Polygons are defined counter-clock-wise in a coordinate system
38 * with the y-axis pointing down. */
40 va_start (ap, num_points);
41 p->num_points = num_points;
42 p->points = g_new (Point, num_points);
44 for (i = 0; i < num_points; i++) {
45 p->points[i].x = va_arg (ap, double);
46 p->points[i].y = va_arg (ap, double);
50 p->normals = g_new (Vector, p->num_points);
51 /* Compute outward pointing normals. p->normals[i] is the normal
52 * for the edged between p->points[i] and p->points[i + 1]. */
53 for (i = 0; i < p->num_points; i++) {
54 j = (i + 1) % p->num_points;
55 dx = p->points[j].x - p->points[i].x;
56 dy = p->points[j].y - p->points[i].y;
57 length = sqrt (dx * dx + dy * dy);
58 p->normals[i].x = -dy / length;
59 p->normals[i].y = dx / length;
64 polygon_init_diamond (Polygon *polygon, double x, double y)
66 return polygon_init (polygon, 5,
75 polygon_init_rectangle (Polygon *polygon, double x0, double y0,
78 return polygon_init (polygon, 4, x0, y0, x0, y1, x1, y1, x1, y0);
82 model_fini (Model *model)
86 g_free (model->objects);
87 g_free (model->sticks);
88 g_free (model->strings);
89 for (i = 0; i < model->num_offsets; i++)
90 g_free (model->offsets[i].objects);
91 g_free (model->springs);
92 g_free (model->offset_springs);
93 for (i = 0; i < model->num_polygons; i++)
94 g_free (model->polygons[i].points);
95 g_free (model->polygons);
97 memset (model, 0, sizeof *model);
101 model_accumulate_forces (Model *model)
104 double x, y, dx, dy, distance, displacement;
108 for (i = 0; i < model->num_objects; i++) {
110 model->objects[i].force.x = 0;
111 model->objects[i].force.y = gravity * model->objects[i].mass;
114 v.x = model->objects[i].position.x - model->objects[i].previous_position.x;
115 v.y = model->objects[i].position.y - model->objects[i].previous_position.y;
116 model->objects[i].force.x -= v.x * friction;
117 model->objects[i].force.y -= v.y * friction;
120 for (i = 0; i < model->num_springs; i++) {
121 x = model->springs[i].a->position.x;
122 y = model->springs[i].a->position.y;
123 dx = model->springs[i].b->position.x - x;
124 dy = model->springs[i].b->position.y - y;
125 distance = sqrt (dx * dx + dy * dy);
128 displacement = distance - model->springs[i].length;
129 model->springs[i].a->force.x += u.x * model->k * displacement;
130 model->springs[i].a->force.y += u.y * model->k * displacement;
131 model->springs[i].b->force.x -= u.x * model->k * displacement;
132 model->springs[i].b->force.y -= u.y * model->k * displacement;
135 for (i = 0; i < model->num_offset_springs; i++) {
137 (model->offset_springs[i].a->position.x +
138 model->offset_springs[i].b->position.x) / 2;
140 (model->offset_springs[i].a->position.y +
141 model->offset_springs[i].b->position.y) / 2;
143 x = middle.x - model->offset_springs[i].dx / 2;
144 y = middle.y - model->offset_springs[i].dy / 2;
146 dx = x - model->offset_springs[i].a->position.x;
147 dy = y - model->offset_springs[i].a->position.y;
149 model->offset_springs[i].a->force.x += dx * model->k;
150 model->offset_springs[i].a->force.y += dy * model->k;
151 model->offset_springs[i].b->force.x -= dx * model->k;
152 model->offset_springs[i].b->force.y -= dy * model->k;
155 for (i = 0; i < model->num_objects; i++) {
157 model->objects[i].force.x * model->objects[i].force.x +
158 model->objects[i].force.y * model->objects[i].force.y;
166 model_integrate (Model *model, double step)
172 for (i = 0; i < model->num_objects; i++) {
173 o = &model->objects[i];
178 x + (x - o->previous_position.x) + o->force.x * step * step;
180 y + (y - o->previous_position.y) + o->force.y * step * step;
182 o->previous_position.x = x;
183 o->previous_position.y = y;
187 /* The square root in the distance computation for the string and
188 * stick constraints can be aproximated using Newton:
191 * (model->sticks[i].length +
192 * (dx * dx + dy * dy) / model->sticks[i].length) / 2;
194 * This works really well, since the constraints aren't typically
195 * violated much. Thus, the distance is really close to the stick
196 * length, which then makes a good initial guess. However, the
197 * approximation seems to be slower that just calling sqrt()...
201 estimate_distance (double dx, double dy, double r)
203 #ifdef APPROXIMATE_SQUARE_ROOTS
204 return (r + (dx * dx + dy * dy) / r) / 2;
206 return sqrt (dx * dx + dy * dy);
211 polygon_contains_point (Polygon *polygon, Point *point)
216 for (i = 0; i < polygon->num_points; i++) {
217 dx = point->x - polygon->points[i].x;
218 dy = point->y - polygon->points[i].y;
220 if (polygon->normals[i].x * dx + polygon->normals[i].y * dy >= 0)
228 polygon_reflect_object (Polygon *polygon, Object *object)
235 for (i = 0; i < polygon->num_points; i++) {
236 d = polygon->normals[i].x * (object->position.x - polygon->points[i].x) +
237 polygon->normals[i].y * (object->position.y - polygon->points[i].y);
243 n = &polygon->normals[i];
247 object->position.x -= (1 + elasticity) * distance * n->x;
248 object->position.y -= (1 + elasticity) * distance * n->y;
251 n->x * (object->previous_position.x - polygon->points[edge].x) +
252 n->y * (object->previous_position.y - polygon->points[edge].y);
254 object->previous_position.x -= (1 + elasticity) * distance * n->x;
255 object->previous_position.y -= (1 + elasticity) * distance * n->y;
259 model_constrain_polygon (Model *model, Polygon *polygon)
263 for (i = 0; i < model->num_objects; i++) {
264 if (polygon_contains_point (polygon, &model->objects[i].position))
265 polygon_reflect_object (polygon, &model->objects[i]);
270 model_constrain_offset (Model *model, Offset *offset)
277 for (i = 0; i < offset->num_objects; i++) {
278 x += offset->objects[i]->position.x;
279 y += offset->objects[i]->position.y;
282 x = x / offset->num_objects - offset->dx * (offset->num_objects - 1) / 2;
283 y = y / offset->num_objects - offset->dy * (offset->num_objects - 1) / 2;
285 for (i = 0; i < offset->num_objects; i++) {
286 offset->objects[i]->position.x = x + offset->dx * i;
287 offset->objects[i]->position.y = y + offset->dy * i;
292 model_constrain (Model *model)
294 double dx, dy, x, y, distance, fraction;
297 /* Anchor object constraint. */
298 if (model->anchor_object != NULL) {
299 model->anchor_object->position.x = model->anchor_position.x;
300 model->anchor_object->position.y = model->anchor_position.y;
301 model->anchor_object->previous_position.x = model->anchor_position.x;
302 model->anchor_object->previous_position.y = model->anchor_position.y;
305 /* String constraints. */
306 for (i = 0; i < model->num_strings; i++) {
307 x = model->strings[i].a->position.x;
308 y = model->strings[i].a->position.y;
309 dx = model->strings[i].b->position.x - x;
310 dy = model->strings[i].b->position.y - y;
311 distance = estimate_distance (dx, dy, model->strings[i].length);
312 if (distance < model->strings[i].length)
314 fraction = (distance - model->strings[i].length) / distance / 2;
315 model->strings[i].a->position.x = x + dx * fraction;
316 model->strings[i].a->position.y = y + dy * fraction;
317 model->strings[i].b->position.x = x + dx * (1 - fraction);
318 model->strings[i].b->position.y = y + dy * (1 - fraction);
321 /* Stick constraints. */
322 for (i = 0; i < model->num_sticks; i++) {
323 x = model->sticks[i].a->position.x;
324 y = model->sticks[i].a->position.y;
325 dx = model->sticks[i].b->position.x - x;
326 dy = model->sticks[i].b->position.y - y;
327 distance = estimate_distance (dx, dy, model->sticks[i].length);
328 fraction = (distance - model->sticks[i].length) / distance / 2;
329 model->sticks[i].a->position.x = x + dx * fraction;
330 model->sticks[i].a->position.y = y + dy * fraction;
331 model->sticks[i].b->position.x = x + dx * (1 - fraction);
332 model->sticks[i].b->position.y = y + dy * (1 - fraction);
335 /* Offset constraints. */
336 for (i = 0; i < model->num_offsets; i++)
337 model_constrain_offset (model, &model->offsets[i]);
339 /* Polygon constraints. */
340 for (i = 0; i < model->num_polygons; i++)
341 model_constrain_polygon (model, &model->polygons[i]);
345 model_step (Model *model, double delta_t)
349 model_accumulate_forces (model);
350 model_integrate (model, delta_t);
351 for (i = 0; i < 50; i++)
352 model_constrain (model);
354 model->theta += delta_t;
358 object_distance (Object *object, double x, double y)
362 dx = object->position.x - x;
363 dy = object->position.y - y;
365 return sqrt (dx*dx + dy*dy);
369 model_find_nearest (Model *model, double x, double y)
372 double distance, min_distance;
375 for (i = 0; i < model->num_objects; i++) {
376 distance = object_distance (&model->objects[i], x, y);
377 if (i == 0 || distance < min_distance) {
378 min_distance = distance;
379 object = &model->objects[i];