10 SDL_Surface *load_image(char *filename);
13 // 2 sets of sprites, sorted by position
14 static Sprite **sprites[2] = { NULL, NULL };
16 // which set are we using?
19 // size of squares into which sprites are sorted.
20 static int grid_size = 0;
22 // screen size in grid squares.
23 static int gw = 0, gh = 0;
25 // lists of free sprites, by type.
26 Sprite *free_sprites[N_TYPES];
34 uint32_t bits = 0, bit, *p;
37 if(s->image->format->BytesPerPixel != 2) {
38 fprintf(stderr, "get_shape(): not a 16-bit image!\n");
42 s->w = s->image->w; s->h = s->image->h;
43 grid_size = max(grid_size, max(s->w, s->h));
44 s->mask_w = ((s->w+31)>>5);
45 s->mask = malloc(s->mask_w*s->h*sizeof(uint32_t));
47 fprintf(stderr, "get_shape(): can't allocate bitmask.\n");
51 SDL_LockSurface(s->image);
52 px = s->image->pixels;
53 transp = s->image->format->colorkey;
55 for(y=0; y<s->image->h; y++) {
57 for(x=0; x<s->image->w; x++) {
58 if(!bit) { bits = 0; bit = 0x80000000; }
59 if(*px++ != transp) { bits |= bit; s->area++; }
61 if(!bit || x == s->image->w - 1) { *(p++) = bits; }
63 px = (uint16_t *) ((uint8_t *) px + s->image->pitch - 2*s->image->w);
65 SDL_UnlockSurface(s->image);
70 load_sprite(Sprite *s, char *filename)
72 s->image = load_image(filename);
73 if(s->image) get_shape(s);
90 grid_size = grid_size * 3 / 2;
91 gw = (XSIZE-1 + 2*grid_size) / grid_size;
92 gh = (YSIZE-1 + 2*grid_size) / grid_size;
94 sprites[0] = malloc(2 * gw * gh * sizeof(Sprite *));
95 sprites[1] = (void *)sprites[0] + gw * gh * sizeof(Sprite *);
97 fprintf(stderr, "init_sprites(): can't allocate grid squares.\n");
100 memset(sprites[0], 0, 2 * gw * gh * sizeof(Sprite *));
104 static inline Sprite **
105 square(int x, int y, int set)
107 int b = (x+grid_size)/grid_size + gw*((y+grid_size)/grid_size);
108 return &sprites[set][b];
112 add_sprite(Sprite *s)
114 insert_sprite(square(s->x, s->y, set), s);
122 for(i=0; i<gw*gh; i++)
123 while(sprites[set][i]) {
124 Sprite *s = remove_sprite(&sprites[set][i]);
125 insert_sprite(&free_sprites[s->type], s);
131 move_sprite(Sprite *s, float ticks)
133 if(s->flags & MOVE) {
134 s->x += (s->dx - screendx)*ticks;
135 s->y += (s->dy - screendy)*ticks;
140 sort_sprite(Sprite *s)
142 // clip it, or sort it into the other set of sprites.
143 if(s->x + s->w < 0 || s->x >= XSIZE
144 || s->y + s->h < 0 || s->y >= YSIZE) {
145 insert_sprite(&free_sprites[s->type], s);
147 } else insert_sprite(square(s->x, s->y, 1-set), s);
151 move_sprites(float ticks)
156 // Move all the sprites
157 for(sq=0; sq<gw*gh; sq++) {
158 head=&sprites[set][sq];
160 Sprite *s = remove_sprite(head);
161 move_sprite(s, ticks); sort_sprite(s);
164 set = 1-set; // switch to other set of sprites.
169 line_collide(int xov, unsigned bit, uint32_t *amask, uint32_t *bmask)
171 int i, words = (xov-1) >> 5;
174 for(i=0; i<words; i++) {
175 abits = *amask++ << bit;
176 abits |= *amask >> (32-bit);
177 if(abits & *bmask++) return true;
179 abits = *amask << bit;
180 if(abits & *bmask) return true;
186 mask_collide(int xov, int yov, Sprite *a, Sprite *b)
189 int xoffset = a->w - xov;
190 int word = xoffset >> 5, bit = xoffset & 31;
191 uint32_t *amask = a->mask, *bmask = b->mask;
194 amask = a->mask + ((a->h - yov) * a->mask_w) + word;
199 bmask = b->mask + ((b->h - yov) * b->mask_w) + word;
202 for(y=0; y<yov; y++) {
203 if(line_collide(xov, bit, amask, bmask)) return 1;
204 amask += a->mask_w; bmask += b->mask_w;
211 collide(Sprite *a, Sprite *b)
213 int dx, dy, xov, yov;
215 if(!COLLIDES(a) || !COLLIDES(b)) return false;
217 if(b->x < a->x) { Sprite *tmp = a; a = b; b = tmp; }
222 xov = max(min(a->w - dx, b->w), 0);
224 if(dy >= 0) yov = max(min(a->h - dy, b->h), 0);
225 else yov = -max(min(b->h - -dy, a->h), 0);
227 if(xov == 0 || yov == 0) return false;
228 else return mask_collide(xov, yov, a, b);
232 collide_with_list(Sprite *s, Sprite *list)
234 for(; list; list=list->next)
235 if(collide(s, list)) do_collision(s, list);
243 for(i=0; i<end; i++) {
244 for(s=sprites[set][i]; s; s=s->next) {
245 collide_with_list(s, s->next);
246 if(i+1 < end) collide_with_list(s, sprites[set][i+1]);
247 if(i+gw < end) collide_with_list(s, sprites[set][i+gw]);
248 if(i+gw+1 < end) collide_with_list(s, sprites[set][i+gw+1]);
254 hit_in_square(Sprite *r, Sprite *s)
257 if(collide(r, s)) break;
268 l = (s->x + grid_size) / grid_size;
269 r = (s->x + s->w + grid_size) / grid_size;
270 t = (s->y + grid_size) / grid_size;
271 b = (s->y + s->h + grid_size) / grid_size;
272 sq = &sprites[set][l + t*gw];
274 if((c = hit_in_square(*sq, s))) return c;
275 if(l > 0 && (c = hit_in_square(*(sq-1), s))) return c;
276 if(t > 0 && (c = hit_in_square(*(sq-gw), s))) return c;
277 if(l > 0 && t > 0 && (c = hit_in_square(*(sq-1-gw), s))) return c;
280 if((c = hit_in_square(*(sq+1), s))) return c;
281 if(t > 0 && hit_in_square(*(sq+1-gw), s)) return c;
284 if((c = hit_in_square(*(sq+gw), s))) return c;
285 if(l > 0 && (c = hit_in_square(*(sq-1+gw), s))) return c;
287 if(r > l && b > t && (c = hit_in_square(*(sq+1+gw), s))) return c;
292 pixel_collide(Sprite *s, int x, int y)
296 if(!COLLIDES(s)) return false;
298 if(x < s->x || y < s->y || x >= s->x + s->w || y >= s->y + s->h) return 0;
300 x -= s->x; y -= s->y;
301 pmask = 0x80000000 >> (x&0x1f);
302 return s->mask[(y*s->mask_w) + (x>>5)] & pmask;
306 pixel_hit_in_square(Sprite *r, float x, float y)
308 for(; r; r=r->next) {
309 if(COLLIDES(r) && pixel_collide(r, x, y)) return r;
315 pixel_collides(float x, float y)
321 l = (x + grid_size) / grid_size; t = (y + grid_size) / grid_size;
322 sq = &sprites[set][l + t*gw];
323 if((ret = pixel_hit_in_square(*sq, x, y))) return ret;
324 if(l > 0 && (ret = pixel_hit_in_square(*(sq-1), x, y))) return ret;
325 if(t > 0 && (ret = pixel_hit_in_square(*(sq-gw), x, y))) return ret;
326 if(l > 0 && t > 0 && (ret = pixel_hit_in_square(*(sq-1-gw), x, y))) return ret;
332 sprite_mass(Sprite *s)
334 if(s->type == SHIP) return s->area;
335 else if(s->type == ROCK) return 3 * s->area;
342 * ****************** In 1 Dimension *****************
344 * For now we will imagine bouncing A and B off each other in 1 dimension (along
345 * a line). We can safely save the other dimension for later.
347 * A and B are the same weight, and are both traveling 1m/sec, to collide right
348 * at the origin. With perfect bounciness, their full momentum is reversed.
350 * If we cut the weight of A down by half, then the center of our colision will
351 * drift towards A (the speeds of A and B are not simply reversed as in our last
352 * example.) However, there is always a place between A and B on the line (I'll
353 * call it x) such that the speeds of A and B relative to x, are simply
354 * reversed. Thus we can find the new speed for A like so:
367 * this point x is the sort of center of momentum. If, instead of bouncing, A
368 * and B just globbed together, x would be center of the new glob.
370 * x is the point where there's an equal amount of force coming in from both
371 * sides. ie the weighted average of the speeds of A and B.
373 * average force = (A force + B force) / total mass
375 * x.speed = (a.speed * a.mass + b.speed * b.mass) / (a.mass + b.mas)
377 * then we apply the formula above for calculating the new A and B.
382 * ****************** In 2 Dimensions *****************
384 * OK, that's how we do it in 1D. Now we need to deal with 2D.
386 * Imagine (or draw) the two balls just as they are bouncing off each other.
387 * Imagine drawing a line through the centers of the balls. The balls are
388 * exerting force on each other only along this axis. So if we rotate
389 * everything, we can do our earlier 1D math along this line.
391 * It doesn't matter what direction the balls are going in, they only exert
392 * force on each other along this line. What we will do is to compute the part
393 * of the balls' momentum that is going along this line, and bounce it according
394 * to our math above. The other part is unaffected by the bounce, and we can
395 * just leave it alone.
397 * To get this component of the balls' momentum, we can use the dot product.
399 * dot(U, V) = length(U) * length(V) * cos(angle between U and V)
401 * If U is a length 1 vector, then dot(U, V) is the length of the component of V
402 * in the direction of U. So the components of V are:
404 * U * dot(U, V) parallel to U
406 * V - U * dot(U, V) perpendicular to U
408 * To do the actual bounce, we compute the unit vector between the center of the
409 * two balls, compute the components of the balls' speeds along this vector (A
410 * and B), and then bounce them according to the math above:
416 * But we rewrite it in relative terms:
424 bounce(Sprite *a, Sprite *b)
426 float x, y, n; // (x, y) is unit vector from a to b.
427 float va, vb; // va, vb are balls' speeds along (x, y)
428 float ma, mb; // ma, mb are the balls' masses.
429 float vc; // vc is the "center of momentum"
431 // (x, y) is unit vector pointing from A's center to B's center.
432 x = (b->x + b->w / 2) - (a->x + a->w / 2);
433 y = (b->y + b->h / 2) - (a->y + a->h / 2);
434 n = sqrt(x*x + y*y); x /= n; y /= n;
436 // velocities along (x, y)
437 va = x*a->dx + y*a->dy;
438 vb = x*b->dx + y*b->dy;
439 if(vb-va > 0) return; // don't bounce if we're already moving away.
441 // get masses and compute "center" speed
442 ma = sprite_mass(a); mb = sprite_mass(b);
443 vc = (va*ma + vb*mb) / (ma+mb);
445 // bounce off the center speed.
446 a->dx += 2*x*(vc-va); a->dy += 2*y*(vc-va);
447 b->dx += 2*x*(vc-vb); b->dy += 2*y*(vc-vb);