+ if((ret = pixel_hit_in_square(*sq, x, y))) return ret;
+ if(l > 0 && (ret = pixel_hit_in_square(*(sq-1), x, y))) return ret;
+ if(t > 0 && (ret = pixel_hit_in_square(*(sq-gw), x, y))) return ret;
+ if(l > 0 && t > 0 && (ret = pixel_hit_in_square(*(sq-1-gw), x, y))) return ret;
+ return 0;
+}
+
+
+float
+sprite_mass(Sprite *s)
+{
+ if(s->type == SHIP) return s->area;
+ else if(s->type == ROCK) return 3 * s->area;
+ else return 0;
+}
+
+/*
+ * BOUNCE THEORY
+ *
+ * ****************** In 1 Dimension *****************
+ *
+ * For now we will imagine bouncing A and B off each other in 1 dimension (along
+ * a line). We can safely save the other dimension for later.
+ *
+ * A and B are the same weight, and are both traveling 1m/sec, to collide right
+ * at the origin. With perfect bounciness, their full momentum is reversed.
+ *
+ * If we cut the weight of A down by half, then the center of our colision will
+ * drift towards A (the speeds of A and B are not simply reversed as in our last
+ * example.) However, there is always a place between A and B on the line (I'll
+ * call it x) such that the speeds of A and B relative to x, are simply
+ * reversed. Thus we can find the new speed for A like so:
+ *
+ * new A = x -(A - x)
+ *
+ * new B = x -(B - x)
+ *
+ * or, simply:
+ *
+ * new A = 2x - A
+ *
+ * new B = 2x - B
+ *
+ *
+ * this point x is the sort of center of momentum. If, instead of bouncing, A
+ * and B just globbed together, x would be center of the new glob.
+ *
+ * x is the point where there's an equal amount of force coming in from both
+ * sides. ie the weighted average of the speeds of A and B.
+ *
+ * average force = (A force + B force) / total mass
+ *
+ * x.speed = (a.speed * a.mass + b.speed * b.mass) / (a.mass + b.mas)
+ *
+ * then we apply the formula above for calculating the new A and B.
+ *
+ *
+ *
+ *
+ * ****************** In 2 Dimensions *****************
+ *
+ * OK, that's how we do it in 1D. Now we need to deal with 2D.
+ *
+ * Imagine (or draw) the two balls just as they are bouncing off each other.
+ * Imagine drawing a line through the centers of the balls. The balls are
+ * exerting force on each other only along this axis. So if we rotate
+ * everything, we can do our earlier 1D math along this line.
+ *
+ * It doesn't matter what direction the balls are going in, they only exert
+ * force on each other along this line. What we will do is to compute the part
+ * of the balls' momentum that is going along this line, and bounce it according
+ * to our math above. The other part is unaffected by the bounce, and we can
+ * just leave it alone.
+ *
+ * To get this component of the balls' momentum, we can use the dot product.
+ *
+ * dot(U, V) = length(U) * length(V) * cos(angle between U and V)
+ *
+ * If U is a length 1 vector, then dot(U, V) is the length of the component of V
+ * in the direction of U. So the components of V are:
+ *
+ * U * dot(U, V) parallel to U
+ *
+ * V - U * dot(U, V) perpendicular to U
+ *
+ * To do the actual bounce, we compute the unit vector between the center of the
+ * two balls, compute the components of the balls' speeds along this vector (A
+ * and B), and then bounce them according to the math above:
+ *
+ * new A = 2x - A
+ *
+ * new B = 2x - B
+ *
+ * But we rewrite it in relative terms:
+ *
+ * new A = A + 2(x-A)
+ *
+ * new B = B + 2(x-B)
+ */
+
+void
+bounce(Sprite *a, Sprite *b)
+{
+ float x, y, n; // (x, y) is unit vector from a to b.
+ float va, vb; // va, vb are balls' speeds along (x, y)
+ float ma, mb; // ma, mb are the balls' masses.
+ float vc; // vc is the "center of momentum"
+
+ // (x, y) is unit vector pointing from A's center to B's center.
+ x = (b->x + b->w / 2) - (a->x + a->w / 2);
+ y = (b->y + b->h / 2) - (a->y + a->h / 2);
+ n = sqrt(x*x + y*y); x /= n; y /= n;
+
+ // velocities along (x, y)
+ va = x*a->dx + y*a->dy;
+ vb = x*b->dx + y*b->dy;
+ if(vb-va > 0) return; // don't bounce if we're already moving away.
+
+ // get masses and compute "center" speed
+ ma = sprite_mass(a); mb = sprite_mass(b);
+ vc = (va*ma + vb*mb) / (ma+mb);
+
+ // bounce off the center speed.
+ a->dx += 2*x*(vc-va); a->dy += 2*y*(vc-va);
+ b->dx += 2*x*(vc-vb); b->dy += 2*y*(vc-vb);