Rotating a 2d array -> reversing a loop - c

Question

I use the following code to rotate a bitmask (a packed 2d array). To be honest I do not have a firm grip of the algorithm used, I copied and modified the rotation code from the pygame library (where it was used to rotate surfaces). Due to the implementation of bitmask I can speed this rotation up a lot by reversing the inner loop. With that I mean, instead of doing foreach y { foreach x { ... } } I need to do foreach x { foreach y { ... } }. I have trouble reversing the loop because the trigonometry has to be adapted in a way I don't currently see at this moment.
Here's the code:
typedef struct bitmask {
int w,h;
BITMASK_W bits[1];
} bitmask_t;
bitmask_t* bitmask_rotate(const bitmask_t *mask, float angle) {
bitmask_t *newmask = NULL;
double radangle, sangle, cangle;
int isin, icos;
double cx, cy, sx, sy;
int x, y, ax, ay, xd, yd, dx, dy;
int nxmax, nymax, xmaxval, ymaxval;
radangle = angle * DEG_TO_RAD;
sangle = sin(radangle);
cangle = cos(radangle);
isin = (int)(sangle * 65536);
icos = (int)(cangle * 65536);
x = mask->w;
y = mask->h;
cx = cangle*x;
cy = cangle*y;
sx = sangle*x;
sy = sangle*y;
nxmax = (int) (MAX (MAX (MAX (fabs (cx + sy), fabs (cx - sy)), fabs (-cx + sy)), fabs (-cx - sy)));
nymax = (int) (MAX (MAX (MAX (fabs (sx + cy), fabs (sx - cy)), fabs (-sx + cy)), fabs (-sx - cy)));
newmask = bitmask_create(nxmax, nymax, 0);
if (!newmask) return NULL;
cy = newmask->h / 2;
xd = ((mask->w - newmask->w) << 15);
yd = ((mask->h - newmask->h) << 15);
ax = ((newmask->w) << 15) - (int)(cangle * ((newmask->w - 1) << 15));
ay = ((newmask->h) << 15) - (int)(sangle * ((newmask->w - 1) << 15));
xmaxval = ((mask->w) << 16) - 1;
ymaxval = ((mask->h) << 16) - 1;
for (y = 0; y < newmask->h; y++) {
dx = (ax + (isin * (cy - y))) + xd;
dy = (ay - (icos * (cy - y))) + yd;
for (x = 0; x < newmask->w; x++) {
if (!(dx < 0 || dy < 0 || dx > xmaxval || dy > ymaxval)) {
if (bitmask_getbit(mask, dx >> 16, dy >> 16)) {
bitmask_setbit(newmask, x, y);
}
}
dx += icos;
dy += isin;
}
}
return newmask;
}
Before people are going to ask "what have you tried?", I looped up rotating matrices on Wikipedia, and I could see what is going on there and how they implemented it in this algorithm (precalculate a starting dx and dy and then increment with icos and isin), but the bitshifts and parameters I don't understand (ax for example) make it hard for me to follow.

Answer 1

for (x = 0; x < newmask->w; x++) {
dx = (ax + (isin * cy + icos * x)) + xd;
dy = (ay - (icos * cy - isin * x)) + yd;
for (y = 0; y < newmask->h; y++) {
if (!(dx < 0 || dy < 0 || dx > xmaxval || dy > ymaxval)) {
if (bitmask_getbit(mask, dx >> 16, dy >> 16)) {
bitmask_setbit(newmask, x, y);
}
}
dx -= isin;
dy += icos;
}
}