Make the shadow actually gaussian

The old shadow kernel formula is not "wrong" per se, as the only judge
is if it looks good. However, the formula used is not really gaussian.
Also, the kernel size calculation doesn't really make sense to me.

This commit change the kernel formula to actually use a gaussian
distribution. As far as I can tell, there is no perceivable difference.
Except now the effective shadow radius is smaller for the same config.

Also, made that part of code a bit more mordern.

Signed-off-by: Yuxuan Shui <yshuiv7@gmail.com>

src/common.h

@@ -426,7 +426,7 @@ typedef uint32_t glx_prog_main_t;
 
 typedef struct conv {
   int size;
-  double *data;
+  double data[];
 } conv;
 
 /// Linked list type of atoms.

src/compton.c

@@ -569,36 +569,42 @@ check_fade_fin(session_t *ps, win **_w) {
 
 static double __attribute__((const))
 gaussian(double r, double x, double y) {
-  return ((1 / (sqrt(2 * M_PI * r))) *
-    exp((- (x * x + y * y)) / (2 * r * r)));
+  // Formula can be found here:
+  // https://en.wikipedia.org/wiki/Gaussian_blur#Mathematics
+  // Except a special case for r == 0 to produce sharp shadows
+  if (r == 0)
+    return 1;
+  return exp(-0.5*(x*x+y*y)/(r*r))/(2*M_PI*r*r);
 }
 
 static conv *
 make_gaussian_map(double r) {
   conv *c;
-  int size = ((int) ceil((r * 3)) + 1) & ~1;
-  int center = size / 2;
-  int x, y;
+  int size = r*2+1;
+  int center = size/2;
   double t;
-  double g;
 
-  c = malloc(sizeof(conv) + size * size * sizeof(double));
+  c = malloc(sizeof(conv)+size*size*sizeof(double));
   c->size = size;
-  c->data = (double *) (c + 1);
   t = 0.0;
 
-  for (y = 0; y < size; y++) {
-    for (x = 0; x < size; x++) {
-      g = gaussian(r, x - center, y - center);
+  /*printf_errf("(): %f", r);*/
+  for (int y = 0; y < size; y++) {
+    for (int x = 0; x < size; x++) {
+      double g = gaussian(r, x-center, y-center);
       t += g;
-      c->data[y * size + x] = g;
+      c->data[y*size+x] = g;
+      /*printf("%f ", c->data[y*size+x]);*/
     }
+    /*printf("\n");*/
   }
 
-  for (y = 0; y < size; y++) {
-    for (x = 0; x < size; x++) {
-      c->data[y * size + x] /= t;
+  for (int y = 0; y < size; y++) {
+    for (int x = 0; x < size; x++) {
+      c->data[y*size+x] /= t;
+      /*printf("%f ", c->data[y*size+x]);*/
     }
+    /*printf("\n");*/
   }
 
   return c;
@@ -4227,7 +4233,7 @@ get_cfg(session_t *ps, int argc, char *const *argv, bool first_pass) {
 
   // Range checking and option assignments
   ps->o.fade_delta = max_i(ps->o.fade_delta, 1);
-  ps->o.shadow_radius = max_i(ps->o.shadow_radius, 1);
+  ps->o.shadow_radius = max_i(ps->o.shadow_radius, 0);
   ps->o.shadow_red = normalize_d(ps->o.shadow_red);
   ps->o.shadow_green = normalize_d(ps->o.shadow_green);
   ps->o.shadow_blue = normalize_d(ps->o.shadow_blue);