update

articles/fast-quad-rotation/page.mmd

@@ -7,15 +7,45 @@ CSS:    /style.css
 A similar in essence trick to [by pi rotation](/articles/vector-pi-rotation.html), but with delta calculated
 for some corner which is reused later with negation and coordinate swap.
 
-Scaling by `M_SQRT1_2` is there to retain the quad size (Pythagorean stuffs).
+Additionally `cos(a) = sqrt(1 - sin(a) ^ 2)` is used to reuse the result of sin(a),
+with `fast_sqrt()` for good measure.
 
 ### Code ###
 ```c
-const t_fvec2 c = frect_center(sprite.rect);
-const t_fvec2 d = {
-    .x = (cosf(sprite.rotation + (float)M_PI_4) * sprite.rect.w) * (float)M_SQRT1_2,
-    .y = (sinf(sprite.rotation + (float)M_PI_4) * sprite.rect.h) * (float)M_SQRT1_2,
+/* http://www.azillionmonkeys.com/qed/sqroot.html */
+static inline float fast_sqrt(float x)
+{
+    union {
+        float f;
+        uint32_t u;
+    } pun = {.f = x};
+
+    pun.u += 127 << 23;
+    pun.u >>= 1;
+
+    return pun.f;
+}
+
+/* instead of calculating cosf again, - use sinf result */
+static inline t_fvec2 fast_cossine(float a) {
+    const float s = sinf(a);
+    return (t_fvec2){
+        .x = fast_sqrt(1.0f - s * s) *
+            (a >= (float)M_PI_2 && a < (float)(M_PI + M_PI_2) ? -1 : 1),
+        .y = s
     };
+}
+
+/* final vertex calculation */
+const t_fvec2 t = fast_cossine(sprite.rotation + (float)M_PI_4);
+
+/* scaling by `M_SQRT1_2` is there to retain the quad size (Pythagorean stuffs). */
+const t_fvec2 d = {
+    .x = t.x * sprite.rect.w * (float)M_SQRT1_2,
+    .y = t.y * sprite.rect.h * (float)M_SQRT1_2,
+};
+
+const t_fvec2 c = frect_center(sprite.rect);
 
 /* upper-left */
 const t_fvec2 v0 = { c.x - d.x, c.y - d.y };