From 16c045ba9781f6f9f3ec3cf631a7ddf6566a8291 Mon Sep 17 00:00:00 2001 From: veclavtalica Date: Tue, 30 Jul 2024 23:28:33 +0300 Subject: [PATCH] update --- articles/fast-quad-rotation/page.mmd | 38 +++++++++++++++++++++++++--- 1 file changed, 34 insertions(+), 4 deletions(-) diff --git a/articles/fast-quad-rotation/page.mmd b/articles/fast-quad-rotation/page.mmd index 791b656..ea4ab74 100644 --- a/articles/fast-quad-rotation/page.mmd +++ b/articles/fast-quad-rotation/page.mmd @@ -7,16 +7,46 @@ 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); +/* 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 = (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, + .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 };