63 lines
1.6 KiB
Plaintext
63 lines
1.6 KiB
Plaintext
Title: Fast Quad Rotation
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Brief: A better way to rotate quads around their centers.
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Date: 1722126213
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Tags: Programming, Optimization, C
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CSS: /style.css
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A similar in essence trick to [by pi rotation](/articles/vector-pi-rotation.html), but with delta calculated
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for some corner which is reused later with negation and coordinate swap.
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Additionally `cos(a) = sqrt(1 - sin(a) ^ 2)` is used to reuse the result of sin(a),
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with `fast_sqrt()` for good measure.
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### Code ###
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```c
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/* http://www.azillionmonkeys.com/qed/sqroot.html */
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static inline float fast_sqrt(float x)
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{
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union {
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float f;
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uint32_t u;
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} pun = {.f = x};
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pun.u += 127 << 23;
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pun.u >>= 1;
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return pun.f;
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}
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/* instead of calculating cosf again, - use sinf result */
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static inline t_fvec2 fast_cossine(float a) {
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const float s = sinf(a);
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return (t_fvec2){
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.x = fast_sqrt(1.0f - s * s) *
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(a >= (float)M_PI_2 && a < (float)(M_PI + M_PI_2) ? -1 : 1),
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.y = s
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};
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}
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/* final vertex calculation */
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const t_fvec2 t = fast_cossine(sprite.rotation + (float)M_PI_4);
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/* scaling by `M_SQRT1_2` is there to retain the quad size (Pythagorean stuffs). */
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const t_fvec2 d = {
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.x = t.x * sprite.rect.w * (float)M_SQRT1_2,
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.y = t.y * sprite.rect.h * (float)M_SQRT1_2,
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};
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const t_fvec2 c = frect_center(sprite.rect);
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/* upper-left */
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const t_fvec2 v0 = { c.x - d.x, c.y - d.y };
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/* bottom-left */
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const t_fvec2 v1 = { c.x - d.y, c.y + d.x };
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/* bottom-right */
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const t_fvec2 v2 = { c.x + d.x, c.y + d.y };
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/* upper-right */
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const t_fvec2 v3 = { c.x + d.y, c.y - d.x };
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```
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