Title:  Fast Quad Rotation
Brief:  A better way to rotate quads around their centers.
Date:   1722126213
Tags:   Programming, Optimization, C
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.

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
/* 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 };

/* bottom-left */
const t_fvec2 v1 = { c.x - d.y, c.y + d.x };

/* bottom-right */
const t_fvec2 v2 = { c.x + d.x, c.y + d.y };

/* upper-right */
const t_fvec2 v3 = { c.x + d.y, c.y - d.x };

```