Various math util functions for cg

Mathutil.cginc

#ifndef _MATHUTIL
#define _MATHUTIL

#define PI 3.141592653589793115997963468544185161590576171875

inline float floorq(float v, float q) {
    return floor(v / q) * q;
}    

inline float ceilq(float v, float q) {
    return ceil(v / q) * q;
}    

inline float roundq(float v, float q) {
    return round(v / q) * q;
}

inline float never0(float v) {
    return (sign(v) + 0.00001) * max(abs(v), 0.00001);
}

inline float smooth(float v) {
    return cos(v * PI + PI) / 2 + .5;
}

inline float circle(float x) {
    return sqrt(1 - pow(x - 1, 2));
}

inline float circlei(float x) {
    return 1 - sqrt(1 - pow((1 - x) - 1, 2));
}

inline float tri(float v) {
    return 1 - abs(v % 1 * 2 - 1);
}

inline float parabola(float x) {
    return x * (0.5 + (1 - x * 2) * 0.5) * 4;
}

inline float bounce(float v) {
    return 1 - pow(abs(v % 1 * 2 - 1), 2);
}

inline float2 rotate2(float2 v, float r) {
    float sinx = sin(r);
    float cosx = cos(r);
    float2x2 m = float2x2(cosx, -sinx, sinx, cosx);
    return mul(v, m);
}

inline float2 bend2(float2 v, float factor)
{
    float x, y, theta, sint, cost;

    x = v.y;
    y = v.x;

    theta = x * factor;
    sint = sin(theta);
    cost = cos(theta);

    if (abs(factor) > 0) {
        return float2(
            (y - 1 / factor) * cost + 1 / factor,
            -(y - 1 / factor) * sint);
    } else {
        return v;
    }
}

inline float lerpx(float a, float b, float v, float bias, float scale)
{
    v = clamp((v - bias) / scale, 0, 1);
    v = a * (1 - v) + b * v;
    return v;
}

inline float2 ray_x_plane(float3 ro, float3 rd, float3 po, float3 pn) {
    /*
    input:
        ro = ray origin;
        rd = ray direction;
        po = plane origin;
        pn = plane normal;
    output:
        x: > 0 = intersection found
        y: distance to plane
    */

    float d = dot(pn, rd);

    if (abs(d) > 0.0001)
    {
        float t = dot(po - ro, pn) / d;
        if (t >= 0)
            return float2(1, t);
    }

    return float2(0, 0);
}

inline float4 ray_x_plane_point(float3 ro, float3 rd, float3 po, float3 pn) {
    float2 res = ray_x_plane(ro, rd, po, pn);

    if (res.x > 0)
        return half4(ro + rd * res.y, res.x);
    else
        return half4(ro, res.x);
}

#endif