// The following comment prevents Unity from auto upgrading the shader. Please keep it to keep backward compatibility.
// UNITY_SHADER_NO_UPGRADE

#ifndef _VLB_SHADER_MATHS_INCLUDED_
#define _VLB_SHADER_MATHS_INCLUDED_

inline float lengthSqr(float2 v) { return dot(v, v); }
inline float dot2(float2 v) { return dot(v,v); }
inline float lerpClamped(float a, float b, float t) { return lerp(a, b, saturate(t)); }
inline float invLerp(float a, float b, float t) { return (t - a) / (b - a); }
inline float invLerpClamped(float a, float b, float t) { return saturate(invLerp(a, b, t)); }
inline float fromABtoCD_Clamped(float valueAB, float A, float B, float C, float D)  { return lerpClamped(C, D, invLerpClamped(A, B, valueAB)); }

// Returns 1.0 if a >= b, 0.0 otherwise
inline float isEqualOrGreater(float a, float b) { return step(b, a); }

// Returns 1.0 if a < b, 0.0 otherwise
inline float isLower(float a, float b) { return 1.0 - step(b, a); }

// Returns 1.0 if all arguments equal 1.0, 0.0 otherwise
inline float ifAnd(float a, float b)            { return isEqualOrGreater(a + b, 1.5); }
inline float ifAnd(float a, float b, float c)   { return isEqualOrGreater(a + b + c, 2.5); }

// Get signed distance of pos from the plane (normal ; d).
// Normal should be normalized.
// If we want to disable this feature, we could set normal and d to 0 (no discard in this case).
inline float DistanceToPlane(float3 pos, float3 normal, float d) { return dot(normal, pos) + d; }

// https://www.iquilezles.org/www/articles/functions/functions.htm
// A nice choice to remap the 0..1 interval into 0..1, such that the corners are mapped to 0 and the center to 1.
// In other words, parabola(0) = parabola(1) = 0, and parabola(1/2) = 1.
inline float parabola( float x, float k )
{
    return pow( 4.0*x*(1.0-x), k );
}

// https://en.wikipedia.org/wiki/Smoothstep
inline float smootherstep(float edge0, float edge1, float x)
{
    // Scale, and clamp x to 0..1 range
    x = clamp((x - edge0) / (edge1 - edge0), 0.0, 1.0);
    // Evaluate polynomial
    return x*x*x*(x*(x * 6 - 15) + 10);
}

inline float flipUV(float uv, float shouldFlip)
{
    // returns uv or 1-uv
    return max(-shouldFlip, 0) + shouldFlip * uv;
}

#endif