/******************************************************************************/
/*
  Project   - MudBun
  Publisher - Long Bunny Labs
              http://LongBunnyLabs.com
  Author    - Ming-Lun "Allen" Chou
              http://AllenChou.net
*/
/******************************************************************************/

#ifndef MUDBUN_SDF_OPERATORS
#define MUDBUN_SDF_OPERATORS

#include "../Math/MathConst.cginc"

// http://www.iquilezles.org/www/articles/smin/smin.htm
// http://www.iquilezles.org/www/articles/distfunctions/distfunctions.htm
// http://mercury.sexy/hg_sdf

#define SQRT_2_INV (0.70710678118f)
#define ONE_OVER_4 (0.25f)
#define ONE_OVER_6 (0.16666666666f)

// union
//-----------------------------------------------------------------------------

// raw union
float sdf_uni(float a, float b)
{
  return min(a, b);
}

// smooth quadratic polynomial union (C1 continuity, order-dependent concatenation)
float sdf_uni_quad(float a, float b, float k)
{
  float h = max(k - abs(a - b), 0.0f) / max(k, kEpsilon);
  return min(a, b) - h * h * k * ONE_OVER_4;
}

// smooth cubic polynomial union (C2 continuity, order-dependent concatenation)
float sdf_uni_cubic(float a, float b, float k)
{
  float h = max(k - abs(a - b), 0.0f) / max(k, kEpsilon);
  return min(a, b) - h * h * h * k * ONE_OVER_6;
}

float sdf_uni_round(float a, float b, float r)
{
  float2 u = max(float2(r - a, r - b), float2(0.0f, 0.0f));
  return max(r, min(a, b)) - length(u);
}

float sdf_uni_chamfer(float a, float b, float r)
{
  return min(min(a, b), (a - r + b) * SQRT_2_INV);
}

// smooth exponential union (infinite continuity, order-independent concatenation)
// max(k, kEpsilon); = 30.0f is a good default
#define sdf_uni_exp_concat_term(x, k) (exp2(-(k) * (x)))
#define sdf_uni_exp_concat_res(sum, k) (-log2(sum) / (k))
float sdf_uni_exp(float a, float b, float k) // 2-term concatenation
{
  float sum = sdf_uni_exp_concat_term(a, k) + sdf_uni_exp_concat_term(b, k);
  return sdf_uni_exp_concat_res(sum, k);
}

// smooth power union (infinite continuity, order-independent concatenation)
// max(k, kEpsilon); = 8.0f is a good default
#define sdf_uni_pow_concat_term(x, k) (pow((x), (k)))
#define sdf_uni_pow_concat_res(sum, prod, k) pow((prod) / (sum), 1.0f / (k))
float sdf_uni_pow(float a, float b, float k) // 2-term concatenation
{
  a = sdf_uni_pow_concat_term(a, k);
  b = sdf_uni_pow_concat_term(b, k);
  return sdf_uni_pow_concat_res(a + b, a * b, k);
}

//-----------------------------------------------------------------------------
// end: union


// intersection
//-----------------------------------------------------------------------------

// raw intersection
float sdf_int(float a, float b)
{
  return max(a, b);
}

// smooth quadratic polynomial intersection (C1 continuity, order-dependent concatenation)
float sdf_int_quad(float a, float b, float k)
{
  float h = max(k - abs(a - b), 0.0f) / max(k, kEpsilon);
  return max(a, b) + h * h * k * ONE_OVER_4;
}

// smooth cubic polynomial intersection (C2 continuity, order-dependent concatenation)
float sdf_int_cubic(float a, float b, float k)
{
  float h = max(k - abs(a - b), 0.0f) / max(k, kEpsilon);
  return max(a, b) + h * h * h * k * ONE_OVER_6;
}

float sdf_int_round(float a, float b, float r)
{
  float2 u = max(float2(r + a, r + b), float2(0.0f, 0.0f));
  return min(-r, max(a, b)) + length(u);
}

float sdf_int_chamfer(float a, float b, float r)
{
  return max(max(a, b), (a + r + b) * SQRT_2_INV);
}

//-----------------------------------------------------------------------------
// end: intersection


// subtraction
//-----------------------------------------------------------------------------

// raw subtraction
float sdf_sub(float a, float b)
{
  return max(a, -b);
}

// smooth quadratic polynomial subtraction (C1 continuity, order-dependent concatenation)
float sdf_sub_quad(float a, float b, float k)
{
  return sdf_int_quad(a, -b, k);
}

// smooth cubic polynomial subtraction (C2 continuity, order-dependent concatenation)
float sdf_sub_cubic(float a, float b, float k)
{
  return sdf_int_cubic(a, -b, k);
}

float sdf_sub_round(float a, float b, float r)
{
  return sdf_int_round(a, -b, r);
}

float sdf_sub_chamfer(float a, float b, float r)
{
  return sdf_int_chamfer(a, -b, r);
}

//-----------------------------------------------------------------------------
// end: subtraction


// misc.
//-----------------------------------------------------------------------------

float sdf_pipe(float a, float b, float r)
{
  return length(float2(a, b)) - r;
}

float sdf_engrave(float a, float b, float r)
{
  return max(a, (a + r - abs(b))) * SQRT_2_INV;
}

//-----------------------------------------------------------------------------
// end: misc.

#endif