Lumenarium/src_v2/patterns/patterns_math.h

#ifndef PATTERNS_MATH_H
#define PATTERNS_MATH_H

r32 fractf(r32 v) { r64 int_part = 0; return (r32)modf((r64)v, &int_part); }

r32
pm_smoothstep_r32(r32 t)
{
  r32 r = (t * t * (3 - (2 * t)));
  return r;
}

r32
pm_smoothstep_range_r32(r32 t, r32 min, r32 max)
{
  r32 tt = pm_smoothstep_r32(t);
  r32 r = lerp(min, tt, max);
  return r;
}

v3
pm_smoothstep_v3(v3 p)
{
  v3 result = {
    .x = pm_smoothstep_r32(p.x),
    .y = pm_smoothstep_r32(p.y),
    .z = pm_smoothstep_r32(p.z),
  };
  return result;
}

r32
pm_easeinout_cubic_r32(r32 v)
{
  assert(v >= 0 && v <= 1);
  // Equation:
  // [0,0.5) = 4 * v^3
  // [0.5,1] = 1 - (-2 * v + 2)^3 / 2
  if (v < 0.5f) {
    return 4 * v * v * v;
  } else {
    r32 a = -2 * v + 2;
    r32 a3 = a * a * a;
    return 1 - a3 / 2;
  }
}

///// vector extensions

v2 pm_lerp_v2(v2 a, r32 t, v2 b) { 
  return (v2){ 
    .x = lerp(a.x, t, b.x),
    .y = lerp(a.y, t, b.y),
  };
}
v3 pm_lerp_v3(v3 a, r32 t, v3 b) { 
  return (v3){ 
    .x = lerp(a.x, t, b.x),
    .y = lerp(a.y, t, b.y),
    .z = lerp(a.z, t, b.z),
  };
}
v4 pm_lerp_v4(v4 a, r32 t, v4 b) { 
  return (v4){ 
    .x = lerp(a.x, t, b.x),
    .y = lerp(a.y, t, b.y),
    .z = lerp(a.z, t, b.z),
    .w = lerp(a.w, t, b.w),
  };
}

v2 pm_abs_v2(v2 v) { return (v2){ .x = fabsf(v.x), .y = fabsf(v.y) }; }
v3 pm_abs_v3(v3 v) { return (v3){ .x = fabsf(v.x), .y = fabsf(v.y), .z = fabsf(v.z) }; }
v4 pm_abs_v4(v4 v) { return (v4){ .x = fabsf(v.x), .y = fabsf(v.y), .z = fabsf(v.z), .w = fabsf(v.w) }; }

v2 pm_floor_v2(v2 v) { return (v2){ .x = floorf(v.x), .y = floorf(v.y) }; }
v3 pm_floor_v3(v3 v) { return (v3){ .x = floorf(v.x), .y = floorf(v.y), .z = floorf(v.z) }; }
v4 pm_floor_v4(v4 v) { return (v4){ .x = floorf(v.x), .y = floorf(v.y), .z = floorf(v.z), .w = floorf(v.w) }; }

v2 pm_fract_v2(v2 v) { return (v2){ .x = fractf(v.x), .y = fractf(v.y) }; }
v3 pm_fract_v3(v3 v) { return (v3){ .x = fractf(v.x), .y = fractf(v.y), .z = fractf(v.z) }; }
v4 pm_fract_v4(v4 v) { return (v4){ .x = fractf(v.x), .y = fractf(v.y), .z = fractf(v.z), .w = fractf(v.w) }; }

r32 pm_sinf_01(r32 v) { return 0.5f + (0.5f * sinf(v)); }
r32 pm_cosf_01(r32 v) { return 0.5f + (0.5f * cosf(v)); }

v2 pm_sin_v2(v2 v) { return (v2){ .x = sinf(v.x), .y = sinf(v.y) }; }
v3 pm_sin_v3(v3 v) { return (v3){ .x = sinf(v.x), .y = sinf(v.y), .z = sinf(v.z) }; }
v4 pm_sin_v4(v4 v) { return (v4){ .x = sinf(v.x), .y = sinf(v.y), .z = sinf(v.z), .w = sinf(v.w) }; }

v2 pm_cos_v2(v2 v) { return (v2){ .x = cosf(v.x), .y = cosf(v.y) }; }
v3 pm_cos_v3(v3 v) { return (v3){ .x = cosf(v.x), .y = cosf(v.y), .z = cosf(v.z) }; }
v4 pm_cos_v4(v4 v) { return (v4){ .x = cosf(v.x), .y = cosf(v.y), .z = cosf(v.z), .w = cosf(v.w) }; }

////// hash functions

r32
pm_hash_v2_to_r32(v2 p)
{
  v2 r = HMM_MultiplyVec2f(p, 0.3183099f);
  r = pm_fract_v2(r);
  r = HMM_MultiplyVec2f(r, 50);
  r32 result = fractf(r.x * r.y * (r.x + r.y));
  return result;
}

r32
pm_hash_r32_to_r32(r32 n)
{
  return fractf(n * 17 * fractf(n * 0.3183099f));
}

v2
pm_hash_r32_to_v2(r32 n)
{
  v2 a = pm_sin_v2((v2){ n, n + 1.0f });
  v2 b = HMM_MultiplyVec2(a, (v2){ 43758.5453123f, 22578.1459123f });
  v2 r = pm_fract_v2(b);
  return r;
}

v2
pm_hash_v2_to_v2(v2 p)
{
  v2 k = (v2){ 0.3183099f, 0.3678794f };
  v2 kp = (v2){k.y, k.x};
  v2 r0 = HMM_MultiplyVec2(p, k);
  v2 r1 = HMM_AddVec2(r0, kp);
  r32 f = 16.0f * fractf(p.x * p.y * (p.x + p.y));
  v2 r2 = HMM_MultiplyVec2f(k, f);
  v2 r3 = pm_fract_v2(r2);
  return r3;
}

v3
pm_hash_v2_to_v3(v2 p)
{
  v3 q = (v3){
    .x = HMM_DotVec2(p, (v2){127.1f, 311.7f}),
    .y = HMM_DotVec2(p, (v2){267.5f, 183.3f}),
    .z = HMM_DotVec2(p, (v2){419.2f, 371.9f})
  };
  v3 r0 = pm_sin_v3(q);
  v3 r1 = HMM_MultiplyVec3f(r0, 43758.5453f);
  v3 r2 = pm_fract_v3(r1);
  return r2;
}

r32
pm_hash_v3_to_r32(v3 p)
{
  v3 p0 = HMM_MultiplyVec3f(p, 0.3183099f);
  v3 p1 = HMM_AddVec3(p0, (v3){ 0.1f, 0.1f, 0.1f });
  v3 p2 = pm_fract_v3(p1);
  v3 p3 = HMM_MultiplyVec3f(p2, 17.0f);
  r32 r0 = fractf(p3.x * p3.y * p3.z * (p3.x + p3.y + p3.z));
  return r0;
}

r32
pm_random_v2_to_r32(v2 n)
{
  v2 v = (v2){ 12.9898f, 4.1414f };
  r32 r0 = HMM_DotVec2(n, v);
  r32 r1 = sinf(r0);
  r32 r2 = fractf(r1 * 43758.5453);
  return r2;
}

internal r32
pm_noise_v3_to_r32(v3 p)
{
  p = pm_abs_v3(p);
  v3 p_fl = pm_floor_v3(p);
  v3 p_fr = pm_fract_v3(p);
  v3 f = pm_smoothstep_v3(p_fr);
  
  v3 p_fl_0 = p_fl;
  v3 p_fl_1 = HMM_AddVec3(p_fl, (v3){1, 0, 0});
  v3 p_fl_2 = HMM_AddVec3(p_fl, (v3){0, 1, 0});
  v3 p_fl_3 = HMM_AddVec3(p_fl, (v3){1, 1, 0});
  v3 p_fl_4 = HMM_AddVec3(p_fl, (v3){0, 0, 1});
  v3 p_fl_5 = HMM_AddVec3(p_fl, (v3){1, 0, 1});
  v3 p_fl_6 = HMM_AddVec3(p_fl, (v3){0, 1, 1});
  v3 p_fl_7 = HMM_AddVec3(p_fl, (v3){1, 1, 1});
  
  r32 h0 = pm_hash_v3_to_r32(p_fl_0);
  r32 h1 = pm_hash_v3_to_r32(p_fl_1);
  r32 h2 = pm_hash_v3_to_r32(p_fl_2);
  r32 h3 = pm_hash_v3_to_r32(p_fl_3);
  r32 h4 = pm_hash_v3_to_r32(p_fl_4);
  r32 h5 = pm_hash_v3_to_r32(p_fl_5);
  r32 h6 = pm_hash_v3_to_r32(p_fl_6);
  r32 h7 = pm_hash_v3_to_r32(p_fl_7);
  
  r32 h0_1 = lerp(h0, f.x, h1);
  r32 h2_3 = lerp(h2, f.x, h3);
  r32 h4_5 = lerp(h4, f.x, h5);
  r32 h6_7 = lerp(h6, f.x, h7);
  r32 h01_23 = lerp(h0_1, f.y, h2_3);
  r32 h45_67 = lerp(h4_5, f.y, h6_7);
  // r32 result = lerp( 
  //   lerp(
  //     lerp(h0, f.x, h1),
  //     f.y, 
  //     lerp(h2, f.x, h3)
  //   ),
  //   f.z,
  //   lerp(
  //     lerp(h4, f.x, h5),
  //     f.y,
  //     lerp(h6, f.x, h7)
  //   )
  // );
  r32 result = lerp(h01_23, f.z, h45_67);
  
  assert(result >= 0 && result <= 1);
  return result;
}

r32
pm_fmb_3d(v3 x, r32 h)
{ 
  // r32 G = powf(2, -h);
  // r32 f = 1.0f;
  // r32 a = 1.0f;
  // r32 t = 0.0f;
  // for(s32 i = 0; i < 4; i++)
  // {
  //   v3 xx = HMM_MultiplyVec3f(x, f);
  //   r32 n = pm_noise_v3_to_r32(xx);
  //   t += a * n;
  //   f *= 2.0f;
  //   a *= G;
  // }
  // return (t - .17f) / 1.2f;
  
  // float t = 0.0;
  // for(s32 i = 0; i < 4; i++)
  // {
  //   r32 f = powf(2.0, (r32)(i));
  //   r32 a = powf(f, -h);
  //   r32 n = pm_noise_v3_to_r32(
  //     HMM_MultiplyVec3f(x, f)
  //   );
  //   r32 ns = a * n;
  //   t += ns; 
  // }
  // return t;
  
  v3 ts = (v3){h, h, h};
  v3 pp = x;
  r32 f = 0.0;
  
  v3 pp0 = HMM_AddVec3(pp, ts);
  v3 pp1 = HMM_SubtractVec3(pp, ts);
  
  f += 0.500000f * pm_noise_v3_to_r32(pp0); pp = HMM_MultiplyVec3f(pp, 2.02);
  f += 0.300000f * pm_noise_v3_to_r32(pp1); pp = HMM_MultiplyVec3f(pp, 2.03);
  f += 0.125000f * pm_noise_v3_to_r32(pp);  pp = HMM_MultiplyVec3f(pp, 2.01);
  f += 0.062500f * pm_noise_v3_to_r32(pp0); pp = HMM_MultiplyVec3f(pp, 2.04);
  
  r32 d = 0.9875f;
  f = f / d;
  return f;
}

// internal r32
// pm_voronoise(v2 p, r32 u, r32 v)
// {
//     r32 k = 1.0f + 63.0f + powf(1.0f - v, 6.0f);

//     v2 i = pm_floor_v2(p);
//     v2 f = pm_fract_v2(p);

//     v2 a = (v2){0, 0};
//     for (s32 y = -2; y <= 2; y++)
//     {
//         for (s32 x = -2; x <= 2; x++)
//         {
//             v2 g = (v2){(r32)x, (r32)y};
//             v2 hi = HMM_AddVec2(g, i);
//             v3 h = pm_hash_v2_to_v3(hi);
//             v3 o = HMM_MultiplyVec3(h, (v3){ u, u, 1.0f });
//             v2 d0 = HMM_SubtractVec2(g, f);
//             v2 d1 = HMM_AddVec2(d0, o.XY);
//             r32 d1m = HMM_LengthVec2(d1);
//             r32 w = powf(1.0f - pm_smoothstep_range_r32(d1m, 0.0f, 1.414f), k);
//             a = HMM_AddVec2(a, (v2){o.z * w, w});
//         }
//     }

//     return a.x / a.y;
// }


// Color ramps

typedef struct {
  r32 pct;
  v3 color;
} Color_Ramp_Anchor;

typedef struct {
  Color_Ramp_Anchor anchors[8];
  u32 anchors_count;
} Color_Ramp;

Color_Ramp
color_ramp_reverse(Color_Ramp ramp)
{
  Color_Ramp result = { .anchors_count = ramp.anchors_count };
  for (u32 i = 0; i < ramp.anchors_count; i++)
  {
    u32 new_i = (ramp.anchors_count - 1) - i;
    assert(new_i < ramp.anchors_count);
    r32 rev_pct = 1.f - ramp.anchors[i].pct;
    result.anchors[new_i] = (Color_Ramp_Anchor){
      .color = ramp.anchors[i].color,
      .pct = rev_pct,
    };
  }
  return result;
}

v3
color_ramp_eval(Color_Ramp ramp, r32 pct)
{
  pct = clamp(0, pct, 1);
  // find nearest two anchors
  // TODO: do a binary search and we just have to assume that the anchors
  // are in order from least to greatest
  Color_Ramp_Anchor nearest_below = { .pct = 0, .color = BLACK_V4.xyz }; 
  Color_Ramp_Anchor nearest_above = { .pct = 1, .color = BLACK_V4.xyz };
  r32 dist_below = 1;
  r32 dist_above = -1;
  for (u32 i = 0; i < ramp.anchors_count; i++) {
    Color_Ramp_Anchor anchor = ramp.anchors[i];
    r32 dist = pct - anchor.pct;
    if (dist >= 0 && dist_below > dist) {
      nearest_below = anchor;
      dist_below = dist;
    }
    if (dist <= 0 && dist_above < dist) {
      nearest_above = anchor;
      dist_above = dist;
    }
  }
  
  // interpolate between them
  r32 anchor_range = nearest_above.pct - nearest_below.pct;
  if (anchor_range == 0) anchor_range = 1;
  r32 pct_remapped = (pct - nearest_below.pct) / anchor_range;
  v3 result = pm_lerp_v3(nearest_below.color, pct_remapped, nearest_above.color);
  return result;
}

// Common SDFs
// all assume the shape is centered at 0, 0, 0

internal r32
sdf_sphere2_d(r32 radius_squared, r32 dist_squared)
{
  r32 d = radius_squared - dist_squared;
  r32 sdf = (d / radius_squared);
  return max(0, sdf);
}

internal r32
sdf_sphere2(r32 radius_squared, v3 p)
{
  r32 d2 = HMM_LengthSquaredVec3(p);
  return sdf_sphere2_d(radius_squared, d2);
}

internal r32
sdf_sphere(r32 radius, v3 p)
{
  return sdf_sphere2(radius * radius, p);
}

internal r32
sdf_sphere_hull2_d(r32 radius_squared, r32 falloff, r32 dist_squared)
{
  r32 d = fabsf(falloff * (radius_squared - dist_squared));
  r32 sdf = 1.0f - (d / radius_squared);
  r32 result = max(0, sdf);
  return result;
}

internal r32
sdf_sphere_hull2(r32 radius_squared, r32 falloff, v3 p)
{
  r32 d2 = HMM_LengthSquaredVec3(p);
  return sdf_sphere_hull2_d(radius_squared, falloff, d2);
}

internal r32
sdf_sphere_hull(r32 radius, r32 falloff, v3 p)
{
  return sdf_sphere_hull2(radius * radius, falloff, p);
}

#endif // PATTERNS_MATH_H