@takram/three-atmosphere/build/shared3.js

A Three.js and R3F implementation of Precomputed Atmospheric Scattering

const e = `// Based on: https://github.com/ebruneton/precomputed_atmospheric_scattering/blob/master/atmosphere/functions.glsl

/**
 * Copyright (c) 2017 Eric Bruneton
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 * 3. Neither the name of the copyright holders nor the names of its
 *    contributors may be used to endorse or promote products derived from
 *    this software without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
 * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
 * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
 * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
 * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
 * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
 * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF
 * THE POSSIBILITY OF SUCH DAMAGE.
 *
 * Precomputed Atmospheric Scattering
 * Copyright (c) 2008 INRIA
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 * 3. Neither the name of the copyright holders nor the names of its
 *    contributors may be used to endorse or promote products derived from
 *    this software without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
 * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
 * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
 * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
 * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
 * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
 * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF
 * THE POSSIBILITY OF SUCH DAMAGE.
 */

Number ClampCosine(const Number mu) {
  return clamp(mu, Number(-1.0), Number(1.0));
}

Length ClampDistance(const Length d) {
  return max(d, 0.0 * m);
}

Length ClampRadius(const AtmosphereParameters atmosphere, const Length r) {
  return clamp(r, atmosphere.bottom_radius, atmosphere.top_radius);
}

Length SafeSqrt(const Area a) {
  return sqrt(max(a, 0.0 * m2));
}

Length DistanceToTopAtmosphereBoundary(const AtmosphereParameters atmosphere,
    const Length r, const Number mu) {
  assert(r <= atmosphere.top_radius);
  assert(mu >= -1.0 && mu <= 1.0);
  Area discriminant = r * r * (mu * mu - 1.0) +
      atmosphere.top_radius * atmosphere.top_radius;
  return ClampDistance(-r * mu + SafeSqrt(discriminant));
}

Length DistanceToBottomAtmosphereBoundary(const AtmosphereParameters atmosphere,
    const Length r, const Number mu) {
  assert(r >= atmosphere.bottom_radius);
  assert(mu >= -1.0 && mu <= 1.0);
  Area discriminant = r * r * (mu * mu - 1.0) +
      atmosphere.bottom_radius * atmosphere.bottom_radius;
  return ClampDistance(-r * mu - SafeSqrt(discriminant));
}

bool RayIntersectsGround(const AtmosphereParameters atmosphere,
    const Length r, const Number mu) {
  assert(r >= atmosphere.bottom_radius);
  assert(mu >= -1.0 && mu <= 1.0);
  return mu < 0.0 && r * r * (mu * mu - 1.0) +
      atmosphere.bottom_radius * atmosphere.bottom_radius >= 0.0 * m2;
}

Number GetTextureCoordFromUnitRange(const Number x, const int texture_size) {
  return 0.5 / Number(texture_size) + x * (1.0 - 1.0 / Number(texture_size));
}

vec2 GetTransmittanceTextureUvFromRMu(const AtmosphereParameters atmosphere,
    const Length r, const Number mu) {
  assert(r >= atmosphere.bottom_radius && r <= atmosphere.top_radius);
  assert(mu >= -1.0 && mu <= 1.0);
  // Distance to top atmosphere boundary for a horizontal ray at ground level.
  Length H = sqrt(atmosphere.top_radius * atmosphere.top_radius -
      atmosphere.bottom_radius * atmosphere.bottom_radius);
  // Distance to the horizon.
  Length rho =
      SafeSqrt(r * r - atmosphere.bottom_radius * atmosphere.bottom_radius);
  // Distance to the top atmosphere boundary for the ray (r,mu), and its minimum
  // and maximum values over all mu - obtained for (r,1) and (r,mu_horizon).
  Length d = DistanceToTopAtmosphereBoundary(atmosphere, r, mu);
  Length d_min = atmosphere.top_radius - r;
  Length d_max = rho + H;
  Number x_mu = (d - d_min) / (d_max - d_min);
  Number x_r = rho / H;
  return vec2(GetTextureCoordFromUnitRange(x_mu, TRANSMITTANCE_TEXTURE_WIDTH),
              GetTextureCoordFromUnitRange(x_r, TRANSMITTANCE_TEXTURE_HEIGHT));
}

DimensionlessSpectrum GetTransmittanceToTopAtmosphereBoundary(
    const AtmosphereParameters atmosphere,
    const TransmittanceTexture transmittance_texture,
    const Length r, const Number mu) {
  assert(r >= atmosphere.bottom_radius && r <= atmosphere.top_radius);
  vec2 uv = GetTransmittanceTextureUvFromRMu(atmosphere, r, mu);
  // @shotamatsuda: Added for the precomputation stage in half-float precision.
  #ifdef TRANSMITTANCE_PRECISION_LOG
  // Manually interpolate the transmittance instead of the optical depth.
  const vec2 size = vec2(TRANSMITTANCE_TEXTURE_WIDTH, TRANSMITTANCE_TEXTURE_HEIGHT);
  const vec3 texel_size = vec3(1.0 / size, 0.0);
  vec2 coord = (uv * size) - 0.5;
  vec2 i = (floor(coord) + 0.5) * texel_size.xy;
  vec2 f = fract(coord);
  vec4 t1 = exp(-texture(transmittance_texture, i));
  vec4 t2 = exp(-texture(transmittance_texture, i + texel_size.xz));
  vec4 t3 = exp(-texture(transmittance_texture, i + texel_size.zy));
  vec4 t4 = exp(-texture(transmittance_texture, i + texel_size.xy));
  return DimensionlessSpectrum(mix(mix(t1, t2, f.x), mix(t3, t4, f.x), f.y));
  #else // TRANSMITTANCE_PRECISION_LOG
  return DimensionlessSpectrum(texture(transmittance_texture, uv));
  #endif // TRANSMITTANCE_PRECISION_LOG
}

DimensionlessSpectrum GetTransmittance(
    const AtmosphereParameters atmosphere,
    const TransmittanceTexture transmittance_texture,
    const Length r, const Number mu, const Length d,
    const bool ray_r_mu_intersects_ground) {
  assert(r >= atmosphere.bottom_radius && r <= atmosphere.top_radius);
  assert(mu >= -1.0 && mu <= 1.0);
  assert(d >= 0.0 * m);

  Length r_d = ClampRadius(atmosphere, sqrt(d * d + 2.0 * r * mu * d + r * r));
  Number mu_d = ClampCosine((r * mu + d) / r_d);

  if (ray_r_mu_intersects_ground) {
    return min(
        GetTransmittanceToTopAtmosphereBoundary(
            atmosphere, transmittance_texture, r_d, -mu_d) /
        GetTransmittanceToTopAtmosphereBoundary(
            atmosphere, transmittance_texture, r, -mu),
        DimensionlessSpectrum(1.0));
  } else {
    return min(
        GetTransmittanceToTopAtmosphereBoundary(
            atmosphere, transmittance_texture, r, mu) /
        GetTransmittanceToTopAtmosphereBoundary(
            atmosphere, transmittance_texture, r_d, mu_d),
        DimensionlessSpectrum(1.0));
  }
}

DimensionlessSpectrum GetTransmittanceToSun(
    const AtmosphereParameters atmosphere,
    const TransmittanceTexture transmittance_texture,
    const Length r, const Number mu_s) {
  Number sin_theta_h = atmosphere.bottom_radius / r;
  Number cos_theta_h = -sqrt(max(1.0 - sin_theta_h * sin_theta_h, 0.0));
  return GetTransmittanceToTopAtmosphereBoundary(
          atmosphere, transmittance_texture, r, mu_s) *
      smoothstep(-sin_theta_h * atmosphere.sun_angular_radius / rad,
                 sin_theta_h * atmosphere.sun_angular_radius / rad,
                 mu_s - cos_theta_h);
}

InverseSolidAngle RayleighPhaseFunction(const Number nu) {
  InverseSolidAngle k = 3.0 / (16.0 * PI * sr);
  return k * (1.0 + nu * nu);
}

InverseSolidAngle MiePhaseFunction(const Number g, const Number nu) {
  InverseSolidAngle k = 3.0 / (8.0 * PI * sr) * (1.0 - g * g) / (2.0 + g * g);
  return k * (1.0 + nu * nu) / pow(1.0 + g * g - 2.0 * g * nu, 1.5);
}

vec4 GetScatteringTextureUvwzFromRMuMuSNu(const AtmosphereParameters atmosphere,
    const Length r, const Number mu, const Number mu_s, const Number nu,
    const bool ray_r_mu_intersects_ground) {
  assert(r >= atmosphere.bottom_radius && r <= atmosphere.top_radius);
  assert(mu >= -1.0 && mu <= 1.0);
  assert(mu_s >= -1.0 && mu_s <= 1.0);
  assert(nu >= -1.0 && nu <= 1.0);

  // Distance to top atmosphere boundary for a horizontal ray at ground level.
  Length H = sqrt(atmosphere.top_radius * atmosphere.top_radius -
      atmosphere.bottom_radius * atmosphere.bottom_radius);
  // Distance to the horizon.
  Length rho =
      SafeSqrt(r * r - atmosphere.bottom_radius * atmosphere.bottom_radius);
  Number u_r = GetTextureCoordFromUnitRange(rho / H, SCATTERING_TEXTURE_R_SIZE);

  // Discriminant of the quadratic equation for the intersections of the ray
  // (r,mu) with the ground (see RayIntersectsGround).
  Length r_mu = r * mu;
  Area discriminant =
      r_mu * r_mu - r * r + atmosphere.bottom_radius * atmosphere.bottom_radius;
  Number u_mu;
  if (ray_r_mu_intersects_ground) {
    // Distance to the ground for the ray (r,mu), and its minimum and maximum
    // values over all mu - obtained for (r,-1) and (r,mu_horizon).
    Length d = -r_mu - SafeSqrt(discriminant);
    Length d_min = r - atmosphere.bottom_radius;
    Length d_max = rho;
    u_mu = 0.5 - 0.5 * GetTextureCoordFromUnitRange(d_max == d_min ? 0.0 :
        (d - d_min) / (d_max - d_min), SCATTERING_TEXTURE_MU_SIZE / 2);
  } else {
    // Distance to the top atmosphere boundary for the ray (r,mu), and its
    // minimum and maximum values over all mu - obtained for (r,1) and
    // (r,mu_horizon).
    Length d = -r_mu + SafeSqrt(discriminant + H * H);
    Length d_min = atmosphere.top_radius - r;
    Length d_max = rho + H;
    u_mu = 0.5 + 0.5 * GetTextureCoordFromUnitRange(
        (d - d_min) / (d_max - d_min), SCATTERING_TEXTURE_MU_SIZE / 2);
  }

  Length d = DistanceToTopAtmosphereBoundary(
      atmosphere, atmosphere.bottom_radius, mu_s);
  Length d_min = atmosphere.top_radius - atmosphere.bottom_radius;
  Length d_max = H;
  Number a = (d - d_min) / (d_max - d_min);
  Length D = DistanceToTopAtmosphereBoundary(
      atmosphere, atmosphere.bottom_radius, atmosphere.mu_s_min);
  Number A = (D - d_min) / (d_max - d_min);
  // An ad-hoc function equal to 0 for mu_s = mu_s_min (because then d = D and
  // thus a = A), equal to 1 for mu_s = 1 (because then d = d_min and thus
  // a = 0), and with a large slope around mu_s = 0, to get more texture
  // samples near the horizon.
  Number u_mu_s = GetTextureCoordFromUnitRange(
      max(1.0 - a / A, 0.0) / (1.0 + a), SCATTERING_TEXTURE_MU_S_SIZE);

  Number u_nu = (nu + 1.0) / 2.0;
  return vec4(u_nu, u_mu_s, u_mu, u_r);
}

vec2 GetIrradianceTextureUvFromRMuS(const AtmosphereParameters atmosphere,
    const Length r, const Number mu_s) {
  assert(r >= atmosphere.bottom_radius && r <= atmosphere.top_radius);
  assert(mu_s >= -1.0 && mu_s <= 1.0);
  Number x_r = (r - atmosphere.bottom_radius) /
      (atmosphere.top_radius - atmosphere.bottom_radius);
  Number x_mu_s = mu_s * 0.5 + 0.5;
  return vec2(GetTextureCoordFromUnitRange(x_mu_s, IRRADIANCE_TEXTURE_WIDTH),
              GetTextureCoordFromUnitRange(x_r, IRRADIANCE_TEXTURE_HEIGHT));
}

IrradianceSpectrum GetIrradiance(
    const AtmosphereParameters atmosphere,
    const IrradianceTexture irradiance_texture,
    const Length r, const Number mu_s) {
  vec2 uv = GetIrradianceTextureUvFromRMuS(atmosphere, r, mu_s);
  return IrradianceSpectrum(texture(irradiance_texture, uv));
}
`, t = `// Based on: https://github.com/ebruneton/precomputed_atmospheric_scattering/blob/master/atmosphere/definitions.glsl

/**
 * Copyright (c) 2017 Eric Bruneton
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 * 3. Neither the name of the copyright holders nor the names of its
 *    contributors may be used to endorse or promote products derived from
 *    this software without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
 * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
 * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
 * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
 * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
 * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
 * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF
 * THE POSSIBILITY OF SUCH DAMAGE.
 */

#define assert(x)

#define Length float
#define Wavelength float
#define Angle float
#define SolidAngle float
#define Power float
#define LuminousPower float

#define Number float
#define InverseLength float
#define Area float
#define Volume float
#define NumberDensity float
#define Irradiance float
#define Radiance float
#define SpectralPower float
#define SpectralIrradiance float
#define SpectralRadiance float
#define SpectralRadianceDensity float
#define ScatteringCoefficient float
#define InverseSolidAngle float
#define LuminousIntensity float
#define Luminance float
#define Illuminance float

// A generic function from Wavelength to some other type.
#define AbstractSpectrum vec3
// A function from Wavelength to Number.
#define DimensionlessSpectrum vec3
// A function from Wavelength to SpectralPower.
#define PowerSpectrum vec3
// A function from Wavelength to SpectralIrradiance.
#define IrradianceSpectrum vec3
// A function from Wavelength to SpectralRadiance.
#define RadianceSpectrum vec3
// A function from Wavelength to SpectralRadianceDensity.
#define RadianceDensitySpectrum vec3
// A function from Wavelength to ScatteringCoefficient.
#define ScatteringSpectrum vec3

// A position in 3D (3 length values).
#define Position vec3
// A unit direction vector in 3D (3 unit-less values).
#define Direction vec3
// A vector of 3 luminance values.
#define Luminance3 vec3
// A vector of 3 illuminance values.
#define Illuminance3 vec3

#define TransmittanceTexture sampler2D
#define AbstractScatteringTexture sampler3D
#define ReducedScatteringTexture sampler3D
#define ScatteringTexture sampler3D
#define ScatteringDensityTexture sampler3D
#define IrradianceTexture sampler2D

const Length m = 1.0;
const Wavelength nm = 1.0;
const Angle rad = 1.0;
const SolidAngle sr = 1.0;
const Power watt = 1.0;
const LuminousPower lm = 1.0;

#if !defined(PI)
const float PI = 3.14159265358979323846;
#endif // !defined(PI)

const Length km = 1000.0 * m;
const Area m2 = m * m;
const Volume m3 = m * m * m;
const Angle pi = PI * rad;
const Angle deg = pi / 180.0;
const Irradiance watt_per_square_meter = watt / m2;
const Radiance watt_per_square_meter_per_sr = watt / (m2 * sr);
const SpectralIrradiance watt_per_square_meter_per_nm = watt / (m2 * nm);
const SpectralRadiance watt_per_square_meter_per_sr_per_nm = watt / (m2 * sr * nm);
const SpectralRadianceDensity watt_per_cubic_meter_per_sr_per_nm = watt / (m3 * sr * nm);
const LuminousIntensity cd = lm / sr;
const LuminousIntensity kcd = 1000.0 * cd;
const Luminance cd_per_square_meter = cd / m2;
const Luminance kcd_per_square_meter = kcd / m2;

struct DensityProfileLayer {
  Length width;
  Number exp_term;
  InverseLength exp_scale;
  InverseLength linear_term;
  Number constant_term;
};

struct DensityProfile {
  DensityProfileLayer layers[2];
};

// See AtmosphereParameter.ts for further details.
struct AtmosphereParameters {
  IrradianceSpectrum solar_irradiance;
  Angle sun_angular_radius;
  Length bottom_radius;
  Length top_radius;
  DensityProfile rayleigh_density;
  ScatteringSpectrum rayleigh_scattering;
  DensityProfile mie_density;
  ScatteringSpectrum mie_scattering;
  ScatteringSpectrum mie_extinction;
  Number mie_phase_function_g;
  DensityProfile absorption_density;
  ScatteringSpectrum absorption_extinction;
  DimensionlessSpectrum ground_albedo;
  Number mu_s_min;
};
`, n = `// Based on: https://github.com/ebruneton/precomputed_atmospheric_scattering/blob/master/atmosphere/functions.glsl

/**
 * Copyright (c) 2017 Eric Bruneton
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 * 3. Neither the name of the copyright holders nor the names of its
 *    contributors may be used to endorse or promote products derived from
 *    this software without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
 * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
 * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
 * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
 * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
 * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
 * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF
 * THE POSSIBILITY OF SUCH DAMAGE.
 *
 * Precomputed Atmospheric Scattering
 * Copyright (c) 2008 INRIA
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 * 3. Neither the name of the copyright holders nor the names of its
 *    contributors may be used to endorse or promote products derived from
 *    this software without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
 * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
 * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
 * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
 * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
 * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
 * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF
 * THE POSSIBILITY OF SUCH DAMAGE.
 */

#ifdef COMBINED_SCATTERING_TEXTURES
vec3 GetExtrapolatedSingleMieScattering(
    const AtmosphereParameters atmosphere, const vec4 scattering) {
  // Algebraically this can never be negative, but rounding errors can produce
  // that effect for sufficiently short view rays.
  // @shotamatsuda: Avoid division by infinitesimal values.
  // See https://github.com/takram-design-engineering/three-geospatial/issues/47
  if (scattering.r < 1e-5) {
    return vec3(0.0);
  }
  return scattering.rgb * scattering.a / scattering.r *
	    (atmosphere.rayleigh_scattering.r / atmosphere.mie_scattering.r) *
	    (atmosphere.mie_scattering / atmosphere.rayleigh_scattering);
}
#endif // COMBINED_SCATTERING_TEXTURES

IrradianceSpectrum GetCombinedScattering(
    const AtmosphereParameters atmosphere,
    const ReducedScatteringTexture scattering_texture,
    const ReducedScatteringTexture single_mie_scattering_texture,
    const Length r, const Number mu, const Number mu_s, const Number nu,
    const bool ray_r_mu_intersects_ground,
    out IrradianceSpectrum single_mie_scattering) {
  vec4 uvwz = GetScatteringTextureUvwzFromRMuMuSNu(
      atmosphere, r, mu, mu_s, nu, ray_r_mu_intersects_ground);
  Number tex_coord_x = uvwz.x * Number(SCATTERING_TEXTURE_NU_SIZE - 1);
  Number tex_x = floor(tex_coord_x);
  Number lerp = tex_coord_x - tex_x;
  vec3 uvw0 = vec3((tex_x + uvwz.y) / Number(SCATTERING_TEXTURE_NU_SIZE),
      uvwz.z, uvwz.w);
  vec3 uvw1 = vec3((tex_x + 1.0 + uvwz.y) / Number(SCATTERING_TEXTURE_NU_SIZE),
      uvwz.z, uvwz.w);
#ifdef COMBINED_SCATTERING_TEXTURES
  vec4 combined_scattering =
      texture(scattering_texture, uvw0) * (1.0 - lerp) +
      texture(scattering_texture, uvw1) * lerp;
  IrradianceSpectrum scattering = IrradianceSpectrum(combined_scattering);
  single_mie_scattering =
      GetExtrapolatedSingleMieScattering(atmosphere, combined_scattering);
#else // COMBINED_SCATTERING_TEXTURES
  IrradianceSpectrum scattering = IrradianceSpectrum(
      texture(scattering_texture, uvw0) * (1.0 - lerp) +
      texture(scattering_texture, uvw1) * lerp);
  single_mie_scattering = IrradianceSpectrum(
      texture(single_mie_scattering_texture, uvw0) * (1.0 - lerp) +
      texture(single_mie_scattering_texture, uvw1) * lerp);
#endif // COMBINED_SCATTERING_TEXTURES
  return scattering;
}

// @shotamatsuda: Added for reading higher-order scattering texture.
#ifdef HAS_HIGHER_ORDER_SCATTERING_TEXTURE
IrradianceSpectrum GetScattering(
    const AtmosphereParameters atmosphere,
    const ReducedScatteringTexture scattering_texture,
    const Length r, const Number mu, const Number mu_s, const Number nu,
    const bool ray_r_mu_intersects_ground) {
  vec4 uvwz = GetScatteringTextureUvwzFromRMuMuSNu(
      atmosphere, r, mu, mu_s, nu, ray_r_mu_intersects_ground);
  Number tex_coord_x = uvwz.x * Number(SCATTERING_TEXTURE_NU_SIZE - 1);
  Number tex_x = floor(tex_coord_x);
  Number lerp = tex_coord_x - tex_x;
  vec3 uvw0 = vec3((tex_x + uvwz.y) / Number(SCATTERING_TEXTURE_NU_SIZE),
      uvwz.z, uvwz.w);
  vec3 uvw1 = vec3((tex_x + 1.0 + uvwz.y) / Number(SCATTERING_TEXTURE_NU_SIZE),
      uvwz.z, uvwz.w);
  IrradianceSpectrum scattering = IrradianceSpectrum(
      texture(scattering_texture, uvw0) * (1.0 - lerp) +
      texture(scattering_texture, uvw1) * lerp);
  return scattering;
}
#endif // HAS_HIGHER_ORDER_SCATTERING_TEXTURE

RadianceSpectrum GetSkyRadiance(
    const AtmosphereParameters atmosphere,
    const TransmittanceTexture transmittance_texture,
    const ReducedScatteringTexture scattering_texture,
    const ReducedScatteringTexture single_mie_scattering_texture,
    Position camera, const Direction view_ray, const Length shadow_length,
    const Direction sun_direction,
    out DimensionlessSpectrum transmittance) {
  // Compute the distance to the top atmosphere boundary along the view ray,
  // assuming the viewer is in space (or NaN if the view ray does not intersect
  // the atmosphere).
  Length r = length(camera);
  Length rmu = dot(camera, view_ray);
  // @shotamatsuda: Use SafeSqrt instead.
  // See: https://github.com/takram-design-engineering/three-geospatial/pull/26
  Length distance_to_top_atmosphere_boundary = -rmu -
      SafeSqrt(rmu * rmu - r * r +
          atmosphere.top_radius * atmosphere.top_radius);
  // If the viewer is in space and the view ray intersects the atmosphere, move
  // the viewer to the top atmosphere boundary (along the view ray):
  if (distance_to_top_atmosphere_boundary > 0.0 * m) {
    camera = camera + view_ray * distance_to_top_atmosphere_boundary;
    r = atmosphere.top_radius;
    rmu += distance_to_top_atmosphere_boundary;
  } else if (r > atmosphere.top_radius) {
    // If the view ray does not intersect the atmosphere, simply return 0.
    transmittance = DimensionlessSpectrum(1.0);
    return RadianceSpectrum(0.0 * watt_per_square_meter_per_sr_per_nm);
  }
  // Compute the r, mu, mu_s and nu parameters needed for the texture lookups.
  Number mu = rmu / r;
  Number mu_s = dot(camera, sun_direction) / r;
  Number nu = dot(view_ray, sun_direction);

  // @shotamatsuda: For rendering points below the bottom atmosphere.
  #ifdef GROUND
  bool ray_r_mu_intersects_ground = RayIntersectsGround(atmosphere, r, mu);
  #else // GROUND
  bool ray_r_mu_intersects_ground = false;
  #endif // GROUND

  transmittance = ray_r_mu_intersects_ground ? DimensionlessSpectrum(0.0) :
      GetTransmittanceToTopAtmosphereBoundary(
          atmosphere, transmittance_texture, r, mu);
  IrradianceSpectrum single_mie_scattering;
  IrradianceSpectrum scattering;
  if (shadow_length == 0.0 * m) {
    scattering = GetCombinedScattering(
        atmosphere, scattering_texture, single_mie_scattering_texture,
        r, mu, mu_s, nu, ray_r_mu_intersects_ground,
        single_mie_scattering);
  } else {
    // Case of light shafts (shadow_length is the total length noted l in our
    // paper): we omit the scattering between the camera and the point at
    // distance l, by implementing Eq. (18) of the paper (shadow_transmittance
    // is the T(x,x_s) term, scattering is the S|x_s=x+lv term).
    Length d = shadow_length;
    Length r_p =
        ClampRadius(atmosphere, sqrt(d * d + 2.0 * r * mu * d + r * r));
    Number mu_p = (r * mu + d) / r_p;
    Number mu_s_p = (r * mu_s + d * nu) / r_p;

    scattering = GetCombinedScattering(
        atmosphere, scattering_texture, single_mie_scattering_texture,
        r_p, mu_p, mu_s_p, nu, ray_r_mu_intersects_ground,
        single_mie_scattering);
    DimensionlessSpectrum shadow_transmittance =
        GetTransmittance(atmosphere, transmittance_texture,
            r, mu, shadow_length, ray_r_mu_intersects_ground);
    // @shotamatsuda: Occlude only single Rayleigh scattering by the shadow.
#ifdef HAS_HIGHER_ORDER_SCATTERING_TEXTURE
    IrradianceSpectrum higher_order_scattering = GetScattering(
        atmosphere, higher_order_scattering_texture,
        r_p, mu_p, mu_s_p, nu, ray_r_mu_intersects_ground);
    IrradianceSpectrum single_scattering = scattering - higher_order_scattering;
    scattering = single_scattering * shadow_transmittance + higher_order_scattering;
#else // HAS_HIGHER_ORDER_SCATTERING_TEXTURE
    scattering = scattering * shadow_transmittance;
#endif // HAS_HIGHER_ORDER_SCATTERING_TEXTURE
    single_mie_scattering = single_mie_scattering * shadow_transmittance;
  }
  return scattering * RayleighPhaseFunction(nu) + single_mie_scattering *
      MiePhaseFunction(atmosphere.mie_phase_function_g, nu);
}

// @shotamatsuda: Returns the point on the ray closest to the origin.
vec3 ClosestPointOnRay(const Position camera, const Position point) {
  Position ray = point - camera;
  Number t = clamp(-dot(camera, ray) / dot(ray, ray), 0.0, 1.0);
  return camera + t * ray;
}

vec2 RaySphereIntersections(
    const Position camera, const Direction direction, const Length radius) {
  float b = 2.0 * dot(direction, camera);
  float c = dot(camera, camera) - radius * radius;
  float discriminant = b * b - 4.0 * c;
  float Q = sqrt(discriminant);
  return vec2(-b - Q, -b + Q) * 0.5;
}

// @shotamatsuda: Clip the view ray at the bottom atmosphere boundary.
bool ClipAtBottomAtmosphere(
    const AtmosphereParameters atmosphere,
    const Direction view_ray, inout Position camera, inout Position point) {
  const Length eps = 0.0;
  Length bottom_radius = atmosphere.bottom_radius + eps;
  Length r_camera = length(camera);
  Length r_point = length(point);
  bool camera_below = r_camera < bottom_radius;
  bool point_below = r_point < bottom_radius;

  vec2 t = RaySphereIntersections(camera, view_ray, bottom_radius);
  Position intersection = camera + view_ray * (camera_below ? t.y : t.x);
  camera = camera_below ? intersection : camera;
  point = point_below ? intersection : point;

  return camera_below && point_below;
}

RadianceSpectrum GetSkyRadianceToPoint(
    const AtmosphereParameters atmosphere,
    const TransmittanceTexture transmittance_texture,
    const ReducedScatteringTexture scattering_texture,
    const ReducedScatteringTexture single_mie_scattering_texture,
    Position camera, Position point, const Length shadow_length,
    const Direction sun_direction, out DimensionlessSpectrum transmittance) {
  // @shotamatsuda: Avoid artifacts when the ray does not intersect the top
  // atmosphere boundary.
  if (length(ClosestPointOnRay(camera, point)) > atmosphere.top_radius) {
    transmittance = vec3(1.0);
    return vec3(0.0);
  }

  Direction view_ray = normalize(point - camera);
  if (ClipAtBottomAtmosphere(atmosphere, view_ray, camera, point)) {
    transmittance = vec3(1.0);
    return vec3(0.0);
  }

  // Compute the distance to the top atmosphere boundary along the view ray,
  // assuming the viewer is in space (or NaN if the view ray does not intersect
  // the atmosphere).
  Length r = length(camera);
  Length rmu = dot(camera, view_ray);
  // @shotamatsuda: Use SafeSqrt instead.
  // See: https://github.com/takram-design-engineering/three-geospatial/pull/26
  Length distance_to_top_atmosphere_boundary = -rmu -
      SafeSqrt(rmu * rmu - r * r +
          atmosphere.top_radius * atmosphere.top_radius);
  // If the viewer is in space and the view ray intersects the atmosphere, move
  // the viewer to the top atmosphere boundary (along the view ray):
  if (distance_to_top_atmosphere_boundary > 0.0 * m) {
    camera = camera + view_ray * distance_to_top_atmosphere_boundary;
    r = atmosphere.top_radius;
    rmu += distance_to_top_atmosphere_boundary;
  }

  // Compute the r, mu, mu_s and nu parameters for the first texture lookup.
  Number mu = rmu / r;
  Number mu_s = dot(camera, sun_direction) / r;
  Number nu = dot(view_ray, sun_direction);
  Length d = length(point - camera);
  bool ray_r_mu_intersects_ground = RayIntersectsGround(atmosphere, r, mu);

  // @shotamatsuda: Hack to avoid rendering artifacts near the horizon, due to
  // finite atmosphere texture resolution and finite floating point precision.
  // See: https://github.com/ebruneton/precomputed_atmospheric_scattering/pull/32
  if (!ray_r_mu_intersects_ground) {
    Number mu_horizon = -SafeSqrt(1.0 -
        (atmosphere.bottom_radius * atmosphere.bottom_radius) / (r * r));
    const Number eps = 0.004;
    mu = max(mu, mu_horizon + eps);
  }

  transmittance = GetTransmittance(atmosphere, transmittance_texture,
      r, mu, d, ray_r_mu_intersects_ground);

  IrradianceSpectrum single_mie_scattering;
  IrradianceSpectrum scattering = GetCombinedScattering(
      atmosphere, scattering_texture, single_mie_scattering_texture,
      r, mu, mu_s, nu, ray_r_mu_intersects_ground,
      single_mie_scattering);

  // Compute the r, mu, mu_s and nu parameters for the second texture lookup.
  // If shadow_length is not 0 (case of light shafts), we want to ignore the
  // scattering along the last shadow_length meters of the view ray, which we
  // do by subtracting shadow_length from d (this way scattering_p is equal to
  // the S|x_s=x_0-lv term in Eq. (17) of our paper).
  d = max(d - shadow_length, 0.0 * m);
  Length r_p = ClampRadius(atmosphere, sqrt(d * d + 2.0 * r * mu * d + r * r));
  Number mu_p = (r * mu + d) / r_p;
  Number mu_s_p = (r * mu_s + d * nu) / r_p;

  IrradianceSpectrum single_mie_scattering_p;
  IrradianceSpectrum scattering_p = GetCombinedScattering(
      atmosphere, scattering_texture, single_mie_scattering_texture,
      r_p, mu_p, mu_s_p, nu, ray_r_mu_intersects_ground,
      single_mie_scattering_p);

  // Combine the lookup results to get the scattering between camera and point.
  DimensionlessSpectrum shadow_transmittance = transmittance;
  if (shadow_length > 0.0 * m) {
    // This is the T(x,x_s) term in Eq. (17) of our paper, for light shafts.
    shadow_transmittance = GetTransmittance(atmosphere, transmittance_texture,
        r, mu, d, ray_r_mu_intersects_ground);
  }
  // @shotamatsuda: Occlude only single Rayleigh scattering by the shadow.
#ifdef HAS_HIGHER_ORDER_SCATTERING_TEXTURE
  IrradianceSpectrum higher_order_scattering = GetScattering(
      atmosphere, higher_order_scattering_texture,
      r, mu, mu_s, nu, ray_r_mu_intersects_ground);
  IrradianceSpectrum single_scattering = scattering - higher_order_scattering;
  IrradianceSpectrum higher_order_scattering_p = GetScattering(
      atmosphere, higher_order_scattering_texture,
      r_p, mu_p, mu_s_p, nu, ray_r_mu_intersects_ground);
  IrradianceSpectrum single_scattering_p =
      scattering_p - higher_order_scattering_p;
  scattering =
      single_scattering - shadow_transmittance * single_scattering_p +
      higher_order_scattering - transmittance * higher_order_scattering_p;
#else // HAS_HIGHER_ORDER_SCATTERING_TEXTURE
  scattering = scattering - shadow_transmittance * scattering_p;
#endif // HAS_HIGHER_ORDER_SCATTERING_TEXTURE

  single_mie_scattering =
      single_mie_scattering - shadow_transmittance * single_mie_scattering_p;
#ifdef COMBINED_SCATTERING_TEXTURES
  single_mie_scattering = GetExtrapolatedSingleMieScattering(
      atmosphere, vec4(scattering, single_mie_scattering.r));
#endif // COMBINED_SCATTERING_TEXTURES

  // Hack to avoid rendering artifacts when the sun is below the horizon.
  single_mie_scattering = single_mie_scattering *
      smoothstep(Number(0.0), Number(0.01), mu_s);

  return scattering * RayleighPhaseFunction(nu) + single_mie_scattering *
      MiePhaseFunction(atmosphere.mie_phase_function_g, nu);
}

IrradianceSpectrum GetSunAndSkyIrradiance(
    const AtmosphereParameters atmosphere,
    const TransmittanceTexture transmittance_texture,
    const IrradianceTexture irradiance_texture,
    const Position point, const Direction normal, const Direction sun_direction,
    out IrradianceSpectrum sky_irradiance) {
  Length r = length(point);
  Number mu_s = dot(point, sun_direction) / r;

  // Indirect irradiance (approximated if the surface is not horizontal).
  sky_irradiance = GetIrradiance(atmosphere, irradiance_texture, r, mu_s) *
      (1.0 + dot(normal, point) / r) * 0.5;

  // Direct irradiance.
  return atmosphere.solar_irradiance *
      GetTransmittanceToSun(
          atmosphere, transmittance_texture, r, mu_s) *
      max(dot(normal, sun_direction), 0.0);
}

// @shotamatsuda: Added for the clouds.
IrradianceSpectrum GetSunAndSkyScalarIrradiance(
    const AtmosphereParameters atmosphere,
    const TransmittanceTexture transmittance_texture,
    const IrradianceTexture irradiance_texture,
    const Position point, const Direction sun_direction,
    out IrradianceSpectrum sky_irradiance) {
  Length r = length(point);
  Number mu_s = dot(point, sun_direction) / r;

  // Indirect irradiance. Integral over sphere yields 2π.
  sky_irradiance = GetIrradiance(atmosphere, irradiance_texture, r, mu_s) *
      2.0 * PI;

  // Direct irradiance. Omit the cosine term.
  return atmosphere.solar_irradiance *
      GetTransmittanceToSun(atmosphere, transmittance_texture, r, mu_s);
}

Luminance3 GetSolarLuminance() {
  return ATMOSPHERE.solar_irradiance /
      (PI * ATMOSPHERE.sun_angular_radius * ATMOSPHERE.sun_angular_radius) *
      SUN_SPECTRAL_RADIANCE_TO_LUMINANCE;
}

Luminance3 GetSkyLuminance(
    const Position camera, Direction view_ray, const Length shadow_length,
    const Direction sun_direction, out DimensionlessSpectrum transmittance) {
  return GetSkyRadiance(ATMOSPHERE, transmittance_texture,
      scattering_texture, single_mie_scattering_texture,
      camera, view_ray, shadow_length, sun_direction,
      transmittance) * SKY_SPECTRAL_RADIANCE_TO_LUMINANCE;
}

Luminance3 GetSkyLuminanceToPoint(
    const Position camera, const Position point, const Length shadow_length,
    const Direction sun_direction, out DimensionlessSpectrum transmittance) {
  return GetSkyRadianceToPoint(ATMOSPHERE, transmittance_texture,
      scattering_texture, single_mie_scattering_texture,
      camera, point, shadow_length, sun_direction, transmittance) *
      SKY_SPECTRAL_RADIANCE_TO_LUMINANCE;
}

Illuminance3 GetSunAndSkyIlluminance(
    const Position p, const Direction normal, const Direction sun_direction,
    out IrradianceSpectrum sky_irradiance) {
  IrradianceSpectrum sun_irradiance = GetSunAndSkyIrradiance(
      ATMOSPHERE, transmittance_texture, irradiance_texture, p, normal,
      sun_direction, sky_irradiance);
  sky_irradiance *= SKY_SPECTRAL_RADIANCE_TO_LUMINANCE;
  return sun_irradiance * SUN_SPECTRAL_RADIANCE_TO_LUMINANCE;
}

// @shotamatsuda: Added for the clouds.
Illuminance3 GetSunAndSkyScalarIlluminance(
    const Position p, const Direction sun_direction,
    out IrradianceSpectrum sky_irradiance) {
  IrradianceSpectrum sun_irradiance = GetSunAndSkyScalarIrradiance(
      ATMOSPHERE, transmittance_texture, irradiance_texture, p,
      sun_direction, sky_irradiance);
  sky_irradiance *= SKY_SPECTRAL_RADIANCE_TO_LUMINANCE;
  return sun_irradiance * SUN_SPECTRAL_RADIANCE_TO_LUMINANCE;
}

#define GetSolarRadiance GetSolarLuminance
#define GetSkyRadiance GetSkyLuminance
#define GetSkyRadianceToPoint GetSkyLuminanceToPoint
#define GetSunAndSkyIrradiance GetSunAndSkyIlluminance
#define GetSunAndSkyScalarIrradiance GetSunAndSkyScalarIlluminance
`, r = `// Based on: https://github.com/ebruneton/precomputed_atmospheric_scattering/blob/master/atmosphere/functions.glsl

/**
 * Copyright (c) 2017 Eric Bruneton
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 * 3. Neither the name of the copyright holders nor the names of its
 *    contributors may be used to endorse or promote products derived from
 *    this software without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
 * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
 * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
 * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
 * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
 * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
 * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF
 * THE POSSIBILITY OF SUCH DAMAGE.
 *
 * Precomputed Atmospheric Scattering
 * Copyright (c) 2008 INRIA
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 * 3. Neither the name of the copyright holders nor the names of its
 *    contributors may be used to endorse or promote products derived from
 *    this software without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
 * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
 * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
 * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
 * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
 * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
 * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF
 * THE POSSIBILITY OF SUCH DAMAGE.
 */

Number GetLayerDensity(const DensityProfileLayer layer, const Length altitude) {
  Number density = layer.exp_term * exp(layer.exp_scale * altitude) +
      layer.linear_term * altitude + layer.constant_term;
  return clamp(density, Number(0.0), Number(1.0));
}

Number GetProfileDensity(const DensityProfile profile, const Length altitude) {
  DensityProfileLayer layers[2] = profile.layers;
  return altitude < layers[0].width
    ? GetLayerDensity(layers[0], altitude)
    : GetLayerDensity(layers[1], altitude);
}

Length ComputeOpticalLengthToTopAtmosphereBoundary(
    const AtmosphereParameters atmosphere, const DensityProfile profile,
    const Length r, const Number mu) {
  assert(r >= atmosphere.bottom_radius && r <= atmosphere.top_radius);
  assert(mu >= -1.0 && mu <= 1.0);
  // Number of intervals for the numerical integration.
  const int SAMPLE_COUNT = 500;
  // The integration step, i.e. the length of each integration interval.
  Length dx =
      DistanceToTopAtmosphereBoundary(atmosphere, r, mu) / Number(SAMPLE_COUNT);
  // Integration loop.
  Length result = 0.0 * m;
  for (int i = 0; i <= SAMPLE_COUNT; ++i) {
    Length d_i = Number(i) * dx;
    // Distance between the current sample point and the planet center.
    Length r_i = sqrt(d_i * d_i + 2.0 * r * mu * d_i + r * r);
    // Number density at the current sample point (divided by the number density
    // at the bottom of the atmosphere, yielding a dimensionless number).
    Number y_i = GetProfileDensity(profile, r_i - atmosphere.bottom_radius);
    // Sample weight (from the trapezoidal rule).
    Number weight_i = i == 0 || i == SAMPLE_COUNT ? 0.5 : 1.0;
    result += y_i * weight_i * dx;
  }
  return result;
}

DimensionlessSpectrum ComputeTransmittanceToTopAtmosphereBoundary(
    const AtmosphereParameters atmosphere, const Length r, const Number mu) {
  assert(r >= atmosphere.bottom_radius && r <= atmosphere.top_radius);
  assert(mu >= -1.0 && mu <= 1.0);
  vec3 optical_depth = (
      atmosphere.rayleigh_scattering *
          ComputeOpticalLengthToTopAtmosphereBoundary(
              atmosphere, atmosphere.rayleigh_density, r, mu) +
      atmosphere.mie_extinction *
          ComputeOpticalLengthToTopAtmosphereBoundary(
              atmosphere, atmosphere.mie_density, r, mu) +
      atmosphere.absorption_extinction *
          ComputeOpticalLengthToTopAtmosphereBoundary(
              atmosphere, atmosphere.absorption_density, r, mu));
  // @shotamatsuda: Added for the precomputation stage in half-float precision.
  #ifdef TRANSMITTANCE_PRECISION_LOG
  return optical_depth;
  #else // TRANSMITTANCE_PRECISION_LOG
  return exp(-optical_depth);
  #endif // TRANSMITTANCE_PRECISION_LOG
}

Number GetUnitRangeFromTextureCoord(const Number u, const int texture_size) {
  return (u - 0.5 / Number(texture_size)) / (1.0 - 1.0 / Number(texture_size));
}

void GetRMuFromTransmittanceTextureUv(const AtmosphereParameters atmosphere,
    const vec2 uv, out Length r, out Number mu) {
  assert(uv.x >= 0.0 && uv.x <= 1.0);
  assert(uv.y >= 0.0 && uv.y <= 1.0);
  Number x_mu = GetUnitRangeFromTextureCoord(uv.x, TRANSMITTANCE_TEXTURE_WIDTH);
  Number x_r = GetUnitRangeFromTextureCoord(uv.y, TRANSMITTANCE_TEXTURE_HEIGHT);
  // Distance to top atmosphere boundary for a horizontal ray at ground level.
  Length H = sqrt(atmosphere.top_radius * atmosphere.top_radius -
      atmosphere.bottom_radius * atmosphere.bottom_radius);
  // Distance to the horizon, from which we can compute r:
  Length rho = H * x_r;
  r = sqrt(rho * rho + atmosphere.bottom_radius * atmosphere.bottom_radius);
  // Distance to the top atmosphere boundary for the ray (r,mu), and its minimum
  // and maximum values over all mu - obtained for (r,1) and (r,mu_horizon) -
  // from which we can recover mu:
  Length d_min = atmosphere.top_radius - r;
  Length d_max = rho + H;
  Length d = d_min + x_mu * (d_max - d_min);
  mu = d == 0.0 * m ? Number(1.0) : (H * H - rho * rho - d * d) / (2.0 * r * d);
  mu = ClampCosine(mu);
}

DimensionlessSpectrum ComputeTransmittanceToTopAtmosphereBoundaryTexture(
    const AtmosphereParameters atmosphere, const vec2 frag_coord) {
  const vec2 TRANSMITTANCE_TEXTURE_SIZE =
      vec2(TRANSMITTANCE_TEXTURE_WIDTH, TRANSMITTANCE_TEXTURE_HEIGHT);
  Length r;
  Number mu;
  GetRMuFromTransmittanceTextureUv(
      atmosphere, frag_coord / TRANSMITTANCE_TEXTURE_SIZE, r, mu);
  return ComputeTransmittanceToTopAtmosphereBoundary(atmosphere, r, mu);
}

void ComputeSingleScatteringIntegrand(
    const AtmosphereParameters atmosphere,
    const TransmittanceTexture transmittance_texture,
    const Length r, const Number mu, const Number mu_s, const Number nu,
    const Length d, const bool ray_r_mu_intersects_ground,
    out DimensionlessSpectrum rayleigh, out DimensionlessSpectrum mie) {
  Length r_d = ClampRadius(atmosphere, sqrt(d * d + 2.0 * r * mu * d + r * r));
  Number mu_s_d = ClampCosine((r * mu_s + d * nu) / r_d);
  DimensionlessSpectrum transmittance =
      GetTransmittance(
          atmosphere, transmittance_texture, r, mu, d,
          ray_r_mu_intersects_ground) *
      GetTransmittanceToSun(
          atmosphere, transmittance_texture, r_d, mu_s_d);
  rayleigh = transmittance * GetProfileDensity(
      atmosphere.rayleigh_density, r_d - atmosphere.bottom_radius);
  mie = transmittance * GetProfileDensity(
      atmosphere.mie_density, r_d - atmosphere.bottom_radius);
}

Length DistanceToNearestAtmosphereBoundary(const AtmosphereParameters atmosphere,
    Length r, Number mu, bool ray_r_mu_intersects_ground) {
  if (ray_r_mu_intersects_ground) {
    return DistanceToBottomAtmosphereBoundary(atmosphere, r, mu);
  } else {
    return DistanceToTopAtmosphereBoundary(atmosphere, r, mu);
  }
}

void ComputeSingleScattering(
    const AtmosphereParameters atmosphere,
    const TransmittanceTexture transmittance_texture,
    const Length r, const Number mu, const Number mu_s, const Number nu,
    const bool ray_r_mu_intersects_ground,
    out IrradianceSpectrum rayleigh, out IrradianceSpectrum mie) {
  assert(r >= atmosphere.bottom_radius && r <= atmosphere.top_radius);
  assert(mu >= -1.0 && mu <= 1.0);
  assert(mu_s >= -1.0 && mu_s <= 1.0);
  assert(nu >= -1.0 && nu <= 1.0);

  // Number of intervals for the numerical integration.
  const int SAMPLE_COUNT = 50;
  // The integration step, i.e. the length of each integration interval.
  Length dx =
      DistanceToNearestAtmosphereBoundary(atmosphere, r, mu,
          ray_r_mu_intersects_ground) / Number(SAMPLE_COUNT);
  // Integration loop.
  DimensionlessSpectrum rayleigh_sum = DimensionlessSpectrum(0.0);
  DimensionlessSpectrum mie_sum = DimensionlessSpectrum(0.0);
  for (int i = 0; i <= SAMPLE_COUNT; ++i) {
    Length d_i = Number(i) * dx;
    // The Rayleigh and Mie single scattering at the current sample point.
    DimensionlessSpectrum rayleigh_i;
    DimensionlessSpectrum mie_i;
    ComputeSingleScatteringIntegrand(atmosphere, transmittance_texture,
        r, mu, mu_s, nu, d_i, ray_r_mu_intersects_ground, rayleigh_i, mie_i);
    // Sample weight (from the trapezoidal rule).
    Number weight_i = (i == 0 || i == SAMPLE_COUNT) ? 0.5 : 1.0;
    rayleigh_sum += rayleigh_i * weight_i;
    mie_sum += mie_i * weight_i;
  }
  rayleigh = rayleigh_sum * dx * atmospher