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paysages3d/src/rendering/atmosphere/atm_bruneton.cpp

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#include "private.h"
/*
* Atmospheric scattering, based on E. Bruneton and F.Neyret work.
* http://evasion.inrialpes.fr/~Eric.Bruneton/
*/
#include <cassert>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include "System.h"
#include "PackStream.h"
#include "tools.h"
#include "tools/cache.h"
#include "tools/texture.h"
#include "tools/parallel.h"
#include "renderer.h"
#include "water/public.h"
/*********************** Constants ***********************/
#define GROUND_OFFSET 0.5
static const double Rg = 6360.0;
static const double Rt = 6420.0;
static const double RL = 6421.0;
static const double exposure = 0.4;
static const double ISun = 100.0;
static const double AVERAGE_GROUND_REFLECTANCE = 0.1;
#if 1
#define RES_MU 128
#define RES_MU_S 32
#define RES_R 32
#define RES_NU 8
#define SKY_W 64
#define SKY_H 16
#define TRANSMITTANCE_W 256
#define TRANSMITTANCE_H 64
#define TRANSMITTANCE_INTEGRAL_SAMPLES 500
#define INSCATTER_INTEGRAL_SAMPLES 50
#define IRRADIANCE_INTEGRAL_SAMPLES 32
#define INSCATTER_SPHERICAL_INTEGRAL_SAMPLES 16
#else
#define RES_MU 64
#define RES_MU_S 16
#define RES_R 16
#define RES_NU 8
#define SKY_W 64
#define SKY_H 16
#define TRANSMITTANCE_W 256
#define TRANSMITTANCE_H 64
#define TRANSMITTANCE_INTEGRAL_SAMPLES 100
#define INSCATTER_INTEGRAL_SAMPLES 10
#define IRRADIANCE_INTEGRAL_SAMPLES 16
#define INSCATTER_SPHERICAL_INTEGRAL_SAMPLES 8
#endif
Texture2D* _transmittanceTexture = NULL;
Texture2D* _irradianceTexture = NULL;
Texture4D* _inscatterTexture = NULL;
/* Rayleigh */
static const double HR = 8.0;
static const Color betaR = {5.8e-3, 1.35e-2, 3.31e-2, 1.0};
/* Mie */
/* DEFAULT */
static const double HM = 1.2;
static const Vector3 betaMSca = {4e-3, 4e-3, 4e-3};
static const Vector3 betaMEx = {4e-3 / 0.9, 4e-3 / 0.9, 4e-3 / 0.9};
static const double mieG = 0.8;
/* CLEAR SKY */
/*static const double HM = 1.2;
static const Vector3 betaMSca = {20e-3, 20e-3, 20e-3};
static const Vector3 betaMEx = {20e-3 / 0.9, 20e-3 / 0.9, 20e-3 / 0.9};
static const double mieG = 0.76;*/
/* PARTLY CLOUDY */
/*static const double HM = 3.0;
static const Vector3 betaMSca = {3e-3, 3e-3, 3e-3};
static const Vector3 betaMEx = {3e-3 / 0.9, 3e-3 / 0.9, 3e-3 / 0.9};
static const double mieG = 0.65;*/
/*********************** Shader helpers ***********************/
#define step(_a_,_b_) ((_b_) < (_a_) ? 0.0 : 1.0)
#define sign(_a_) ((_a_) < 0.0 ? -1.0 : ((_a_) > 0.0 ? 1.0 : 0.0))
#define mix(_x_,_y_,_a_) ((_x_) * (1.0 - (_a_)) + (_y_) * (_a_))
static inline double min(double a, double b)
{
return a < b ? a : b;
}
static inline double max(double a, double b)
{
return a > b ? a : b;
}
static inline Color vec4mix(Color v1, Color v2, double a)
{
v1.r = mix(v1.r, v2.r, a);
v1.g = mix(v1.g, v2.g, a);
v1.b = mix(v1.b, v2.b, a);
v1.a = mix(v1.a, v2.a, a);
return v1;
}
static inline double clamp(double x, double minVal, double maxVal)
{
if (x < minVal)
{
x = minVal;
}
return (x > maxVal) ? maxVal : x;
}
static inline double smoothstep(double edge0, double edge1, double x)
{
double t = clamp((x - edge0) / (edge1 - edge0), 0.0, 1.0);
return t * t * (3.0 - 2.0 * t);
}
static inline void _fixVec4Min(Color* vec, double minVal)
{
if (vec->r < minVal) { vec->r = minVal; }
if (vec->g < minVal) { vec->g = minVal; }
if (vec->b < minVal) { vec->b = minVal; }
if (vec->a < minVal) { vec->a = minVal; }
}
static inline Color vec4max(Color vec, double minVal)
{
if (vec.r < minVal) { vec.r = minVal; }
if (vec.g < minVal) { vec.g = minVal; }
if (vec.b < minVal) { vec.b = minVal; }
if (vec.a < minVal) { vec.a = minVal; }
return vec;
}
static inline Vector3 vec3(double x, double y, double z)
{
Vector3 result;
result.x = x;
result.y = y;
result.z = z;
return result;
}
static inline Color vec4(double r, double g, double b, double a)
{
Color result;
result.r = r;
result.g = g;
result.b = b;
result.a = a;
return result;
}
/*********************** Texture manipulation ***********************/
static Color _texture4D(Texture4D* tex, double r, double mu, double muS, double nu)
{
if (r < Rg + 0.00000001) r = Rg + 0.00000001;
double H = sqrt(Rt * Rt - Rg * Rg);
double rho = sqrt(r * r - Rg * Rg);
double rmu = r * mu;
double delta = rmu * rmu - r * r + Rg * Rg;
Color cst = (rmu < 0.0 && delta > 0.0) ? vec4(1.0, 0.0, 0.0, 0.5 - 0.5 / (double)(RES_MU)) : vec4(-1.0, H * H, H, 0.5 + 0.5 / (double)(RES_MU));
double uR = 0.5 / (double)(RES_R) + rho / H * (1.0 - 1.0 / (double)(RES_R));
double uMu = cst.a + (rmu * cst.r + sqrt(delta + cst.g)) / (rho + cst.b) * (0.5 - 1.0 / (double)(RES_MU));
double uMuS = 0.5 / (double)(RES_MU_S) + (atan(max(muS, -0.1975) * tan(1.26 * 1.1)) / 1.1 + (1.0 - 0.26)) * 0.5 * (1.0 - 1.0 / (double)(RES_MU_S));
return texture4DGetLinear(tex, uMu, uMuS, nu, uR);
}
/*********************** Physics functions ***********************/
/* Rayleigh phase function */
static double _phaseFunctionR(double mu)
{
return (3.0 / (16.0 * M_PI)) * (1.0 + mu * mu);
}
/* Mie phase function */
static double _phaseFunctionM(double mu)
{
return 1.5 * 1.0 / (4.0 * M_PI) * (1.0 - mieG * mieG) * pow(1.0 + (mieG * mieG) - 2.0 * mieG * mu, -3.0 / 2.0) * (1.0 + mu * mu) / (2.0 + mieG * mieG);
}
/* approximated single Mie scattering (cf. approximate Cm in paragraph "Angular precision") */
static Color _getMie(Color rayMie)
{
Color result;
result.r = rayMie.r * rayMie.a / max(rayMie.r, 1e-4) * (betaR.r / betaR.r);
result.g = rayMie.g * rayMie.a / max(rayMie.r, 1e-4) * (betaR.r / betaR.g);
result.b = rayMie.b * rayMie.a / max(rayMie.r, 1e-4) * (betaR.r / betaR.b);
result.a = 1.0;
return result;
}
/* optical depth for ray (r,mu) of length d, using analytic formula
(mu=cos(view zenith angle)), intersections with ground ignored
H=height scale of exponential density function */
static double _opticalDepth(double H, double r, double mu, double d)
{
double a = sqrt((0.5 / H) * r);
double ax = a * (mu);
double ay = a * (mu + d / r);
double axs = sign(ax);
double ays = sign(ay);
double axq = ax * ax;
double ayq = ay * ay;
double x = ays > axs ? exp(axq) : 0.0;
double yx = axs / (2.3193 * fabs(ax) + sqrt(1.52 * axq + 4.0));
double yy = ays / (2.3193 * fabs(ay) + sqrt(1.52 * ayq + 4.0)) * exp(-d / H * (d / (2.0 * r) + mu));
return sqrt((6.2831 * H) * r) * exp((Rg - r) / H) * (x + yx - yy);
}
static inline void _getTransmittanceUV(double r, double mu, double* u, double* v)
{
if (r < Rg + 0.00000001) r = Rg + 0.00000001;
double dr = (r - Rg) / (Rt - Rg);
*v = sqrt(dr);
*u = atan((mu + 0.15) / (1.0 + 0.15) * tan(1.5)) / 1.5;
}
/* transmittance(=transparency) of atmosphere for infinite ray (r,mu)
(mu=cos(view zenith angle)), intersections with ground ignored */
static Color _transmittance(double r, double mu)
{
double u, v;
_getTransmittanceUV(r, mu, &u, &v);
return texture2DGetLinear(_transmittanceTexture, u, v);
}
/* transmittance(=transparency) of atmosphere between x and x0
* assume segment x,x0 not intersecting ground
* d = distance between x and x0, mu=cos(zenith angle of [x,x0) ray at x) */
static Color _transmittance3(double r, double mu, double d)
{
Color result, t1, t2;
double r1 = sqrt(r * r + d * d + 2.0 * r * mu * d);
double mu1 = (r * mu + d) / r1;
if (mu > 0.0)
{
t1 = _transmittance(r, mu);
t2 = _transmittance(r1, mu1);
}
else
{
t1 = _transmittance(r1, -mu1);
t2 = _transmittance(r, -mu);
}
result.r = min(t1.r / t2.r, 1.0);
result.g = min(t1.g / t2.g, 1.0);
result.b = min(t1.b / t2.b, 1.0);
result.a = 1.0;
return result;
}
static void _getIrradianceRMuS(double x, double y, double* r, double* muS)
{
*r = Rg + y * (Rt - Rg);
*muS = -0.2 + x * (1.0 + 0.2);
}
/* nearest intersection of ray r,mu with ground or top atmosphere boundary
* mu=cos(ray zenith angle at ray origin) */
static double _limit(double r, double mu)
{
double dout = -r * mu + sqrt(r * r * (mu * mu - 1.0) + RL * RL);
double delta2 = r * r * (mu * mu - 1.0) + Rg * Rg;
if (delta2 >= 0.0)
{
double din = -r * mu - sqrt(delta2);
if (din >= 0.0) {
dout = min(dout, din);
}
}
return dout;
}
/* transmittance(=transparency) of atmosphere for ray (r,mu) of length d
(mu=cos(view zenith angle)), intersections with ground ignored
uses analytic formula instead of transmittance texture */
static Vector3 _analyticTransmittance(double r, double mu, double d)
{
Vector3 result;
result.x = exp(-betaR.r * _opticalDepth(HR, r, mu, d) - betaMEx.x * _opticalDepth(HM, r, mu, d));
result.y = exp(-betaR.g * _opticalDepth(HR, r, mu, d) - betaMEx.y * _opticalDepth(HM, r, mu, d));
result.z = exp(-betaR.b * _opticalDepth(HR, r, mu, d) - betaMEx.z * _opticalDepth(HM, r, mu, d));
return result;
}
/* transmittance(=transparency) of atmosphere for infinite ray (r,mu)
(mu=cos(view zenith angle)), or zero if ray intersects ground */
static Color _transmittanceWithShadow(double r, double mu)
{
return mu < -sqrt(1.0 - (Rg / r) * (Rg / r)) ? COLOR_BLACK : _transmittance(r, mu);
}
static void _texCoordToMuMuSNu(double x, double y, double z, double r, Color dhdH, double* mu, double* muS, double* nu)
{
double d;
x /= (double)RES_MU;
y /= (double)RES_MU_S;
z /= (double)RES_NU;
if (x < 0.5)
{
d = 1.0 - x / 0.5;
d = min(max(dhdH.b, d * dhdH.a), dhdH.a * 0.999);
*mu = (Rg * Rg - r * r - d * d) / (2.0 * r * d);
*mu = min(*mu, -sqrt(1.0 - (Rg / r) * (Rg / r)) - 0.001);
}
else
{
d = (x - 0.5) / 0.5;
d = min(max(dhdH.r, d * dhdH.g), dhdH.g * 0.999);
*mu = (Rt * Rt - r * r - d * d) / (2.0 * r * d);
}
*muS = tan((2.0 * y - 1.0 + 0.26) * 1.1) / tan(1.26 * 1.1);
*nu = -1.0 + z / 2.0;
}
static void _getIrradianceUV(double r, double muS, double* uMuS, double* uR)
{
*uR = (r - Rg) / (Rt - Rg);
*uMuS = (muS + 0.2) / (1.0 + 0.2);
}
static Color _irradiance(Texture2D* sampler, double r, double muS)
{
double u, v;
_getIrradianceUV(r, muS, &u, &v);
return texture2DGetLinear(sampler, u, v);
}
/*********************** transmittance.glsl ***********************/
static void _getTransmittanceRMu(double x, double y, double* r, double* muS)
{
*r = Rg + (y * y) * (Rt - Rg);
*muS = -0.15 + tan(1.5 * x) / tan(1.5) * (1.0 + 0.15);
}
static double _opticalDepthTransmittance(double H, double r, double mu)
{
double result = 0.0;
double dx = _limit(r, mu) / (double)TRANSMITTANCE_INTEGRAL_SAMPLES;
double yi = exp(-(r - Rg) / H);
int i;
for (i = 1; i <= TRANSMITTANCE_INTEGRAL_SAMPLES; ++i) {
double xj = (double)i * dx;
double yj = exp(-(sqrt(r * r + xj * xj + 2.0 * xj * r * mu) - Rg) / H);
result += (yi + yj) / 2.0 * dx;
yi = yj;
}
return mu < -sqrt(1.0 - (Rg / r) * (Rg / r)) ? 1e9 : result;
}
static void _precomputeTransmittanceTexture()
{
int x, y;
for (x = 0; x < TRANSMITTANCE_W; x++)
{
for (y = 0; y < TRANSMITTANCE_H; y++)
{
double r, muS;
_getTransmittanceRMu((double)(x + 0.5) / TRANSMITTANCE_W, (double)(y + 0.5) / TRANSMITTANCE_H, &r, &muS);
double depth1 = _opticalDepthTransmittance(HR, r, muS);
double depth2 = _opticalDepthTransmittance(HM, r, muS);
Color trans;
trans.r = exp(-(betaR.r * depth1 + betaMEx.x * depth2));
trans.g = exp(-(betaR.g * depth1 + betaMEx.y * depth2));
trans.b = exp(-(betaR.b * depth1 + betaMEx.z * depth2));
trans.a = 1.0;
texture2DSetPixel(_transmittanceTexture, x, y, trans); /* Eq (5) */
}
}
}
/*********************** irradiance1.glsl ***********************/
static void _precomputeIrrDeltaETexture(Texture2D* destination)
{
int x, y;
/* Irradiance program */
for (x = 0; x < SKY_W; x++)
{
for (y = 0; y < SKY_H; y++)
{
double r, muS;
Color trans, irr;
_getIrradianceRMuS((double)x / SKY_W, (double)y / SKY_H, &r, &muS);
trans = _transmittance(r, muS);
irr.r = trans.r * max(muS, 0.0);
irr.g = trans.g * max(muS, 0.0);
irr.b = trans.b * max(muS, 0.0);
irr.a = 1.0;
texture2DSetPixel(destination, x, y, irr);
}
}
}
static void _getLayerParams(int layer, double* _r, Color* _dhdH)
{
double r = layer / (RES_R - 1.0);
r = r * r;
r = sqrt(Rg * Rg + r * (Rt * Rt - Rg * Rg)) + (layer == 0 ? 0.01 : (layer == RES_R - 1 ? -0.001 : 0.0));
double dmin = Rt - r;
double dmax = sqrt(r * r - Rg * Rg) + sqrt(Rt * Rt - Rg * Rg);
double dminp = r - Rg;
double dmaxp = sqrt(r * r - Rg * Rg);
*_r = r;
_dhdH->r = dmin;
_dhdH->g = dmax;
_dhdH->b = dminp;
_dhdH->a = dmaxp;
}
/*********************** inscatter1.glsl ***********************/
static void _integrand1(double r, double mu, double muS, double nu, double t, Color* ray, Color* mie)
{
double ri = sqrt(r * r + t * t + 2.0 * r * mu * t);
double muSi = (nu * t + muS * r) / ri;
ri = max(Rg, ri);
if (muSi >= -sqrt(1.0 - Rg * Rg / (ri * ri)))
{
Color t1, t2;
t1 = _transmittance3(r, mu, t);
t2 = _transmittance(ri, muSi);
double fR = exp(-(ri - Rg) / HR);
double fM = exp(-(ri - Rg) / HM);
ray->r = fR * t1.r * t2.r;
ray->g = fR * t1.g * t2.g;
ray->b = fR * t1.b * t2.b;
mie->r = fM * t1.r * t2.r;
mie->g = fM * t1.g * t2.g;
mie->b = fM * t1.b * t2.b;
}
else
{
ray->r = ray->g = ray->b = 0.0;
mie->r = mie->g = mie->b = 0.0;
}
}
static void _inscatter1(double r, double mu, double muS, double nu, Color* ray, Color* mie)
{
ray->r = ray->g = ray->b = 0.0;
mie->r = mie->g = mie->b = 0.0;
double dx = _limit(r, mu) / (double)(INSCATTER_INTEGRAL_SAMPLES);
Color rayi;
Color miei;
_integrand1(r, mu, muS, nu, 0.0, &rayi, &miei);
int i;
for (i = 1; i <= INSCATTER_INTEGRAL_SAMPLES; ++i)
{
double xj = (double)(i) * dx;
Color rayj;
Color miej;
_integrand1(r, mu, muS, nu, xj, &rayj, &miej);
ray->r += (rayi.r + rayj.r) / 2.0 * dx;
ray->g += (rayi.g + rayj.g) / 2.0 * dx;
ray->b += (rayi.b + rayj.b) / 2.0 * dx;
mie->r += (miei.r + miej.r) / 2.0 * dx;
mie->g += (miei.g + miej.g) / 2.0 * dx;
mie->b += (miei.b + miej.b) / 2.0 * dx;
rayi = rayj;
miei = miej;
}
ray->r *= betaR.r;
ray->g *= betaR.g;
ray->b *= betaR.b;
mie->r *= betaMSca.x;
mie->g *= betaMSca.y;
mie->b *= betaMSca.z;
}
typedef struct
{
Texture4D* ray;
Texture4D* mie;
} Inscatter1Params;
static int _inscatter1Worker(ParallelWork* work, int layer, void* data)
{
Inscatter1Params* params = (Inscatter1Params*)data;
UNUSED(work);
double r;
Color dhdH;
_getLayerParams(layer, &r, &dhdH);
int x, y, z;
for (x = 0; x < RES_MU; x++)
{
for (y = 0; y < RES_MU_S; y++)
{
for (z = 0; z < RES_NU; z++)
{
Color ray = COLOR_BLACK;
Color mie = COLOR_BLACK;
double mu, muS, nu;
_texCoordToMuMuSNu((double)x, (double)y, (double)z, r, dhdH, &mu, &muS, &nu);
_inscatter1(r, mu, muS, nu, &ray, &mie);
/* store separately Rayleigh and Mie contributions, WITHOUT the phase function factor
* (cf "Angular precision") */
texture4DSetPixel(params->ray, x, y, z, layer, ray);
texture4DSetPixel(params->mie, x, y, z, layer, mie);
}
}
}
return 1;
}
/*********************** inscatterS.glsl ***********************/
static Color _inscatterS(double r, double mu, double muS, double nu, int first, Texture2D* deltaE, Texture4D* deltaSR, Texture4D* deltaSM)
{
Color raymie = COLOR_BLACK;
double dphi = M_PI / (double)(INSCATTER_SPHERICAL_INTEGRAL_SAMPLES);
double dtheta = M_PI / (double)(INSCATTER_SPHERICAL_INTEGRAL_SAMPLES);
r = clamp(r, Rg, Rt);
mu = clamp(mu, -1.0, 1.0);
muS = clamp(muS, -1.0, 1.0);
double var = sqrt(1.0 - mu * mu) * sqrt(1.0 - muS * muS);
nu = clamp(nu, muS * mu - var, muS * mu + var);
double cthetamin = -sqrt(1.0 - (Rg / r) * (Rg / r));
Vector3 v = vec3(sqrt(1.0 - mu * mu), 0.0, mu);
double sx = v.x == 0.0 ? 0.0 : (nu - muS * mu) / v.x;
Vector3 s = vec3(sx, sqrt(max(0.0, 1.0 - sx * sx - muS * muS)), muS);
/* integral over 4.PI around x with two nested loops over w directions (theta,phi) -- Eq (7) */
int itheta;
for (itheta = 0; itheta < INSCATTER_SPHERICAL_INTEGRAL_SAMPLES; ++itheta)
{
double theta = ((double)(itheta) + 0.5) * dtheta;
double ctheta = cos(theta);
double greflectance = 0.0;
double dground = 0.0;
Color gtransp = {0.0, 0.0, 0.0, 0.0};
if (ctheta < cthetamin)
{
/* if ground visible in direction w
* compute transparency gtransp between x and ground */
greflectance = AVERAGE_GROUND_REFLECTANCE / M_PI;
dground = -r * ctheta - sqrt(r * r * (ctheta * ctheta - 1.0) + Rg * Rg);
gtransp = _transmittance3(Rg, -(r * ctheta + dground) / Rg, dground);
}
int iphi;
for (iphi = 0; iphi < 2 * INSCATTER_SPHERICAL_INTEGRAL_SAMPLES; ++iphi)
{
double phi = ((double)(iphi) + 0.5) * dphi;
double dw = dtheta * dphi * sin(theta);
Vector3 w = vec3(cos(phi) * sin(theta), sin(phi) * sin(theta), ctheta);
double nu1 = v3Dot(s, w);
double nu2 = v3Dot(v, w);
double pr2 = _phaseFunctionR(nu2);
double pm2 = _phaseFunctionM(nu2);
/* compute irradiance received at ground in direction w (if ground visible) =deltaE */
Vector3 gnormal;
gnormal.x = dground * w.x / Rg;
gnormal.y = dground * w.y / Rg;
gnormal.z = (r + dground * w.z) / Rg;
Color girradiance = _irradiance(deltaE, Rg, v3Dot(gnormal, s));
Color raymie1; /* light arriving at x from direction w */
/* first term = light reflected from the ground and attenuated before reaching x, =T.alpha/PI.deltaE */
raymie1.r = greflectance * girradiance.r * gtransp.r;
raymie1.g = greflectance * girradiance.g * gtransp.g;
raymie1.b = greflectance * girradiance.b * gtransp.b;
/* second term = inscattered light, =deltaS */
if (first)
{
/* first iteration is special because Rayleigh and Mie were stored separately,
* without the phase functions factors; they must be reintroduced here */
double pr1 = _phaseFunctionR(nu1);
double pm1 = _phaseFunctionM(nu1);
Color ray1 = _texture4D(deltaSR, r, w.z, muS, nu1);
Color mie1 = _texture4D(deltaSM, r, w.z, muS, nu1);
raymie1.r += ray1.r * pr1 + mie1.r * pm1;
raymie1.g += ray1.g * pr1 + mie1.g * pm1;
raymie1.b += ray1.b * pr1 + mie1.b * pm1;
}
else
{
Color col = _texture4D(deltaSR, r, w.z, muS, nu1);
raymie1.r += col.r;
raymie1.g += col.g;
raymie1.b += col.b;
}
/* light coming from direction w and scattered in direction v
= light arriving at x from direction w (raymie1) * SUM(scattering coefficient * phaseFunction)
see Eq (7) */
raymie.r += raymie1.r * (betaR.r * exp(-(r - Rg) / HR) * pr2 + betaMSca.x * exp(-(r - Rg) / HM) * pm2) * dw;
raymie.g += raymie1.g * (betaR.g * exp(-(r - Rg) / HR) * pr2 + betaMSca.y * exp(-(r - Rg) / HM) * pm2) * dw;
raymie.b += raymie1.b * (betaR.b * exp(-(r - Rg) / HR) * pr2 + betaMSca.z * exp(-(r - Rg) / HM) * pm2) * dw;
}
}
/* output raymie = J[T.alpha/PI.deltaE + deltaS] (line 7 in algorithm 4.1) */
return raymie;
}
typedef struct
{
Texture4D* result;
Texture2D* deltaE;
Texture4D* deltaSR;
Texture4D* deltaSM;
int first;
} jParams;
static int _jWorker(ParallelWork* work, int layer, void* data)
{
jParams* params = (jParams*)data;
UNUSED(work);
double r;
Color dhdH;
_getLayerParams(layer, &r, &dhdH);
int x, y, z;
for (x = 0; x < RES_MU; x++)
{
for (y = 0; y < RES_MU_S; y++)
{
for (z = 0; z < RES_NU; z++)
{
Color raymie;
double mu, muS, nu;
_texCoordToMuMuSNu((double)x, (double)y, (double)z, r, dhdH, &mu, &muS, &nu);
raymie = _inscatterS(r, mu, muS, nu, params->first, params->deltaE, params->deltaSR, params->deltaSM);
texture4DSetPixel(params->result, x, y, z, layer, raymie);
}
}
}
return 1;
}
/*********************** irradianceN.glsl ***********************/
void _irradianceNProg(Texture2D* destination, Texture4D* deltaSR, Texture4D* deltaSM, int first)
{
int x, y;
double dphi = M_PI / (double)(IRRADIANCE_INTEGRAL_SAMPLES);
double dtheta = M_PI / (double)(IRRADIANCE_INTEGRAL_SAMPLES);
for (x = 0; x < SKY_W; x++)
{
for (y = 0; y < SKY_H; y++)
{
double r, muS;
int iphi;
_getIrradianceRMuS((double)x / SKY_W, (double)y / SKY_H, &r, &muS);
Vector3 s = vec3(max(sqrt(1.0 - muS * muS), 0.0), 0.0, muS);
Color result = COLOR_BLACK;
/* integral over 2.PI around x with two nested loops over w directions (theta,phi) -- Eq (15) */
for (iphi = 0; iphi < 2 * IRRADIANCE_INTEGRAL_SAMPLES; ++iphi)
{
double phi = ((double)(iphi) + 0.5) * dphi;
int itheta;
for (itheta = 0; itheta < IRRADIANCE_INTEGRAL_SAMPLES / 2; ++itheta)
{
double theta = ((double)(itheta) + 0.5) * dtheta;
double dw = dtheta * dphi * sin(theta);
Vector3 w = vec3(cos(phi) * sin(theta), sin(phi) * sin(theta), cos(theta));
double nu = v3Dot(s, w);
if (first)
{
/* first iteration is special because Rayleigh and Mie were stored separately,
without the phase functions factors; they must be reintroduced here */
double pr1 = _phaseFunctionR(nu);
double pm1 = _phaseFunctionM(nu);
Color ray1 = _texture4D(deltaSR, r, w.z, muS, nu);
Color mie1 = _texture4D(deltaSM, r, w.z, muS, nu);
result.r += (ray1.r * pr1 + mie1.r * pm1) * w.z * dw;
result.g += (ray1.g * pr1 + mie1.g * pm1) * w.z * dw;
result.b += (ray1.b * pr1 + mie1.b * pm1) * w.z * dw;
}
else
{
Color col = _texture4D(deltaSR, r, w.z, muS, nu);
result.r += col.r * w.z * dw;
result.g += col.g * w.z * dw;
result.b += col.b * w.z * dw;
}
}
}
texture2DSetPixel(destination, x, y, result);
}
}
}
/*********************** inscatterN.glsl ***********************/
typedef struct
{
Texture4D* destination;
Texture4D* deltaJ;
} InscatterNParams;
static Color _integrand2(Texture4D* deltaJ, double r, double mu, double muS, double nu, double t)
{
double ri = sqrt(r * r + t * t + 2.0 * r * mu * t);
double mui = (r * mu + t) / ri;
double muSi = (nu * t + muS * r) / ri;
Color c1, c2;
c1 = _texture4D(deltaJ, ri, mui, muSi, nu);
c2 = _transmittance3(r, mu, t);
c1.r *= c2.r;
c1.g *= c2.g;
c1.b *= c2.b;
c1.a = 1.0;
return c1;
}
static Color _inscatterN(Texture4D* deltaJ, double r, double mu, double muS, double nu)
{
Color raymie = COLOR_BLACK;
double dx = _limit(r, mu) / (double)(INSCATTER_INTEGRAL_SAMPLES);
Color raymiei = _integrand2(deltaJ, r, mu, muS, nu, 0.0);
int i;
for (i = 1; i <= INSCATTER_INTEGRAL_SAMPLES; ++i)
{
double xj = (double)(i) * dx;
Color raymiej = _integrand2(deltaJ, r, mu, muS, nu, xj);
raymie.r += (raymiei.r + raymiej.r) / 2.0 * dx;
raymie.g += (raymiei.g + raymiej.g) / 2.0 * dx;
raymie.b += (raymiei.b + raymiej.b) / 2.0 * dx;
raymiei = raymiej;
}
return raymie;
}
static int _inscatterNWorker(ParallelWork* work, int layer, void* data)
{
UNUSED(work);
InscatterNParams* params = (InscatterNParams*)data;
double r;
Color dhdH;
_getLayerParams(layer, &r, &dhdH);
int x, y, z;
for (x = 0; x < RES_MU; x++)
{
for (y = 0; y < RES_MU_S; y++)
{
for (z = 0; z < RES_NU; z++)
{
double mu, muS, nu;
_texCoordToMuMuSNu((double)x, (double)y, (double)z, r, dhdH, &mu, &muS, &nu);
texture4DSetPixel(params->destination, x, y, z, layer, _inscatterN(params->deltaJ, r, mu, muS, nu));
}
}
}
return 1;
}
/*********************** copyInscatterN.glsl ***********************/
typedef struct
{
Texture4D* source;
Texture4D* destination;
} CopyInscatterNParams;
static int _copyInscatterNWorker(ParallelWork* work, int layer, void* data)
{
CopyInscatterNParams* params = (CopyInscatterNParams*)data;
UNUSED(work);
double r;
Color dhdH;
_getLayerParams(layer, &r, &dhdH);
int x, y, z;
for (x = 0; x < RES_MU; x++)
{
for (y = 0; y < RES_MU_S; y++)
{
for (z = 0; z < RES_NU; z++)
{
double mu, muS, nu;
_texCoordToMuMuSNu((double)x, (double)y, (double)z, r, dhdH, &mu, &muS, &nu);
Color col1 = texture4DGetPixel(params->source, x, y, z, layer);
Color col2 = texture4DGetPixel(params->destination, x, y, z, layer);
col2.r += col1.r / _phaseFunctionR(nu);
col2.g += col1.g / _phaseFunctionR(nu);
col2.b += col1.b / _phaseFunctionR(nu);
texture4DSetPixel(params->destination, x, y, z, layer, col2);
}
}
}
return 1;
}
/*********************** Final getters ***********************/
static inline Color _applyInscatter(Color inscatter, Color attmod, Color samp)
{
inscatter.r = inscatter.r - attmod.r * samp.r;
inscatter.g = inscatter.g - attmod.g * samp.g;
inscatter.b = inscatter.b - attmod.b * samp.b;
inscatter.a = inscatter.a - attmod.a * samp.a;
return vec4max(inscatter, 0.0);
}
/* inscattered light along ray x+tv, when sun in direction s (=S[L]-T(x,x0)S[L]|x0) */
static Color _getInscatterColor(Vector3* _x, double* _t, Vector3 v, Vector3 s, double* _r, double* _mu, Vector3* attenuation)
{
Color result;
double r = v3Norm(*_x);
double mu = v3Dot(*_x, v) / r;
double d = -r * mu - sqrt(r * r * (mu * mu - 1.0) + Rt * Rt);
attenuation->x = attenuation->y = attenuation->z = 0.0;
if (d > 0.0)
{
/* if x in space and ray intersects atmosphere
move x to nearest intersection of ray with top atmosphere boundary */
_x->x += d * v.x;
_x->y += d * v.y;
_x->z += d * v.z;
*_t -= d;
mu = (r * mu + d) / Rt;
r = Rt;
}
double t = *_t;
Vector3 x = *_x;
if (r <= Rt)
{
/* if ray intersects atmosphere */
double nu = v3Dot(v, s);
double muS = v3Dot(x, s) / r;
double phaseR = _phaseFunctionR(nu);
double phaseM = _phaseFunctionM(nu);
Color inscatter = vec4max(_texture4D(_inscatterTexture, r, mu, muS, nu), 0.0);
if (t > 0.0)
{
Vector3 x0 = v3Add(x, v3Scale(v, t));
double r0 = v3Norm(x0);
double rMu0 = v3Dot(x0, v);
double mu0 = rMu0 / r0;
double muS0 = v3Dot(x0, s) / r0;
/* avoids imprecision problems in transmittance computations based on textures */
*attenuation = _analyticTransmittance(r, mu, t);
if (r0 > Rg + 0.001)
{
/* computes S[L]-T(x,x0)S[L]|x0 */
Color attmod = {attenuation->x, attenuation->y, attenuation->z, attenuation->x};
Color samp = _texture4D(_inscatterTexture, r0, mu0, muS0, nu);
inscatter = _applyInscatter(inscatter, attmod, samp);
/* avoids imprecision problems near horizon by interpolating between two points above and below horizon */
const double EPS = 0.02;
double muHoriz = -sqrt(1.0 - (Rg / r) * (Rg / r));
if (fabs(mu - muHoriz) < EPS)
{
double a = ((mu - muHoriz) + EPS) / (2.0 * EPS);
mu = muHoriz - EPS;
r0 = sqrt(r * r + t * t + 2.0 * r * t * mu);
mu0 = (r * mu + t) / r0;
Color inScatter0 = _texture4D(_inscatterTexture, r, mu, muS, nu);
Color inScatter1 = _texture4D(_inscatterTexture, r0, mu0, muS0, nu);
Color inScatterA = _applyInscatter(inScatter0, attmod, inScatter1);
mu = muHoriz + EPS;
r0 = sqrt(r * r + t * t + 2.0 * r * t * mu);
mu0 = (r * mu + t) / r0;
inScatter0 = _texture4D(_inscatterTexture, r, mu, muS, nu);
inScatter1 = _texture4D(_inscatterTexture, r0, mu0, muS0, nu);
Color inScatterB = _applyInscatter(inScatter0, attmod, inScatter1);
inscatter = vec4mix(inScatterA, inScatterB, a);
}
}
}
/* avoids imprecision problems in Mie scattering when sun is below horizon */
inscatter.a *= smoothstep(0.00, 0.02, muS);
Color mie = _getMie(inscatter);
result.r = inscatter.r * phaseR + mie.r * phaseM;
result.g = inscatter.g * phaseR + mie.g * phaseM;
result.b = inscatter.b * phaseR + mie.b * phaseM;
result.a = 1.0;
_fixVec4Min(&result, 0.0);
}
else
{
/* x in space and ray looking in space */
result = COLOR_BLACK;
}
*_r = r;
*_mu = mu;
result.r *= ISun;
result.g *= ISun;
result.b *= ISun;
result.a = 1.0;
return result;
}
/* direct sun light for ray x+tv, when sun in direction s (=L0) */
static Color _sunColor(Vector3 v, Vector3 s, double r, double mu, double radius)
{
Color transmittance = r <= Rt ? _transmittanceWithShadow(r, mu) : COLOR_WHITE; /* T(x,xo) */
double d = _limit(r, mu);
radius *= (1.0 + 10.0 * d / Rt); /* Inflating due to lens effect near horizon */
double isun = step(cos(radius * M_PI / 180.0), v3Dot(v, s)) * ISun; /* Lsun */
transmittance.r *= isun;
transmittance.g *= isun;
transmittance.b *= isun;
transmittance.a = 1.0;
return transmittance; /* Eq (9) */
}
/*********************** Cache/debug methods ***********************/
static int _tryLoadCache2D(Texture2D* tex, const char* tag, int order)
{
CacheFile* cache;
int xsize, ysize;
texture2DGetSize(tex, &xsize, &ysize);
cache = cacheFileCreateAccessor("atmo-br", "cache", tag, xsize, ysize, 0, 0, order);
if (cacheFileIsReadable(cache))
{
PackStream stream;
stream.bindToFile(cacheFileGetPath(cache));
texture2DLoad(&stream, tex);
cacheFileDeleteAccessor(cache);
return 1;
}
else
{
cacheFileDeleteAccessor(cache);
return 0;
}
}
static void _saveCache2D(Texture2D* tex, const char* tag, int order)
{
CacheFile* cache;
int xsize, ysize;
texture2DGetSize(tex, &xsize, &ysize);
cache = cacheFileCreateAccessor("atmo-br", "cache", tag, xsize, ysize, 0, 0, order);
if (cacheFileIsWritable(cache))
{
PackStream stream;
stream.bindToFile(cacheFileGetPath(cache));
texture2DSave(&stream, tex);
}
cacheFileDeleteAccessor(cache);
}
static void _saveDebug2D(Texture2D* tex, const char* tag, int order)
{
CacheFile* cache;
int xsize, ysize;
texture2DGetSize(tex, &xsize, &ysize);
cache = cacheFileCreateAccessor("atmo-br", "png", tag, xsize, ysize, 0, 0, order);
if (cacheFileIsWritable(cache))
{
texture2DSaveToFile(tex, cacheFileGetPath(cache));
}
cacheFileDeleteAccessor(cache);
}
static int _tryLoadCache4D(Texture4D* tex, const char* tag, int order)
{
CacheFile* cache;
int xsize, ysize, zsize, wsize;
texture4DGetSize(tex, &xsize, &ysize, &zsize, &wsize);
cache = cacheFileCreateAccessor("atmo-br", "cache", tag, xsize, ysize, zsize, wsize, order);
if (cacheFileIsReadable(cache))
{
PackStream stream;
stream.bindToFile(cacheFileGetPath(cache));
texture4DLoad(&stream, tex);
cacheFileDeleteAccessor(cache);
return 1;
}
else
{
cacheFileDeleteAccessor(cache);
return 0;
}
}
static void _saveCache4D(Texture4D* tex, const char* tag, int order)
{
CacheFile* cache;
int xsize, ysize, zsize, wsize;
texture4DGetSize(tex, &xsize, &ysize, &zsize, &wsize);
cache = cacheFileCreateAccessor("atmo-br", "cache", tag, xsize, ysize, zsize, wsize, order);
if (cacheFileIsWritable(cache))
{
PackStream stream;
stream.bindToFile(cacheFileGetPath(cache));
texture4DSave(&stream, tex);
}
cacheFileDeleteAccessor(cache);
}
static void _saveDebug4D(Texture4D* tex, const char* tag, int order)
{
CacheFile* cache;
int xsize, ysize, zsize, wsize;
texture4DGetSize(tex, &xsize, &ysize, &zsize, &wsize);
cache = cacheFileCreateAccessor("atmo-br", "png", tag, xsize, ysize, zsize, wsize, order);
if (cacheFileIsWritable(cache))
{
texture4DSaveToFile(tex, cacheFileGetPath(cache));
}
cacheFileDeleteAccessor(cache);
}
/*********************** Public methods ***********************/
void brunetonInit()
{
int x, y, z, w, order;
ParallelWork* work;
assert(_inscatterTexture == NULL);
/* TODO Deletes */
_transmittanceTexture = texture2DCreate(TRANSMITTANCE_W, TRANSMITTANCE_H);
_irradianceTexture = texture2DCreate(SKY_W, SKY_H);
_inscatterTexture = texture4DCreate(RES_MU, RES_MU_S, RES_NU, RES_R);
/* try loading from cache */
if (_tryLoadCache2D(_transmittanceTexture, "transmittance", 0)
&& _tryLoadCache2D(_irradianceTexture, "irradiance", 0)
&& _tryLoadCache4D(_inscatterTexture, "inscatter", 0))
{
return;
}
Texture2D* _deltaETexture = texture2DCreate(SKY_W, SKY_H);
Texture4D* _deltaSMTexture = texture4DCreate(RES_MU, RES_MU_S, RES_NU, RES_R);
Texture4D* _deltaSRTexture = texture4DCreate(RES_MU, RES_MU_S, RES_NU, RES_R);
Texture4D* _deltaJTexture = texture4DCreate(RES_MU, RES_MU_S, RES_NU, RES_R);
/* computes transmittance texture T (line 1 in algorithm 4.1) */
_precomputeTransmittanceTexture();
_saveDebug2D(_transmittanceTexture, "transmittance", 0);
/* computes irradiance texture deltaE (line 2 in algorithm 4.1) */
_precomputeIrrDeltaETexture(_deltaETexture);
_saveDebug2D(_deltaETexture, "deltaE", 0);
/* computes single scattering texture deltaS (line 3 in algorithm 4.1)
* Rayleigh and Mie separated in deltaSR + deltaSM */
Inscatter1Params params = {_deltaSRTexture, _deltaSMTexture};
work = parallelWorkCreate(_inscatter1Worker, RES_R, &params);
parallelWorkPerform(work, -1);
parallelWorkDelete(work);
_saveDebug4D(_deltaSRTexture, "deltaSR", 0);
_saveDebug4D(_deltaSMTexture, "deltaSM", 0);
/* copies deltaE into irradiance texture E (line 4 in algorithm 4.1) */
/* ??? all black texture (k=0.0) ??? */
texture2DFill(_irradianceTexture, COLOR_BLACK);
/* copies deltaS into inscatter texture S (line 5 in algorithm 4.1) */
for (x = 0; x < RES_MU; x++)
{
for (y = 0; y < RES_MU_S; y++)
{
for (z = 0; z < RES_NU; z++)
{
for (w = 0; w < RES_R; w++)
{
Color result = texture4DGetPixel(_deltaSRTexture, x, y, z, w);
Color mie = texture4DGetPixel(_deltaSMTexture, x, y, z, w);
result.a = mie.r;
texture4DSetPixel(_inscatterTexture, x, y, z, w, result);
}
}
}
}
_saveDebug4D(_inscatterTexture, "inscatter", 0);
/* loop for each scattering order (line 6 in algorithm 4.1) */
for (order = 2; order <= 4; ++order)
{
/* computes deltaJ (line 7 in algorithm 4.1) */
jParams jparams = {_deltaJTexture, _deltaETexture, _deltaSRTexture, _deltaSMTexture, order == 2};
work = parallelWorkCreate(_jWorker, RES_R, &jparams);
parallelWorkPerform(work, -1);
parallelWorkDelete(work);
_saveDebug4D(_deltaJTexture, "deltaJ", order);
/* computes deltaE (line 8 in algorithm 4.1) */
_irradianceNProg(_deltaETexture, _deltaSRTexture, _deltaSMTexture, order == 2);
_saveDebug2D(_deltaETexture, "deltaE", order);
/* computes deltaS (line 9 in algorithm 4.1) */
InscatterNParams iparams = {_deltaSRTexture, _deltaJTexture};
work = parallelWorkCreate(_inscatterNWorker, RES_R, &iparams);
parallelWorkPerform(work, -1);
parallelWorkDelete(work);
_saveDebug4D(_deltaSRTexture, "deltaSR", order);
/* adds deltaE into irradiance texture E (line 10 in algorithm 4.1) */
texture2DAdd(_deltaETexture, _irradianceTexture);
_saveDebug2D(_irradianceTexture, "irradiance", order);
/* adds deltaS into inscatter texture S (line 11 in algorithm 4.1) */
CopyInscatterNParams cparams = {_deltaSRTexture, _inscatterTexture};
work = parallelWorkCreate(_copyInscatterNWorker, RES_R, &cparams);
parallelWorkPerform(work, -1);
parallelWorkDelete(work);
_saveDebug4D(_inscatterTexture, "inscatter", order);
}
_saveCache2D(_transmittanceTexture, "transmittance", 0);
_saveCache2D(_irradianceTexture, "irradiance", 0);
_saveCache4D(_inscatterTexture, "inscatter", 0);
texture2DDelete(_deltaETexture);
texture4DDelete(_deltaSMTexture);
texture4DDelete(_deltaSRTexture);
texture4DDelete(_deltaJTexture);
}
AtmosphereResult brunetonGetSkyColor(Renderer* renderer, Vector3 eye, Vector3 direction, Vector3 sun_position, Color base)
{
UNUSED(base);
double yoffset = GROUND_OFFSET - renderer->water->getHeightInfo(renderer).base_height;
eye.y += yoffset;
if (eye.y < 0.0)
{
eye.y = 0.0;
}
Vector3 x = {0.0, Rg + eye.y * WORLD_SCALING, 0.0};
Vector3 v = v3Normalize(direction);
Vector3 s = v3Normalize(v3Sub(sun_position, x));
double r = v3Norm(x);
double mu = v3Dot(x, v) / r;
double t = -r * mu - sqrt(r * r * (mu * mu - 1.0) + Rg * Rg);
AtmosphereResult result;
Vector3 attenuation;
Color sunColor = _sunColor(v, s, r, mu, renderer->atmosphere->definition->sun_radius); /* L0 */
atmosphereInitResult(&result);
/*result.base.r = base.r + sunColor.r;
result.base.g = base.g + sunColor.g;
result.base.b = base.b + sunColor.b;*/
result.base = sunColor;
result.inscattering = _getInscatterColor(&x, &t, v, s, &r, &mu, &attenuation); /* S[L]-T(x,xs)S[l]|xs */
/* TODO Use atmosphere attenuation */
result.distance = SPHERE_SIZE;
atmosphereUpdateResult(&result);
return result;
}
AtmosphereResult brunetonApplyAerialPerspective(Renderer* renderer, Vector3 location, Color base)
{
Vector3 eye = renderer->getCameraLocation(renderer, location);
Vector3 sun_position = v3Scale(renderer->atmosphere->getSunDirection(renderer), SUN_DISTANCE);
double yoffset = GROUND_OFFSET - renderer->water->getHeightInfo(renderer).base_height;
eye.y += yoffset;
location.y += yoffset;
if (eye.y < 0.0)
{
eye.y = 0.0;
}
if (location.y < 0.0)
{
location.y = 0.0;
}
Vector3 direction = v3Scale(v3Sub(location, eye), WORLD_SCALING);
Vector3 x = {0.0, Rg + eye.y * WORLD_SCALING, 0.0};
Vector3 v = v3Normalize(direction);
Vector3 s = v3Normalize(v3Sub(sun_position, x));
if (v.y == 0.0)
{
v.y = -0.000001;
}
double r = v3Norm(x);
double mu = v3Dot(x, v) / r;
double t = v3Norm(direction);
AtmosphereResult result;
Vector3 attenuation;
atmosphereInitResult(&result);
result.base = base;
result.inscattering = _getInscatterColor(&x, &t, v, s, &r, &mu, &attenuation); /* S[L]-T(x,xs)S[l]|xs */
result.attenuation.r = attenuation.x;
result.attenuation.g = attenuation.y;
result.attenuation.b = attenuation.z;
result.distance = t / WORLD_SCALING;
atmosphereUpdateResult(&result);
return result;
}
void brunetonGetLightingStatus(Renderer* renderer, LightStatus* status, Vector3 normal, int opaque)
{
UNUSED(normal);
UNUSED(opaque);
LightDefinition sun, irradiance;
double muS;
double altitude = lightingGetStatusLocation(status).y;
double yoffset = GROUND_OFFSET - renderer->water->getHeightInfo(renderer).base_height;
altitude += yoffset;
if (altitude < 0.0)
{
altitude = 0.0;
}
double r0 = Rg + altitude * WORLD_SCALING;
Vector3 up = {0.0, 1.0, 0.0};
Vector3 sun_position = v3Scale(renderer->atmosphere->getSunDirection(renderer), SUN_DISTANCE);
Vector3 x = {0.0, r0, 0.0};
Vector3 s = v3Normalize(v3Sub(sun_position, x));
muS = v3Dot(up, s);
sun.color = _transmittanceWithShadow(r0, muS);
sun.direction = v3Scale(s, -1.0);
sun.reflection = ISun;
sun.altered = 1;
lightingPushLight(status, &sun);
irradiance.color = _irradiance(_irradianceTexture, r0, muS);
irradiance.direction = VECTOR_DOWN;
irradiance.reflection = 0.0;
irradiance.altered = 0;
lightingPushLight(status, &irradiance);
}
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