Hello all, I'm new to the forum. Even though what I'm trying to achieve is not game related, I've found the most useful resources (and knowledge) here while trying to solve my problem.

For some time now I've been wanting to make a 2D representation of the sky for a given location at any date/time of day. I found the Preetham paper and followed through it, looked for several examples online and made my own implementation. Along the way I came across a couple of (as of now, very old) threads from here as well (http://www.gamedev.net/topic/100346-having-trouble-implementing-a-sky-colouring-algorithm and http://www.gamedev.net/topic/184552-preethams-daylight-paper-problem-50k-of-images/). I must say that, before doing this, I had no experience whatsoever in color management/theories, nor do I have any kind of knowledge on 3D programming.

After a couple of weeks I finished my implementation, but the colors are way off. I produced a series of images, from midnight to midnight for today at my current location. The image sequence is on my Dropbox (https://www.dropbox.com/sh/rklgyfvfhh2knij/AABRe_7V2OhT3Bprwj9yAMuga) and I also produced a video of it (https://www.dropbox.com/s/ispwejh3otf4zba/sunsky.mp4).

My current C code (also on pastebin: http://pastebin.com/EctzJFmF)

#define M_PI 3.14159265358979323846264338327950288 #define radians(x) ((x) / 180.f * M_PI) typedef struct { double A, B, C, D, E; } PerezCoefficient; typedef struct { PerezCoefficient Y, x, y; } PerezYxyCoefficients; typedef struct { float red, green, blue; } RGBColor; typedef struct { double Y, y, x; } YyxColor; double getJulianDayNumber(int year, int month, int day, int hour, int minute, int second, double timezone) { double dayDecimal, julianDay, a, b; double timeDecimal = ((hour - timezone) / 24.) + (minute / (60. * 24.)) + (second / (60. * 60. * 24.)); dayDecimal = day + timeDecimal; if (month < 3) { month += 12; year--; } a = (int)floor(year / 100.); b = 2 - a + floor(a / 4.); julianDay = (int)floor(365.25 * (year + 4716.)) + (int)floor(30.6001 * (month + 1)) + dayDecimal + b - 1524.5; return julianDay; } double getDecimalTime(int hour, int minute, int second) { return hour + ((double)minute / 60.) + ((double)second / 3600.); } double getSolarTime(double julianDayNumber, double decimalTime, double timezone, double longitude) { return decimalTime + .17f*sin(4.*M_PI*((julianDayNumber - 80) / 373)) - .129f*sin(2.*M_PI*((julianDayNumber - 8) / 355.)) - ((15*timezone - longitude) / 15.); } double getSolarDeclination(double julianDayNumber) { return .4093f * sin((2*M_PI * (julianDayNumber - 81)) / 368.); } double getSolarAltitude(double solarDeclination, double solarTime, double latitude) { return asin(sin(radians(latitude)) * sin(solarDeclination) - cos (radians(latitude)) * cos (solarDeclination) * cos (M_PI * solarTime / 12.)); } double getSolarAzimuth(double solarDeclination, double solarTime, double latitude) { return atan((-cos(solarDeclination) * sin(M_PI * solarTime / 12.)) / (cos(radians(latitude)) * sin(solarDeclination) - sin(radians(latitude)) * cos(solarDeclination) * cos(M_PI * solarTime / 12.))); } double getPerezLuminance(double zenith, double gamma, PerezCoefficient coeff) { double cosZenith = (zenith == M_PI_2 ? .0000001f : cos(zenith)); return (1 + coeff.A * exp(coeff.B / cosZenith)) * (1 + coeff.C * exp(coeff.D * gamma) + coeff.E * pow(cos(gamma), 2)); } double getPerezGamma(float zenith, float azimuth, float solarzenith, float solarazimuth) { double a = sin(zenith) * sin(solarzenith) * cos(solarazimuth - azimuth) + cos(zenith) * cos(solarzenith); if(a > 1) return 0; if(a < -1) return M_PI; return acos(a); } PerezYxyCoefficients getPerezCoefficientsForTurbidity(double turbidity) { PerezCoefficient coeffY, coeffx, coeffy; coeffY.A = .17872f * turbidity - 1.46303f; coeffY.B = -.3554f * turbidity + .42749f; coeffY.C = -.02266f * turbidity + 5.32505f; coeffY.D = .12064f * turbidity - 2.57705f; coeffY.E = -.06696f * turbidity + .37027f; coeffx.A = -.01925f * turbidity - .25922f; coeffx.B = -.06651f * turbidity + .00081f; coeffx.C = -.00041f * turbidity + .21247f; coeffx.D = -.06409f * turbidity + .89887f; coeffx.E = -.00325f * turbidity + .04517f; coeffy.A = -.01669f * turbidity - .26078f; coeffy.B = -.09495f * turbidity + .00921f; coeffy.C = -.00792f * turbidity + .21023f; coeffy.D = -.04405f * turbidity - 1.65369f; coeffy.E = -.01092f * turbidity + .05291f; return (PerezYxyCoefficients){ .Y = coeffY, .x = coeffx, .y = coeffy }; } YyxColor getYyxColorForZenithAndTurbidity(double zenith, double turbidity) { YyxColor color; double zenith2 = pow(zenith, 2); double zenith3 = pow(zenith, 3); double turbidity2 = pow(turbidity, 2); color.Y = ((4.0453f * turbidity - 4.971f) * tan((4.f/9.f - turbidity / 120.f) * (M_PI - 2*zenith)) - 0.2155f * turbidity + 2.4192f) * 1000.f; color.x = (.00165f * zenith3 - .00375f * zenith2 + .00209f * zenith + 0.f) * turbidity2 + (-0.02903f * zenith3 + .06377f * zenith2 - .03202f * zenith + .00394f) * turbidity + (.11693f * zenith3 - .21196f * zenith2 + .06052f * zenith + .25886f); color.y = (.00275f * zenith3 - .0061f * zenith2 + .00317f * zenith + 0.f) * turbidity2 + (-0.04214f * zenith3 + .0897f * zenith2 - .04153f * zenith + .00516f) * turbidity + (.15346f * zenith3 - .26756f * zenith2 + .0667f * zenith + .26688f); return color; } RGBColor getRGBColorFromYxy(YyxColor YyxColor) { double Y = YyxColor.Y; double x = YyxColor.x; double y = YyxColor.y; double X = x / y * Y; double Z = ((1. - x - y) / y) * Y; RGBColor color; color.red = 3.2404f * X - 1.5371f * Y - .4985f * Z; color.green = -.9692f * X + 1.8759f * Y + .0415f * Z; color.blue = .0556f * X - .2040f * Y + 1.0573f * Z; float expo = -(1.f / 15000.f); color.red = fmax(0., fmin(1., 1.f - exp(expo * color.red))); color.green = fmax(0., fmin(1., 1.f - exp(expo * color.green))); color.blue = fmax(0., fmin(1., 1.f - exp(expo * color.blue))); return color; } void getPixels() { struct timeval tv; struct tm *tm; gettimeofday(&tv, NULL); tm = localtime(&tv.tv_sec); int year = tm->tm_year + 1900; int month = tm->tm_mon + 1; int day = tm->tm_mday; int hour = tm->tm_hour; int min = tm->tm_min; int sec = tm->tm_sec; double timezone = (tm->tm_gmtoff / 3600.); double latitude = -33.3142516; double longitude = -71.4143858; double julianDay = getJulianDayNumber(year, month, day, hour, min, sec, timezone); double decimalTime = getDecimalTime(hour, min, sec); double solarTime = getSolarTime(julianDay, decimalTime, timezone, longitude); double solarDeclination = getSolarDeclination(julianDay); double solarAltitude = getSolarAltitude(solarDeclination, solarTime, latitude); double thetaS = (M_PI / 2.) - solarAltitude; double phiS = getSolarAzimuth(solarDeclination, solarTime, latitude); double T = 2.; PerezYxyCoefficients coeffs = getPerezCoefficientsForTurbidity(T); YyxColor sunYyx = getYyxColorForZenithAndTurbidity(thetaS, T); static const int WIDTH = 720; static const int HEIGHT = 180; for(int row = 0.; row < HEIGHT; row ++) { for(int col = 0.; col < WIDTH; col ++) { double zenith = radians((double)row / 2.); double azimuth = radians((double)col / 2.); YyxColor Yyx; double gamma = getPerezGamma(zenith, azimuth, thetaS, phiS); Yyx.Y = sunYyx.Y * getPerezLuminance(zenith, gamma, coeffs.Y) / getPerezLuminance(0, thetaS, coeffs.Y); Yyx.x = sunYyx.x * getPerezLuminance(zenith, gamma, coeffs.x) / getPerezLuminance(0, thetaS, coeffs.x); Yyx.y = sunYyx.y * getPerezLuminance(zenith, gamma, coeffs.y) / getPerezLuminance(0, thetaS, coeffs.y); RGBColor rgb = getRGBColorFromYxy(Yyx); addPixelColor(rgb); } } free(pixels); }

The resulting images are for a turbidity (T) value of 2. I checked the resulting values from the solar functions with an online calculator and mine seem to be fine.

Any help would be greatly appreciated.