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## Preetham sky for 2D - wicked colors. Sample images and video.

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### #1boliva  Members

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Posted 19 July 2014 - 07:05 PM

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);

}
}
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.

### #2Nico Schertler  Members

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Posted 21 July 2014 - 03:48 AM

Hi,

there are two things that attracted my attention (which are different from my code, http://nicoschertler.wordpress.com/2013/04/03/simulating-a-days-sky):

Your Yxy to RGB conversion includes an exponentiation. You should check if this is intended.

In my code I had to scale down sunYyx.Y by the maximum possible luminance. Otherwise the code would have produced out-of-range results. It's the Yz / Y0 part of the code.

Nico

### #3boliva  Members

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Posted 25 July 2014 - 02:38 PM

I finally managed to solve my issue: I had a wrongly signed value in the Perez coefficients and I replaced the atan in getSolarAzimuth with an atan2 to solve the cases where the angle was negative. I also had a problem with the color components ordering in my image algorithm...

The end result is nice but still somewhat not entirely perfect: the sky should be more red than the yellowish that appears at dawn/sunset, the horizon is a bit too red and the top of the sky a little too dark for my taste.

Nico, the Yyx->RGB includes an exposure function to better scale the values. This is similar to what you mentioned with the Yz/Y0 in your code, which in my case resulted in a very 'saturated' sun.

Video here:

Any tips or guidance on make the colors at dawn/dusk more real life like?

[edit: fixed code: http://pastebin.com/zVFJ8uZn]

Edited by boliva, 25 July 2014 - 02:58 PM.

### #4necrowizzard  Members

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Posted 31 July 2014 - 06:08 AM

Thanks for the code. So basically in the Preetham sun position formulas they mixed up longitude and latitude? Are your longitude/latitude coordinates on the southern hemisphere?

edit: also thanks alot fot the atan2 hint ;)

Edited by necrowizzard, 31 July 2014 - 06:12 AM.

### #5boliva  Members

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Posted 31 July 2014 - 04:05 PM

Hi necrowizzard, I don't see where they mixed up the coordinates. Yes, I am in the southern hemisphere, that's why for my simulation the sun is always up north. Glad you could make use of the atan2.

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