HSI to RGB without Math.Cos() - colors

Question

Well the question says it all. I am looking for an algorithm to convert HSI (not HSL and not HSV) to RGB, assuming that all H, S, and I are > 0 and < 1.
I was hoping I could produce something like: http://en.wikipedia.org/wiki/HSL_and_HSV#From_HSV but for HSI w/o using cosine function. I am not quite sure if it is possible. Is there a way to compute C and m (as referred to in Wikipedia article for HSV and HSL) for HSI?
Thanks.
FYI, I am using this function for RGB to HSI (so I am trying to make the inverse):
public static void toHSI(byte R, byte G, byte B, out double H, out double S, out double I)
{
byte MAX, MIN;
if (R > G) { if (R > B) { MAX = R; MIN = (G < B ? G : B); } else { MAX = B; MIN = (G < R ? G : R); } }
else { if (G > B) { MAX = G; MIN = (R < B ? R : B); } else { MAX = B; MIN = (G < R ? G : R); } }
I = (double)(R + G + B) / 765;
if (I == 0) { H = S = 0; } // achromatic
else
{
double DIF = (double)(MAX - MIN);
S = 1 - (double)MIN / (255 * I);
if (MAX == R) { H = (double)(G - B) / DIF + (G < B ? 6 : 0); }
else if (MAX == G) { H = (double)(B - R) / DIF + 2; }
else { H = (double)(R - G) / DIF + 4; }
H /= 6;
}
}

Answer 1

You could try this I am not sure if it is helpful but you need to treat your values in the functions as floats. Hue is a number between 0-360. Saturation is 0.00 -1.00 and anything in between. Intensity aka Value is also used and is also a value of 0.00 -1.00 and anything in between. The result of the function are three values of an array which can then be used for rgb colorspace of values 0-255.
///I use this
// the function result will be the values of the array rgb[3] and will be the rgb values 0-255
///float H is values 0-360 because there are 360 degrees of color in hsi colorspace
///float S is 0.00 - 1.00 and aything in between
///float I is 0.00 - 1.00 and aything in between
///The input to our function is going to be hsi_to_rgb (Hue, Saturation, Intensity(brightness))
int rgb[3]; ///number of channels rgb = 3
void hsi_to_rgb(float H, float S, float I) {
int r, g, b;
if (H > 360) {
H = H - 360;
}
H = fmod(H, 360); // cycle H around to 0-360 degrees
H = 3.14159 * H / (float)180; // Convert to radians.
S = S > 0 ? (S < 1 ? S : 1) : 0; // clamp S and I to interval [0,1]
I = I > 0 ? (I < 1 ? I : 1) : 0;
if (H < 2.09439) {
r = 255 * I / 3 * (1 + S * cos(H) / cos(1.047196667 - H));
g = 255 * I / 3 * (1 + S * (1 - cos(H) / cos(1.047196667 - H)));
b = 255 * I / 3 * (1 - S);
} else if (H < 4.188787) {
H = H - 2.09439;
g = 255 * I / 3 * (1 + S * cos(H) / cos(1.047196667 - H));
b = 255 * I / 3 * (1 + S * (1 - cos(H) / cos(1.047196667 - H)));
r = 255 * I / 3 * (1 - S);
} else {
H = H - 4.188787;
b = 255 * I / 3 * (1 + S * cos(H) / cos(1.047196667 - H));
r = 255 * I / 3 * (1 + S * (1 - cos(H) / cos(1.047196667 - H)));
g = 255 * I / 3 * (1 - S);
}
//set the output to the array
rgb[0] = r;
rgb[1] = g;
rgb[2] = b;
}