Algorithm to convert RGB to HSV and HSV to RGB in range 0-255 for both
I've used these for a long time - no idea where they came from at this point... Note that the inputs and outputs, except for the angle in degrees, are in the range of 0 to 1.0.
NOTE: this code does no real sanity checking on inputs. Proceed with caution!
typedef struct {
double r; // a fraction between 0 and 1
double g; // a fraction between 0 and 1
double b; // a fraction between 0 and 1
} rgb;
typedef struct {
double h; // angle in degrees
double s; // a fraction between 0 and 1
double v; // a fraction between 0 and 1
} hsv;
static hsv rgb2hsv(rgb in);
static rgb hsv2rgb(hsv in);
hsv rgb2hsv(rgb in)
{
hsv out;
double min, max, delta;
min = in.r < in.g ? in.r : in.g;
min = min < in.b ? min : in.b;
max = in.r > in.g ? in.r : in.g;
max = max > in.b ? max : in.b;
out.v = max; // v
delta = max - min;
if (delta < 0.00001)
{
out.s = 0;
out.h = 0; // undefined, maybe nan?
return out;
}
if( max > 0.0 ) { // NOTE: if Max is == 0, this divide would cause a crash
out.s = (delta / max); // s
} else {
// if max is 0, then r = g = b = 0
// s = 0, h is undefined
out.s = 0.0;
out.h = NAN; // its now undefined
return out;
}
if( in.r >= max ) // > is bogus, just keeps compilor happy
out.h = ( in.g - in.b ) / delta; // between yellow & magenta
else
if( in.g >= max )
out.h = 2.0 + ( in.b - in.r ) / delta; // between cyan & yellow
else
out.h = 4.0 + ( in.r - in.g ) / delta; // between magenta & cyan
out.h *= 60.0; // degrees
if( out.h < 0.0 )
out.h += 360.0;
return out;
}
rgb hsv2rgb(hsv in)
{
double hh, p, q, t, ff;
long i;
rgb out;
if(in.s <= 0.0) { // < is bogus, just shuts up warnings
out.r = in.v;
out.g = in.v;
out.b = in.v;
return out;
}
hh = in.h;
if(hh >= 360.0) hh = 0.0;
hh /= 60.0;
i = (long)hh;
ff = hh - i;
p = in.v * (1.0 - in.s);
q = in.v * (1.0 - (in.s * ff));
t = in.v * (1.0 - (in.s * (1.0 - ff)));
switch(i) {
case 0:
out.r = in.v;
out.g = t;
out.b = p;
break;
case 1:
out.r = q;
out.g = in.v;
out.b = p;
break;
case 2:
out.r = p;
out.g = in.v;
out.b = t;
break;
case 3:
out.r = p;
out.g = q;
out.b = in.v;
break;
case 4:
out.r = t;
out.g = p;
out.b = in.v;
break;
case 5:
default:
out.r = in.v;
out.g = p;
out.b = q;
break;
}
return out;
}
I wrote this in HLSL for our rendering engine, it has no conditions in it:
float3 HSV2RGB( float3 _HSV )
{
_HSV.x = fmod( 100.0 + _HSV.x, 1.0 ); // Ensure [0,1[
float HueSlice = 6.0 * _HSV.x; // In [0,6[
float HueSliceInteger = floor( HueSlice );
float HueSliceInterpolant = HueSlice - HueSliceInteger; // In [0,1[ for each hue slice
float3 TempRGB = float3( _HSV.z * (1.0 - _HSV.y),
_HSV.z * (1.0 - _HSV.y * HueSliceInterpolant),
_HSV.z * (1.0 - _HSV.y * (1.0 - HueSliceInterpolant)) );
// The idea here to avoid conditions is to notice that the conversion code can be rewritten:
// if ( var_i == 0 ) { R = V ; G = TempRGB.z ; B = TempRGB.x }
// else if ( var_i == 2 ) { R = TempRGB.x ; G = V ; B = TempRGB.z }
// else if ( var_i == 4 ) { R = TempRGB.z ; G = TempRGB.x ; B = V }
//
// else if ( var_i == 1 ) { R = TempRGB.y ; G = V ; B = TempRGB.x }
// else if ( var_i == 3 ) { R = TempRGB.x ; G = TempRGB.y ; B = V }
// else if ( var_i == 5 ) { R = V ; G = TempRGB.x ; B = TempRGB.y }
//
// This shows several things:
// . A separation between even and odd slices
// . If slices (0,2,4) and (1,3,5) can be rewritten as basically being slices (0,1,2) then
// the operation simply amounts to performing a "rotate right" on the RGB components
// . The base value to rotate is either (V, B, R) for even slices or (G, V, R) for odd slices
//
float IsOddSlice = fmod( HueSliceInteger, 2.0 ); // 0 if even (slices 0, 2, 4), 1 if odd (slices 1, 3, 5)
float ThreeSliceSelector = 0.5 * (HueSliceInteger - IsOddSlice); // (0, 1, 2) corresponding to slices (0, 2, 4) and (1, 3, 5)
float3 ScrollingRGBForEvenSlices = float3( _HSV.z, TempRGB.zx ); // (V, Temp Blue, Temp Red) for even slices (0, 2, 4)
float3 ScrollingRGBForOddSlices = float3( TempRGB.y, _HSV.z, TempRGB.x ); // (Temp Green, V, Temp Red) for odd slices (1, 3, 5)
float3 ScrollingRGB = lerp( ScrollingRGBForEvenSlices, ScrollingRGBForOddSlices, IsOddSlice );
float IsNotFirstSlice = saturate( ThreeSliceSelector ); // 1 if NOT the first slice (true for slices 1 and 2)
float IsNotSecondSlice = saturate( ThreeSliceSelector-1.0 ); // 1 if NOT the first or second slice (true only for slice 2)
return lerp( ScrollingRGB.xyz, lerp( ScrollingRGB.zxy, ScrollingRGB.yzx, IsNotSecondSlice ), IsNotFirstSlice ); // Make the RGB rotate right depending on final slice index
}
You can also try this code without floats (faster but less accurate):
typedef struct RgbColor
{
unsigned char r;
unsigned char g;
unsigned char b;
} RgbColor;
typedef struct HsvColor
{
unsigned char h;
unsigned char s;
unsigned char v;
} HsvColor;
RgbColor HsvToRgb(HsvColor hsv)
{
RgbColor rgb;
unsigned char region, remainder, p, q, t;
if (hsv.s == 0)
{
rgb.r = hsv.v;
rgb.g = hsv.v;
rgb.b = hsv.v;
return rgb;
}
region = hsv.h / 43;
remainder = (hsv.h - (region * 43)) * 6;
p = (hsv.v * (255 - hsv.s)) >> 8;
q = (hsv.v * (255 - ((hsv.s * remainder) >> 8))) >> 8;
t = (hsv.v * (255 - ((hsv.s * (255 - remainder)) >> 8))) >> 8;
switch (region)
{
case 0:
rgb.r = hsv.v; rgb.g = t; rgb.b = p;
break;
case 1:
rgb.r = q; rgb.g = hsv.v; rgb.b = p;
break;
case 2:
rgb.r = p; rgb.g = hsv.v; rgb.b = t;
break;
case 3:
rgb.r = p; rgb.g = q; rgb.b = hsv.v;
break;
case 4:
rgb.r = t; rgb.g = p; rgb.b = hsv.v;
break;
default:
rgb.r = hsv.v; rgb.g = p; rgb.b = q;
break;
}
return rgb;
}
HsvColor RgbToHsv(RgbColor rgb)
{
HsvColor hsv;
unsigned char rgbMin, rgbMax;
rgbMin = rgb.r < rgb.g ? (rgb.r < rgb.b ? rgb.r : rgb.b) : (rgb.g < rgb.b ? rgb.g : rgb.b);
rgbMax = rgb.r > rgb.g ? (rgb.r > rgb.b ? rgb.r : rgb.b) : (rgb.g > rgb.b ? rgb.g : rgb.b);
hsv.v = rgbMax;
if (hsv.v == 0)
{
hsv.h = 0;
hsv.s = 0;
return hsv;
}
hsv.s = 255 * long(rgbMax - rgbMin) / hsv.v;
if (hsv.s == 0)
{
hsv.h = 0;
return hsv;
}
if (rgbMax == rgb.r)
hsv.h = 0 + 43 * (rgb.g - rgb.b) / (rgbMax - rgbMin);
else if (rgbMax == rgb.g)
hsv.h = 85 + 43 * (rgb.b - rgb.r) / (rgbMax - rgbMin);
else
hsv.h = 171 + 43 * (rgb.r - rgb.g) / (rgbMax - rgbMin);
return hsv;
}
Note that this algorithm uses 0-255 as it's range (not 0-360) as that was requested by the author of this question.