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Algorithm to convert RGB to HSV and HSV to RGB in range 0-255 for both

Posted by: admin November 30, 2017 Leave a comment

Questions:

I am looking for color space converter from RGB to HSV, specifically for the range 0 to 255 for both color spaces.

Answers:

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;     
}

Questions:
Answers:

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;
}

Questions:
Answers:

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
    }

Questions:
Answers:

Here’s a C implementation based on Agoston’s Computer Graphics and Geometric Modeling: Implementation and Algorithms p. 304, with H ∈ [0, 360] and S,V ∈ [0, 1].

#include <math.h>

typedef struct {
    double r;       // ∈ [0, 1]
    double g;       // ∈ [0, 1]
    double b;       // ∈ [0, 1]
} rgb;

typedef struct {
    double h;       // ∈ [0, 360]
    double s;       // ∈ [0, 1]
    double v;       // ∈ [0, 1]
} hsv;

rgb hsv2rgb(hsv HSV)
{
    rgb RGB;
    double H = HSV.h, S = HSV.s, V = HSV.v,
            P, Q, T,
            fract;

    (H == 360.)?(H = 0.):(H /= 60.);
    fract = H - floor(H);

    P = V*(1. - S);
    Q = V*(1. - S*fract);
    T = V*(1. - S*(1. - fract));

    if      (0. <= H && H < 1.)
        RGB = (rgb){.r = V, .g = T, .b = P};
    else if (1. <= H && H < 2.)
        RGB = (rgb){.r = Q, .g = V, .b = P};
    else if (2. <= H && H < 3.)
        RGB = (rgb){.r = P, .g = V, .b = T};
    else if (3. <= H && H < 4.)
        RGB = (rgb){.r = P, .g = Q, .b = V};
    else if (4. <= H && H < 5.)
        RGB = (rgb){.r = T, .g = P, .b = V};
    else if (5. <= H && H < 6.)
        RGB = (rgb){.r = V, .g = P, .b = Q};
    else
        RGB = (rgb){.r = 0., .g = 0., .b = 0.};

    return RGB;
}

Questions:
Answers:

this should be on here:
it works anyway. And it looks good compared to the above ones.

        float3 Hue(float H)
        {
            half R = abs(H * 6 - 3) - 1;
            half G = 2 - abs(H * 6 - 2);
            half B = 2 - abs(H * 6 - 4);
            return saturate(half3(R,G,B));
        }

        half4 HSVtoRGB(in half3 HSV)
        {
            return half4(((Hue(HSV.x) - 1) * HSV.y + 1) * HSV.z,1);
        }

float3 is 16 bit precision vector3 data type, i.e. float3 hue() is returns a data type (x,y,z) e.g. (r,g,b), half is same with half precision, 8bit, a float4 is (r,g,b,a) 4 values.

Questions:
Answers:

This isn’t C, but it’s certainly does work. All the other methods I see here work by casing everything into parts of a hexagon, and approximating “angles” from that. By instead starting with a different equation using cosines, and solving for h s and v, you get a lot nicer relationship between hsv and rgb, and tweening becomes smoother (at the cost of it being way slower).

Assume everything is floating point. If r g and b go from 0 to 1, h goes from 0 to 2pi, v goes from 0 to 4/3, and s goes from 0 to 2/3.

The following code is written in Lua. It’s easily translatable into anything else.

local hsv do
    hsv         ={}
    local atan2 =math.atan2
    local cos   =math.cos
    local sin   =math.sin

    function hsv.fromrgb(r,b,g)
        local c=r+g+b
        if c<1e-4 then
            return 0,2/3,0
        else
            local p=2*(b*b+g*g+r*r-g*r-b*g-b*r)^0.5
            local h=atan2(b-g,(2*r-b-g)/3^0.5)
            local s=p/(c+p)
            local v=(c+p)/3
            return h,s,v
        end
    end

    function hsv.torgb(h,s,v)
        local r=v*(1+s*(cos(h)-1))
        local g=v*(1+s*(cos(h-2.09439)-1))
        local b=v*(1+s*(cos(h+2.09439)-1))
        return r,g,b
    end

    function hsv.tween(h0,s0,v0,h1,s1,v1,t)
        local dh=(h1-h0+3.14159)%6.28318-3.14159
        local h=h0+t*dh
        local s=s0+t*(s1-s0)
        local v=v0+t*(v1-v0)
        return h,s,v
    end
end

Questions:
Answers:

@fins’s answer has an overflow issue on Arduio as you turn the saturation down. Here it is with some values converted to int to prevent that.

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, p, q, t;
    unsigned int h, s, v, remainder;

    if (hsv.s == 0)
    {
        rgb.r = hsv.v;
        rgb.g = hsv.v;
        rgb.b = hsv.v;
        return rgb;
    }

    // converting to 16 bit to prevent overflow
    h = hsv.h;
    s = hsv.s;
    v = hsv.v;

    region = h / 43;
    remainder = (h - (region * 43)) * 6; 

    p = (v * (255 - s)) >> 8;
    q = (v * (255 - ((s * remainder) >> 8))) >> 8;
    t = (v * (255 - ((s * (255 - remainder)) >> 8))) >> 8;

    switch (region)
    {
        case 0:
            rgb.r = v;
            rgb.g = t;
            rgb.b = p;
            break;
        case 1:
            rgb.r = q;
            rgb.g = v;
            rgb.b = p;
            break;
        case 2:
            rgb.r = p;
            rgb.g = v;
            rgb.b = t;
            break;
        case 3:
            rgb.r = p;
            rgb.g = q;
            rgb.b = v;
            break;
        case 4:
            rgb.r = t;
            rgb.g = p;
            rgb.b = v;
            break;
        default:
            rgb.r = 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;
}

Questions:
Answers:

GLSL Shader version based on Patapoms answer:

vec3 HSV2RGB( vec3 hsv )
{
    hsv.x = mod( 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
    vec3  TempRGB = vec3(   hsv.z * (1.0 - hsv.y), hsv.z * (1.0 - hsv.y * HueSliceInterpolant), hsv.z * (1.0 - hsv.y * (1.0 - HueSliceInterpolant)) );
    float   IsOddSlice = mod( 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)
    vec3  ScrollingRGBForEvenSlices = vec3( hsv.z, TempRGB.zx );           // (V, Temp Blue, Temp Red) for even slices (0, 2, 4)
    vec3  ScrollingRGBForOddSlices = vec3( TempRGB.y, hsv.z, TempRGB.x );  // (Temp Green, V, Temp Red) for odd slices (1, 3, 5)
    vec3  ScrollingRGB = mix( ScrollingRGBForEvenSlices, ScrollingRGBForOddSlices, IsOddSlice );
    float   IsNotFirstSlice = clamp( ThreeSliceSelector, 0.0,1.0 );                   // 1 if NOT the first slice (true for slices 1 and 2)
    float   IsNotSecondSlice = clamp( ThreeSliceSelector-1.0, 0.0,1. );              // 1 if NOT the first or second slice (true only for slice 2)
    return  mix( ScrollingRGB.xyz, mix( ScrollingRGB.zxy, ScrollingRGB.yzx, IsNotSecondSlice ), IsNotFirstSlice );    // Make the RGB rotate right depending on final slice index
}

Questions:
Answers:

This link has formulas for what you want. Then it’s a matter of performance (numerical techniques) if you want it fast.

Questions:
Answers:

Here’s one which i just wrote this morning based on pretty much the same math as above:

/* math adapted from: http://www.rapidtables.com/convert/color/rgb-to-hsl.htm
 * reasonably optimized for speed, without going crazy */
void rgb_to_hsv (int r, int g, int b, float *r_h, float *r_s, float *r_v) {
  float rp, gp, bp, cmax, cmin, delta, l;
  int cmaxwhich, cminwhich;

  rp = ((float) r) / 255;
  gp = ((float) g) / 255;
  bp = ((float) b) / 255;

  //debug ("rgb=%d,%d,%d rgbprime=%f,%f,%f", r, g, b, rp, gp, bp);

  cmax = rp;
  cmaxwhich = 0; /* faster comparison afterwards */
  if (gp > cmax) { cmax = gp; cmaxwhich = 1; }
  if (bp > cmax) { cmax = bp; cmaxwhich = 2; }
  cmin = rp;
  cminwhich = 0;
  if (gp < cmin) { cmin = gp; cminwhich = 1; }
  if (bp < cmin) { cmin = bp; cminwhich = 2; }

  //debug ("cmin=%f,cmax=%f", cmin, cmax);
  delta = cmax - cmin;

  /* HUE */
  if (delta == 0) {
    *r_h = 0;
  } else {
    switch (cmaxwhich) {
      case 0: /* cmax == rp */
        *r_h = HUE_ANGLE * (fmod ((gp - bp) / delta, 6));
      break;

      case 1: /* cmax == gp */
        *r_h = HUE_ANGLE * (((bp - rp) / delta) + 2);
      break;

      case 2: /* cmax == bp */
        *r_h = HUE_ANGLE * (((rp - gp) / delta) + 4);
      break;
    }
    if (*r_h < 0)
      *r_h += 360;
  }

  /* LIGHTNESS/VALUE */
  //l = (cmax + cmin) / 2;
  *r_v = cmax;

  /* SATURATION */
  /*if (delta == 0) {
    *r_s = 0;
  } else {
    *r_s = delta / (1 - fabs (1 - (2 * (l - 1))));
  }*/
  if (cmax == 0) {
    *r_s = 0;
  } else {
    *r_s = delta / cmax;
  }
  //debug ("rgb=%d,%d,%d ---> hsv=%f,%f,%f", r, g, b, *r_h, *r_s, *r_v);
}


void hsv_to_rgb (float h, float s, float v, int *r_r, int *r_g, int *r_b) {
  if (h > 360)
    h -= 360;
  if (h < 0)
    h += 360;
  h = CLAMP (h, 0, 360);
  s = CLAMP (s, 0, 1);
  v = CLAMP (v, 0, 1);
  float c = v * s;
  float x = c * (1 - fabsf (fmod ((h / HUE_ANGLE), 2) - 1));
  float m = v - c;
  float rp, gp, bp;
  int a = h / 60;

  //debug ("h=%f, a=%d", h, a);

  switch (a) {
    case 0:
      rp = c;
      gp = x;
      bp = 0;
    break;

    case 1:
      rp = x;
      gp = c;
      bp = 0;
    break;

    case 2:
      rp = 0;
      gp = c;
      bp = x;
    break;

    case 3:
      rp = 0;
      gp = x;
      bp = c;
    break;

    case 4:
      rp = x;
      gp = 0;
      bp = c;
    break;

    default: // case 5:
      rp = c;
      gp = 0;
      bp = x;
    break;
  }

  *r_r = (rp + m) * 255;
  *r_g = (gp + m) * 255;
  *r_b = (bp + m) * 255;

  //debug ("hsv=%f,%f,%f, ---> rgb=%d,%d,%d", h, s, v, *r_r, *r_g, *r_b);
}