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

Question

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

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

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

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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    gt  gt  8      q    hsv v    255 -   hsv s   remainder   gt  gt  8     gt  gt  8      t    hsv v    255 -   hsv s    255 - remainder    gt  gt  8     gt  gt  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  lt  rgb g    rgb r  lt  rgb b   rgb r   rgb b     rgb g  lt  rgb b   rgb g   rgb b       rgbMax   rgb r  gt  rgb g    rgb r  gt  rgb b   rgb r   rgb b     rgb g  gt  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

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I m not C   developer so I will not provide code  But I can provide simple hsv2rgb  algorithm  rgb2hsv here  which I currently discover -  I update wiki with description  HSV and HLS  Main improvement is that I carefully observe r g b as hue functions and introduce simpler shape function to describe them  without loosing accuracy   The Algorithm - on input we have  h  0-255   s  0-255   v 0-255   r   255 f 5     g   255 f 3     b   255 f 1    We use function f described as follows  f n    v 255 -  v 255   s 255  max min k 4-k 1  0    where  mod can return fraction part  k is floating point number   k    n h 360  255 60   mod 6    Here are snippets PoV in SO in JS  HSV and HSL

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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  lt math h gt   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   lt   H  amp  amp  H  lt  1           RGB    rgb   r   V   g   T   b   P       else if  1   lt   H  amp  amp  H  lt  2           RGB    rgb   r   Q   g   V   b   P       else if  2   lt   H  amp  amp  H  lt  3           RGB    rgb   r   P   g   V   b   T       else if  3   lt   H  amp  amp  H  lt  4           RGB    rgb   r   P   g   Q   b   V       else if  4   lt   H  amp  amp  H  lt  5           RGB    rgb   r   T   g   P   b   V       else if  5   lt   H  amp  amp  H  lt  6           RGB    rgb   r   V   g   P   b   Q       else         RGB    rgb   r   0    g   0    b   0         return RGB

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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 lt 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

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Here is an online converter with an article after explaining all the algorithms for color conversion   You probably would prefer a ready-made C version but it should not be long to apply and it could help other people trying to do the same in another language or with another color space

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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

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This pair of functions convert HSL to RGB and vice-versa     It s pretty optimized for execution speed  typedef unsigned char       BYTE typedef struct  RGB       BYTE R      BYTE G      BYTE B    RGB   pRGB  typedef struct  HSL       float   H      color Hue  0 0 to 360 0 degrees      float   S      color Saturation  0 0 to 1 0      float   L      Luminance  0 0 to 1 0      float   V      Value  0 0 to 1 0    HSL   pHSL   float    fMin        float  a  float  b        return  a  lt    b   a   b     float    fMax        float  a  float  b        return  a  gt    b  a   b     void    RGBtoHSL     pRGB rgb  pHSL hsl       See https   en wikipedia org wiki HSL and HSV    rgb- gt R  rgb- gt G  rgb- gt B   0 to 255      float r          float  rgb- gt R   255      float g          float  rgb- gt G   255      float b          float  rgb- gt B   255      float  min      fMin fMin  amp r   amp g    amp b       float  max      fMax fMax  amp r   amp g    amp b       float delta      max -  min      L  V  0 0 to 1 0      hsl- gt L     max    min  2      hsl- gt V    max     Special case for H and S     if  delta    0                hsl- gt H   0 0f          hsl- gt S   0 0f            else          Special case for S         if   max    0       min    1               hsl- gt S   0          else    S  0 0 to 1 0              hsl- gt S    2    max - 2 hsl- gt L   1 - fabsf 2 hsl- gt L - 1       H  0 0 to 360 0          if       max     amp r      hsl- gt H   fmod  g - b  delta  6         max is R         else if  max     amp g      hsl- gt H    b - r  delta   2             max is G         else                    hsl- gt H    r - g  delta   4             max is B         hsl- gt H    60           void    HSLtoRGB     pHSL hsl  pRGB rgb       See https   en wikipedia org wiki HSL and HSV     float a  k  fm1  fp1  f1  f2   f3     L  V  S   0 0 to 1 0     rgb- gt R  rgb- gt G  rgb- gt B   0 to 255      fm1   -1      fp1   1      f1   1-hsl- gt L      a   hsl- gt S    fMin  amp hsl- gt L   amp f1       k   fmod 0   hsl- gt H 30  12       f1   k - 3      f2   9 - k      f3   fMin fMin  amp f1   amp f2    amp fp1        rgb- gt R    BYTE   255    hsl- gt L - a    fMax f3   amp fm1          k   fmod 8   hsl- gt H 30  12       f1   k - 3      f2   9 - k      f3   fMin fMin  amp f1   amp f2    amp fp1        rgb- gt G    BYTE   255    hsl- gt L - a    fMax f3   amp fm1          k   fmod 4   hsl- gt H 30  12       f1   k - 3      f2   9 - k      f3   fMin fMin  amp f1   amp f2    amp fp1        rgb- gt B    BYTE   255    hsl- gt L - a    fMax f3   amp fm1

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I created a possibly faster implementation by using 0-1 range for RGBS and V and 0-6 range for Hue  avoiding the division   and grouping the cases into two categories    include  lt math h gt   include  lt float h gt   void fromRGBtoHSV float rgb    float hsv            for int i 0  i lt 3    i            rgb i    max 0 0f  min 1 0f  rgb i           hsv 0    0 0f       hsv 2    max rgb 0   max rgb 1   rgb 2          const float delta   hsv 2  - min rgb 0   min rgb 1   rgb 2           if  delta  lt  FLT MIN           hsv 1    0 0f       else                 hsv 1    delta   hsv 2            if  rgb 0   gt   hsv 2                           hsv 0     rgb 1  - rgb 2     delta               if  hsv 0   lt  0 0f                   hsv 0     6 0f                      else if  rgb 1   gt   hsv 2                hsv 0    2 0f    rgb 2  - rgb 0     delta           else              hsv 0    4 0f    rgb 0  - rgb 1     delta                void fromHSVtoRGB const float hsv    float rgb          if hsv 1   lt  FLT MIN          rgb 0    rgb 1    rgb 2    hsv 2       else               const float h   hsv 0           const int i    int h          const float f   h - i          const float p   hsv 2     1 0f - hsv 1             if  i  amp  1                const float q   hsv 2     1 0f -  hsv 1    f                switch i                case 1                  rgb 0    q                  rgb 1    hsv 2                   rgb 2    p                  break              case 3                  rgb 0    p                  rgb 1    q                  rgb 2    hsv 2                   break              default                  rgb 0    hsv 2                   rgb 1    p                  rgb 2    q                  break                                  else                       const float t   hsv 2     1 0f -  hsv 1     1 0f - f                 switch i                case 0                  rgb 0    hsv 2                   rgb 1    t                  rgb 2    p                  break              case 2                  rgb 0    p                  rgb 1    hsv 2                   rgb 2    t                  break              default                  rgb 0    t                  rgb 1    p                  rgb 2    hsv 2                   break                                    For 0-255 range just   255 0f   0 5f and assign it to an unsigned char  or divide by 255 0 to get the opposite

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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

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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    gt  gt  8      q    v    255 -   s   remainder   gt  gt  8     gt  gt  8      t    v    255 -   s    255 - remainder    gt  gt  8     gt  gt  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  lt  rgb g    rgb r  lt  rgb b   rgb r   rgb b     rgb g  lt  rgb b   rgb g   rgb b       rgbMax   rgb r  gt  rgb g    rgb r  gt  rgb b   rgb r   rgb b     rgb g  gt  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

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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  gt  cmax    cmax   gp  cmaxwhich   1      if  bp  gt  cmax    cmax   bp  cmaxwhich   2      cmin   rp    cminwhich   0    if  gp  lt  cmin    cmin   gp  cminwhich   1      if  bp  lt  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  lt  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 --- gt  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  gt  360      h -  360    if  h  lt  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  --- gt  rgb  d  d  d   h  s  v   r r   r g   r b

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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  lt  in g   in r   in g      min   min   lt  in b   min    in b       max   in r  gt  in g   in r   in g      max   max   gt  in b   max    in b       out v   max                                    v     delta   max - min      if  delta  lt  0 00001                out s   0          out h   0     undefined  maybe nan          return out            if  max  gt  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  gt   max                                 gt  is bogus  just keeps compilor happy         out h     in g - in b     delta            between yellow  amp  magenta     else     if  in g  gt   max           out h   2 0     in b - in r     delta      between cyan  amp  yellow     else         out h   4 0     in r - in g     delta      between magenta  amp  cyan      out h    60 0                                  degrees      if  out h  lt  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  lt   0 0              lt  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  gt   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

[c++] Algorithm to convert RGB to HSV and HSV to RGB in range 0-255 for both

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