[zt]Photoshop Blend Mode Math

from http://www.nathanm.com/photoshop-blending-math/

Been working on programmatically blending bitmaps. Below are the macros that I’ve come up, borrowing the some of the formulas from other websites (see sources at the bottom of this post).

Channel blending

#define ChannelBlend_Normal(B,L)     ((uint8)(B))
#define ChannelBlend_Lighten(B,L)    ((uint8)((L > B) ? L:B))
#define ChannelBlend_Darken(B,L)     ((uint8)((L > B) ? B:L))
#define ChannelBlend_Multiply(B,L)   ((uint8)((B * L) / 255))
#define ChannelBlend_Average(B,L)    ((uint8)((B + L) / 2))
#define ChannelBlend_Add(B,L)        ((uint8)(min(255, (B + L))))
#define ChannelBlend_Subtract(B,L)   ((uint8)((B + L < 255) ? 0:(B + L - 255)))
#define ChannelBlend_Difference(B,L) ((uint8)(abs(B - L)))
#define ChannelBlend_Negation(B,L)   ((uint8)(255 - abs(255 - B - L)))
#define ChannelBlend_Screen(B,L)     ((uint8)(255 - (((255 - B) * (255 - L)) >> 8)))
#define ChannelBlend_Exclusion(B,L)  ((uint8)(B + L - 2 * B * L / 255))
#define ChannelBlend_Overlay(B,L)    ((uint8)((L < 128) ? (2 * B * L / 255):(255 - 2 * (255 - B) * (255 - L) / 255)))
#define
 ChannelBlend_SoftLight(B,L)  ((uint8)((L < 
128)?(2*((B>>1)+64))*((float)L/255):(255-(2*(255-((B>>1)+64))*(float)(255-L)/255))))
#define ChannelBlend_HardLight(B,L)  (ChannelBlend_Overlay(L,B))
#define ChannelBlend_ColorDodge(B,L) ((uint8)((L == 255) ? L:min(255, ((B << 8 ) / (255 - L)))))
#define ChannelBlend_ColorBurn(B,L)  ((uint8)((L == 0) ? L:max(0, (255 - ((255 - B) << 8 ) / L))))
#define ChannelBlend_LinearDodge(B,L)(ChannelBlend_Add(B,L))
#define ChannelBlend_LinearBurn(B,L) (ChannelBlend_Subtract(B,L))
#define
 ChannelBlend_LinearLight(B,L)((uint8)(L < 
128)?ChannelBlend_LinearBurn(B,(2 * L)):ChannelBlend_LinearDodge(B,(2 * 
(L - 128))))
#define
 ChannelBlend_VividLight(B,L) ((uint8)(L < 
128)?ChannelBlend_ColorBurn(B,(2 * L)):ChannelBlend_ColorDodge(B,(2 * (L
 - 128))))
#define
 ChannelBlend_PinLight(B,L)   ((uint8)(L < 
128)?ChannelBlend_Darken(B,(2 * L)):ChannelBlend_Lighten(B,(2 * (L - 
128))))
#define ChannelBlend_HardMix(B,L)    ((uint8)((ChannelBlend_VividLight(B,L) < 128) ? 0:255))
#define ChannelBlend_Reflect(B,L)    ((uint8)((L == 255) ? L:min(255, (B * B / (255 - L)))))
#define ChannelBlend_Glow(B,L)       (ChannelBlend_Reflect(L,B))
#define ChannelBlend_Phoenix(B,L)    ((uint8)(min(B,L) - max(B,L) + 255))
#define ChannelBlend_Alpha(B,L,O)    ((uint8)(O * B + (1 - O) * L))
#define ChannelBlend_AlphaF(B,L,F,O) (ChannelBlend_Alpha(F(B,L),B,O))

B is the base channel and L is the blend channel. For example you to blend using Glow you simply call:

Target[i] = ChannelBlend_Glow(Base[i], Blend[i]);

The great thing about these macros is that you can apply the blending effect simply by passing in the channel value, without regard to which channel is red, green, or blue.

To use the blending along with opacity you can use the following.

Target[i] = ChannelBlend_AlphaF(Base[i], Blend[i], Blend_Subtract, 0.5F)

Color blending

To add certain blend modes that utilize hue, luminosity, and saturation we have to construct a per-color interface instead of per-channel interface. For these macros we assume that A and B are buffer pointers and they point to bytes with channels red, green, and blue in that order.

#define ColorBlend_Buffer(T,B,L,M)      (T)[0] = ChannelBlend_##M((B)[0], (L)[0]), \
                                        (T)[1] = ChannelBlend_##M((B)[1], (L)[1]), \
                                        (T)[2] = ChannelBlend_##M((B)[2], (L)[2])
#define ColorBlend_Normal(T,B,L)        (ColorBlend_Buffer(T,B,L,Normal))
#define ColorBlend_Lighten(T,B,L)       (ColorBlend_Buffer(T,B,L,Lighten))
#define ColorBlend_Darken(T,B,L)        (ColorBlend_Buffer(T,B,L,Darken))
#define ColorBlend_Multiply(T,B,L)      (ColorBlend_Buffer(T,B,L,Multiply))
#define ColorBlend_Average(T,B,L)       (ColorBlend_Buffer(T,B,L,Average))
#define ColorBlend_Add(T,B,L)           (ColorBlend_Buffer(T,B,L,Add))
#define ColorBlend_Subtract(T,B,L)      (ColorBlend_Buffer(T,B,L,Subtract))
#define ColorBlend_Difference(T,B,L)    (ColorBlend_Buffer(T,B,L,Difference))
#define ColorBlend_Negation(T,B,L)      (ColorBlend_Buffer(T,B,L,Negation))
#define ColorBlend_Screen(T,B,L)        (ColorBlend_Buffer(T,B,L,Screen))
#define ColorBlend_Exclusion(T,B,L)     (ColorBlend_Buffer(T,B,L,Exclusion))
#define ColorBlend_Overlay(T,B,L)       (ColorBlend_Buffer(T,B,L,Overlay))
#define ColorBlend_SoftLight(T,B,L)     (ColorBlend_Buffer(T,B,L,SoftLight))
#define ColorBlend_HardLight(T,B,L)     (ColorBlend_Buffer(T,B,L,HardLight))
#define ColorBlend_ColorDodge(T,B,L)    (ColorBlend_Buffer(T,B,L,ColorDodge))
#define ColorBlend_ColorBurn(T,B,L)     (ColorBlend_Buffer(T,B,L,ColorBurn))
#define ColorBlend_LinearDodge(T,B,L)   (ColorBlend_Buffer(T,B,L,LinearDodge))
#define ColorBlend_LinearBurn(T,B,L)    (ColorBlend_Buffer(T,B,L,LinearBurn))
#define ColorBlend_LinearLight(T,B,L)   (ColorBlend_Buffer(T,B,L,LinearLight))
#define ColorBlend_VividLight(T,B,L)    (ColorBlend_Buffer(T,B,L,VividLight))
#define ColorBlend_PinLight(T,B,L)      (ColorBlend_Buffer(T,B,L,PinLight))
#define ColorBlend_HardMix(T,B,L)       (ColorBlend_Buffer(T,B,L,HardMix))
#define ColorBlend_Reflect(T,B,L)       (ColorBlend_Buffer(T,B,L,Reflect))
#define ColorBlend_Glow(T,B,L)          (ColorBlend_Buffer(T,B,L,Glow))
#define ColorBlend_Phoenix(T,B,L)       (ColorBlend_Buffer(T,B,L,Phoenix))
#define ColorBlend_Hue(T,B,L)            ColorBlend_Hls(T,B,L,HueL,LuminationB,SaturationB)
#define ColorBlend_Saturation(T,B,L)     ColorBlend_Hls(T,B,L,HueB,LuminationB,SaturationL)
#define ColorBlend_Color(T,B,L)          ColorBlend_Hls(T,B,L,HueL,LuminationB,SaturationL)
#define ColorBlend_Luminosity(T,B,L)     ColorBlend_Hls(T,B,L,HueB,LuminationL,SaturationB)
 
#define ColorBlend_Hls(T,B,L,O1,O2,O3) {                                        \
    float64 HueB, LuminationB, SaturationB;                                     \
    float64 HueL, LuminationL, SaturationL;                                     \
    Color_RgbToHls((B)[2],(B)[1],(B)[0], &HueB, &LuminationB, &SaturationB);    \
    Color_RgbToHls((L)[2],(L)[1],(L)[0], &HueL, &LuminationL, &SaturationL);    \
    Color_HlsToRgb(O1,O2,O3,&(T)[2],&(T)[1],&(T)[0]);                           \
    }
 
int32 Color_HueToRgb(float64 M1, float64 M2, float64 Hue, float64 *Channel)
{
    if (Hue < 0.0)
        Hue += 1.0;
    else if (Hue > 1.0)
        Hue -= 1.0;
 
    if ((6.0 * Hue) < 1.0)
        *Channel = (M1 + (M2 - M1) * Hue * 6.0);
    else if ((2.0 * Hue) < 1.0)
        *Channel = (M2);
    else if ((3.0 * Hue) < 2.0)
        *Channel = (M1 + (M2 - M1) * ((2.0F / 3.0F) - Hue) * 6.0);
    else
        *Channel = (M1);
 
    return TRUE;
}
 
int32 Color_RgbToHls(uint8 Red, uint8 Green, uint8 Blue, float64 *Hue, float64 *Lumination, float64 *Saturation)
{
    float64 Delta;
    float64 Max, Min;
    float64 Redf, Greenf, Bluef;
 
    Redf    = ((float64)Red   / 255.0F);
    Greenf  = ((float64)Green / 255.0F);
    Bluef   = ((float64)Blue  / 255.0F); 
 
    Max     = max(max(Redf, Greenf), Bluef);
    Min     = min(min(Redf, Greenf), Bluef);
 
    *Hue        = 0;
    *Lumination = (Max + Min) / 2.0F;
    *Saturation = 0;
 
    if (Max == Min)
        return TRUE;
 
    Delta = (Max - Min);
 
    if (*Lumination < 0.5)
        *Saturation = Delta / (Max + Min);
    else
        *Saturation = Delta / (2.0 - Max - Min);
 
    if (Redf == Max)
        *Hue = (Greenf - Bluef) / Delta;
    else if (Greenf == Max)
        *Hue = 2.0 + (Bluef - Redf) / Delta;
    else
        *Hue = 4.0 + (Redf - Greenf) / Delta;
 
    *Hue /= 6.0; 
 
    if (*Hue < 0.0)
        *Hue += 1.0;       
 
    return TRUE;
}
 
int32 Color_HlsToRgb(float64 Hue, float64 Lumination, float64 Saturation, uint8 *Red, uint8 *Green, uint8 *Blue)
{
    float64 M1, M2;
    float64 Redf, Greenf, Bluef;
 
    if (Saturation == 0)
        {
        Redf    = Lumination;
        Greenf  = Lumination;
        Bluef   = Lumination;
        }
    else
        {
        if (Lumination <= 0.5)
            M2 = Lumination * (1.0 + Saturation);
        else
            M2 = Lumination + Saturation - Lumination * Saturation;
 
        M1 = (2.0 * Lumination - M2);
 
        Color_HueToRgb(M1, M2, Hue + (1.0F / 3.0F), &Redf);
        Color_HueToRgb(M1, M2, Hue, &Greenf);
        Color_HueToRgb(M1, M2, Hue - (1.0F / 3.0F), &Bluef);
        }
 
    *Red    = (uint8)(Redf * 255);
    *Blue   = (uint8)(Bluef * 255);
    *Green  = (uint8)(Greenf * 255);
 
    return TRUE;
}

So now we can use the hue, saturation, color, and luminosity blend modes along with the rest of the blend modes. To use the ColorBlend macros we just position our bitmap’s pointers to the next RGB iteration and call,

ColorBlend_Glow(Target + iTarget, Base + iBase, Blend + iBlend);

Color macros

Here are some color macros for combining and extracting channels colors out of an integer. One macro that I find a lot of use for is HexToRgb. With it I can copy and paste a hex color value out of the Photoshop color dialog and use the macro to do all the conversion for me to an rgb value.

#define COLOR_OPAQUE                (0)
#define COLOR_TRANSPARENT           (127)
 
#define RGB_SIZE                    (3)
#define RGB_BPP                     (24)
#define RGB_MAXRED                  (255)
#define RGB_MAXGREEN                (255)
#define RGB_MAXBLUE                 (255)
 
#define ARGB_SIZE                   (4)
#define ARGB_BPP                    (32)
#define ARGB_MAXALPHA               (127)
#define ARGB_MAXRED                 (RGB_MAXRED)
#define ARGB_MAXGREEN               (RGB_MAXGREEN)
#define ARGB_MAXBLUE                (RGB_MAXBLUE)
 
/*********************************************************************/
 
#define Color_GetChannel(c,shift)   ((uint8)((c) >> (shift)))
#define
 Color_Reverse(c,bpp)        ((((uint8)(c) << 24) | ((uint8)((c) 
>> 8 ) << 16) | ((uint8)((c) >> 16) << 8 ) | \
                                    ((uint8)((c) >> 24))) >> (32 - (bpp)))
 
#define Rgb_ByteWidth(width)        ((width) * RGB_SIZE)
#define Rgb_PixelWidth(width)       ((width) / RGB_SIZE)
 
#define Rgb_GetRed(rgb)             (Color_GetChannel(rgb, 0))
#define Rgb_GetGreen(rgb)           (Color_GetChannel(rgb, 8))
#define Rgb_GetBlue(rgb)            (Color_GetChannel(rgb, 16))
 
#define Rgba_GetRed(rgba)           (Color_GetChannel(rgba, 24))
#define Rgba_GetGreen(rgba)         (Color_GetChannel(rgba, 16))
#define Rgba_GetBlue(rgba)          (Color_GetChannel(rgba, 8))
#define Rgba_GetAlpha(rgba)         (Color_GetChannel(rgba, 0))
 
#define Argb_GetAlpha(argb)         (Color_GetChannel(argb, 24))
#define Argb_GetRed(argb)           (Color_GetChannel(argb, 16))
#define Argb_GetGreen(argb)         (Color_GetChannel(argb, 8))
#define Argb_GetBlue(argb)          (Color_GetChannel(argb, 0))
 
#define MakeRgb(r,g,b)              (((uint32)(uint8)(b) << 16) | ((uint16)(uint8)(g) << 8 ) | (uint8)(r))
#define
 MakeRgba(r,g,b,a)           (((uint32)(uint8)(r) << 24) | 
((uint16)(uint8)(g) << 16) | ((uint16)(uint8)(b) << 8 ) | 
(uint8)(a))
#define
 MakeArgb(a,r,g,b)           (((uint32)(uint8)(a) << 24) | 
((uint32)(uint8)(r) << 16) | ((uint16)(uint8)(g) << 8 ) | 
(uint8)(b))
 
#define
 HexToRgb(hex)               (MakeRgb(((hex & 0xFF0000) >> 
16), ((hex & 0x00FF00) >> 8 ), (hex & 0xFF)))

Image blending

To show you what each effect does I’ve blended the following two photos.

Base Layer
Source

Blend Layer
Source

And the results..

Blend_Lighten	Blend_Darken	Blend_Multiply
Blend_Average	Blend_Add	Blend_Subtract
Blend_Difference	Blend_Negation	Blend_Screen
Blend_Exclusion	Blend_Overlay	Blend_SoftLight
Blend_HardLight	Blend_ColorDodge	Blend_ColorBurn
Blend_LinearDodge	Blend_LinearBurn	Blend_LinearLight
Blend_VividLight	Blend_PinLight	Blend_HardMix
Blend_Reflect	Blend_Glow	Blend_Phoenix
Blend_Hue	Blend_Saturation	Blend_Color
Blend_Luminosity

And the gradients..

Base Layer

Blend Layer

And the results..

Blend_Lighten	Blend_Darken	Blend_Multiply
Blend_Average	Blend_Add	Blend_Subtract
Blend_Difference	Blend_Negation	Blend_Screen
Blend_Exclusion	Blend_Overlay	Blend_SoftLight
Blend_HardLight	Blend_ColorDodge	Blend_ColorBurn
Blend_LinearDodge	Blend_LinearBurn	Blend_LinearLight
Blend_VividLight	Blend_PinLight	Blend_HardMix
Blend_Reflect	Blend_Glow	Blend_Phoenix
Blend_Hue	Blend_Saturation	Blend_Color
Blend_Luminosity