Photoshop blends two images together by performing a blend operation on each pixel in image A against its corresponding pixel in image B. Each pixel is a color consisting of multiple channels. Assuming we are working with RGB pixels, the channels in each pixel would be red, green and blue. To blend two pixels we blend their respective channels.
The blend operation that occurs for each blend mode in Photoshop can be summed up in the following macros:
#define ChannelBlend_Normal(A,B) ((uint8)(A))
#define ChannelBlend_Lighten(A,B) ((uint8)((B > A) ? B:A))
#define ChannelBlend_Darken(A,B) ((uint8)((B > A) ? A:B))
#define ChannelBlend_Multiply(A,B) ((uint8)((A * B) / 255))
#define ChannelBlend_Average(A,B) ((uint8)((A + B) / 2))
#define ChannelBlend_Add(A,B) ((uint8)(min(255, (A + B))))
#define ChannelBlend_Subtract(A,B) ((uint8)((A + B < 255) ? 0:(A + B - 255)))
#define ChannelBlend_Difference(A,B) ((uint8)(abs(A - B)))
#define ChannelBlend_Negation(A,B) ((uint8)(255 - abs(255 - A - B)))
#define ChannelBlend_Screen(A,B) ((uint8)(255 - (((255 - A) * (255 - B)) >> 8)))
#define ChannelBlend_Exclusion(A,B) ((uint8)(A + B - 2 * A * B / 255))
#define ChannelBlend_Overlay(A,B) ((uint8)((B < 128) ? (2 * A * B / 255):(255 - 2 * (255 - A) * (255 - B) / 255)))
#define ChannelBlend_SoftLight(A,B) ((uint8)((B < 128)?(2*((A>>1)+64))*((float)B/255):(255-(2*(255-((A>>1)+64))*(float)(255-B)/255))))
#define ChannelBlend_HardLight(A,B) (ChannelBlend_Overlay(B,A))
#define ChannelBlend_ColorDodge(A,B) ((uint8)((B == 255) ? B:min(255, ((A << 8 ) / (255 - B)))))
#define ChannelBlend_ColorBurn(A,B) ((uint8)((B == 0) ? B:max(0, (255 - ((255 - A) << 8 ) / B))))
#define ChannelBlend_LinearDodge(A,B)(ChannelBlend_Add(A,B))
#define ChannelBlend_LinearBurn(A,B) (ChannelBlend_Subtract(A,B))
#define ChannelBlend_LinearLight(A,B)((uint8)(B < 128)?ChannelBlend_LinearBurn(A,(2 * B)):ChannelBlend_LinearDodge(A,(2 * (B - 128))))
#define ChannelBlend_VividLight(A,B) ((uint8)(B < 128)?ChannelBlend_ColorBurn(A,(2 * B)):ChannelBlend_ColorDodge(A,(2 * (B - 128))))
#define ChannelBlend_PinLight(A,B) ((uint8)(B < 128)?ChannelBlend_Darken(A,(2 * B)):ChannelBlend_Lighten(A,(2 * (B - 128))))
#define ChannelBlend_HardMix(A,B) ((uint8)((ChannelBlend_VividLight(A,B) < 128) ? 0:255))
#define ChannelBlend_Reflect(A,B) ((uint8)((B == 255) ? B:min(255, (A * A / (255 - B)))))
#define ChannelBlend_Glow(A,B) (ChannelBlend_Reflect(B,A))
#define ChannelBlend_Phoenix(A,B) ((uint8)(min(A,B) - max(A,B) + 255))
#define ChannelBlend_Alpha(A,B,O) ((uint8)(O * A + (1 - O) * B))
#define ChannelBlend_AlphaF(A,B,F,O) (ChannelBlend_Alpha(F(A,B),A,O))
To blend a single RGB pixel you would do the following:
ImageTColorR = ChannelBlend_Glow(ImageAColorR, ImageBColorR);
ImageTColorB = ChannelBlend_Glow(ImageAColorB, ImageBColorB);
ImageTColorG = ChannelBlend_Glow(ImageAColorG, ImageBColorG);
ImageTColor = RGB(ImageTColorR, ImageTColorB, ImageTColorG);
If we wanted to perform a blend operation with a particular opacity, say 50%:
ImageTColorR = ChannelBlend_AlphaF(ImageAColorR, ImageBColorR, Blend_Subtract, 0.5F);
If you have pointers to the image data for images A, B, and T (our target), we can simplify the blending of all three channels using this macro:
#define ColorBlend_Buffer(T,A,B,M) (T)[0] = ChannelBlend_##M((A)[0], (B)[0]),
(T)[1] = ChannelBlend_##M((A)[1], (B)[1]),
(T)[2] = ChannelBlend_##M((A)[2], (B)[2])
And can derive the following RGB color blend macros:
#define ColorBlend_Normal(T,A,B) (ColorBlend_Buffer(T,A,B,Normal))
#define ColorBlend_Lighten(T,A,B) (ColorBlend_Buffer(T,A,B,Lighten))
#define ColorBlend_Darken(T,A,B) (ColorBlend_Buffer(T,A,B,Darken))
#define ColorBlend_Multiply(T,A,B) (ColorBlend_Buffer(T,A,B,Multiply))
#define ColorBlend_Average(T,A,B) (ColorBlend_Buffer(T,A,B,Average))
#define ColorBlend_Add(T,A,B) (ColorBlend_Buffer(T,A,B,Add))
#define ColorBlend_Subtract(T,A,B) (ColorBlend_Buffer(T,A,B,Subtract))
#define ColorBlend_Difference(T,A,B) (ColorBlend_Buffer(T,A,B,Difference))
#define ColorBlend_Negation(T,A,B) (ColorBlend_Buffer(T,A,B,Negation))
#define ColorBlend_Screen(T,A,B) (ColorBlend_Buffer(T,A,B,Screen))
#define ColorBlend_Exclusion(T,A,B) (ColorBlend_Buffer(T,A,B,Exclusion))
#define ColorBlend_Overlay(T,A,B) (ColorBlend_Buffer(T,A,B,Overlay))
#define ColorBlend_SoftLight(T,A,B) (ColorBlend_Buffer(T,A,B,SoftLight))
#define ColorBlend_HardLight(T,A,B) (ColorBlend_Buffer(T,A,B,HardLight))
#define ColorBlend_ColorDodge(T,A,B) (ColorBlend_Buffer(T,A,B,ColorDodge))
#define ColorBlend_ColorBurn(T,A,B) (ColorBlend_Buffer(T,A,B,ColorBurn))
#define ColorBlend_LinearDodge(T,A,B) (ColorBlend_Buffer(T,A,B,LinearDodge))
#define ColorBlend_LinearBurn(T,A,B) (ColorBlend_Buffer(T,A,B,LinearBurn))
#define ColorBlend_LinearLight(T,A,B) (ColorBlend_Buffer(T,A,B,LinearLight))
#define ColorBlend_VividLight(T,A,B) (ColorBlend_Buffer(T,A,B,VividLight))
#define ColorBlend_PinLight(T,A,B) (ColorBlend_Buffer(T,A,B,PinLight))
#define ColorBlend_HardMix(T,A,B) (ColorBlend_Buffer(T,A,B,HardMix))
#define ColorBlend_Reflect(T,A,B) (ColorBlend_Buffer(T,A,B,Reflect))
#define ColorBlend_Glow(T,A,B) (ColorBlend_Buffer(T,A,B,Glow))
#define ColorBlend_Phoenix(T,A,B) (ColorBlend_Buffer(T,A,B,Phoenix))
And example would be:
ColorBlend_Glow(TargetPtr, ImageAPtr, ImageBPtr);
The remainder of the photoshop blend modes involve converting RGB to HLS and back again.
#define ColorBlend_Hue(T,A,B) ColorBlend_Hls(T,A,B,HueB,LuminationA,SaturationA)
#define ColorBlend_Saturation(T,A,B) ColorBlend_Hls(T,A,B,HueA,LuminationA,SaturationB)
#define ColorBlend_Color(T,A,B) ColorBlend_Hls(T,A,B,HueB,LuminationA,SaturationB)
#define ColorBlend_Luminosity(T,A,B) ColorBlend_Hls(T,A,B,HueA,LuminationB,SaturationA)
#define ColorBlend_Hls(T,A,B,O1,O2,O3) {
float64 HueA, LuminationA, SaturationA;
float64 HueB, LuminationB, SaturationL;
Color_RgbToHls((A)[2],(A)[1],(A)[0], &HueA, &LuminationA, &SaturationA);
Color_RgbToHls((B)[2],(B)[1],(B)[0], &HueB, &LuminationB, &SaturationB);
Color_HlsToRgb(O1,O2,O3,&(T)[2],&(T)[1],&(T)[0]);
}
These functions will be helpful in converting RGB to HLS.
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;
}
There are more resources on this topic, mainly: