透明颜色混合算法

一般数学计算中，颜色取值是：$R,G,B \in \left [ 0, 255 \right ], A\in \left [ 0, 1 \right ]$
所以对于一般的颜色混合有：$Color(RGBA) = Color(R_{1}G_{1}B_{1}A_{1}) + Color(R_{2}G_{2}B_{2}A_{2})$

标准的颜色混合算法如下：
$A = 1 - \left ( 1-\alpha _{1} \right )*\left ( 1-\alpha _{2} \right)$
$R = \frac{1}{A}(\alpha _{1}R_{1}+ (1 - \alpha _{1})\alpha _{2}R_{2})$
$G = \frac{1}{A}(\alpha _{1}G_{1}+ (1 - \alpha _{1})\alpha _{2}G_{2})$
$B = \frac{1}{A}(\alpha _{1}B_{1}+ (1 - \alpha _{1})\alpha _{2}B_{2})$

但是在计算机图像中，透明度alpha通常也是$A \in \left [ 0, 255 \right ]$
所以，根据变化得到的代码是：

//浮点数版
float a1 = A1 / 256.0;
float a2 = A2 / 256.0;
float a = 1 - (1 - a1)*(1 - a2);

R = (a1*R1 + (1 - a1)*a2*R2) / a;
G = (a1*G1 + (1 - a1)*a2*G2) / a;
B = (a1*B1 + (1 - a1)*a2*B2) / a;
A = a * 256;

但是浮点数运算终究不快，经过优化后有如下算法

uint32_t a1 = A1;
uint32_t a2 = A2 - ((a1*A2) >> 8);

A = clamp(a1 + a2, 1, 255);
R = (a1*R1 + a2*R2) / A;
G = (a1*G1 + a2*G2) / A;
B = (a1*B1 + a2*B2) / A;