GDI alpha如何混合颜色？

Question

I simply need a function which takes two colors and returns the mixed version of them. It should mix them in the same way that GDI does.

I figured that the alpha value you get when mixing two ARGB colors in GDI is calculated like this:

Private Function blend(alphaBelow As Single, alphaAbove As Single) As Single
    Return alphaBelow + (1.0 - alphaBelow) * alphaAbove
End Function

I also found this page where Microsoft says that the R, G and B values are calculated using this formula:

displayColor = sourceColor × alpha / 255 + backgroundColor × (255 – alpha) / 255

however, I can't get that to work:

Color1:          A=164, R=111, G=78, B=129
Color2:          A=241, R=152, G=22, B=48
Blended in GDI:  A=250, R=150, G=24, B=50

R:
150 = 152 * x / 255 + 111 * (255 - x) / 255
x = 9945/41 = 242.5609756097560975609756097561

G:
24 = 22 * x / 255 + 78 * (255 - x) / 255
x = 6885/28 = 245.89285714285714285714285714286

B:
50 = 48 * x / 255 + 129 * (255 - x) / 255
x = 6715/27 = 248.7037037037037037037037037037

As you can see, I get different alpha values for each of the R, G and B values. How is this number calculated?

EDIT:

Color1 and Color2 is just some random ARGB colors I want to mix together. "Blended in GDI" is what you get if you draw them on top of eachother in a bitmap.

The code which mixes the colors with GDI:

    Dim B As New Bitmap(Width, Height, Imaging.PixelFormat.Format32bppPArgb)
    Dim G = Graphics.FromImage(B)
    Dim w = B.Width - 1, h = B.Height - 1

    G.SmoothingMode = Drawing2D.SmoothingMode.AntiAlias

    Dim pth As New Drawing2D.GraphicsPath
    pth.AddRectangle(New Rectangle(0, 0, w, h))

    Dim c1 = RandomColor(), c2 = RandomColor()
    G.FillPath(New SolidBrush(c1), pth)
    G.FillPath(New SolidBrush(c2), pth)

    Dim resoult As Color = B.GetPixel(w / 2, h / 2)

Answer 1

After hours of searching I solved my problem. I'm just gonna post it here in case anypony need it in the future.

Private Function MixColors(c1 As Color, c2 As Color) As Color
    Dim c1a = c1.A / 255, c2a = c2.A / 255, alp = AlphaBlend(c1a, c2a)

    Dim a = alp * 255
    Dim r = ColorBlend(c1.R, c1a, c2.R, c2a, alp)
    Dim g = ColorBlend(c1.G, c1a, c2.G, c2a, alp)
    Dim b = ColorBlend(c1.B, c1a, c2.B, c2a, alp)

    Return Color.FromArgb(CInt(a), CInt(r), CInt(g), CInt(b))
End Function

Private Function ColorBlend(c1r%, c1a#, c2r%, c2a#, alp#) As Single
    Return (c2r * c2a + c1r * c1a * (1 - c2a)) / alp
End Function

Private Function AlphaBlend(alphaBelow!, alphaAbove!) As Double
    Return alphaBelow + (1.0 - alphaBelow) * alphaAbove
End Function

Please note that I developed this function by myself and did not get it from Microsoft or anything, so I cannot prove that it calculates mixing of colors in the same way that GDI does. All tho I have not expirienced that the function missbehaves myself, I cannot guarantee that it will return the excact same resoult as GDI does, but it should be very very close.