Interpolation or other math formula

Question

I have a math problem.

I am dealing with a graphics function that defines a gradient size. However this size is not in pixels but in a value ranging from 0 to 1.

I would like to find a formula to automatically determine the desired value for any size.

But just using my eyes I have discovered that

• if the size is 1000 pixels, the value should be ~0.96.
• if the size is 498 pixels, the value should be ~0.93.
• if the size is 306 pixels, the value should be ~0.9.
• if the size is 239 pixels, the value should be ~0.86.
• if the size is 175 pixels, the value should be ~0.79.
• if the size is 50 pixels, the value should be ~0.25.

Does anybody know a formula to calculate the size of a the value for a given pixel size? Or does anybody with a good mathematical understanding see the underlying formula right away? The values are not perfectly right, I think. I had to use my eyes to determine which value is required to produce the gradient I need:

Answer 1

Try this formula. It's not completely accurate, but I hope it's accurate enough:

FocusScale = 1 - 37.251 / uSize

Answer 2

Private Function pGetFocusScale(ByVal uSize As Double) As Double

    Dim d As Double
    d = 20 / (uSize / 2)

    Return 1 - d

End Function

It is used for

        Dim nPathGradientBrush As New PathGradientBrush(somePath)
        Dim dblFocusX As Double = pGetFocusScale(someRect.Width)
        Dim dblFocusY As Double = pGetFocusScale(someRect.Height)
        nPathGradientBrush.FocusScales = New System.Drawing.PointF(dblFocusX, dblFocusY)

http://msdn.microsoft.com/de-de/library/system.drawing.drawing2d.pathgradientbrush.focusscales%28v=vs.110%29.aspx