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For my own purposes I have been trying to write a program that draws a radial gradient. In computer graphics, a radial gradient blends a colour from the edge of a circle to a focus point within. When the focus is at the centre of the circle, it is simple enough to treat the gradient as a right circular cone with a height of 1.0. Given a pixel at position x and y, z will represent the ratio with which to interpolate between colours. The equation I used is:
A gradient with a non-centred focus is an oblique cone, but I am having a difficult time finding the equation used to represent an oblique cone. The extent of my math education is single variable calculus about a dozen years ago, so I am not up to the task of trying to derive the equation myself. Does such an equation exist? Or is an oblique cone simply a right cone whose base is an inclined section? Any help would be appreciated.
Thank you.