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Expanding a convex hull

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I have a list of points that describe the convex hull of an image. I can't use internal graphics scaling because I'm already using it for zoom in and out generally. The image is centered in a square so I know the center point of the hull (middle of the square), call it O. What I need for each point P in the hull is the X and Y coordinates of a point Pa along the line OP such that the distance OPa is Z more than the distance OP. I can conceive that I may need to take into account special cases where there is no change of X or Y from O to some point P, though it should never be possible that both are the same (that'd be a picture of one dot, which would be... weird).

Example: O is 25,25, P is 12,13, Z is 5. The distance OP is 17.69. I need a point along the line OP that is 22.69 away from O, and in the same direction.

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