blending two color images

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Because Red and Green (and also Blue if you have a third input) are separate color channels, it is not necessary to apply the convex combination constraint.

The convex combination constraint is the rule that says the coefficients for input A (i.e. alpha) and for input B (beta) should add up to 1.0. If we consider the trajectory of the point (alpha, beta) in R2 space, the trajectory will be a straight line connecting (1.0, 0.0) and (0.0, 1.0), which blends the image from "all of A, none of B", to "all of B, none of A".

If this constraint is removed, then you can draw up any smooth curve connecting the two corner points (1.0, 0.0) and (0.0, 1.0), and the result will still be a smooth animated transition between the two images. The only requirement is that the curve cannot go beyond the "unit square", which is the cartesian product of [0.0, 1.0] x [0.0, 1.0].

In fact, the image result "c" is formed from a blending parameter of (1.0, 1.0), meaning that it is the pixelwise sum of A and B. This is perfectly legal, because A only contains non-zero red values and B only contains non-zero green values. Their pixelwise sum does not cause an overflow in pixel value.