This approach reminds me of how images calculate their pixel values after a transformation. A pixel in the post-transformation image does not always correspond to a whole pixel in the pre-transformation image perfectly. In other words, the pixel at (10, 10) may correspond to the coordinate at (9.4, 11.7). So in order to calculate the correct pixel value (i.e. RGB) post-transformation, we can use a similar approach to interpolate its color, where basically each of the four pixels surrounding the pre-transformation coordinate contribute proportionally to the final composite color. In the (9.4, 11.7) -> (10, 10) example, the pixel color at (9, 11) will contribute (1 - 0.4) * (1 - 0.7) of the final color. Similarly, the one at (10, 11) will contribute 0.4 * (1 - 0.7).
brandonlouie
One way that helps me understand the quantities alpha, beta, and gamma is thinking of them as the influence or "pull" their respective vertices have on a point. In other words, alpha describes how much the vertex A pulls a point away from BC, beta describes how much the vertex B pulls a point away from AC, and gamma describes how much the vertex C pulls a point away from AB. We can think of alpha = 1 as vertex A pulling the point the hardest (beta and gamma would be 0), thus by intuition this would result in the point being at vertex A
This approach reminds me of how images calculate their pixel values after a transformation. A pixel in the post-transformation image does not always correspond to a whole pixel in the pre-transformation image perfectly. In other words, the pixel at (10, 10) may correspond to the coordinate at (9.4, 11.7). So in order to calculate the correct pixel value (i.e. RGB) post-transformation, we can use a similar approach to interpolate its color, where basically each of the four pixels surrounding the pre-transformation coordinate contribute proportionally to the final composite color. In the (9.4, 11.7) -> (10, 10) example, the pixel color at (9, 11) will contribute (1 - 0.4) * (1 - 0.7) of the final color. Similarly, the one at (10, 11) will contribute 0.4 * (1 - 0.7).
One way that helps me understand the quantities alpha, beta, and gamma is thinking of them as the influence or "pull" their respective vertices have on a point. In other words, alpha describes how much the vertex A pulls a point away from BC, beta describes how much the vertex B pulls a point away from AC, and gamma describes how much the vertex C pulls a point away from AB. We can think of alpha = 1 as vertex A pulling the point the hardest (beta and gamma would be 0), thus by intuition this would result in the point being at vertex A