Lecture 5: Texture Mapping (23)

So far we have seen two geometric viewpoints (distance & area) to interpolate values inside. Are there any rules or norms to help us determine when to use which? Or this choice is commonly made subjectively?


As you will see in Project 1, the previous method for computing barycentric coordinates (using distance) will be quite natural as it is one step away from the point-in-triangle test. Since you will need to determine if a point is inside the triangle, and then determine the color, you may be able to save some computation.


This is true because the area of AAA_A is the height α\alpha times the length of BC¯\bar{BC} and 1/2, so if we say distance from point A to BC is 1 WLOG to find the ratio, then the area of the triangle is then length of BC * 1/2. So the result is of AAA_A over the entire area of the triangle is α\alpha


Are there any advantages or disadvantages to the different ways of computing these Barycentric Coordinates?

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