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?

didvi

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.

briana-jin-zhang

This is true because the area of $A_A$ is the height $\alpha$ times the length of $\bar{BC}$ 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 $A_A$ over the entire area of the triangle is $\alpha$

KindaCallam-io

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

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 $A_A$ is the height $\alpha$ times the length of $\bar{BC}$ 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 $A_A$ over the entire area of the triangle is $\alpha$

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