Whats the terminology for defining a point on a triangle?

Question

There are 2 common methods of representing a point on a 2d/3d triangle.

• 2 numbers (often called "UV coordinates" in 3D graphics):
  Where 2 edges of the triangle are axes, which the point is translated along.
• 3 numbers (barycentric weights):
  The point is the product of the triangle, where each point is multiplied by the corresponding weight.

I've seen some source-code that makes references to both methods as barycentric coordinates.

Whats the correct terminology for these 2 methods of defining a point on a triangle?

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Note, I may know the answer to these but looking on-line I didn't find good definitive explanations that distinguish between these 2 methods.

Answer 1

The first way is typically bilinear interpolation in which a triangle is seen as a rectangle with two coincident vertices by collapsing an edge. Each edge you choose will given a different parametrization of the triangle.

The second way is barycentric interpolation or barycentric coordinates.

The two methods are different because the isoparametric curves $u=u_0$ and $v=v_0$ are different.