Barycentric Coordinates, or 'Area Coordinates' (or uv's) provide a linear interpolation of coordinates in terms of the space of a triangle (or polytope), and have applications from collision detection to texture mapping.

In essence any point P on a triangle with vertices A,B,C can be described as:

P = A + u * (C - A) + v * (B - A)

this is the parametric form of describing a triangle. (ie: Make A the origin, and describe the coordinates in terms of a linear combination of C and B)

The barycentric coordinates are illustrated in

blackpawn's barycentric flash application
## 1 comment:

Thanks for the visual explanation. I had a rather hard time getting my head round this after reading Wolfram and Wikipedia. But this just made it look easy.

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