Quiz 10: Geometry Stuff

Question 1: Element Ratio

A very useful relationship to be aware of is that in any triangle mesh, the ratio of vertices to edges to faces is roughly

V : E : F = 1 : 3 : 2

(In fact, they'll approach this ratio exactly as the number of elements goes to infinity, independent of the shape of the surface or choice of triangulation.) A formal proof of this fact takes a bit of work (but is not beyond your ability!).

For this quiz question, you should just give a very rough argument for why mesh elements might appear in this ratio. (Hint: think about the manifold property, the notion of regular valence, and the fact that we are only considering triangle meshes.)

Question 2: Bezier/Hermite Conversion

The second part of your quiz is written up here: BezierHermiteConversion.pdf