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Computational Geometry

Computers are being used more and more to solve geometric problems, like modeling physical objects such as brains and bridges.

Grids

How many different possible triangulations can be constructed for a regular hexagon?

How many triangles will the triangulation of a simple polygon with \(51\) sides contain?

Suppose a convex polygon has vertices \( v_{0}, \ldots, v_{n}\). In any triangulation we can assign a weight to each triangle to be the length of its perimeter. Let the cost of a triangulation be the sum of the weights of its component triangles. Write an algorithm to find a triangulation with the minimum cost.

If \(A\) the minimum cost of triangulation for a convex polygon with the the coordinates below, what is the value of \(\left\lfloor A \right\rfloor \)?

\[(-2,3), (4,0), (8,7), (5,10), (1,10)\]

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