Basic Examples (2) 

Compute an interpolation of vertex values at the center of a equilateral triangle:

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Calculate the vertices of a pentagon:

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Compute the value of a function at each vertex:

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Find the value of an interpolation of the values at a point within the polygon:

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Scope (2) 

A triangle:

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Define values at the triangle's vertices for a linear function:

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Evaluate the interpolant at a single point:

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Evaluate the interpolant at multiple points:

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Plot the interpolant over the triangle:

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A star-shaped Polygon:

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Values at the polygon's vertices:

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Evaluate the interpolant at a single point:

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Evaluate the interpolant at multiple points:

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Plot the interpolant along with the original function over the star-shaped polygon:

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Applications (3) 

Vertices for a bean-shaped polygon, and colors specified as RGB components:

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Visualize the polygon colored using PolygonInterpolation:

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Compare with the result of using the VertexColors option of Polygon:

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Neat Examples (4) 

Define a polygon using FindShortestTour over grid points:

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See the polygon:

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Define an arbitrary function and map it over all the vertices:

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For 64 vertices, visualizing the results takes a few seconds:

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