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Volume 9, Issue 3

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Algebraic Construction of Smooth Interpolants on Polygonal Domains
Elisabeth Anna Malsch
Gautam Dasgupta

Concave Polygons

For concave polygons, the zeroArea[a,b,c] function is replaced with the zeroPerim[a,b,c] function.

The shape functions for a concave quadrilateral can easily be constructed. The interpolant contains a square root. The branch points of the square root terms add a discontinuity in the gradient of the interpolant. This discontinuity is necessary for the modeling of re-entrant corners.

Figure 5. Interpolants on concave polygons do not require tesselation.



     
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