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Smoothing the dges of a polygon

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Hello every body, I have a simple polygon consisting of 26 points as shown in the attached file. I would like to smothen the edges of the polygon. Could any one help me with some simple ways to smoothen the edges? Thanks in advance.

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If you are working in 2D, I would use Catmull-Rom splines to draw the edges (google it).

if 3D, I would start by smoothing the normals (although that might improve the shading but not the geometry).

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