Mesecina is a software to visualize and study the medial axis and related computational geometry structures in the plane.
We illustrate a simple algorithm for approximating the medial axis of a 2D shape with smooth boundary from a sample of this boundary. The algorithm is compared to a more general approximation method that builds on the same idea, namely, to approximate the shape by a union of balls. While not as general, our algorithm is simpler, faster and numerically more stable. Both algorithms are visualized using the Mesecina tool, which is also described.
Streaming flash version (move the mouse over the image below and use the player bar to start viewing the video):
Miklos, Giesen, Pauly: Medial Axis Approximation from Inner Voronoi Balls: A Demo of the Mesecina Tool - the accompanying extended abstract.
Giesen, Miklos, Pauly: The Medial Axis of the Union of Inner Voronoi Balls in the Plane - manuscript with the complete proof of the structural result visualized in the video. Submitted and under review for Computational Geometry: Theory and Applications.
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