Medial Axes and Mean Curvature Motion I: Regular Points
✍ Scribed by Ralph Costa Teixeira
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 157 KB
- Volume
- 13
- Category
- Article
- ISSN
- 1047-3203
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✦ Synopsis
What happens to the medial axis of a curve that evolves through MCM (mean curvature motion)? We explore some theoretical results regarding properties of both medial axes and curvature motions. Specifically, we present a set of conditions on the local validity of a medial axis transform and a differential equation for the change of smooth parts of the medial axis when its generating curve evolves under MCM. Finally, we also introduce a differential equation that describes the evolution of the distance transform of a curve under MCM. A companion article will use singularity theory to classify all generic changes in the medial axis of a curve evolving through MCM.