Reconstructing Two-Dimensional Manifolds from Scattered Data: Motivation and Background
نویسندگان
چکیده
In this report we introduce and motivate the problem of reconstructing shapes from partial information. An appropriate mathematical abstraction capturing the notion of a shape in three-dimensional space is a two-dimensional manifold. The concept of the topological type of a manifold plays an important role in reconstruction, and we present a synopsis of the pertinent definitions and results. We then discuss ways of representing two-dimensional manifolds. Finally, we focus on the specific problem of reconstructing a two-dimensional manifold from an unorganized collection of points assumed to be scattered on or about the manifold, and give a survey of previous work on this topic.
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