Surface reconstruction using alpha shapes

We describe a method for reconstructing an unknown surface from a set of data points. The basic approach is to extract the surface as a polygon mesh from an α-shape. Even though alpha shapes are generalized polytopes having complicated internal structures, we show that manifold surfaces, with or without boundaries, can be efficiently generated, and these surfaces completely describe the α-shapes to the extent that they are visible from outside. Unlike the original α-shapes, the polygonal surfaces can be easily simplified to yield compact models suitable for a variety of geometric modeling applications such as surface fitting.