Edelsbrunner, HerbertISTA ; Mücke, Ernst P
Frequently, data in scientific computing is in its abstract form a finite point set in space, and it is sometimes useful or required to compute what one might call the `'shape” of the set. For that purpose, this article introduces the formal notion of the family of alpha-shapes of a finite point set in R3. Each shape is a well-defined polytope, derived from the Delaunay triangulation of the point set, with a parameter alpha is-an-element-of R controlling the desired level of detail. An algorithm is presented that constructs the entire family of shapes for a given set of size n in time O(n2), worst case. A robust implementation of the algorithm is discussed, and several applications in the area of scientific computing are mentioned.
ACM Transactions on Graphics
National Science Foundation under grant CCR-8921421 and Alan T. Waterman award, grant CCR-9118874.
43 - 72
Edelsbrunner H, Mücke E. Three-dimensional alpha shapes. ACM Transactions on Graphics. 1994;13(1):43-72. doi:10.1145/174462.156635
Edelsbrunner, H., & Mücke, E. (1994). Three-dimensional alpha shapes. ACM Transactions on Graphics. ACM. https://doi.org/10.1145/174462.156635
Edelsbrunner, Herbert, and Ernst Mücke. “Three-Dimensional Alpha Shapes.” ACM Transactions on Graphics. ACM, 1994. https://doi.org/10.1145/174462.156635.
H. Edelsbrunner and E. Mücke, “Three-dimensional alpha shapes,” ACM Transactions on Graphics, vol. 13, no. 1. ACM, pp. 43–72, 1994.
Edelsbrunner H, Mücke E. 1994. Three-dimensional alpha shapes. ACM Transactions on Graphics. 13(1), 43–72.
Edelsbrunner, Herbert, and Ernst Mücke. “Three-Dimensional Alpha Shapes.” ACM Transactions on Graphics, vol. 13, no. 1, ACM, 1994, pp. 43–72, doi:10.1145/174462.156635.