Topic
Alpha shape
About: Alpha shape is a research topic. Over the lifetime, 265 publications have been published within this topic receiving 9864 citations.
Papers published on a yearly basis
Papers
TL;DR: This article introduces the formal notion of the family of α-shapes of a finite point set in R 3 .
Abstract: 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 a-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 a e 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 0(n2), worst case. A robust implementation of the algorithm is discussed, and several applications in the area of scientific computing are mentioned.
2,274 citations
TL;DR: A generalization of the convex hull of a finite set of points in the plane leads to a family of straight-line graphs, "alpha -shapes," which seem to capture the intuitive notions of "fine shape" and "crude shape" of point sets.
Abstract: A generalization of the convex hull of a finite set of points in the plane is introduced and analyzed. This generalization leads to a family of straight-line graphs, " \alpha -shapes," which seem to capture the intuitive notions of "fine shape" and "crude shape" of point sets. It is shown that a-shapes are subgraphs of the closest point or furthest point Delaunay triangulation. Relying on this result an optimal O(n \log n) algorithm that constructs \alpha -shapes is developed.
1,977 citations
1 Dec 1992
TL;DR: This article introduces the formal notion of the family of α-shapes of a finite point set in R, a well-defined polytope, derived from the Delaunay triangulation of the point set, with a parameter α ε R controlling the desired level of detail.
Abstract: 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 a-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 a e 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 0(n2), worst case. A robust implementation of the algorithm is discussed, and several applications in the area of scientific computing are mentioned.
1,176 citations
Posted Content•
TL;DR: In this paper, the authors introduce the formal notion of the family of α-shapes of a finite point set in real time, where α is a well-defined polytope, derived from the Delaunay triangulation of the point set.
Abstract: 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 paper introduces the formal notion of the family of $\alpha$-shapes of a finite point set in $\Real^3$. Each shape is a well-defined polytope, derived from the Delaunay triangulation of the point set, with a parameter $\alpha \in \Real$ 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 $O(n^2)$, worst case. A robust implementation of the algorithm is discussed and several applications in the area of scientific computing are mentioned.
1,145 citations
768 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 3 |
| 2020 | 6 |
| 2019 | 8 |
| 2018 | 5 |
| 2017 | 8 |
| 2016 | 6 |