Computational geometry: an introduction
Computational geometry: an introduction
Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms
ACM Transactions on Graphics (TOG)
Randomized incremental construction of Delaunay and Voronoi diagrams
Proceedings of the seventeenth international colloquium on Automata, languages and programming
Three-dimensional alpha shapes
ACM Transactions on Graphics (TOG)
The union of balls and its dual shape
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
An incremental algorithm for Betti numbers of simplicial complexes
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Scanline surfacing: building separating surfaces from planar contours
Proceedings of the conference on Visualization '00
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We present a new technique for the visualization and analysis of the results from Monte Carlo simulations based on α-complexes and α-shapes. The specific application we present in this article is the analysis of the quantum-mechanical behavior of hydrogen molecules and helium atoms on a surface at very low temperatures. Our technique is an improvement over existing techniques in two respects. First, our approach allows one to visualize the points on a random walk at varying levels of detail and interactively select the level of detail that is most appropriate. Second using α-shapes one can obtain quantitative measures of spatial properties of the system, such as the boundary length and interior area of clusters, that would be difficult to obtain otherwise.