Animation of Geometric Algorithms: A Video Review

Geometric algorithms and data structures are often easiest to understand visually, in terms of the geometric objects they manipulate. Indeed, most papers in computational geometry rely on diagrams to communicate the intuition behind the results. Algorithm animation uses dynamic visual images to explain algorithms. Thus it is natural to present geometric algorithms, which are inherently dynamic, via algorithm animation. The accompanying videotape presents a video review of geometric animations; the review was premiered at the 1992 ACM Symposium on Computational Geometry. The video review includes single-algorithm animations and sample graphic displays from “workbench” systems for implementing multiple geometric algorithms. This report contains short descriptions of each video segment.

[1]  Bernard Chazelle,et al.  Triangulating a non-convex polytype , 1989, SCG '89.

[2]  Tiow Seng Tan,et al.  An O(n2 log n) Time Algorithm for the Minmax Angle Triangulation , 1992, SIAM J. Sci. Comput..

[3]  F. P. Preparata,et al.  Convex hulls of finite sets of points in two and three dimensions , 1977, CACM.

[4]  Robert Sedgewick,et al.  Techniques for Algorithm Animation , 1985, IEEE Software.

[5]  Klaus H. Hinrichs,et al.  Plane-Sweep Solves the Closest Pair Problem Elegantly , 1988, Inf. Process. Lett..

[6]  Robert E. Tarjan,et al.  An O(n log log n)-Time Algorithm for Triangulating a Simple Polygon , 1988, SIAM J. Comput..

[7]  Leonidas J. Guibas,et al.  An efficient algorithm for finding the CSG representation of a simple polygon , 1988, SIGGRAPH.

[8]  Ronald L. Graham,et al.  An Efficient Algorithm for Determining the Convex Hull of a Finite Planar Set , 1972, Inf. Process. Lett..

[9]  Simon Kahan,et al.  A model for data in motion , 1991, STOC '91.

[10]  Bernard Chazelle,et al.  Convex Partitions of Polyhedra: A Lower Bound and Worst-Case Optimal Algorithm , 1984, SIAM J. Comput..

[11]  D. T. Lee,et al.  Euclidean shortest paths in the presence of rectilinear barriers , 1984, Networks.

[12]  Simon Kahan.  Real-time processing of moving data , 1992 .

[13]  Marc H. Brown,et al.  Zeus: a system for algorithm animation and multi-view editing , 1991, Proceedings 1991 IEEE Workshop on Visual Languages.

[14]  Jürg Nievergelt,et al.  XYZ: A Project in Experimental Geometric Computation , 1991, Workshop on Computational Geometry.

[15]  John Hershberger.  Compliant motion in a simple polygon , 1993, SCG '93.

[16]  Raimund Seidel,et al.  On the difficulty of tetrahedralizing 3-dimensional non-convex polyhedra , 1989, SCG '89.

[17]  David Eppstein,et al.  Edge insertion for optimal triangulations , 1993, Discret. Comput. Geom..

[18]  Peter Schorn.  Robust algorithms in a program library for geometric computation , 1991, Informatik-Dissertationen ETH Zürich.

[19]  Leonidas J. Guibas,et al.  Topologically sweeping an arrangement , 1986, STOC '86.

[20]  David Eppstein,et al.  Edge Insertion for Optional Triangulations , 1992, LATIN.

[21]  Jean-Claude Latombe,et al.  Robot motion planning , 1970, The Kluwer international series in engineering and computer science.

[22]  S. Suri.  Minimum link paths in polygons and related problems , 1987 .

[23]  Thomas Ottmann,et al.  Algorithms for Reporting and Counting Geometric Intersections , 1979, IEEE Transactions on Computers.

[24]  Robert E. Tarjan,et al.  Triangulating a Simple Polygon , 1978, Inf. Process. Lett..

[25]  Bruce Randall Donald,et al.  A Geometric Approach to Error Detection and Recovery for Robot Motion Planning with Uncertainty , 1987, Artif. Intell..

[26]  John Hershberger,et al.  Colour and sound in algorithm animation , 1991, Proceedings 1991 IEEE Workshop on Visual Languages.