As an example application of jump flooding, the paper discusses a constant time algorithm on the GPU to compute an approximation to the Voronoi diagram of a given set of seeds in a 2D grid. The errors due to the differences between the approximation and the actual Voronoi diagram are hardly noticeable to the naked eye in all presented experiments. The same approach can also compute in constant time an approximation to the distance transform of a set of seeds in a 2D grid. In practice, such constant time algorithm is useful to many interactive applications involving, for example, rendering and image processing.
Includes bibliographical references p. Guarding an Art Gallery. Knowing Where You Are.
The Post Office Problem. Supersampling in Ray Tracing. Getting Where You Want to Be.
Finding the Shortest Route. Nielsen Book Data Publisher's Summary This well-accepted introduction to computational geometry is a textbook for high-level undergraduate and low-level graduate courses.
The focus is on algorithms and hence the book is well suited for students in computer science and engineering. Motivation is provided from the application areas: For students, this motivation will be especially welcome.
Modern insights in computational geometry are used to provide solutions that are both efficient and easy to understand and implement.
All the basic techniques and topics from computational geometry, as well as several more advanced topics, are covered. The book is largely self-contained and can be used for self-study by anyone with a basic background in algorithms. In the second edition, besides revisions to the first edition, a number of new exercises have been added.
Nielsen Book Data Subjects.Computational Geometry CS JE, Spring WF , Siebel Center Lecture notes and research papers will also be distributed on the course web site. Either a survey paper, a programming project, or (my favorite) original research.
Details TBA. The computational geometry research commu-nity could, of course, spend a considerable amount of In this paper we present a system designed to address these issues, give examplea of applications sup-ported by the current prototype implementation, and discuss further extensions.
Comments: 21 pages, 20 figures. To appear in The Journal of Computer Aided Geometric Design's Special Issue on Heat Diffusion Equation and Optimal Transport in . Computational Geometry From infinite to the paper folding. By the time of a Russian mathematician name Nikolai Ivanovich Lobachevsky proposed his research that fundamentally differed from the established approach.
Marc Khoury, Jonathan Shewchuk Symposium on Computational Geometry (SoCG), We prove that the restricted Delaunay triangulation, thought of as an operator that takes as input a surface and a point set, iteratively applied to an input surface eventually reaches a fixed point.
Quick Navigation through the Mathematics Research Paper Topics Page: Sample Pages of a Research Paper; Research paper topics pertaining to Algebra; Computational Geometry is a branch of the discrete mathematics that deals with the algorithms for the solving of the geometric problems.