# Robust Geometric Computation

@inproceedings{Yap2016RobustGC, title={Robust Geometric Computation}, author={Chee-Keng Yap and Vikram Sharma}, booktitle={Encyclopedia of Algorithms}, year={2016} }

Nonrobustness refers to qualitative or catastrophic failures in geometric algorithms arising from numerical errors. Section 45.1 provides background on these problems. Although nonrobustness is already an issue in “purely numerical” computation, the problem is compounded in “geometric computation.” In Section 45.2 we characterize such computations. Researchers trying to create robust geometric software have tried two approaches: making fixed-precision computation robust (Section 45.3), and…

## 29 Citations

### Lecture 5 Geometric Approaches

- Mathematics

We look at some geometric approaches to nonrobustness. An intriguing idea here is the notion of " fixed precision geometry ". After all, if nonrobustness is a geometric phenomenon, it makes sense to…

### Lecture 1 Introduction to Numerical Nonrobustness

- Mathematics

This chapter gives an initial orientation to some key issues that concern us. What is the nonrobustness phenomenon? Why does it appear so intractable? Of course, the prima facie reason for…

### Towards Soft Exact Computation (Invited Talk)

- Computer ScienceCASC
- 2019

A bird’s eye view of the recent work with collaborators in two principle areas: computing zero sets and robot path planning and a systematic pathway to go from the abstract algorithmic description to an effective algorithm in the subdivision framework are discussed.

### Efficient non-incremental constructive solid geometry evaluation for triangular meshes

- Computer ScienceGraph. Model.
- 2018

### ImatiSTL - Fast and Reliable Mesh Processing with a Hybrid Kernel

- Computer ScienceTrans. Comput. Sci.
- 2017

A novel approach is presented to deal with geometric computations while joining the efficiency of floating point representations with the robustness of exact arithmetic. Our approach is based on a…

### Lecture 1 on Numerical Nonrobustness

- Computer Science

This chapter gives an initial orientation to some key issues that concernNonrobustness arises when benign errors leads a computation to commit catastrophic errors, and often the program crashes as a result.

### Lecture 6 Exact Geometric Computation

- Mathematics

You might object that it would be reasonable enough for me to try to expound the differential calculus, or the theory of numbers, to you, because the view that I might find something of interest to…

### Lecture 2 MODES OF NUMERICAL COMPUTATION

- Mathematics

It is better to solve the right problem the wrong way than to solve the wrong problem the right way. The purpose of computing is insight, not numbers. To understand numerical nonrobustness, we need…

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