Robust geometric computation: Difference between revisions

Revision as of 06:09, 11 March 2019

Revision as of 06:11, 11 March 2019

Line 1:

{{Userspace draft|source=ArticleWizard|date=February 2014}}

(Extremely rough draft #1)

== Introduction ==

Geometric objects on a digital computer are composed of two types of data: numerical and combinatorial. Examples of numerical data include the Cartesian coordinates of a point in 3-space, the length of a line segment connecting two such points, or the angle between two such line segments. Examples of combinatorial information include grouping two points as an edge, grouping a collection of edges as a face, or grouping a collection of faces as a surface.

Line 13 ⟶ 9:

Geometric nonrobustness results from this unfortunate disconnect between continuous theoretical formulations and the reality of discrete machine implementation. In most instances, the numerical data composing geometric objects is an approximation to a real value. Predicates that assume exact values but are fed approximate values are liable to make incorrect determinations. Constructions compound the situation by taking exact values and producing approximate ones, or by taking approximate values and producing even coarser approximations. In short, geometric nonrobustness is a problem wherein branching decisions in geometric algorithms are predicated on approximate numerical computations, leading to various forms of unreliability including ill-formed output and software failure through crashing or infinite loops.

== Section 2 ==

== Section 3 ==

blah blah

== Section 4 ==

blah blah blah

== References ==

{{Reflist}}<references />

<!--- See http://en.wikipedia.org/wiki/Wikipedia:Footnotes on how to create references using <ref></ref> tags which will then appear here automatically -->

{{Reflist}}<references />

== External links ==