Last update: Sat Apr 14 02:01:36 MDT 2018
@InProceedings{Tupper:2001:RTD,
author = "Jeff Tupper",
title = "Reliable two-dimensional graphing methods for
mathematical formulae with two free variables",
crossref = "ACM:2001:SCP",
pages = "77--86",
year = "2001",
bibdate = "Tue Mar 26 06:05:07 MST 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/siggraph2000.bib",
URL = "http://www.dgp.toronto.edu/people/mooncake/papers/SIGGRAPH2001_Tupper.pdf",
abstract = "This paper presents a series of new algorithms for
reliably graphing two-dimensional implicit equations
and inequalities. A clear standard for interpreting the
graphs generated by two-dimensional graphing software
is introduced and used to evaluate the presented
algorithms. The first approach presented uses a
standard interval arithmetic library. This approach is
shown to be faulty; an analysis of the failure reveals
a limitation of standard interval arithmetic.
Subsequent algorithms are developed in parallel with
improvements and extensions to the interval arithmetic
used by the graphing algorithms. Graphs exhibiting a
variety of mathematical and artistic phenomena are
shown to be graphed correctly by the presented
algorithms. A brief comparison of the final algorithm
presented to other graphing algorithms is included.",
acknowledgement = ack-nhfb,
classification = "G.1.0 [Numerical Analysis]: General Interval
Arithmetic; G.4 [Mathematical Software]: Reliability
and Robustness; I.3.3 [Computer Graphics]:
Picture/Image Generation Display Algorithms",
keywords = "interval arithmetic,Tupper interval
arithmetic,interval analysis,implicit curves,algebraic
curves, relation graphing,formula graphing,GrafEq",
}