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Article

Reliable two-dimensional graphing methods for mathematical formulae with two free variables

Author:

Jeff TupperAuthors Info & Claims

SIGGRAPH '01: Proceedings of the 28th annual conference on Computer graphics and interactive techniques

Pages 77 - 86

https://doi.org/10.1145/383259.383267

Published: 01 August 2001 Publication History

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.

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Cited By

Jazar KKry P(2023)Temporal Set Inversion for Animated ImplicitsACM Transactions on Graphics10.1145/359244842:4(1-18)Online publication date: 26-Jul-2023
https://dl.acm.org/doi/10.1145/3592448
Herath Mudiyanselage NMoroz GPouget MMaza MZhi L(2022)Fast High-Resolution Drawing of Algebraic CurvesProceedings of the 2022 International Symposium on Symbolic and Algebraic Computation10.1145/3476446.3535483(449-458)Online publication date: 4-Jul-2022
https://dl.acm.org/doi/10.1145/3476446.3535483
Oliveira JStolfi JNehab DFigueiredo L(2016)Rigorous bounds for polynomial Julia setsJournal of Computational Dynamics10.3934/jcd.20160063:2(113-137)Online publication date: Nov-2016
https://doi.org/10.3934/jcd.2016006
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Index Terms

Reliable two-dimensional graphing methods for mathematical formulae with two free variables

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cover image ACM Conferences

SIGGRAPH '01: Proceedings of the 28th annual conference on Computer graphics and interactive techniques

August 2001

600 pages

ISBN:158113374X

DOI:10.1145/383259

Chairman:
Lynn Pocock
New York Inst. of Technology

Copyright © 2001 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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SIGGRAPH: ACM Special Interest Group on Computer Graphics and Interactive Techniques

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New York, NY, United States

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Published: 01 August 2001

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SIGGRAPH '01 Paper Acceptance Rate 65 of 300 submissions, 22%;

Overall Acceptance Rate 1,822 of 8,601 submissions, 21%

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Cited By

Jazar KKry P(2023)Temporal Set Inversion for Animated ImplicitsACM Transactions on Graphics10.1145/359244842:4(1-18)Online publication date: 26-Jul-2023
https://dl.acm.org/doi/10.1145/3592448
Herath Mudiyanselage NMoroz GPouget MMaza MZhi L(2022)Fast High-Resolution Drawing of Algebraic CurvesProceedings of the 2022 International Symposium on Symbolic and Algebraic Computation10.1145/3476446.3535483(449-458)Online publication date: 4-Jul-2022
https://dl.acm.org/doi/10.1145/3476446.3535483
Oliveira JStolfi JNehab DFigueiredo L(2016)Rigorous bounds for polynomial Julia setsJournal of Computational Dynamics10.3934/jcd.20160063:2(113-137)Online publication date: Nov-2016
https://doi.org/10.3934/jcd.2016006
Goldsztejn AGranvilliers L(2010)A new framework for sharp and efficient resolution of NCSP with manifolds of solutionsConstraints10.1007/s10601-009-9082-315:2(190-212)Online publication date: 1-Apr-2010
https://dl.acm.org/doi/10.1007/s10601-009-9082-3
Gomes AMorgado JPereira E(2009)A BSP-based algorithm for dimensionally nonhomogeneous planar implicit curves with topological guaranteesACM Transactions on Graphics10.1145/1516522.151652828:2(1-24)Online publication date: 13-May-2009
https://dl.acm.org/doi/10.1145/1516522.1516528
Goldsztejn AGranvilliers L(2008)A New Framework for Sharp and Efficient Resolution of NCSP with Manifolds of SolutionsProceedings of the 14th international conference on Principles and Practice of Constraint Programming10.1007/978-3-540-85958-1_13(190-204)Online publication date: 14-Sep-2008
https://dl.acm.org/doi/10.1007/978-3-540-85958-1_13
Stoutemyer D(2007)Useful computations need useful numbersACM Communications in Computer Algebra10.1145/1358190.135819241:3(75-99)Online publication date: 1-Sep-2007
https://dl.acm.org/doi/10.1145/1358190.1358192
Shou HShen JYoon D(2006)Robust Plotting of Polar Algebraic Curves, Space Algebraic Curves, and Offsets of Planar Algebraic CurvesReliable Computing10.1007/s11155-006-9005-612:4(323-335)Online publication date: 29-Jul-2006
https://doi.org/10.1007/s11155-006-9005-6
Loop CBlinn J(2005)Resolution independent curve rendering using programmable graphics hardwareACM SIGGRAPH 2005 Papers10.1145/1186822.1073303(1000-1009)Online publication date: 31-Jul-2005
https://dl.acm.org/doi/10.1145/1186822.1073303
Loop CBlinn J(2005)Resolution independent curve rendering using programmable graphics hardwareACM Transactions on Graphics10.1145/1073204.107330324:3(1000-1009)Online publication date: 1-Jul-2005
https://dl.acm.org/doi/10.1145/1073204.1073303
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