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A parametric algorithm for drawing pictures of solid objects composed of quadric surfaces

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Joshua LevinAuthors Info & Claims

Communications of the ACM, Volume 19, Issue 10

Pages 555 - 563

https://doi.org/10.1145/360349.360355

Published: 01 October 1976 Publication History

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Abstract

An algorithm for drawing pictures of three-dimensional objects, with surfaces made up of patches of quadric surfaces, is described. The emphasis of this algorithm is on calculating the intersections of quadric surfaces. A parameterization scheme is used. Each quadric surface intersection curve (QSIC) is represented as a set of coefficients and parameter limits. Each value of the parameter represents at most two points, and these may easily be distinguished. This scheme can find the coordinates of points of even quartic (fourth-order) intersection curves, using equations of no more than second order. Methods of parameterization for each type of QSIC are discussed, as well as surface bounding and hidden surface removal.

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Shao WChen F(2024)Topologically Correct Intersection Curves of Two Trimmed Quadrics with Tolerance ControlJournal of Systems Science and Complexity10.1007/s11424-024-2519-337:5(2207-2239)Online publication date: 30-Aug-2024
https://doi.org/10.1007/s11424-024-2519-3
Shao WChen F(2023)Topological classification of the intersection curves of two quadrics using a set of discriminantsComputer Aided Geometric Design10.1016/j.cagd.2023.102244107(102244)Online publication date: Dec-2023
https://doi.org/10.1016/j.cagd.2023.102244
Franklin WAkman VVerrilli C(2023)Voronoi diagrams with barriers and on polyhedra for minimal path planningThe Visual Computer: International Journal of Computer Graphics10.1007/BF018983571:2(133-150)Online publication date: 22-Mar-2023
https://dl.acm.org/doi/10.1007/BF01898357
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A parametric algorithm for drawing pictures of solid objects composed of quadric surfaces
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
2. Theory of computation
  1. Randomness, geometry and discrete structures

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Published In

Communications of the ACM Volume 19, Issue 10

Oct. 1976

46 pages

ISSN:0001-0782

EISSN:1557-7317

DOI:10.1145/360349

Editor:
Robert L. Ashenhurst
Univ. of Chicago, Chicago, IL

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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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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 October 1976

Published in CACM Volume 19, Issue 10

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Shao WChen F(2024)Topologically Correct Intersection Curves of Two Trimmed Quadrics with Tolerance ControlJournal of Systems Science and Complexity10.1007/s11424-024-2519-337:5(2207-2239)Online publication date: 30-Aug-2024
https://doi.org/10.1007/s11424-024-2519-3
Shao WChen F(2023)Topological classification of the intersection curves of two quadrics using a set of discriminantsComputer Aided Geometric Design10.1016/j.cagd.2023.102244107(102244)Online publication date: Dec-2023
https://doi.org/10.1016/j.cagd.2023.102244
Franklin WAkman VVerrilli C(2023)Voronoi diagrams with barriers and on polyhedra for minimal path planningThe Visual Computer: International Journal of Computer Graphics10.1007/BF018983571:2(133-150)Online publication date: 22-Mar-2023
https://dl.acm.org/doi/10.1007/BF01898357
Gonzalez-Vega LTrocado A(2021)Tools for analyzing the intersection curve between two quadrics through projection and liftingJournal of Computational and Applied Mathematics10.1016/j.cam.2021.113522393:COnline publication date: 1-Sep-2021
https://dl.acm.org/doi/10.1016/j.cam.2021.113522
Ahmed MZiauddin SMarshall JGreenspan M(2021)Point Cloud Registration Using Virtual Interest Points from Macaulay’s Resultant of Quadric SurfacesJournal of Mathematical Imaging and Vision10.1007/s10851-020-01013-z63:4(457-471)Online publication date: 1-May-2021
https://dl.acm.org/doi/10.1007/s10851-020-01013-z
Hamdi SLevin DMorse B(2020)Exact Parametric Solutions for the Intersections of Quadric Surfaces Using MAPLEMaple in Mathematics Education and Research10.1007/978-3-030-41258-6_8(101-113)Online publication date: 28-Feb-2020
https://doi.org/10.1007/978-3-030-41258-6_8
Gonzalez-Vega LTrocado A(2020)Using Maple to Compute the Intersection Curve of Two Quadrics: Improving the Intersectplot CommandMaple in Mathematics Education and Research10.1007/978-3-030-41258-6_7(92-100)Online publication date: 28-Feb-2020
https://doi.org/10.1007/978-3-030-41258-6_7
Fu GRiedel CHolmes TLiu J(2019)Geometric Modeling of the Z-Surface and Z-Curve of GNSS Signals and Their Solution TechniquesIEEE Transactions on Geoscience and Remote Sensing10.1109/TGRS.2018.285304657:1(212-223)Online publication date: Jan-2019
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Zhao MJia XTu CMourrain BWang W(2019)Enumerating the morphologies of non-degenerate Darboux cyclidesComputer Aided Geometric Design10.1016/j.cagd.2019.10177675(101776)Online publication date: Nov-2019
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Brozos-Vázquez MPereira-Sáez MSouto-Salorio MTarrío-Tobar A(2019)Classification of the relative positions between a small ellipsoid and an elliptic paraboloidComputer Aided Geometric Design10.1016/j.cagd.2019.05.002Online publication date: May-2019
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A parametric algorithm for drawing pictures of solid objects bounded by quadric surfaces

A parametric algorithm for drawing pictures of solid objects bounded by quadric surfaces

Blending parametric surfaces

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