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    Computation of Self-Intersections of Offsets of Bézier Surface Patches

    Source: Journal of Mechanical Design:;1997:;volume( 119 ):;issue: 002::page 275
    Author:
    Takashi Maekawa
    ,
    Wonjoon Cho
    ,
    Nicholas M. Patrikalakis
    DOI: 10.1115/1.2826247
    Publisher: The American Society of Mechanical Engineers (ASME)
    Abstract: Self-intersection of offsets of regular Bézier surface patches due to local differential geometry and global distance function properties is investigated. The problem of computing starting points for tracing self-intersection curves of offsets is formulated in terms of a system of nonlinear polynomial equations and solved robustly by the interval projected polyhedron algorithm. Trivial solutions are excluded by evaluating the normal bounding pyramids of the surface subpatches mapped from the parameter boxes computed by the polynomial solver with a coarse tolerance. A technique to detect and trace self-intersection curve loops in the parameter domain is also discussed. The method has been successfully tested in tracing complex self-intersection curves of offsets of Bézier surface patches. Examples illustrate the principal features and robustness characteristics of the method.
    keyword(s): Intersections , Computation , Polynomials , Robustness , Equations , Geometry AND Algorithms ,
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      Computation of Self-Intersections of Offsets of Bézier Surface Patches

    URI
    http://yetl.yabesh.ir/yetl1/handle/yetl/119135
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    • Journal of Mechanical Design

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    contributor authorTakashi Maekawa
    contributor authorWonjoon Cho
    contributor authorNicholas M. Patrikalakis
    date accessioned2017-05-08T23:54:15Z
    date available2017-05-08T23:54:15Z
    date copyrightJune, 1997
    date issued1997
    identifier issn1050-0472
    identifier otherJMDEDB-27645#275_1.pdf
    identifier urihttp://yetl.yabesh.ir/yetl/handle/yetl/119135
    description abstractSelf-intersection of offsets of regular Bézier surface patches due to local differential geometry and global distance function properties is investigated. The problem of computing starting points for tracing self-intersection curves of offsets is formulated in terms of a system of nonlinear polynomial equations and solved robustly by the interval projected polyhedron algorithm. Trivial solutions are excluded by evaluating the normal bounding pyramids of the surface subpatches mapped from the parameter boxes computed by the polynomial solver with a coarse tolerance. A technique to detect and trace self-intersection curve loops in the parameter domain is also discussed. The method has been successfully tested in tracing complex self-intersection curves of offsets of Bézier surface patches. Examples illustrate the principal features and robustness characteristics of the method.
    publisherThe American Society of Mechanical Engineers (ASME)
    titleComputation of Self-Intersections of Offsets of Bézier Surface Patches
    typeJournal Paper
    journal volume119
    journal issue2
    journal titleJournal of Mechanical Design
    identifier doi10.1115/1.2826247
    journal fristpage275
    journal lastpage283
    identifier eissn1528-9001
    keywordsIntersections
    keywordsComputation
    keywordsPolynomials
    keywordsRobustness
    keywordsEquations
    keywordsGeometry AND Algorithms
    treeJournal of Mechanical Design:;1997:;volume( 119 ):;issue: 002
    contenttypeFulltext
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    DSpace software copyright © 2002-2015  DuraSpace
    نرم افزار کتابخانه دیجیتال "دی اسپیس" فارسی شده توسط یابش برای کتابخانه های ایرانی | تماس با یابش
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