Rice Univesrity Logo
    • FAQ
    • Deposit your work
    • Login
    View Item 
    •   Rice Scholarship Home
    • Faculty & Staff Research
    • George R. Brown School of Engineering
    • Computer Science
    • Computer Science Technical Reports
    • View Item
    •   Rice Scholarship Home
    • Faculty & Staff Research
    • George R. Brown School of Engineering
    • Computer Science
    • Computer Science Technical Reports
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Surface Approximation By Low Degree Patches With Multiple Representations

    Thumbnail
    Name:
    TR92-191.pdf
    Size:
    4.913Mb
    Format:
    PDF
    View/Open
    Author
    Lodha, Suresh Kumar
    Date
    August 1992
    Abstract
    Computer Aided Geometric Design (CAGD) is concerned with the representation and approximation of curves and surfaces when these objects have to be processed by a computer. Parametric representations are very popular because they allow considerable flexibility for shaping and design. Implicit representations are convenient for determining whether a point is inside, outside or on the surface. These representations offer many complimentary advantages. Therefore, it is desirable to build geometric models with surfaces which have both parametric and implicit representations. Maintaining the degree of the surfaces low is important for practical reasons. Both the size of the surface representation, as well as the difficulties encountered in the algorithms, e.g. root finding algorithms, grow quickly with increasing degree. This thesis introduces low degree surfaces with both parametric and implicit representations and investigates their properties. A new method is described for creating quadratic triangular Bezier surface patches which lie on implicit quadric surfaces. Another method is described for creating biquadratic tensor product Bezier surface patches which lie on implicit cubic surfaces. The resulting surface patches satisfy all of the standard properties of parametric Bezier surfaces, including interpolation of the corners of the control polyhedron and the convex hull property. The second half of this work describes a scheme for filling n-sided holes and for approximating the resulting smooth surface consisting of high degree parametric Bezier surface patches by a continuous surface consisting of low degree patches with both parametric and implicit representations. A new technique is described for filling an n-sided hole smoothly using a single parametric surface patch with a geometrically intuitive compact representation. Next, a new degree reduction algorithm is applied to approximate high degree parametric Bezier surfaces by low degree Bezier surfaces. Finally, a variant of the least squares technique is used to approximate parametric Bezier surfaces of low degree by low degree surfaces with both parametric and implicit representations. The resulting surfaces have boundary continuity and approximation properties.
    Description
    This work was also published as a Rice University thesis/dissertation: http://hdl.handle.net/1911/16647
    Citation
    Lodha, Suresh Kumar. "Surface Approximation By Low Degree Patches With Multiple Representations." (1992) https://hdl.handle.net/1911/96429.
    Type
    Technical report
    Citable link to this page
    https://hdl.handle.net/1911/96429
    Rights
    You are granted permission for the noncommercial reproduction, distribution, display, and performance of this technical report in any format, but this permission is only for a period of forty-five (45) days from the most recent time that you verified that this technical report is still available from the Computer Science Department of Rice University under terms that include this permission. All other rights are reserved by the author(s).
    Metadata
    Show full item record
    Collections
    • Computer Science Technical Reports [245]

    Home | FAQ | Contact Us | Privacy Notice | Accessibility Statement
    Managed by the Digital Scholarship Services at Fondren Library, Rice University
    Physical Address: 6100 Main Street, Houston, Texas 77005
    Mailing Address: MS-44, P.O.BOX 1892, Houston, Texas 77251-1892
    Site Map

     

    Searching scope

    Browse

    Entire ArchiveCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsTypeThis CollectionBy Issue DateAuthorsTitlesSubjectsType

    My Account

    Login

    Statistics

    View Usage Statistics

    Home | FAQ | Contact Us | Privacy Notice | Accessibility Statement
    Managed by the Digital Scholarship Services at Fondren Library, Rice University
    Physical Address: 6100 Main Street, Houston, Texas 77005
    Mailing Address: MS-44, P.O.BOX 1892, Houston, Texas 77251-1892
    Site Map