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dc.contributor.authorLodha, Suresh Kumar
dc.date.accessioned 2017-08-02T22:03:18Z
dc.date.available 2017-08-02T22:03:18Z
dc.date.issued 1992-08
dc.identifier.urihttps://hdl.handle.net/1911/96429
dc.descriptionThis work was also published as a Rice University thesis/dissertation: http://hdl.handle.net/1911/16647
dc.description.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.
dc.format.extent 120 pp
dc.language.iso eng
dc.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).
dc.title Surface Approximation By Low Degree Patches With Multiple Representations
dc.type Technical report
dc.date.note August 1992
dc.identifier.digital TR92-191
dc.type.dcmi Text
dc.identifier.citation Lodha, Suresh Kumar. "Surface Approximation By Low Degree Patches With Multiple Representations." (1992) https://hdl.handle.net/1911/96429.


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