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dc.contributor.authorHabib, Ayman W.
dc.date.accessioned 2017-08-02T22:03:38Z
dc.date.available 2017-08-02T22:03:38Z
dc.date.issued 1997-05
dc.identifier.urihttps://hdl.handle.net/1911/96481
dc.descriptionThis work was also published as a Rice University thesis/dissertation: http://hdl.handle.net/1911/19165
dc.description.abstract Modeling free-form curves and surfaces is one of the fundamental problems in computer aided geometric design. To solve this problem, several modeling techniques have been proposed. Three of these techniques, are investigated. The unifying theme of these three techniques is the use and the control of geometric continuity. The first technique deals with constructing parametric spline curves with controlled continuity between the spline segments at the knots. An axiomatic approach to geometric continuity for parametric representations is proposed. Based on this totally algebraic approach, many new flexible notions of continuity are developed. Corresponding to these notions, new spline curves are constructed in a way that gives the designer more control over the curve shape. Many examples are given. When derivative information is available Hermite interpolation can be used to build high continuity surfaces.A dynamic programming algorithm that solves the problem of interpolating bivariate Hermite data where the interpolation positions are aligned on a triangular grid is developed and analyzed. The third geometric continuity problem arises when modeling with subdivision surfaces, in reducing the continuity of these surfaces to allow for the insertion of sharp edges/vertices on these surfaces. A new approach to solving this problem is introduced and analyzed with illustrative examples.
dc.format.extent 192 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 Three Approaches to Building Curves and Surfaces in Computer Aided Geometric Design
dc.type Technical report
dc.date.note May 1997
dc.identifier.digital TR97-312
dc.type.dcmi Text
dc.identifier.citation Habib, Ayman W.. "Three Approaches to Building Curves and Surfaces in Computer Aided Geometric Design." (1997) https://hdl.handle.net/1911/96481.


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