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Construction and Composite of Cubic Triangular Bézier Surface from a Given Spatial Cubic Bézier Geodesic Curve

Author: ZhangGuanSheng
Tutor: GuoQingWei
School: Hefei University of Technology
Course: Computational Mathematics
Keywords: Bézier curve triangular Bézier surface Geodesic control points continuity
CLC: TP391.7
Type: Master's thesis
Year: 2013
Downloads: 2
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Abstract


Geodesic is a curve that geodesic curvature is zero everywhere in the surface.Using the necessary and sufficient condition to determine a curve to be the geodesiccurve of a surface, this thesis deals with how to structure a cubic triangular Béziersurface with a given3D Bézier curve as geodesic boundary in a triangular region.Theexplicit expression of the control points for the constructed cubic triangular Béziersurface is obtained by using the control points of the given3D cubic Bézier curve, soas to determine the required surface. In addition, the continuity of two cubic triangularBézier patches is discussed, which possess common pregeodesic. Several numericalexamples are given to illustrate the effectiveness of the given method. This thesis iscomposed of five chapters：In the first chapter,the author briefly introduces the background and the maincontent of this thesis.The second chapter introducts the required theoretical knowledge of constructionand composite of cubic triangular Bézier surface from a given spatial cubic Béziergeodesic curve，the definition and nature of Bézier curve and Bézier surface Béziersurface, as well as composite of cubic triangular Bézier surface.The third chapter introducts the definitions, properties and applications ofgeodesic.The fourth chapter proposes a method of construction and composite of cubictriangular Bézier surface from a given spatial cubic Bézier geodesic curve，discussesthe continuity of cubic triangular Bézier surface with a given spatial cubic Béziergeodesic curve, then we some examples are given to illustrate the validity of thismethod.The fifth chapter sums up the full text and propose the next assumption.

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