Application of generalized barycentric coordinates in computer aided geometric design

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Supervisor:
Dr. Várady Tamás László
Department of Control Engineering and Information Technology

By means of generalized barycentric coordinates several tasks can be accomplished in computer-aided design, geometry and computer graphics. Their definition for triangles is relatively easy; however, their extension for n-sided convex, concave and nested sets of polygons raises several interesting problems. In this project we introduce the generalized barycentric coordinates, and analyze its most important properties. We will focus on the so-called Mean Value coordinates. By means of several interesting examples, we demonstrate the distribution of these coordinates along constant isolines, and we also deal with interpolating various scalar and vector quantities. Next, several applications of deformation related to editing grids and parts of images are described. A special local method will be used to edit only a part of a picture. Four important algorithms will be presented in details. We have developed a test program, that helped our investigations and by means of which several application examples were generated.

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