By means of generalized barycentric coordinates several important tasks can be accomplished in computer-aided design and computer graphics. Their definition for triangles is well-known; however, their extension for n-sided convex and concave polygons, nested sets of polygons and 3D polyhedrons raises several interesting problems.
In this project we introduce the generalized barycentric coordinates, and analyze their most important properties. We will focus on the so-called 3D Mean Value coordinates, and revisit the 2D coordinates having investigated formerly in my BSc diploma work, as well. By means of several interesting examples, we demonstrate the distribution of these coordinates along constant isolines in a given plane, and also deal with the interpolation of various scalar and vector quantities in the 3D space. Next, several applications to deform and animate the geometry of 3D objects are described. The most important algorithms will be presented in details. We have developed a test program, that supported our investigations and by means of which several application examples have been generated.