In my master thesis I study barycentric coordinates, which can be used to describe a point inside a polygon as a convex combination of its vertices. In the introduction I introduce barycentric coordinates for triangles and then generalize the idea to polygons. First I derived some basic properties of general barycentric coordinates, and later focus on two specific coordinates, which are Wachspress coordinates and mean value coordinates. I also present the application of these coordinates for interpolating functions of two variables. In the second part of the thesis I consider the use of general barycentrc coordinates in computer graphics. I take a look at a type of mapping called the barycentric mapping and the effect it has on planar shapes. Later I describe a way that this mapping can be used for image warping. I present a way of implementing the mapping and then show the results of the implementation on some specific images, among which is also a portrait. On the portrait the mapping is used to make the face narrower. At the end I present mean value coordinates in space and their role in manipulating three-dimensional shapes.
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