# The application of T-spline surfaces in computer aided design

OData: XML JSON What's this?NURBS is the most commonly used surface representation for modeling free-form surfaces in computer-aided design. This representation is worthily popular as it is easily editable and provides the generation of aesthetic and smooth surfaces. One of its disadvantages is that the basis functions, which define the surface, are defined by two global knot vectors, which implies that a regular control grid is created, whose usage is quite tedious and often quite redundant. The T-spline representation has been developed for the elimination of this. It is defined over an optimized structure, which means that control points need to be defined only at those places, where they are really needed. Consequently, not only the number of control points decreases, but also the design process becomes easier.

In this thesis I introduce the T-spline surface representation and analyze its most important properties. By means of several examples I present algorithms for expanding and simplificating the structure of the surface, which includes adding and deleting control points and the automatic simplification of the surface. I demonstrate how to merge two patches smoothly and efficiently, and also describe an algorithm for the approximation of point clouds.

After this the main parts and functions of the demonstration framework system is presented. I specify the implementation of the algorithms and their user interface. By means of several interesting examples I demonstrate the advantages of T-spline surfaces over NURBS.

Finally, I summarize my results, and propose some ideas for further development.