Techniques for geometric modelling using NURBS

Abstract

Computational Geometry(CG) is a challenging and remarkably important area. This thesis presents the prevailing geometric modelling techniques ; Bezier, B-Spline and the Non-Uniform Rational B-Spline (NURBS) which deserves special emphasis in CG and implements some smoothing algorithms. Bezier curves limits the flexibility of the resulting curve because of the two characteristics of the Bernstein basis; first, the dependent relation between the number of control points and the degree of the resulting polynomial that defines the curve, secondly, global control property. On the other hand, NURBS curve and surface can be locally controlled by the knots, weights and the degree of the basis functions, as we want. NURBS provides a single precise mathematical form capable of representing the analytical shapes. That is, we can see clearly the flexibility of NURBS, and by this reason, it is used in Maya, representative animation software in the world and Computer Tomography(CT), and also in a scanning device, etc. However, there is no program using knots for the accuracy of modelling. In conclusion, we suggest the active application of NURBS and the addition function using knot for the accuracy of geometric modelling. And thus Computer Graphics has great possibilities with NURBS.