Pre-evaluation and interactive editing of B-spline and GERBS curves and surfaces

Abstract

Interactive computer based geometry editing is very useful for designers and artists. Our goal has been to develop useful tools for geometry editing in a way that increases the ability for creative design. When we interactively editing geometry, we want to see the change happening gradually and smoothly on the screen. Pre-evaluation is a tool for increasing the speed of the graphics when doing interactive affine operation on control points and control surfaces. It is then possible to add details on surfaces, and change shape in a smooth and continuous way. We use pre-evaluation on basis functions, on blending functions and on local surfaces. Pre-evaluation can be made hierarchi-cally and is thus useful for local refinements. Sampling and plotting of curves, surfaces and volumes can today be handled by the GPU and it is therefore important to have a structured organization and updating system to be able to make interactive editing as smooth and user friendly as possible. In the following, we will show a structure for pre-evaluation and an optimal organisation of the computation and we will show the effect of implementing both of these techniques.