Bezier Subdivision Based Image Rendering Software

Ir. M.T. Verelst

Bezier surfaces are known for their controlled smooth nature in computer graphics. Subdivision is an attractive rendering method, which also maps well onto low level computation primitives. A compact program is presented which renders bezier surfaces using repeated subdivision and a simple shading algorithm, which allows reasonably fast viewing of bezier surface based scenes. Many optimisations are possible, the program is an very short example of how one can transform and render in a graphics processing sequence with beziers alone down to a low level rectange paint primitive.

Originally (at least for the author), some of the ideas come from an article by Pulleyblank and Kapenga about the feasibility of a chip design for bezier subdivision, and similar software has been written as part of the authors' master thesis research:

M.T. Verelst,
     ``A CAGD System Framework with Rational Cubic Bezier Surfaces as
     Graphics Primitives'',
     Technical Report, Dept. Electrical Engineering, Delft University of Technology, 1991

at the time done at Network Theory section, currently:

Circuits and Systems group (16th/17th floor),
   Delft University of Technology
   dept. of Electrical Engineering
   Mekelweg 4
   Delft, the Netherlands

Graduation committee P. Dewilde, A. v.d Veen, E. Deprettere. After I graduated on the basis of that thesis, I got hired in the same section (not as promotion student, but paid as employee) in a STW funded project where the goal was to make a specialized computer hardware design for speeding up photorealistic graphics an order of magnitude compared to state of the art (example pub outside PRO-RISC STW conferences: Jansen, F.W., Kok, A.J.F., Verelst, T., Hardware Challenges for Ray Tracing and Radiosity Algorithms. Seventh Workshop on Graphics Hardware, Cambridge England, September 1992, EG Technical Report 1992, pp. 123-134.).

My thesis contained an accurate theory description of the mathematical properties of  bezier and rational bezier curves and surfaces, for the case of degree surfaces. For interesting introductions and advanced reading about these and related curved surface subjects with mathematical angle, look for articles Prof Les Piegl from around and before '88 (When I graduated there was a short communication between us when he proposed taking part in a joint project).

Bezier curves, basics

There are various ways of making smooth curves and surfaces, such as direct polynomical approximations (grow instable with order quickly), spline like solutions (mostly measurement points need not coïncide with spline curve anywhere), and bezier type of curves.

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