Interactive modelling of shape preserving design curves : A dissertation submitted in partial fulfilment of the degree of Bachelor of Commerce and Management (Honours)

Abstract

Computer aided design is a very widely used tool in industrial design and has been applied to such areas as car, airplane and boat design, to name a few. What is required as a result are applications that allow a designer to interact with a design. Designers want to be able to change, in real time, the shape of curves and surfaces while maintaining desirable properties such as smoothness or locality of a change.

This project investigates a scheme that places a "shape preserving" curve through a set of datapoints. The default curve that is obtained is a rational piecewise cubic curve represented in Bezier form.

From the scheme used to produce our default curve we derive four methods that can be used to make changes to the curve while maintaining a predefined level of smoothness and maintaining the shape preserving properties.

The "Bezier Curve Manipulator" is a tool, written using OpenGL 1. 1, which is used to interactively make changes to a segment using one of the four movement methods mentioned above. This program allows designers to see, in real time, the change to the shape of the curve while maintaining a desired level of smoothness. A change is made by direct manipulation of a Bezier control point, or a weight value associated with each segment.

As well as maintaining a smooth curve, other factors such as the locality of the change and the predictability of the change are considered.

It is the effect on the shape of the curve using these four methods that is discussed with relevance to those criteria.