Biharmonic Polynomial Surfaces for Boundary-Based Smooth Shape Design
This is a collaborative research project (between Dr H Ugail and Dr J Monterde) funded by Engineering and Physical Sciences Research Council (EPSRC) and the Spanish Ministry of Science.
Project Summary
There exists a wide variety of tools to design complex geometric shapes on the computer. Many of these tools utilise algorithms, which are based on polynomial equations called splines. There are several issues with spline-based shape design systems that prohibit them being utilised fully in practical design applications. For example, for spline shapes, the prime tool for interactive shape manipulation is the use of the associated control points and weights, which are often unevenly distributed across the surface. For complex geometry, in practice, the relationship between the changes in geometry upon the manipulation of the control points is not intuitive. Furthermore, in many cases a large percentage of control points are superfluous and therefore significantly interfere with the design process. Another issue with the splines is the generation of shapes conforming to the user required smoothness. In this research we aim to develop a new methodology for smooth spline shapes, whereby one could exercise intuitive control over the shape of surface by using the boundaries or the character lines that define the shape, rather than a set of control points distributed over the interior of the surface. In order to do this, we propose a novel idea, which we have been experimenting with recently. That is, we propose to explore the interface between splines and a branch of mathematics called boundary-value problems, which are widely utilised to solve problems relating to science and, in particular, engineering.
Project Duration
Starts: 1 March 2005
Ends: 30 November 2006
Project Funding
£10,070