Specialeforsvar af Ann-Sofie Fisker – Københavns Universitet

Specialeforsvar af Ann-Sofie Fisker

Den 10. december kl. 10.00 forsvarer Ann-Sofie Fisker sit speciale i Matematik med titlen 'Design and Rationalization with Ruled Surfaces'.

Abstract

In this thesis we discuss the problem of designing a surface within a CAD (Computer Aided Design) system and how to rationalize an arbitrary CAD surface i.e. given a CAD surface we will consider how to perform a segmentation of this into regions that are suitable for an approximation with ruled patches and approximate these regions with ruled patches. We will develop algorithms that construct ruled surfaces, classify regions on a CAD surface as suitable for an approximation with ruled patches and approximate these. Furthermore we will consider the hot wire cutting technique. This is a construction technique where a robot moves a hot wire through a block of EPS (expanded polystyrene) and thereby cuts out a ruled surface. We will in the algorithms include some of the production constraints. The constraints that we include are: The EPS block size, the relative speed on the wire and some of the impossible cuts.

We implement all the algorithms in the CAD system Rhinoceros 5, perform tests and reflect on their limitations/possibilities. To develop these algorithms a good theoretical foundation is needed. We therefore begin this thesis with a theory section where we introduce some fundamental, but necessary, concepts and results from differential geometry.

Afterwards we introduce a section on NURBS (non-uniform rational rational B-spline) curves and surfaces, since these objects are the standard curves and surfaces in a CAD system. Besides differential geometry and NURBS surfaces and curves we will include a section on optimization where we will introduce some optimization algorithms, which we will include in the algorithms that we develop.

Vejledere

  • Francois Bernard Lauze, Lektor, DIKU
  • David Brander, Associate Professor, DTU Compute

Censor

  • Martin Svensson, Dept. of Mathematics & Computer Science, University of Southern Denmark