PhD Thesis Proposal Defence


"Surface intersection problems and new solutions based on quadric
subdivision"

By

Mr. Jinyuan Jia


Abstract

Surface intersection is a fundamental and important problem in CAD/CAM
and CG. Many algorithms have been suggested to solve this difficult
problem during the past decades, however, developing an efficient,
accurate, robust algorithm to compute intersection curves of two general
surfaces still remains an extremely challenging task nowadays.

Due to the difficulties for solving intersection problem on general
surfaces, many researchers pay more attentions to the intersection
problems on special surfaces, e.g. quadratic surfaces, surfaces of
revolution and canal surfaces in geometric modeling. In my proposal,
quadric subdivision is proposed to solve this difficult problem. It
subdivides a surface into piecewise quadric facets, instead of traditional
triangular facets. Different with triangular subdivision, it is much
bigger than triangular facet in size, and much fewer quadric facets are
needed to approximate the same surface than triangular facets. More
important, it can reach C^1 continuity.

Quadric subdivision reduces the complex surface intersection problems to
the simpler quadric intersection problems, which has closed form solutions
and produces piecewise C^1 QSIC parameterization and easier to detect
closed components of intersection curves. Firstly, we choose surfaces of
revolution to testify to quadric subdivision and achieve very good
performances in the three applications, (i) ray intersecting surfaces,
(ii) plane intersecting surfaces and (iii) intersections of two surfaces
of revolution.

In future work, firstly, we will investigate an efficient quadric
subdivision for canal surfaces, then apply it to the three intersection
problems of a canal surface and a ray (plane and another canal surface).
Finally, our goal is to explore a new solution to general surface
intersection problem based on quadric subdivision.


Date:				Thursday, 15 May 2003

Time:				3:00p.m.-5:00p.m.

Venue:				Room 2404
				Lifts 17-18

Committee Members:		Dr. Andrew Horner (Supervisor)
				Dr. Kai Tang (MECH, Supervisor)
				Dr. Long Quan (Chairman)
				Dr. Michael Brown
				Dr. Chiew-Lan Tai
				Dr. Ajay Joneja (IEEM)


**** ALL are Welcome ****