PDE based shape modelling and manipulation of complex geometry Hassan Ugail School of Informatics University of Bradford, United Kingdom

NURBS: Commonly used in 3D modelling Time consuming and not so intuitive 

Method based on boundaries or character lines © H.Ugail, University of Bradford

u=0 p1p1 p2p2 P2P2 Interactive Definition of Shape Demo © H.Ugail, University of Bradford

u=0 d2d2 Examples of PDE Geometry P2P2 © H.Ugail, University of Bradford

u=0 d2d2 PDE Geometry Manipulations P2P2 © H.Ugail, University of Bradford

Geometry manipulation using the spine © H.Ugail, University of Bradford composite surface Corresponding spine described PDE aircraft geometry Boundary curves and spine

Examples © H.Ugail, University of Bradford

Examples …

© H.Ugail, University of Bradford Examples …

Connection with splines © H.Ugail, University of Bradford Presently trying to understand the connections between Bezier surfaces and PDEs. (in collaboration with Prof. Monterde from University of Valencia, Spain). Theorem: Theorem: Given a Bihamonic Bezier Surface of degree n then the inner control points are completely determined by the boundary control points. (Monterde & Ugail, Computer Aided Geometric Design, To Appear)

Some Relevant Literature © H.Ugail, University of Bradford Publications Ugail H, Bloor M I and Wilson M J (1999): "Techniques for Interactive Design Using the PDE Method“, ACM Transactions on Graphics, 18 (2): Ugail H (2004): "Spine Based Shape Parameterisaion for PDE Surfaces" Journal of Computing, 72, Monterde L, Ugail H (2004), “On Harmonic and Bi-harmonic Bezier Surfaces, Computer Aided Geometric Design”, To Appear.Patent: “Method for Complex Geometry Re-Modelling”, British patent (no. GB ) has recently been filed.