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

© H.Ugail, University of Bradford

u=0

p1

p2

P2

Interactive Definition of Shape Interactive Definition of Shape

Demo

© H.Ugail, University of Bradford

u=0

d2

Examples of PDE Geometry Examples of PDE Geometry

P2

© H.Ugail, University of Bradford

u=0

d2

PDE Geometry Manipulations PDE Geometry Manipulations

P2

© H.Ugail, University of Bradford

Geometry manipulation using the spineGeometry manipulation using the spine

© H.Ugail, University of Bradford

composite surface Corresponding spine described

PDE aircraft geometry Boundary curves and spine

ExamplesExamples

© H.Ugail, University of Bradford

© H.Ugail, University of Bradford

Examples …Examples …

© H.Ugail, University of Bradford

Examples …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): 195-212.

Ugail H (2004): "Spine Based Shape Parameterisaion for PDE Surfaces" Journal of Computing, 72, 195-206.

Monterde L, Ugail H (2004), “On Harmonic and Bi-harmonic Bezier Surfaces, Computer Aided Geometric Design”, To Appear.

Patent: Patent:

““Method for Complex Geometry Re-Modelling”, British patent (no. Method for Complex Geometry Re-Modelling”, British patent (no. GB 0410096.2) has recently been filed.GB 0410096.2) has recently been filed.