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

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.