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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.
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