Generating blend surfaces using partial differential equations
Computer-Aided Design
A butterfly subdivision scheme for surface interpolation with tension control
ACM Transactions on Graphics (TOG)
The NURBS book
Techniques for interactive design using the PDE method
ACM Transactions on Graphics (TOG)
Computational Geometry for Design and Manufacture
Computational Geometry for Design and Manufacture
From Conics to NURBS: A Tutorial and Survey
IEEE Computer Graphics and Applications
A subdivision algorithm for computer display of curved surfaces.
A subdivision algorithm for computer display of curved surfaces.
Spine based shape parameterisation for PDE surfaces
Computing - Geometric modelling dagstuhl 2002
A general 4th-order PDE method to generate Bézier surfaces from the boundary
Computer Aided Geometric Design
Industrial geometry: recent advances and applications in CAD
Computer-Aided Design
Technical Section: PDE blending surfaces with C2 continuity
Computers and Graphics
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This paper presents an efficient method for representing complex geometry using an elliptic Partial Differential Equation (PDE) formulation. The integral part of this work is the use of three-dimensional curves within the physical space which act as boundary conditions to solve the PDE. The chosen PDE is solved explicitly for a given general set of curves representing the original shape and thus making the method very efficient. In order to improve the quality of results for shape representation we utilize an automatic parameterization scheme on the chosen curves. With this formulation we discuss our methodology for shape representation using a series of practical examples.