Generating blend surfaces using partial differential equations
Computer-Aided Design
Representing PDE surfaces in terms of B-splines
Computer-Aided Design
Using partial differential equations to generate free-form surfaces: 91787
Computer-Aided Design
Techniques for interactive design using the PDE method
ACM Transactions on Graphics (TOG)
Journal of Computational and Applied Mathematics
Boundary penalty finite element methods for blending surfaces — II: biharmonic equations
Journal of Computational and Applied Mathematics
Rapid Generation of C2 Continuous Blending Surfaces
ICCS '02 Proceedings of the International Conference on Computational Science-Part II
Dynamic PDE Surfaces with Flexible and General Geometric Constraints
PG '00 Proceedings of the 8th Pacific Conference on Computer Graphics and Applications
Finite Difference Surface Representation Considering Effect of Boundary Curvature
IV '01 Proceedings of the Fifth International Conference on Information Visualisation
Integrating Physics-Based Modeling with PDE Solids for Geometric Design
PG '01 Proceedings of the 9th Pacific Conference on Computer Graphics and Applications
Surface Representation Using Second, Fourth and Mixed Order Partial Differential Equations
SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
Generating blend surfaces using a perturbation method
Mathematical and Computer Modelling: An International Journal
An analytic pseudo-spectral method to generate a regular 4-sided PDE surface patch
Computer Aided Geometric Design
An analytic pseudo-spectral method to generate a regular 4-sided PDE surface patch
Computer Aided Geometric Design
Facial geometry parameterisation based on Partial Differential Equations
Mathematical and Computer Modelling: An International Journal
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In our previous work, a more general fourth order partial differential equation (PDE) with three vector-valued parameters was introduced. This equation is able to generate a superset of the blending surfaces of those produced by other existing fourth order PDEs found in the literature. Since it is usually more difficult to solve PDEs analytically than numerically, many references are only concerned with numerical solutions, which unfortunately are often inefficient. In this paper, we have developed a fast and accurate resolution method, the pseudo-Lévy series method. Due to its analytical nature, the comparison with other existing methods indicates that the developed method can generate blending surfaces almost as quickly and accurately as the closed form resolution method, and has higher computational accuracy and efficiency than existing Fourier series and pseudo-spectral methods as well as other numerical methods. In addition, it can be used to solve complex surface blending problems which cannot be tackled by the closed form resolution method. To demonstrate the potential of this new method we have applied it to various surface blending problems, including the generation of the blending surface between parametric primary surfaces, general second and higher degree surfaces, and surfaces defined by explicit equations.