Generating blend surfaces using partial differential equations
Computer-Aided Design
Constant-radius blending in surface modelling
Computer-Aided Design
Representing PDE surfaces in terms of B-splines
Computer-Aided Design
Computer Aided Geometric Design
Computer Aided Geometric Design
Computer Aided Geometric Design
Differential geometry of G1 variable radius rolling ball blend surfaces
Computer Aided Geometric Design
Blending two cones with Dupin cyclides
Computer Aided Geometric Design
Journal of Computational and Applied Mathematics
Boundary penalty finite element methods for blending surfaces — II: biharmonic equations
Journal of Computational and Applied Mathematics
Surface Representation Using Second, Fourth and Mixed Order Partial Differential Equations
SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
Computer-Aided Design
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Most surface-blending methods are able to blend surfaces with tangent continuity. However, curvature continuity has become increasingly important in geometric modelling and its applications, such as computer animation, computer-aided design and virtual reality. In this paper, we present a method which is able to achieve C2 continuity based on the use of partial differential equations (PDE). A sixth order partial differential equation with one vector-valued parameter is introduced to produce such blending surfaces. Since computational efficiency is crucial for interactive computer graphics applications, we have developed a unified closed form (analytical) method for the resolution of this sixth order PDE. Therefore blending surfaces of up to C2 smoothness can be generated in real time.