SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Generating blend surfaces using partial differential equations
Computer-Aided Design
Representing PDE surfaces in terms of B-splines
Computer-Aided Design
Deformable curve and surface finite-elements for free-form shape design
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
Curvature continuity between adjacent rational Be´zier patches
Computer Aided Geometric Design
Dynamic NURBS with geometric constraints for interactive sculpting
ACM Transactions on Graphics (TOG) - Special issue on interactive sculpting
Triangular NURBS and their dynamic generalizations
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
Modeling inelastic deformation: viscolelasticity, plasticity, fracture
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
Dynamic Modeling of Butterfly Subdivision Surfaces
IEEE Transactions on Visualization and Computer Graphics
A web based system to capture outlines of Arabic fonts
Information Sciences—Informatics and Computer Science: An International Journal - Internet computing
Surface Representation Using Second, Fourth and Mixed Order Partial Differential Equations
SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
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Surface representation as a boundary-valued problem of partial differential equations (PDE) is an important topic of computer graphics and computer aided design. In existing references, various free-from surfaces were created with a fourth order PDE which is only able to meet the tangential conditions at the surface boundaries. The need for a sixth order PDE in surface modeling arises in two situations: one is to generate surfaces with curvature continuity; and the other is to use curvature values as a user handle for surface shape manipulation. In this chapter, we introduce such a sixth order PDE for free-form surface generation and develop a finite difference method to solve this PDE. We also investigate the effects of boundary curvature and the vector-valued shape parameters on the surface shape.