Techniques for interactive design using the PDE method

Interactive design of practical surfaces using the partial differential equation (PDE) method is considered. The PDE method treats surface design as a boundary value problem (ensuring that surfaces can be defined using a small set of design parameters). Owing to the elliptic nature of the PDE operator, the boundary conditions imposed around the edges of the surface control the internal shape of the surface. Moreover, surfaces obtained in this manner tend to be smooth and fair. The PDE chosen has a closed form solution allowing the interactive manipulation of the surfaces in real time. Thus we present efficient techniques by which we show how surfaces of practical significance can be constructed interactively in real time.

[1]  C. W. Dekanski,et al.  Partial Differential Equation Surface Generation and Functional Shape Optimization of a Swirl Port , 1997 .

[2]  Pierre Bezier,et al.  The Mathematical Basis of the Unisurf CAD System , 1986 .

[3]  Malcolm I. G. Bloor,et al.  Functionality in blend design , 1991, Comput. Aided Des..

[4]  C. W. Dekanski,et al.  The generation of propeller blade geometries using the PDE method , 1995 .

[5]  C. Woodward.  Skinning techniques for interactive B-spline surface interpolation , 1988 .

[6]  Demetri Terzopoulos,et al.  Physically based models with rigid and deformable components , 1988, IEEE Computer Graphics and Applications.

[7]  R. Noyé,et al.  Numerical Solutions of Partial Differential Equations , 1983 .

[8]  Joachim Loos,et al.  Data Dependent Thin Plate Energy and its use in Interactive Surface Modeling , 1996, Comput. Graph. Forum.

[9]  W. D. Evans,et al.  PARTIAL DIFFERENTIAL EQUATIONS , 1941 .

[10]  Yacov Hel-Or,et al.  Interactive design of smooth objects with probabilistic point constraints , 1994, TOGS.

[11]  Michael J. Wilson,et al.  Generating blend surfaces using partial differential equations , 1989 .

[12]  Hong Qin,et al.  Dynamic NURBS with geometric constraints for interactive sculpting , 1994, TOGS.

[13]  L. Piegl,et al.  Curve and surface constructions using rational B-splines , 1987 .

[14]  Malcolm I. G. Bloor,et al.  9. Interactive Design Using Partial Differential Equations , 1994, Designing Fair Curves and Surfaces.

[15]  L. Schumaker.  Spline Functions: Basic Theory , 1981 .

[16]  Ari Rappoport,et al.  Simple constrained deformations for geometric modeling and interactive design , 1994, TOGS.

[17]  Malcolm I. G. Bloor,et al.  Spectral approximations to PDE surfaces , 1996, Comput. Aided Des..

[18]  Michael J. Wilson,et al.  The automatic functional design of hull surface geometry , 1994 .

[19]  Malcolm I. G. Bloor,et al.  Using partial differential equations to generate free-form surfaces , 1990, Comput. Aided Des..

[20]  Malcolm I. G. Bloor,et al.  Complex PDE Surface Generation for Analysis and Manufacture , 1993, Geometric Modelling.

[21]  Malcolm I. G. Bloor,et al.  Efficient parametrization of generic aircraft geometry , 1995 .

[22]  G. M.,et al.  Partial Differential Equations I , 2023, Applied Mathematical Sciences.

[23]  Wayne Tiller,et al.  Rational B-Splines for Curve and Surface Representation , 1983, IEEE Computer Graphics and Applications.