Generating blend surfaces using partial differential equations
Computer-Aided Design
Constant-radius blending in surface modelling
Computer-Aided Design
Using partial differential equations to generate free-form surfaces: 91787
Computer-Aided Design
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Functional optimization for fair surface design
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Differential geometry of G1 variable radius rolling ball blend surfaces
Computer Aided Geometric Design
ACM SIGGRAPH 2008 papers
Blending two parametric curves
Computer-Aided Design
A vertex-first parametric algorithm for polyhedron blending
Computer-Aided Design
Gn blending multiple surfaces in polar coordinates
Computer-Aided Design
Blends of canal surfaces from polyhedral medial transform representations
Computer-Aided Design
Constructive G1 connection of multiple freeform pipes in arbitrary poses
Computer Aided Geometric Design
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A method for generating parametric G^n blending surfaces based on reparameterization of partial surface patches of the base surfaces is presented. In the method, partial regions, called reparameterized local base surfaces, near the contact curves on both base surfaces are reparameterized first. Then a parametric G^n blending surface is generated by a linear combination of the two reparameterized local base surface patches by using Erich Hartmann's method. Here, contact curves can be arbitrarily defined by users according to practical requirements. Some methods for determining the reparameterized local base surfaces are given, and thereafter the influences of the reparameterized local base surfaces on the blending surface are discussed in detail. In addition, in order to achieve the fairness of the blending surface, a shape optimization method for minimizing the strain energy of the surface is proposed. Finally, some examples, including a G^2 blending surface generated with the method between an aerofoil and a missile body, are given to demonstrate the effectiveness of the proposed approach.