Generating blend surfaces using partial differential equations
Computer-Aided Design
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Bezier and B-Spline Techniques
Bezier and B-Spline Techniques
C2 free-form surfaces of degree (3,5)
Computer Aided Geometric Design
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
SIAM Journal on Numerical Analysis
A finite element method for surface restoration with smooth boundary conditions
Computer Aided Geometric Design
The Gaussian and mean curvature criteria for curvature continuity between surfaces
Computer Aided Geometric Design
Discrete surface modelling using partial differential equations
Computer Aided Geometric Design
Bicubic B-spline blending patches with optimized shape
Computer-Aided Design
Spline surfaces of arbitrary topology with continuous curvature and optimized shape
Computer-Aided Design
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Two constructions of surfaces filling polygonal holes in piecewise B-spline bicubic surfaces with tangent plane continuity are described. The filling surfaces are obtained by minimization of functionals which impose penalty on curvature discontinuities. One of the functionals is a quadratic form, while the other functional is defined with a parameterization-independent formula. The resulting surfaces may be used instead of class G2 surfaces in practical applications; the penalty approach enables simplification of the construction, and reduction in the degree of patches filling the hole from (9,9) to (5,5) without any visible quality degradation. The notion of class Gn quasi Gm surfaces, i.e. class Gn surfaces optimized to approximate class Gm surfaces, is proposed.