A survey of curve and surface methods in CAGD
Computer Aided Geometric Design
Shape-Preserving Spline Interpolation for Specifying Bivariate Functions on Grids
IEEE Computer Graphics and Applications
Piecewise algebraic surface computation and smoothing from a discrete model
Computer Aided Geometric Design
Automatic surface modelling of a ship hull
Computer-Aided Design
Approximation of minimum energy surfaces using optimal twists
Mathematical and Computer Modelling: An International Journal
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The generation of smooth and shape-preserving surfaces from a mesh of three-dimensional data points is a very important problem in the field of Computer Aided Geometric Design. If a mesh of curves has been obtained in a first interpolation step and they fulfil the user requirements, the surface generation algorithm must avoid further oscillations within the patches. However, it is known that unwanted oscillations may appear using C^2 surfaces. In the present paper, a smoothing algorithm for bicubic spline surfaces is presented. Having the piecewise cubic boundaries of the patches fixed, the algorithm chooses adequate twists factors in order to increase the smoothness. At the end, although the surface is only C^1, unwanted oscillations have been reduced. Practical examples and test results are presented and discussed.