A survey of curve and surface methods in CAGD
Computer Aided Geometric Design
Automatic smoothing with geometric surface patches
Computer Aided Geometric Design
Curves and surfaces for computer aided geometric design
Curves and surfaces for computer aided geometric design
Optimal twist vectors as a tool for interpolating a network of curves with a minimum energy surface
Computer Aided Geometric Design
A method of bivariate interpolation and smooth surface fitting based on local procedures
Communications of the ACM
A Survey of the Representation and Design of Surfaces
IEEE Computer Graphics and Applications
Shape-Preserving Spline Interpolation for Specifying Bivariate Functions on Grids
IEEE Computer Graphics and Applications
Surfaces in computer aided geometric design: a survey with new results
Computer Aided Geometric Design
Thin plate splines with tension
Computer Aided Geometric Design
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Construction of a surface is usually executed from the viewpoint of either interpolation or approximation (in other words, conceptual design). From the viewpoint of interpolation, smooth interpolation among given points that is compatible with physical phenomena is often essential. A surface with the minimum strain energy is known as a smooth surface satisfying those requirements. Some methods for construction of an interpolation surface use the strain energy approximated in a suitable way and generate a surface for which the approximated strain energy is minimum. Nevertheless, generated surfaces sometimes contain ''wiggles'' or ''bumps'' for data which implies large gradients. The purpose of this paper is to initiate the method for generating the surface with little ''wiggles'' or ''bumps'' for data which implies large gradients. For this purpose, we first adopt the minimization of the meansquare curvature in the x- and y-directions in a surface as a criterion to estimate the propriety of the interpolation. Next, we derive the optimum equation satisfied by the surface with the minimum meansquare curvature by representing the surface in the form of the C^1 Coons patch and then applying dynamic programming to the minimization problem. Finally, the solution to the optimality equation is obtained by a numerical method, and the surface with the minimum meansquare curvature is generated.