Abstract
In this paper, a new class of rational quadratic/linear trigonometric Hermite functions with two shape parameters is proposed. Based on these Hermite functions, new improved first class of Side-Side (FCSS), second class of Side-Side (SCSS), first class of Side-Vertex (FCSV) and second class of Side-Vertex (SCSV) interpolation operators are proposed respectively, which can be used to construct C1 Coons surfaces over triangular domain. By altering the values of two shape parameters, the shape of the Coons surface patch can be adjusted flexibly, but without affecting the function values and partial derivatives of the boundaries. For constructing the triangular surface patches with the center of mass passing through a fixed point, we also give a center of mass function value control method, by which we can solve the corresponding shape parameter values. Moreover, we also apply these four improved interpolation operators to image interpolation. Compared with some widely used image interpolation methods, our methods achieve competitive performance.
Highlights
The problem of constructing surfaces through a given set of scattered data points has a wide range of applications in many fields, such as medical imaging, scientific visualization, architectural design and aerospace materials manufacturing
The purpose of this paper is to propose the improved first class of Side-Side (FCSS), second class of Side-Side (SCSS), first class of Side-Vertex (FCSV) and second class of Side-Vertex (SCSV) interpolation operators using a new class of rational quadratic/linear trigonometric Hermite functions
Based on the property that the surface shape can be adjusted through parameters, we introduce a center of mass function value control method, by which we can construct surface patches with the center of mass passing through a fixed point
Summary
The problem of constructing surfaces through a given set of scattered data points has a wide range of applications in many fields, such as medical imaging, scientific visualization, architectural design and aerospace materials manufacturing. The purpose of this paper is to propose the improved first class of Side-Side (FCSS), second class of Side-Side (SCSS), first class of Side-Vertex (FCSV) and second class of Side-Vertex (SCSV) interpolation operators using a new class of rational quadratic/linear trigonometric Hermite functions We use these methods to construct Coons surface patches and implement C1 surface stitching. Based on the property that the surface shape can be adjusted through parameters, we introduce a center of mass function value control method, by which we can construct surface patches with the center of mass passing through a fixed point We apply these proposed interpolation methods to image interpolation for upscaling the images with factor 2,3 and 4, and make comparisons between our methods and some existing image interpolation methods. In order to facilitate the discussion over triangular domain, we first need to convert the Cartesian coordinates to the barycentric coordinates
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