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INTERPOLATION ON A NET OF CONVEX QUADRILATERALS

Morton A. Kaplan, R. A. Papetti

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Abstract

Abstract : The problem of forming a surface of interpolation over a mesh of convex quadrilateral cells is investigated. The requirements that the surface be continuous and practical to generate lead to the consideration of interpolation across a space quadrilateral by a set of ruled surfaces. A single surface is selected from this set by use of certain invariance requirements and by simplicity. This surface, an hyperboloid of one sheet, is shown to achieve its maximum and minimum values on its boundary and to have no relative maxima or minima in its interior. The resulting interpolation scheme reproduces the most widely used form of rectangular interpolation in the special case when the quadrilateral is a rectangle. Triangular interpolation is also discussed. (Author)

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What this paper is about

Abstract : The problem of forming a surface of interpolation over a mesh of convex quadrilateral cells is investigated. The requirements that the surface be continuous and practical to generate lead to the consideration of interpolation across a space quadrilateral by a set of ruled surfaces. A single surface is selected from this set by use of certain invariance requirements and by simplicity. This surface, an hyperboloid of one sheet, is shown to achieve its maximum and minimum values on its boundary and to have no relative maxima or minima in its interior. The resulting interpolation scheme reproduces the most widely used form of rectangular interpolation in the special case when the quadrilateral is a rectangle. Triangular interpolation is also discussed. (Author)

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Available abstract

Abstract : The problem of forming a surface of interpolation over a mesh of convex quadrilateral cells is investigated. The requirements that the surface be continuous and practical to generate lead to the consideration of interpolation across a space quadrilateral by a set of ruled surfaces. A single surface is selected from this set by use of certain invariance requirements and by simplicity. This surface, an hyperboloid of one sheet, is shown to achieve its maximum and minimum values on its boundary and to have no relative maxima or minima in its interior. The resulting interpolation scheme reproduces the most widely used form of rectangular interpolation in the special case when the quadrilateral is a rectangle. Triangular interpolation is also discussed. (Author)

Key concepts: Quadrilateral, Interpolation (computer graphics), Mathematics, Bilinear interpolation, Nearest-neighbor interpolation, Boundary (topology), Trilinear interpolation, Rectangle

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