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Full-Text Articles in Physical Sciences and Mathematics
Image Reconstruction Using Data-Dependent Triangulation, Thomas W. Sederberg, Xiaohua Yu, Bryan S. Morse
Image Reconstruction Using Data-Dependent Triangulation, Thomas W. Sederberg, Xiaohua Yu, Bryan S. Morse
Faculty Publications
Image reconstruction based on data-dependent triangulation with new cost functions and optimization can create higher quality images than traditional bilinear or bicubic spline reconstruction. The article presents a novel method for image reconstruction using a piecewise linear intensity surface whose elements don't generally align with the coordinate axes. This method is based on the technique of data-dependent triangulation (DDT) that N. Dyn et al. (1990) introduced and has proven capable of producing more pleasing reconstructions than axis-aligned methods.
Approximation By Interval Bezier Curves, Thomas W. Sederberg, Rida T. Farouki
Approximation By Interval Bezier Curves, Thomas W. Sederberg, Rida T. Farouki
Faculty Publications
The interval Bezier curve, which, unlike other curve and surface approximation schemes, can transfer a complete description of approximation errors between diverse CAD/CAM systems that impose fundamentally incompatible constraints on their canonical representation schemes, is described. Interval arithmetic, which offers an essentially infallible way to monitor error propagation in numerical algorithms that use floating-point arithmetic is reviewed. Affine maps, the computations of which are key operations in the de Casteljau subdivision and degree-elevation algorithms for Bezier curves, the floating-point error propagation in such computations, approximation by interval polynomials, and approximation by interval Bezier curves are discussed.
Techniques For Cubic Algebraic Surfaces I, Thomas W. Sederberg
Techniques For Cubic Algebraic Surfaces I, Thomas W. Sederberg
Faculty Publications
The tutorial presents some tools for free-form modeling with algebraic surfaces, that is, surfaces that can be defined using an implicit polynomial equation f(x, y, z )=0. Cubic algebraic surfaces (defined by an implicit equation of degree 3) are emphasized. While much of this material applies only to cubic surfaces, some applies to algebraic surfaces of any degree. This area of the tutorial introduces terminology, presents different methods for defining and modeling with cubic surfaces, and examines the power basis representation of algebraic surfaces. Methods of forcing an algebraic surface to interpolate a set of points or a space curve …