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The Regularized Spline (R-Spline) Method for Function Approximation
Computational Mathematics and Modeling, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dmitriev, V. I., Ingtem, J. G.
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2011
This is the second volume of A Manual of Computer Graphics. This textbook/reference is big because the discipline of computer graphics is big. There are simply many topics, techniques, and algorithms to discuss, explain, and illustrate by examples. Because of the large number of pages, the book has been produced in two volumes.
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This is the second volume of A Manual of Computer Graphics. This textbook/reference is big because the discipline of computer graphics is big. There are simply many topics, techniques, and algorithms to discuss, explain, and illustrate by examples. Because of the large number of pages, the book has been produced in two volumes.
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Practical spline approximation
1982This two-part paper describes the use of polynomial spline functions for purposes of interpolation and approximation. The emphasis is on practical utility rather than detailed theory. Part I introduces polynomial splines, defines B-splines and treats the representation of splines in terms of B-splines.
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Approximate conversion of spline curves
Computer Aided Geometric Design, 1987An algorithm is presented that approximates: a) a high degree spline curve by one of lower degree and with more segments, or b) a low degree spline curve by one of higher degree but with more pieces. The curvature of the approximations is studied. The method involved concepts of geometric continuity.
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Approximation by Discrete GB-Splines
Numerical Algorithms, 2001Discrete generalized splines are continuous piecewise defined functions which meet some smoothness conditions for the first and second divided difference at the knots. They are a generalization both of smooth generalized splines and classic discrete cubic splines. The paper is devoted to the study of generalized splines.
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Approximation. Interpolation, Splines
1994The problem of approximating a given or a sought function by a function which is in some sense simpler is very frequent in numerical analysis. Usually, the approximating function is a linear combination of a finite number of functions which are given in advance.
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Spline approximation of offset curves
Computer Aided Geometric Design, 1988By using Bézier-splines and rational Bézier-splines, the author discusses the approximation of offset curves. In order to determine the approximating splines, the author presents algorithms for Bézier- splines with G 1 and G 2-continuity, and for rational Bézier-splines with G 1-continuity. An example illustrates the usefulness of the algorithms.
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1988
If (n+1) ordered position vectors Q0, Q1, ..., Qn−1, Q n are given (Fig. 6.1), consider the (n−2) linear combinations: $$ {P_i}(t) = {X_0}(t){Q_{i - 1}} + {X_1}(t){Q_i} + {X_2}(t){Q_{i + 1}} + {X_3}(t){Q_{i + 2}}(i = 1,2,...,n - 2)$$ (6.1) each formed from four successive points.
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If (n+1) ordered position vectors Q0, Q1, ..., Qn−1, Q n are given (Fig. 6.1), consider the (n−2) linear combinations: $$ {P_i}(t) = {X_0}(t){Q_{i - 1}} + {X_1}(t){Q_i} + {X_2}(t){Q_{i + 1}} + {X_3}(t){Q_{i + 2}}(i = 1,2,...,n - 2)$$ (6.1) each formed from four successive points.
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