Thin plate splines have been used successfully to model curves and surfaces. A new application is in data mining where they are used to model interaction terms. These interaction splines break the \curse of dimensionality" by reducing the high-dimensional nonparametric regression problem to the determination of a set of interdependent surfaces. However, the determination of the corresponding th...

C 1-surface splines deene tangent continuous surfaces from control points in the manner of tensor-product (B-)splines, but allow a wider class of control meshes capable of outlining arbitrary free-form surfaces with or without boundary. In particular, irregular meshes with non quadrilateral cells and more or fewer than four cells meeting at a point can be input and are treated in the same conce...

We characterize of the Bernstein-Bezier (BB) form of an implicitly deened bivariate polynomial over a triangle, such that the zero contour of the polynomial deenes a smooth and single sheeted real algebraic curve segment. We call a piecewise G k-continuous chain of such real algebraic curve segments in BB-form as an A-spline (short for algebraic spline). We prove that the degree n A-splines can...

In this paper we consider equidistant polynomial splines S(x) which may grow as O|x|s. We present an integral representation of such splines with a distribution kernel. This representation is related to the Fourier integral of slowly growing functions. The part of the Fourier exponentials herewith play the so called exponential splines by Schoenberg. The integral representation provides a flexi...

Springer, 2008. Hardcover. Book Condition: New. Digital image processing and machine vision have grown considerably during the last few decades. Of the various techniques, developed so far splines play a positive and significant role in many of them. Strong mathematical theory and ease of implementations is one of the keys of their success in many research issues. This book deals with various i...

Catmull-Rom (C-R) splines offer many useful modeling properties, such as affine invariance, global smoothness, and local control. They are therefore of great interest to Computer Aided Design (CAD) users. C-R splines are easily evaluated and are a good choice for interactive applications because they interpolate their control points and therefore provide an intuitive way to represent and edit c...

Splines are a well-known construction originally developed for engineering applications but now used widely in algorithms in computer graphics, differential equations, numerical analysis, and other fields. Billera and others pioneered a more theoretical approach to splines using high-powered techniques from algebra. Over the last fifteen years, geometers and topologists independently rediscover...

In this paper some of the relationships between B-splines and linear control theory is examined. In particular, the controls that produce the B-spline basis is constructed and compared to the basis elements for dynamic splines.