This paper presents a novel method for converting any unstructured quadrilateral or hexahedral mesh to a generalized T-spline surface or solid T-spline, based on the rational T-spline basis functions. Our conversion algorithm consists of two stages: the topology stage and the geometry stage. In the topology stage, the input quadrilateral or hexahedral mesh is taken as the initial T-mesh. To con...

In this paper we give a brief survey of penalized spline smoothing. Penalized spline smoothing is a general non-parametric estimation technique which allows to fit smooth but else unspecified functions to empirical data. While penalized spline regressions are quite popular in natural sciences only few applications can be found in economics. We present an example demonstrating how this non-param...

An adaptive spline method for smoothing is proposed which combines features from both regression spline and smoothing spline approaches One of its advantages is the ability to vary the amount of smoothing in response to the inhomogeneous curvature of true functions at di erent locations This method can be applied to many multivariate function estimation problems which is illustrated in this pap...

Human faces are neither exactly Lambertian nor entirely convex and hence most models in literature which make the Lambertian assumption, fall short when dealing with specularities and cast shadows. In this paper, we present a novel anti-symmetric tensor spline (a spline for tensorvalued functions) based method for the estimation of the Apparent BRDF (ABRDF) field for human faces that seamlessly...

Stitching or merging B-spline curves is a frequently used technique in geometric modeling, and is usually implemented in CAD-systems. These algorithms are basically numerical interpolations using the least squares method. The problem, how to replace two or more curves which are generated separately and defined as B-spline curves, has well functioning numerical solutions, therefore, relatively f...

The application of spline subdivision schemes to data consisting of convex compact sets with addition replaced by Minkowski sums of sets is investigated These methods generate in the limit set valued functions which can be expressed explicitly in terms of linear com binations of integer shifts of B splines with the initial data as coe cients The subdivision techniques are used to conclude that ...

Geronimo, Hardin, et al have previously been able construct orthogonal and biorthogonal scaling vectors by extending a spline scaling vector with functions supported on [0, 1]. Many of these constructions occurred before the concept of balanced scaling vectors was introduced. This paper will show that adding functions on [0, 1] is insufficient for extending spline scaling vectors to scaling vec...

In this paper we study penalized regression splines (P-splines), which are low–order basis function splines with a penalty to avoid undersmoothing. Such P–splines are typically not spatially adaptive, and hence can have trouble when functions are varying rapidly. While frequentist methods are available to address this issue, no Bayesian techniques have been developed. Our approach is to model t...

Iterative learning of B-spline basis functions model for the output probability density function (PDF) control of non-Gaussian systems is studied in this paper using the recursive least square algorithm. Within each control interval, the basis functions are fixed and the control input design is performed that controls the shape of the output PDFs. However, between each control interval, periodi...

We present an explicit formula for spline kernels; these are defined as the convolution of several B-splines of variable widths hi and degrees ni. The spline kernels are useful for continuous signal processing algorithms that involve Bspline inner-products or the convolution of several spline basis functions. We apply our results to the derivation of spline-based algorithms for two classes of p...