We present multiresolution B-spline surfaces of arbitrary order defined over triangular domains. Unlike existing methods, the basic idea of our approach is to construct the triangular basis functions from their tensor product relatives in the spirit of box splines by projecting them onto the barycentric plane. The scheme works for splines of any order where the fundamental building blocks of th...

4 Generalized and Optimized Spline Calculation 8 4.1 Multidimensional Array Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 4.2 Condensing Matrix Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 4.3 Eliminating Nested Loops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 4.4 Reduction of Product Tens...

It is proved that, among all nonnegative bases of its space, the B-spline basis is optimally stable for evaluating spline functions.

Recently, a novel laser data based SLAM algorithm using B-Spline as features has been developed in [Pedraza et al., 2007]. EKF is used in the proposed BS-SLAM algorithm and the state vector contains the current robot pose together with the control points of the splines. The obervation model used for the EKF update is the intersections of the laser beams with the splines contained in the map. In...

This work presents a scalable Discrete Wavelet Transform architecture based on the B-spline factorization. In particular, we show that several wavelet filters of practical interest have a common structure in the distributed part of their B-spline factorization. This common structure is effectively exploited to achieve scalability and to save multipliers compared with a direct polyphase B-spline...

We propose an algorithm that integrates geometry parametrization and mesh movement using the control points of a B-spline mesh. An initial mesh is created using B-spline volumes in such a way that the control points mimic a coarse grid. The control points corresponding to the surface nodes are adopted as the design variables. Mesh movement is achieved by applying a standard movement algorithm t...

We give necessary and sufficient conditions for the total positivity of certain connection matrices arising in piecewise exponential spline spaces. These total positivity conditions are sufficient for existence of B-splines in such spaces, but they are far from being necessary. We give a necessary and sufficient condition for existence of B-splines in the case of piecewise exponential spline sp...

Spline curves are useful in a variety of geometric modeling and graphics applications and covering problems abound in practical settings. This work defines a class of covering decision problems for shapes bounded by spline curves. As a first step in addressing these problems, this paper treats translational spline covering for planar, uniform, cubic B-splines. Inner and outer polygonal approxim...

In the present paper, a numerical algorithm using fifth degree quintic B-spline for fourth order singular perturbation problem has been developed. The most of the numerical methods used for higher order singularly perturbed boundary value problems transform the problems into equivalent system of first and/or second order differential equations. However, in the present method, fifth degree B-spl...

Evaluation routines are essential for any application that uses triangular B-spline surfaces. This paper describes an algorithm to efficiently evaluate triangular B-spline surfaces with arbitrary many variables. The novelty of the algorithm is its generality: there is no restriction on the degree of the B-spline surfaces or on the dimension of the domain. Constructing an evaluation graph allows...