Related papers: A fast Mixed Model B-splines algorithm
B-spline modeling is fundamental to CAD systems, and its evaluation and manipulation algorithms currently in use were developed decades ago, specifically for CPU architectures. While remaining effective for many applications, these…
The Numerical Recipes series of books are a useful resource, but all the algorithms they contain cannot be used within open-source projects. In this paper we develop drop-in alternatives to the two algorithms they present for cubic spline…
This paper deals with simultaneously fast and in-place algorithms for formulae where the result has to be linearly accumulated: some of the output variables are also input variables, linked by a linear dependency. Fundamental examples…
This paper demonstrates how an efficient representation of the planned path using B-splines, and a construction procedure that takes advantage of the neural network's inductive bias, speed up both the inference and training of a DNN-based…
Many scientific fields and applications require compact representations of multivariate functions. For this problem, decoupling methods are powerful techniques for representing the multivariate functions as a combination of linear…
Multi-degree splines are piecewise polynomial functions having sections of different degrees. They offer significant advantages over the classical uniform-degree framework, as they allow for modeling complex geometries with fewer degrees of…
Developments of nonlocal operators for modeling processes that traditionally have been described by local differential operators have been increasingly active during the last few years. One example is peridynamics for brittle materials and…
Reachable Minimally supported (RM) B-splines have been recently introduced as a novel B-spline--like basis. They feature local linear independence and admit a fast de Boor--like evaluation algorithm. These properties make them particularly…
A new differential-recurrence relation for the B-spline functions of the same degree is proved. From this relation, a recursive method of computing the coefficients of B-spline functions of degree $m$ in the Bernstein-B\'{e}zier form is…
This paper deals with simultaneously fast and in-place algorithms for formulae where the result has to be linearly accumulated: some output variables are also input variables, linked by a linear dependency. Fundamental examples include the…
Matrix multiplication is a fundamental computation in many scientific disciplines. In this paper, we show that novel fast matrix multiplication algorithms can significantly outperform vendor implementations of the classical algorithm and…
In high-dimensional generalized linear models, it is crucial to identify a sparse model that adequately accounts for response variation. Although the best subset section has been widely regarded as the Holy Grail of problems of this type,…
Multi-degree splines are smooth piecewise-polynomial functions where the pieces can have different degrees. We describe a simple algorithmic construction of a set of basis functions for the space of multi-degree splines, with similar…
Continuous formulations of trajectory planning problems have two main benefits. First, constraints are guaranteed to be satisfied at all times. Secondly, dynamic obstacles can be naturally considered with time. This paper introduces a novel…
The paper is devoted to problem of spline approximation. A new method of nodes location for curves and surfaces computer construction by means of B-splines and results of simulink-modeling is presented. The advantages of this paper is that…
Matching pursuit algorithms are an important class of algorithms in signal processing and machine learning. We present a blended matching pursuit algorithm, combining coordinate descent-like steps with stronger gradient descent steps, for…
We formulate as an inverse problem the construction of sparse parametric continuous curve models that fit a sequence of contour points. Our prior is incorporated as a regularization term that encourages rotation invariance and sparsity. We…
A noise-reduction algorithm for time-series of non-linear systems is presented. The algorithm smoothes the attractors in phase space using B-splines, allowing a more accurate measure of their dynamics. The algorithm is tested on numerical…
Interpolation and smoothing using cubic and generalized splines are fundamental tools in data analysis and statistical modeling. Recently, fast computational algorithms were developed for natural $L$-splines of order four, which arise as…
We propose a novel method for fitting planar B-spline curves to unorganized data points. In traditional methods, optimization of control points and foot points are performed in two very time-consuming steps in each iteration: 1) control…