Related papers: An error reduced and uniform parameter approximati…
As a parametric polynomial curve family, B\'ezier curves are widely used in safe and smooth motion design of intelligent robotic systems from flying drones to autonomous vehicles to robotic manipulators. In such motion planning settings,…
Recently the author and U. Reif introduced the concept of diversification of uniform tensor product B-splines. Based on this concept, we give a new constructive modification of non-uniform B-splines. The resulting spline spaces are…
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 extended definition of the polynomial B-splines may give a chance to improve the results obtained by the classical cubic polynomial B-splines. Determination of the optimum value of the extension parameter can be achieved by scanning…
This article proposes a technique for the geometrically stable modeling of high-degree B-spline curves based on S-polygon in a float format, which will allow the accurate positioning of the end points of curves and the direction of the…
Inspired by shape constrained estimation under general nonnegative derivative constraints, this paper considers the B-spline approximation of constrained functions and studies the asymptotic performance of the constrained B-spline…
In this work, we present some new integration formulas for any order of accuracy as an application of the B-spline relations obtained in [1]. The resulting rules are defined as a perturbation of the trapezoidal integration method. We prove…
Contours may be viewed as the 2D outline of the image of an object. This type of data arises in medical imaging as well as in computer vision and can be modeled as data on a manifold and can be studied using statistical shape analysis.…
The least squares fit to a straight line, when both variables are affected by all equal uncorrelated errors, leads to very simple results for both the estimated parameters and their standard errors, of widespread applicability. In this…
Functions on a bounded domain in scientific computing are often approximated using piecewise polynomial approximations on meshes that adapt to the shape of the geometry. We study the problem of function approximation using splines on a…
This paper presents a learning-based method to solve the traditional parameterization and knot placement problems in B-spline approximation. Different from conventional heuristic methods or recent AI-based methods, the proposed method does…
Unmeasured, spatially-structured factors can confound associations between spatial environmental exposures and health outcomes. Adding flexible splines to a regression model is a simple approach for spatial confounding adjustment, but the…
Construction of spline surfaces from given boundary curves is one of the classical problems in computer aided geometric design, which regains much attention in isogeometric analysis in recent years and is called domain parameterization.…
This paper develops a unified theory of natural superconvergence points for polynomial spline approximations to second-order elliptic problems. Beginning with the one-dimensional case, we establish that when a point $x_0$ is a local…
The space of $C^1$ cubic Clough-Tocher splines is a classical finite element approximation space over triangulations for solving partial differential equations. However, for such a space there is no B-spline basis available, which is a…
Locally refined spline surfaces (LRB) is a representation well suited for scattered data approximation. When a data set has local details in some areas and is largely smooth in other, LR B-splines allow the spatial distribution of degrees…
Normal multi-scale transform [4] is a nonlinear multi-scale transform for representing geometric objects that has been recently investigated [1, 7, 10]. The restrictive role of the exact order of polynomial reproduction $P_e$ of the…
We derive a variational model to fit a composite B\'ezier curve to a set of data points on a Riemannian manifold. The resulting curve is obtained in such a way that its mean squared acceleration is minimal in addition to remaining close the…
A method is proposed for constructing a spline curve of the Bezier type, which is continuous along with its first derivative by a piecewise polynomial function. Conditions for its existence and uniqueness are given. The constructed curve…
Non-uniform B-spline dictionaries on a compact interval are discussed. For each given partition, dictionaries of B-spline functions for the corresponding spline space are constructed. It is asserted that, by dividing the given partition…