Related papers: Fast B-spline Curve Fitting by L-BFGS
Approximating data points in three or higher dimension space based on cubic B-spline curve is presented. Representations for planar curves, are merged and extended to the higher dimension. The curve is fitted to the order of data points, or…
This paper explores an efficient Lagrangian approach for evolving point cloud data on smooth manifolds. In this preliminary study, we focus on analyzing plane curves, and our ultimate goal is to provide an alternative to the conventional…
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…
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…
A fast algorithm for B-splines in mixed models is presented. B-splines have local support and are computational attractive, because the corresponding matrices are sparse. A key element of the new algorithm is that the local character of…
We propose a novel B-spline trajectory optimization method for autonomous racing. We consider the unavailability of sophisticated race car and race track dynamics in early-stage autonomous motorsports development and derive methods that…
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…
We present a method for fitting monotone curves using cubic B-splines, which is equivalent to putting a monotonicity constraint on the coefficients. We explore different ways of enforcing this constraint and analyze their theoretical and…
We extend our recent curve-evolution framework based on localized B-spline interpolation to present an adaptive Lagrangian framework for the geometric evolution of point-cloud data representing smooth, codimension-one surfaces in…
Large-scale unconstrained optimization is a fundamental and important class of, yet not well-solved problems in numerical optimization. The main challenge in designing an algorithm is to require a few storage locations or very inexpensive…
This paper introduces a computationally efficient method that converges globally to B-stationary points of mathematical programs with equilibrium constraints (MPECs). B-stationarity is necessary for optimality and means that no feasible…
Particle tracing through numerical integration is a well-known approach to generating pathlines for visualization. However, for particle simulations, the computation of pathlines is expensive, since the interpolation method is complicated…
Being able to reverse engineer from point cloud data to obtain 3D models is important in modeling. As our main contribution, we present a new method to obtain a tensor product B-spline representation from point cloud data by fitting…
Background and Objective. B-spline interpolation (BSI) is a popular technique in the context of medical imaging due to its adaptability and robustness in 3D object modeling. A field that utilizes BSI is Image Guided Surgery (IGS). IGS…
This paper describes an implementation of the L-BFGS method designed to deal with two adversarial situations. The first occurs in distributed computing environments where some of the computational nodes devoted to the evaluation of the…
Fitting B-splines to discrete data is especially challenging when the given data contain noise, jumps, or corners. Here, we describe how periodic data sets with these features can be efficiently and robustly approximated with B-splines by…
The limited memory BFGS (L-BFGS) method is one of the popular methods for solving large-scale unconstrained optimization. Since the standard L-BFGS method uses a line search to guarantee its global convergence, it sometimes requires a large…
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…
We propose a modified BFGS algorithm for multiobjective optimization problems with global convergence, even in the absence of convexity assumptions on the objective functions. Furthermore, we establish the superlinear convergence of the…
For large-scale data fitting, the least-squares progressive iterative approximation is a widely used method in many applied domains because of its intuitive geometric meaning and efficiency. In this work, we present a randomized progressive…