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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…
In mathematics curves are typically defined as the images of continuous real functions (parametrizations) defined on a closed interval. They can also be defined as connected one-dimensional compact subsets of points. For simple curves of…
The property of preserving the convexity and concavity of the Bernstein polynomial and of the B\'{e}zier curves is used to generate a method of approximating the reliability polynomial of a hammock network. The mutual behaviour of the…
Implicit neural representations have emerged as a powerful approach for encoding complex geometries as continuous functions. These implicit models are widely used in computer vision and 3D content creation, but their integration into…
A recent type of B-spline functions, namely trigonometric cubic B-splines, are adapted to the collocation method for the numerical solutions of the Kuramoto-Sivashinsky equation. Having only first and second order derivatives of the…
Representing complex shapes with simple primitives in high accuracy is important for a variety of applications in computer graphics and geometry processing. Existing solutions may produce suboptimal samples or are complex to implement. We…
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…
This chapter presents an approach to embed the input/state/output constraints in a unified manner into the trajectory design for differentially flat systems. To that purpose, we specialize the flat outputs (or the reference trajectories) as…
A new global basis of B-splines is defined in the space of generalized quadratic splines (GQS) generated by Merrien subdivision algorithm. Then, refinement equations for these B-splines and the associated corner-cutting algorithm are given.…
Extracting shape information from object bound- aries is a well studied problem in vision, and has found tremen- dous use in applications like object recognition. Conversely, studying the space of shapes represented by curves satisfying…
The smooth piecewise-linear models cover a wide range of applications nowadays. Basically, there are two classes of them: models are transitional or hyperbolic according to their behaviour at the phase-transition zones. This study explored…
An intuitive design method is proposed for generating developable ruled B-spline surfaces from a sequence of straight line segments indicating the surface shape. The first and last line segments are enforced to be the head and tail ruling…
As a parametric motion representation, B\'ezier curves have significant applications in polynomial trajectory optimization for safe and smooth motion planning of various robotic systems, including flying drones, autonomous vehicles, and…
We present a novel approach enabling interactive visualization of volumetric Locally Refined B-splines (LR-splines). To this end we propose a highly efficient algorithm for direct visualization of scalar and vector fields given by an…
Like bisimulations, simulations and directed simulations are used for analyzing graph-based structures such as automata, labeled transition systems, linked data networks, Kripke models and interpretations in description logic. Simulations…
This paper investigates a variational model for splines in the image metamorphosis model for the smooth interpolation of key frames in the space of images. The Riemannian manifold of images based on the metamorphosis model defines shortest…
Spherical $t$-designs are finite point sets on the unit sphere that enable exact integration of polynomials of degree at most $t$ via equal-weight quadrature. This concept has recently been extended to spherical $t$-design curves by the use…
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…
This note is the updated outline of the article "Interpolational properties of planar spiral curves", Fund. and Applied Math., 2001, Vol.7, N.2, 441-463, published in Russian. The main result establishes boundary regions for spiral and…
Subdivision surfaces are considered as an extension of splines to accommodate models with complex topologies, making them useful for addressing PDEs on models with complex topologies in isogeometric analysis. This has generated a lot of…