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Discovering population dynamics from point cloud data has experienced increased popularity in various applications, including GPS behavior prediction, multi-target tracking, and single cell analysis. Existing methods require data in multiple time ...

We present a novel benchmark suite for implementations of vector fields in high-performance computing environments to aid developers in quantifying and ranking their performance. We decompose the design space of such benchmarks into access patterns and ...

We introduce a framework for representing face-based directional fields of an arbitrary piecewise-polynomial order. Our framework is based on a primal-dual decomposition of fields, where the exact component of a field is the gradient of piecewise-...

Given a family of locally Lipschitz vector fields $X(x)=(X_1(x),\dots,X_m(x))$ on $\mathbb{R}^n$, $m\leq n$, we study integral functionals depending on $X$. Using the results in [A. Maione, A. Pinamonti, and F. Serra Cassano, J. Math. Pures Appl. (9), 139 (...

We present a novel linear subdivision scheme for face-based tangent directional fields on triangle meshes. Our subdivision scheme is based on a novel coordinate-free representation of directional fields as halfedge-based scalar quantities, bridging the ...

Vector fields arise in a variety of quantity measure and visualization techniques, such as fluid flow imaging, motion estimation, deformation measures, and color imaging, leading to a better understanding of physical phenomena. Recent progress in vector ...

This paper investigates the possibility of evolving new particle swarm equations representing a collective search mechanism, acting in environments with unknown external dynamics, using Geometric Semantic Genetic Programming (GSGP). The proposed method ...

Rip current are fast moving and narrow currents that are strongest near the beach. They are dangerous not only for novice but also experienced swimmers. Once caught in the current, the flow of the water pulls the person away from the beach. Many people ...

We study local controllability and optimal control problems for invertible discrete-time systems. We present second order necessary and sufficient conditions for optimality and for local controllability. The conditions are stated in geometric terms, using ...

This paper is concerned with closed orbits of non-smooth vector fields on the plane. For a class of non-smooth vector fields we provide necessary and sufficient conditions for the existence of closed poly-trajectorie. By means of a regularization ...

We show how to model geometric patterns on surfaces. We build on the concept of shape grammars to allow the grammars to be guided by a vector or tensor field. Our approach affords greater artistic freedom in design and enables the use of grammars to ...

This paper presents a computational framework that allows for a robust extraction of the extremal structure of scalar and vector fields on 2D manifolds embedded in 3D. This structure consists of critical points, separatrices, and periodic orbits. The ...

Gradient vector flow snakes are a very common method in bio-medical image segmentation. The use of gradient vector flow herein brings some major advantages like a large capture range and a good adaption of the snakes in concave regions. In some cases ...

We develop a direct and accurate approach for local resampling in vector fields, and then use the approach to synthesise textures on 2D manifold surfaces directly from a texture exemplar. Regular-grid patches produced by the local resampling are used as ...

We introduce stochastic models for flow fields with parameters that dictate the scale-dependent (self-similar) character of the field and control the balance between its rotational vs compressive behaviour. The development of our models is motivated by ...

We consider a dynamical system X on a compact differentiable manifold M and the induced dynamical system X ( ) on the universal covering space $$ \tilde M $$ of M . We develop algebraic topology methods for estimating the lower bounds on the number of ...

The article is devoted to a motion control problem for a differentially driven mobile robot in the task of trajectory tracking ...

This paper is devoted to the way point following motion task of a unicycle where the motion planning and the closed-loop motion realization ...

We introduce and illustrate a design framework whereby tabletop documents are oriented according to vector fields that can be visualized and altered by end users. We explore and illustrate the design space using interactive 2D mockups and show how this ...

This work introduces a new approach to modeling object trajectories in image sequences. Trajectories performed by natural objects (e.g., people, animals) typically depend on the position of each object in the scene and can change in an unpredictable ...