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Geofences have attracted significant attention in the design of spatial and virtual regions for managing and engaging spatiotemporal events. By using geofences to monitor human activity across their boundaries, content providers can create…
Barrier function-based inequality constraints are a means to enforce safety specifications for control systems. When used in conjunction with a convex optimization program, they provide a computationally efficient method to enforce safety…
In this paper we present methods for triangulation of infinite cylinders from image line silhouettes. We show numerically that linear estimation of a general quadric surface is inherently a badly posed problem. Instead we propose to…
Computing a quasi-developable strip surface bounded by design curves finds wide industrial applications. Existing methods compute discrete surfaces composed of developable lines connecting sampling points on input curves which are not…
Segmentation, a useful/powerful technique in pattern recognition, is the process of identifying object outlines within images. There are a number of efficient algorithms for segmentation in Euclidean space that depend on the variational…
Monocular Odometry systems can be broadly categorized as being either Direct, Indirect, or a hybrid of both. While Indirect systems process an alternative image representation to compute geometric residuals, Direct methods process the image…
The three-dimensional cylindrical regression problem is a problem of finding a cylinder best fitting a group of points in three-dimensional Euclidean space. The words best fitting are usually understood in the sense of the minimum root mean…
The design process and complexity of existing safety controls are heavily determined by the geometrical properties of the environment, which affects the proof of convergence, design scalability, performance robustness, and numerical…
The paper focuses on synthesizing optimal contact curves that can be used to ensure a rolling constraint between two bodies in relative motion. We show that geodesic based contact curves generated on both the contacting surfaces are…
A new gridding technique for the solution of partial differential equations in cubical geometry is presented. The method is based on volume penalization, allowing for the imposition of a cubical geometry inside of its circumscribing sphere.…
In this paper we study similarity measures for moving curves which can, for example, model changing coastlines or retreating glacier termini. Points on a moving curve have two parameters, namely the position along the curve as well as time.…
We propose an online planning approach for racing that generates the time-optimal trajectory for the upcoming track section. The resulting trajectory takes the current vehicle state, effects caused by \acl{3D} track geometries, and speed…
The paper studies the problem of making Getz's bicycle model traverse a strictly convex Jordan curve with bounded roll angle and bounded speed. The approach to solving this problem is based on the virtual holonomic constraint (VHC) method.…
The Voronoi diagram-based dual-front active contour models are known as a powerful and efficient way for addressing the image segmentation and domain partitioning problems. In the basic formulation of the dual-front models, the evolving…
The finite strain theory is reformulated in the frame of the Tangential Differential Calculus (TDC) resulting in a unification in a threefold sense. Firstly, ropes, membranes and three-dimensional continua are treated with one set of…
We propose a robust nonlinear model predictive control (MPC) scheme for trajectory-tracking control of autonomous vehicles at the limits of handling on non-planar road surfaces. We derive the dynamics from first principles and selectively…
Rule-based methods are often used for assigning fiber orientation to cardiac anatomical models. However, existing methods have been developed using data mostly from the left ventricle. As a consequence, fiber information obtained from…
This paper is concerned with the use of the stereographic projection to map the points of a design on the sphere in three dimensions onto a two-dimensional stereogram. Details of the projection and its attendant stereogram are given and the…
This paper constructs hyperbolic polyhedral metrics via circle packings. We introduce the curvature of circles as a parameter to include all three types of constant curvature curves in the hyperbolic geometry. This provides a unified…
Equilibrium solutions are believed to structure the pathways for ergodic trajectories in a dynamical system. However, equilibria are atypical for systems with continuous symmetries, i.e. for systems with homogeneous spatial dimensions,…