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This paper deals with a kind of design of a ruled surface. It combines concepts from the fields of computer aided geometric design and kinematics. A dual unit spherical B\'ezier-like curve on the dual unit sphere (DUS) is obtained with…
Geometric frameworks for analyzing curves are common in applications as they focus on invariant features and provide visually satisfying solutions to standard problems such as computing invariant distances, averaging curves, or registering…
In this paper, we study the spherical indicatrices of W-direction curves in three dimensional Euclidean space which were defined by using the unit Darboux vector field W of a Frenet curve, in [11]. We obtain the Frenet apparatus of these…
This thesis is devoted to the Differential Geometry of curves and surfaces along with applications in Quantum Mechanics. In the 1st part we introduce the well known Frenet frame. Later, we show that the curvature function is a lower bound…
We develop a transfer matrix formalism to visualize the framing of discrete piecewise linear curves in three dimensional space. Our approach is based on the concept of an intrinsically discrete curve, which enables us to more effectively…
The distance geometry problem asks to find a realization of a given simple edge-weighted graph in a Euclidean space of given dimension K, where the edges are realized as straight segments of lengths equal (or as close as possible) to the…
New quadrotor UAV control algorithms are developed, based on nonlinear surfaces composed of tracking errors that evolve directly on the nonlinear configuration manifold, thus inherently including in the control design the nonlinear…
Visual odometry techniques typically rely on feature extraction from a sequence of images and subsequent computation of optical flow. This point-to-point correspondence between two consecutive frames can be costly to compute and suffers…
Ruled surface is widely used in engineering design such as parting surface design of injection mold and checking surface design of checking fixture, which are usually generated by offsetting 3D curves. However, in 3D curve offset, there…
Unit disk graphs are intersection graphs of circles of unit radius in the plane. We present simple and provably good heuristics for a number of classical NP-hard optimization problems on unit disk graphs. The problems considered include…
This paper describes the foundations of a differential geometry of a quaternionic curves. The Frenet-Serret equations and the evolutes and evolvents of a particular quaternionic curve are accordingly determined. This new formulation takes…
In this study, we define the generalized normal ruled surface of a curve in the Euclidean 3-space $E^3$. We study the geometry of such surfaces by calculating the Gaussian and mean curvatures to determine when the surface is flat or minimal…
In this paper, we investigate the ruled surfaces generated by a straight line according to rotation minimizing frame (RMF). Using this frame of a straight line, we obtained the necessary and sufficient conditions when the ruled surface is…
The main objective of this work is to describe a general and original approach for computing an off-line solution for a set of parameters describing the geometry of the domain. That is, a solution able to include information for different…
Aiming at an obstacle avoidance problem with dynamic constraints for Unmanned Surface Vehicle (USV), a method based on Circle Grid Trajectory Cell (CGTC) is proposed. Firstly, the ship model and standardization rules are constructed to…
This paper presents a novel feedback method on the motion planning for unicycle robots in environments with static obstacles, along with an extension to the distributed planning and coordination in multi-robot systems. The method employs a…
We define discrete constant mean curvature (cmc) surfaces in the three-dimensional Euclidean and Lorentz spaces in terms of sphere packings with orthogonally intersecting circles. These discrete cmc surfaces can be constructed from…
In this paper, we define a new type of ruled surface called ruled surface by using the alternative frame of a base curve. Then, we study its differential geometric properties such as striction line, distribution parameter, fundamental…
Simple geometric models of ice surface shape and equations of motion of objects on these surfaces can be used to explain ejection of sliders from ice tracks. Simulations using these can be used to explain why certain design features can be…
This paper proposes to generalize linear subdivision schemes to nonlinear subdivision schemes for curve and surface modeling by refining vertex positions together with refinement of unit control normals at the vertices. For each round of…