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The purpose of the present article is the study of duals of functional codes on algebraic surfaces. We give a direct geometrical description of them, using differentials. Even if this geometrical description is less trivial, it can be…
Convex geometries form a subclass of closure systems with unique criticals, or $UC$-systems. We show that the $F$-basis introduced in [1] for $UC$-systems, becomes optimum in convex geometries, in two essential parts of the basis: right…
This work deals with shape optimization for contact mechanics. More specifically, the linear elasticity model is considered under the small deformations hypothesis, and the elastic body is assumed to be in contact (sliding or with Tresca…
Optimization under structural constraints is typically analyzed through projection or penalty methods, obscuring the geometric mechanism by which constraints shape admissible dynamics. We propose an operator-theoretic formulation in which…
In a physical design problem, the designer chooses values of some physical parameters, within limits, to optimize the resulting field. We focus on the specific case in which each physical design parameter is the ratio of two field…
We investigate the singularities of two-ruled hypersurfaces in the Euclidean four-space. By considering the points that minimize the distance between adjacent rulings, we obtain a characterization the striction curve. We introduce the…
The research on developing planar curves to produce visually pleasing products (ranges from electric appliances to car body design) and indentifying/modifying planar curves for special purposes namely for railway design, highway design and…
In the present article, we consider Algebraic Geometry codes on some rational surfaces. The estimate of the minimum distance is translated into a point counting problem on plane curves. This problem is solved by applying the upper bound…
We study geometry of curves passing through a Whitney umbrella by using a Darboux frame along it. We define three invariants by using Frenet-Serre type formula relating to the geodesic curvature, the normal curvature, and the geodesic…
Implementing virtual fixtures in guiding tasks constrains the movement of the robot's end effector to specific curves within its workspace. However, incorporating guiding frameworks may encounter discontinuities when optimizing the…
It is shown how a complete set of hydrodynamic equations describing an unsteady three-dimensional viscous flow nearby a solid body, can be reduced to a closed system of surface equations using the method of dimension reduction of…
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…
In this study, we define some new types of ruled surfaces called slant ruled surfaces. We give some characterizations for a regular ruled surface to be a slant ruled surface in Euclidean 3- space. We show that if the slant ruled surface is…
In order to determine the optimal strategy to run a race on a curved track according to the lane number, we introduce a model based on differential equations for the velocity, the propulsive force and the anaerobic energy which takes into…
We propose and experimentally test a method to fabricate patterns of steep, sharp features on surfaces, by exploiting the nonlinear dynamics of uniformly ion bombarded surfaces. We show via theory, simulation, and experiment, that the…
In this paper we give a brief overview of the geometry of involute gears, from a mathematical more than an engineering perspective. We also list some of the many variant geared mechanisms and discuss some of our 3D printed mechanisms.
We analyze human poses and motion by introducing three sequences of easily calculated surface descriptors that are invariant under reparametrizations and Euclidean transformations. These descriptors are obtained by associating to each…
We survey the role of symmetry in diffeomorphic registration of landmarks, curves, surfaces, images and higher-order data. The infinite dimensional problem of finding correspondences between objects can for a range of concrete data types be…
A ruled surface is a shape swept out by moving a line in 3D space. Due to their simple geometric forms, ruled surfaces have applications in various domains such as architecture and engineering. In the past, various approaches have been…
This letter studies a distributed collision avoidance control problem for a group of rigid bodies on a sphere. A rigid body network, consisting of multiple rigid bodies constrained to a spherical surface and an interconnection topology, is…