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Control over the physical properties of materials is ubiquitously required in many fields. One means by which this can be achieved is controlling the internal structure of multi-component materials with an eye to enhancing mechanical…
Algorithms based on gradient descent for computing the elastic shape registration of two simple surfaces in 3-dimensional space and therefore the elastic shape distance between them have been proposed by Kurtek, Jermyn, et al., and more…
The Arbitrary Pattern Formation problem asks to design a distributed algorithm that allows a set of autonomous mobile robots to form any specific but arbitrary geometric pattern given as input. The problem has been extensively studied in…
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…
Texture is an essential property of physical objects that affects aesthetics, usability, and functionality. However, designing and applying textures to 3D objects with existing tools remains difficult and time-consuming; it requires…
Surfaces of revolution in three-dimensional Euclidean space are considered. Several new examples of surfaces of revolution associated with well-known solvable cases of the Schoedinger equation (infinite well, harmonic oscillator, Coulomb…
We investigate through computational simulations with a pore network model the formation of patterns caused by erosion-deposition mechanisms. In this model, the geometry of the pore space changes dynamically as a consequence of the coupling…
The one-sided offset surface Fd of a given surface F is, roughly speaking, obtained by shifting the tangent planes of F in direction of its oriented normal vector. The conchoid surface Gd of a given surface G is roughly speaking obtained by…
Triangles are everywhere in the virtual world. The surface of nearly every graphical object is saved as a triangular mesh on a computer. Light effects and movements of virtual objects are computed on the basis of triangulations. Besides…
We give a new formula for the rotation number (or Whitney index) of a smooth closed plane curve. This formula is obtained from the winding numbers associated with the regions and the crossing points of the curve. One difference with the…
We consider surfaces of revolution in the three-dimensional Euclidean space which are of coordinate finite type with respect to the third fundamental form. We show that a surface of revolution satisfying the preceding relation is a catenoid…
We show under some natural smoothness assumptions that pure in-plane drill rotations as deformation mappings of a $C^2$-smooth regular shell surface to another one parametrized over the same domain are impossible provided that the rotations…
Inspired by traditional handmade crafts, where a person improvises assemblies based on the available objects, we formally introduce the Craft Assembly Task. It is a robotic assembly task that involves building an accurate representation of…
Consider the two-dimensional inverse elastic wave scattering by an infinite rough surface with a Dirichlet boundary condition. A non-interative sampling technique is proposed for detecting the rough surface by taking elastic wave…
We extend the design of radially symmetric three-dimensional invisibility cloaks through transformation optics to cloaks with a surface of revolution. We derive the expression of the transformation matrix and show that one of its…
The good mesh quality of an evolving discretized surface or domain is often compromised during time evolution. In recent years this phenomena have been overcome in a couple of ways, one of them uses arbitrary Lagrangian Eulerian maps.…
We introduce an operation that measures the self intersections of paths on a surface. As applications, we give a criterion of the realizability of a generalized Dehn twist, and derive a geometric constraint on the image of the Johnson…
We present a novel surface convolution operator acting on vector fields that is based on a simple observation: instead of combining neighboring features with respect to a single coordinate parameterization defined at a given point, we have…
A common task in robotics is unloading identical goods from a tray with rectangular grid structure. This naturally leads to the idea of programming the process at one grid position only and translating the motion to the other grid points,…
A circle pattern is a configuration of circles in the plane whose combinatorics is given by a planar graph G such that to each vertex of G corresponds a circle. If two vertices are connected by an edge in G, the corresponding circles…