Related papers: Compass Constructions
Line planning, i.e. choosing paths which are operated by one vehicle end-to-end, is an important aspect of public transport planning. While there exists heuristic procedures for generating lines from scratch, most theoretical observations…
It is shown in this paper that it is possible, at least in principle, to construct a traversable wormhole that is stable to linearized radial perturbations by specifying relatively simple conditions on the shape and redshift functions.
We study the topological construction called Mapper in the context of simply connected domains, in particular on images. The Mapper construction can be considered as a generalization for contour, split, and joint trees on simply connected…
This paper introduces a method for learning to generate line drawings from 3D models. Our architecture incorporates a differentiable module operating on geometric features of the 3D model, and an image-based module operating on view-based…
With the increasing integration of robots into human life, their role in architectural spaces where people spend most of their time has become more prominent. While motion capabilities and accurate localization for automated robots have…
This paper describes new, simple, recursive methods of construction for orientable sequences, i.e. periodic binary sequences in which any n-tuple occurs at most once in a period in either direction. As has been previously described, such…
A construction of polytopes is given based on integers. These geometries are constructed through a mapping to pure numbers and have multiple applications, including statistical mechanics and computer science. The number form is useful in…
The problem of providing meaningful routing directions over road networks is of great importance. In many real-life cases, the fastest route may not be the ideal choice for providing directions in written, spoken text, or for an unfamiliar…
In three spatial dimensions, communication channels are free to pass over or under each other so as to cross without intersecting; in two dimensions, assuming channels of strictly positive thickness, this is not the case. It is natural,…
For every $n$, we construct two curves in the plane that intersect at least $n$ times and do not form spirals. The construction is in three stages: we first exhibit closed curves on the torus that do not form double spirals, then arcs on…
This work, which may be seen as a companion paper to \cite{RS2}, handles the way the intersection points made by the diagonals of a regular polygon are distributed. It was stated recently by the authors that these points lie exclusively on…
We give a general procedure for gluing together possibly noncompact manifolds of constant scalar curvature which satisfy an extra nondegeneracy hypothesis. Our aim is to provide a simple paradigm for making `analytic' connected sums. In…
A random jigsaw puzzle is constructed by arranging $n^2$ square pieces into an $n \times n$ grid and assigning to each edge of a piece one of $q$ available colours uniformly at random, with the restriction that touching edges receive the…
A drawing of a graph is said to be a {\em straight-line drawing} if the vertices of $G$ are represented by distinct points in the plane and every edge is represented by a straight-line segment connecting the corresponding pair of vertices…
Bach et al. [1] recently presented an algorithm for constructing confluent drawings, by leveraging power graph decomposition to generate an auxiliary routing graph. We identify two issues with their method which we call the node split and…
We suggest a geometric visualization of the process of constructing a triangle with prescribed bisectors that makes the existence of such a triangle geometrically evident.
We prove that the golden angle (an angle that divides the circle in the golden ratio) is not constructible using straightedge and compass.
Let P be a point inside a convex quadrilateral ABCD. The lines from P to the vertices of the quadrilateral divide the quadrilateral into four triangles. If we locate a triangle center in each of these triangles, the four triangle centers…
A method to construct transition curves using a family of the quartic Bezier spiral is described. The transition curves discussed are S-shape and C-shape of contact, between two separated circles. A spiral is a curve of monotone increasing…
We prove that a surface in real 3-space containing a line and a circle through each point is a quadric. We also give some particular results on the classification of surfaces containing several circles through each point.