Related papers: Plane-filling trails
Intersection algorithms are very important in computation of geometrical problems. Algorithms for a line intersection with linear or quadratic surfaces are quite efficient. However, algorithms for a line intersection with other surfaces are…
The efficiency of modern computer graphics allows us to explore collections of space curves simultaneously with "drag-to-rotate" interfaces. This inspires us to replace "scatterplots of points" with "scatterplots of curves" to…
A covering path for a finite set $P$ of points in the plane is a polygonal path such that every point of $P$ lies on a segment of the path. The vertices of the path need not be at points of $P$. A covering path is plane if its segments do…
Visualizing very large matrices involves many formidable problems. Various popular solutions to these problems involve sampling, clustering, projection, or feature selection to reduce the size and complexity of the original task. An…
A survey of tilings in the plane for a general audience.
We investigate the curves in the complex plane which are generated by sequences of real numbers being the lifts of the points on the orbit of an orientation preserving circle homeomorphism. Geometrical properties of these curves such as…
Models for predicting aircraft motion are an important component of modern aeronautical systems. These models help aircraft plan collision avoidance maneuvers and help conduct offline performance and safety analyses. In this article, we…
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…
Given two points in the plane, a set of obstacles defined by closed curves, and an integer $k$, does there exist a path between the two designated points intersecting at most $k$ of the obstacles? This is a fundamental and well-studied…
Machine learning models fit complex algorithms to arbitrarily large datasets. These algorithms are well-known to be high on performance and low on interpretability. We use interactive visualization of slices of predictor space to address…
We derive a local criterion for a plane near-triangulated graph to be perfect. It is shown that a plane near-triangulated graph is perfect if and only if it does not contain either a vertex, an edge or a triangle, the neighbourhood of which…
Object tracking systems play important roles in tracking moving objects and overcoming problems such as safety, security and other location-related applications. Problems arise from the difficulties in creating a well-defined and…
Coverage path planning is a fundamental challenge in robotics, with diverse applications in aerial surveillance, manufacturing, cleaning, inspection, agriculture, and more. The main objective is to devise a trajectory for an agent that…
Surveillance and surveying are two important applications of empirical research. A major part of terrain modelling is supported by photographic surveys which are used for capturing expansive natural surfaces using a wide range of sensors --…
We consider here square tilings of the plane. By extending the formalism introduced in [3] we build a correspondence between plane maps endowed with an harmonic vector and square tilings satisfying a condition of regularity. In the case of…
We study the geometry of spaces of planes on smooth complete intersections of three quadrics, with a view toward rationality questions.
We introduce an estimator for the curvature of curves and surfaces by using finite sample points drawn from sampling a probability distribution that has support on the curve or surface. First we give an algorithm for estimation of the…
We define LCL decompositions of the plane and investigate the advantages of using such decompositions in the context of digital topology. We show that discretization schemes based on such decompositions associate, to each LCL tiling of the…
We study the sets of planes in an even dimensional real vector space $V$ which are simultaneously stabilised by a pair of complex structures on $V$. We completely describe these sets of planes for pairs of orthogonal complex structures.…
Skeleton is a new notion designed for constructing space-filling curves of self-similar sets. It is shown in [Dai, Rao and Zhang, Space-filling curves of self-similar sets (II): Edge-to-trail substitution…