A two-step method is proposed for solving this problem. At the first step, using the Dulac–Cherkas test, we find nested closed curves that have no common points and split the simply connected domain into doubly connected subdomains, with each curve being transversal to the vector field of ...
Let $P$ be a polygonal curve in $\mathbb{R}^D$ of length $n$, and $S$ be a point set of size $k$. The Curve/Point Set Matching problem consists of finding a polygonal curve $Q$ on $S$ such that its Fr\'echet distance from $P$ is less than a given $\varep
Conformal transformation of the circles through the origin in the (x, y)-plane (left) into lines in the (u, v)-plane (right) Full size image 5.1.2 Hough Transform The Hough transform [2] is a technique that finds clusters of points that lie on or close to a parametric curve such ...
Animals have evolved mechanisms to travel safely and efficiently within different habitats. On a journey in dense terrains animals avoid collisions and cross narrow passages while controlling an overall course. Multiple hypotheses target how animals solv
If it is, then you have to deal with individual polyline segments rather than the entire polyline, and use Curve.GetPointAtDist() in a loop to calculate the points, and when your distance exceeds the length of the segment, you just use the segment's endpoint. If the segment is always ...
Find the length of the curve e^t \sin t\vec i - e^t\vec j + e^t \cos t\vec k from t = 0 to t = 1. Find \frac{d}{dx} [\int_0^{x^3} \sin t \,dt ] Find ds/dt for s = (1 - sin t ) / (2 +...
(habitable planets) per planetary system, fl = the fraction of habitable planets that develop primitive life, fi = the fraction of planets with life that evolve intelligent life and civilizations, fc = the fraction of civilizations that become ACCs, L = the length of time ...
This measurement reflects the usefulness of the module for a given a design goal. Using modules with high utility values should result in superior designs. We propose a heuristic which iteratively perturbs module utility values until they lead to good module selections. Our experiments show that ...
Self-shaping systems offer a promising approach for making complex 3D geometries from the material-driven transformation of 2D sheets. However, current res
We give exact O(n3)-time algorithms and (1−ε)-approximation algorithms that take time O(ε−1/2logn+ε−3/2). (For maximizing the perimeter we allow the degenerate solution consisting of a single segment whose perimeter is twice its length.) To the best of our knowledge, ...