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The fundamental method to create a buffer around a geographic feature stored in a vector data model, with a given radius r is as follows: [4] Single point: Create a circle around the point with radius r. Polyline, which consists of an ordered list of points (vertices) connected by straight lines. This is also used for the boundary of a polygon.
A cyclocycloid is a roulette traced by a point attached to a circle of radius r rolling around, a fixed circle of radius R, where the point is at a distance d from the center of the exterior circle. The red curve is a cyclocycloid (in this case an hypocycloid ) drawn as the smaller black circle rolls around inside the larger blue circle ...
We know which of the points P i defining Q j is closer to the each point of the halfline containing center of the enclosing circle of the constrained problem solution. This point could be discarded. The half-plane where the unconstrained solution lies could be determined by the points P i on the boundary of the constrained circle solution. (The ...
Gauss's circle problem asks how many points there are inside this circle of the form (,) where and are both integers. Since the equation of this circle is given in Cartesian coordinates by x 2 + y 2 = r 2 {\displaystyle x^{2}+y^{2}=r^{2}} , the question is equivalently asking how many pairs of integers m and n there are such that
Set the new radius for v to be the value for which k circles of radius r would give a covering angle of exactly 2π. Each of these steps may be performed with simple trigonometric calculations, and as Collins and Stephenson argue, the system of radii converges rapidly to a unique fixed point for which all covering angles are exactly 2π. Once ...
The point P is the inversion point of Q; the polar is the line through P that is perpendicular to the line containing O, P and Q. If point R is the inverse of point P then the lines perpendicular to the line PR through one of the points is the polar of the other point (the pole). Poles and polars have several useful properties: