maximum intersectionIn this note we study the following question: Given n halfplanes, find the maximum-area bounded intersection of k halfplanes out of them. We solve this problem in O ( n 3 k ) time and O ( n 2 k ) space.
(The curves have been sectioned here for the intersection points, so that the control points shown do not reflect the original, unintersected curves.) Now here is a plot of the non-linear, two-dimensional distance function between these two curves. The horizontal axis of the plot is the ...
An airplane leaves Chicago and makes the 3000-km trip to Los Angeles in 5.0 h. A second plane leaves Chicago one-half hour later and arrives in Los Angeles at the same time. Compare the average velocities of the two planes. Ignore the curvature of Earth and the difference in...
Given two functions {eq}f(x) \leq g(x) {/eq} on the interval {eq}[a, b], {/eq} we can calculate the area between the graphs of the functions using the integral {eq}\displaystyle\int_a^b g(x) - f(x) \: dx. {/eq} Answer and Explan...
When fitting planes to 4 out of the 7 points, only a single plane can be found. Middle, Right: Examples where the point-to-model assignment fails at the intersection of planes. erate many instances by repeatedly selecting minimal point sets and fitting model instan...
In this section we show that this is not the case: the complexity of the space of rectangles that fit inside P, that is, the complexity of the intersection of Π(P) with the manifold 〈u,v〉=0, is already Θ(n3) in the worst case. Therefore, asymptotically we are not losing anythi...
An obvious approach to our problem is to precompute all intersections between the objects and store the intersections in a suitable intersection-searching data structure. This may give fast query times, but in the worst case any two objects intersect, so\Omega (n^2)is a lower bound on the ...
the angles between the direction to the object and given reference planes. In universal (two-coordinate) direction finders, both angles that determine the bearing are measured. In the azimuthal type, only one of the angles (the azimuth) is obtained; this method is employed in maritime ...
The weather has a major impact on the profitability, safety, and environmental sustainability of the routes sailed by seagoing vessels. The prevailing weat
Basins of attractions are phase-planes that demonstrate iterations employed by the iterative method, which can assume different choices for the initial guess z 0 . Such 2D regions are esthetically so beautiful that their applications are not only found in applied mathematics, but also people working...