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I consider Point Location Problem in Polygon in repetitive mode in the case of simple polygon. In computational geometry,Point Location Problem in Polygon problem asks whether a given point in the pl …

The exercise is Given a set of point $S$ and a point $p$. Decide in $O(n)$ time if $p$ is a vertex of convex polygon formed from points of $S$. The problem is I am a little bit confused with t …

I try to find an approach to the following problem: Given the set of point $S$ and radius $r$, find the center point of circle, such that the circle contains the maximum number of points from the …

Definition: A polygon $P$ in the plane is called monotone with respect to a straight line $L$, if every line orthogonal to $L$ intersects $P$ at most twice. Given a polygon $P$, is it possible to …

Unfortunately I am still not so strong in understanding Sweep Line Algorithm. All papers and textbooks on the topic are already read, however understanding is still far away. Just in order to make it …

I have problem with solving the following exercise Given the set $P$ on $n$ points in two dimensions, build in time $O(n\log n)$ a data structure of $P$ such that given a horizontal segment $s$ fi …

I am trying to solve the following computational geometry problem. Let $S$ be a set of $n$ axis-parallel rectangles in the plane, so that the bottom edge of each rectangle in $S$ lies on the $x$-axis …

Given a set $S$ of points $p_1,..,p_2$ give the most efficient algorithm for determining if any 3 points of the set are collinear. The problem is I started with general definition but I cannot co …

I am given an exercise unfortunately I didn't succeed by myself. There is a set of rectangles $R_{1}..R_{n}$ and a rectangle $R_{0}$. Using plane sweeping algorithm determine if $R_{0}$ is complet …

It's well known that monotone polygons play a crucial role in polygon triangulation. Definition: A polygon $P$ in the plane is called monotone with respect to a straight line $L$, if every line o …

Given two sets $A$ and $B$ each containing $n$ disjoint points in the plane, compute the shortest distance between a point in $A$ and a point in $B$, i.e., $\min \space \{\mbox{ } \text{dist}(p, …

If there is a way to identify if two sets of points can be separated by a line? We have two sets of points $A$ and $B$ if there is a line that separates $A$ and $B$ such that all points of $A$ and …

I try to solve the following coverage problem. There are $n$ transmitters with coverage area of 1km and $n$ receivers. Decide in $O(n\log n)$ that all receivers are covered by any transmitter. Al …

I am wondering if there are any connection between convex polygon and castable object? What can we say about castability of the object if we know that the object is convex polygon and vice versa. Let' …

For a given planar graph $G(V,E)$ embedded in the plane, defined by a set of line segments $E= \left \{ e_1,...,e_m \right \} $, each segment $e_i$ is represented by its endpoints $\left \{ L_i,R_i …