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Computer Science Stack Exchange

Questions tagged [computational-geometry]

Questions about algorithmic solutions of geometric problems, or other algorithms making usage of geometry.

863 questions
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How generate n equidistant points in a n-1 dimensional space

As said, i want to build a program to generate n equidistant points in an euclidian space. From what i know 1d : all couple of points 2d : all equilateral triangles 3d : all equilateral tetrahedra up to 3d : i suppose it's called an equilateral…
KyBe
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Find a straight line to divide two convex polygons by equal area

Suppose, we have two non-overlapping convex polygons $A$ and $B$. How can we draw one straight line which divides $A$ into two parts of equal area and also divides $B$ into two equal area parts? Also, can we do this in complexity $O(n^2)$ or better?…
John Reese
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3 answers

Partitioning connected graphs in the plane

This is a geographic problem, where we have several connected graphs embedded on the plane, where none of them have overlapping edges/nodes. How can we divide the plane using line segments in such a way that each subdivision contains exactly one…
b9s
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King of the North: Placing bannermen surrounding castle

I was trying to solve the King of the North problem in Kattis. Basically, the problem is, the king has a castle to protect. To do this, he wants to place bannermen across the open areas surrounding the castle (some parts are closed thanks to natural…
hola
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6
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Extrema and saddle point of 3D field at different scales

I have a scalar 3D field $f(x, y, z)$ with $x,y,z$ on a regular grid. I would like to know the location of the maxima, minima, saddle points and their relation as a function of a smoothing scale. For that, I'm convolving my field $f$ with a…
cphyc
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6
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1 answer

Point in Polygon on the sphere

I'm looking at geometric objects on the sphere and need to determine if a point on the sphere is inside a spherical polygon. In our case a spherical polygon is a an ordered set of vertices $v_1v_2...v_n$ and the edges $v_iv_{i+1}$ are given by great…
Philip Mayer
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6
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1 answer

Number of vertices and edges lies on the boundary of bounded cells in line arrangement

I am learning computational geometry by myself using these lecture notes from ETH Zurich. Here is an exercise (8.9) I have been stuck for a few days: For a line arrangement $A$ of a set of $n$ lines in $R^2$, let $F$ denote the union of the closure…
CeibaM
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6
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Find the point with minimum max distance to any point in a set

Say I have a set of points on a 2d plane, how do I find the point(s) where the maximum euclidian distance to any of the points in the set is minimized?
BvdBijl
5
votes
1 answer

Checking for intersection of $d$-dimensional spheres

Is there a simple algorithm to check whether $n$ different balls (of the same radius) in $\mathbb{R}^d$ intersect? That is, coordinates of their centers $x_i$ are given, radius $R$ is given and we need to determine if there exists a point $p$ such…
Mathemage
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3D mesh segmentation simple algorithm

I am developing the algorithm reported in this article: Lest square conformal mapping Here is presented an algorithm to flat a 3d mesh on the parametric space, but i don't understand the segmentation step. Does anyone know an alternative…
Mugna
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1 answer

Computing the set of points nearest to a point in a polygon boundary

Let $P$ be a polygon. For each point $x$ on the boundary of $P$, denote by $N_P(x)$ the set of points in $P$, that are nearer to $x$ than to any other point on the boundary of $P$. Given a subset $X$ of the boundary (e.g. an interval contained in…
Erel Segal-Halevi
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5
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Smallest convex set containing given point

Given a set $M$ of $m$ points in $R^n$, where the number of points $m$ is much larger than the dimension $n$, and given a point $x$ in $R^n$ that we may assume is in the convex closure of $M$, is there an (efficient) algorithm that finds…
Mahir Lokvancic
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1 answer

Maximal expansion of a convex polygon

There is a convex polygon $X$ contained in another polygon $Z$ (which can be non-convex and even have holes). I would like to expand $X$ to a larger convex polygon $Y$ such that: $X\subseteq Y\subseteq Z$ $Y$ is maximal, i.e, there is no other…
Erel Segal-Halevi
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4
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delaunay sweep circle initialization

I recently came accross an interesting "sweep circle" algorithm for delaunay triangulation [1]. It's basic idea is seeding with a trivial triangulation (3 points), then gradually extending it outwards (points are sorted by their distance from a…
elad
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4
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Rotating sort algorithm

Take a set of $n$ points in the plane. You want to sort them by increasing abscissa. But you also want to sort them by abscissa after several arbitrary rotations, say $k$, in increasing angles. The obvious brute-force solution takes time $O(kn\log…
user16034
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