All Questions
Tagged with computational-geometry algorithms
67 questions
3
votes
1
answer
589
views
How to partition a graph into N groups with M elements nearest?
This problem probably already here but I could not find the right words to find it.
I have a list with 1700 points (geographic coordinates) and a need to separate into 17 groups with 100 nearest. I ...
- 131
4
votes
3
answers
2k
views
How to find the minimum number of hyperplanes to define a convex hull?
I have the following problem:
I have a convex hull $\Omega$ defined by a set of n-dimensional hyperplanes $S = [(n_1,d_1), (n_2,d_2),...,(n_k,d_k)]$ such that a point $p \in \Omega$ if $n_i^T p \geq ...
- 143
4
votes
2
answers
1k
views
Polyline averaging
I'm trying to find a method that can take a collection of polylines, each described by a list of connected points on a plane, and find an "average" path through them. The input lines do not loop.
...
- 51
3
votes
1
answer
2k
views
practical algorithm for constrained triangulation in two dimensions?
I'm looking for an algorithm that is easy to implement in practice (resulting in small amount of code), preferably incremental. As far as I know, the biggest problem with incremental constrained ...
- 131
9
votes
3
answers
3k
views
Complexity of matching red and blue points in the plane.
I'm just asking because I'm curious.
I was seeking references on the following problem, that a friend exposed to me last holidays :
Problem
Given $n$ red points and $n$ blue points in the plane in ...
- 4,123
13
votes
2
answers
664
views
Complexity of a weirdo two-dimensional sorting problem
Please forgive me if this is easy for some reason.
Suppose given $S$, a set of $n^2$ points in $\mathbb{R}^2$.
I want to choose a bijective map $f$ from $S$ to the set of lattice points in $\lbrace ...
- 19.2k
21
votes
8
answers
4k
views
Determine if circle is covered by some set of other circles
Suppose you have a set of circles $\mathcal{C} = \{ C_1, \ldots, C_n \}$ each with a fixed radius $r$ but varying centre coordinates. Next, you are given a new circle $C_{n+1}$ with the same radius $r$...
- 311
20
votes
2
answers
25k
views
Partitioning a polygon into convex parts
I'm looking for an algorithm to partition any simple closed polygon into convex sub-polygons--preferably as few as possible.
I know almost nothing about this subject, so I've been searching on Google ...
- 201
2
votes
2
answers
687
views
Where to submit a new convex hull algorithm?
Recently, I devised a new convex hull algorithm. Is there any forum where I can submit my work?
- 25
14
votes
2
answers
1k
views
Subfields of a function field
Is there an algorithm for generating (some or all) subfields of a certain genus of a given function field (even a random one,I mean for example generating a random elliptic subfield of a certain given ...
- 601
9
votes
5
answers
13k
views
Get a point inside a polygon
I have a 2D polygon of arbitrary geometry. I need to find any point that is inside of that polygon. Taking the center won't work, because the polygon might not be convex. Is there a way to quickly ...
- 201
3
votes
1
answer
818
views
Algorithm for Ham Sandwich with Points
I just recently learned the Ham Sandwich Theorem in my algebraic topology class. If we take the measure to be the counting measure and let $n=2$, then the theorem tells us that given a set of black ...
- 53
2
votes
2
answers
2k
views
Anuloid (Torus) x line intersection
Hi,
I need calculate ray (line) intersection with torus for my ray-tracing program (I know, its to graphics, but i need math behind it).
I can solve equation of order x^4, but thats too way slow (...
- 21
3
votes
3
answers
2k
views
Is there a simple criterion to determine if two parallelograms intersect?
Assume we are given two parallelograms in the plane. How can I check if their intersection is nonempty?
Note that I do not need to actually find the intersection.
- 979
5
votes
3
answers
478
views
What is the most general class of metric spaces for which the closest pair of points in a finite subset can be found in time O(n^(1+eps))?
What is the most general class of metric spaces for which the closest pair of points in any finite subset can be found in time O(n^(1+eps))? I have studied how to do this in O(n log(n)) in the plane, ...
- 2,302
11
votes
2
answers
3k
views
Algorithm for embedding a graph with metric constraints
Suppose I have a graph $G$ with vertex set $V$, edge set $E \subseteq {V \choose 2}$, a poistive integer $d$, and a weight function $w:E \to \mathbb{R}^{+}$. Is there a nice algorithmic way to decide ...
- 7,857
4
votes
1
answer
1k
views
Finding integer points on an N-d convex hull
Suppose we have a convex hull computed as the solution to a linear programming problem (via whatever method you want). Given this convex hull (and the inequalities that formed the convex hull) is ...
- 1,801