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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 ...
1 vote
1 answer
264 views

Could somebody suggest a way to determine if a parallelogram contains another parallelogram?

I thought of one way to do this. Using the algorithm which determines if a point is inside a parallelogram, one can determine if the polygon contains the point within $2N$ steps ($N=2$ for ...
0 votes
1 answer
1k views

Fast way to generate random points in 2D according to a density function

I'm looking for a fast way to generate random points in 2D according to a given 2D density function. For instance something like this: Right now I'm using a modified version of "Poisson disc&...
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.
4 votes
2 answers
213 views

Algorithm for reporting all triangles with unique interior point

What is known about the complexity of and/or practical algorithms for reporting all triplets of points from finite set of at least four points of which no three are collinear in the Euclidean plane, ...
4 votes
2 answers
4k views

Curves similarity metric [closed]

I am working on an optical character recognition algorithm that takes vector data (i.e. polylines) as input rather than raster picture. E.g., we have N polyline samples, and when certain polyline is ...
3 votes
1 answer
288 views

Generalization of notion of convexity

I am searching for the correct term for the following, if it exists. A set $X\subset \mathbb{R}^2$ is called $r$-convex if for any two points $x_1, x_2\in X$ such that there exists an arc of radius $...