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Questions tagged [polygons]

63 questions
8
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3 answers

Partial polygon matching

I am looking for fast procedures for polygon matching, i.e. checking polygon similarity under different transforms translation only, translation + rotation, translation + scaling, translation + rotation + scaling (= similarity). The matching can…
user16034
5
votes
1 answer

Is there a computationally optimal point-in-polygon solution (for a dynamic scenario)?

I am approaching a problem where, among other things, I will have to repeatedly check if a point is within a (set of) polygon(s) in the 2D plane. the polygons are either convex or star-shaped with a non-singular kernel if multiple polygons, they…
Federico
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1 answer

Can we find the largest intersecting subfamily of convex polygons in quadratic time?

Let $\mathcal{F} = \{P_1, P_2,\ldots,P_m\}$ be a family of (closed) convex polygons in the plane, each represented by their vertices in (say) clockwise order. Let $n$ be the total number of vertices (you can assume general position, no two vertices…
Tassle
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3 answers

How can I determine if two vertices on a polygon are consecutive?

Suppose I have a set of points that construct a convex polygon in the Cartesian plane with the points as its vertices. I randomly choose two vertices and want to know if they are consecutive vertices on the polygon. Does anyone know of an algorithm…
martinba314
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4
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0 answers

Construct polygons from axis-aligned intervals

Scenario Consider one or more curved shapes in 2D space, clipped to a rectangular viewport. For example: Unfortunately, data that would describe these shapes precisely, is not available. Input data All that is available are the intersections of the…
smls
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4
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1 answer

An algorithm to find the area of intersection between a convex polygon and a 3D polyhedron?

Suppose I have a set of points in 3D which are all co-planar, and which describe the vertices of a convex polygon. I know the coordinates of all of these vertices, I know the unit normal to the plane of the polygon, and I know the order (in a…
John Barber
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4
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1 answer

Convex-hull of a star shaped polygon in O(n)

I'm trying to develop an algorithm to find a convex hull of a star shaped polygon in $O(n)$ time. The specific problem, which is also described here, is as follows: A polygon $P$ is star-shaped if there exists a point $p$ in the interior of $P$…
user20691
4
votes
1 answer

Finding all faces in a wireframe mesh

I'm trying to find an algorithm for finding all faces in a wireframe mesh. Wireframe means only the vertices and edges are given as input. There is no restriction on the number of edges a resulting face can have and the face can be convex or…
hgs3
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3 answers

Is there an efficient algorithm to extract the farthest ends of a thin contour?

Let's say you have pixel bitmaps that look something like this: From this I can easily extract a contour, which will be a concave polygon defined by a set of 2D points. The question is what is the fastest algorithm to pick, from the set of polygon…
glopes
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4
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3 answers

Repeated point in polygon: preprocessing complexity given logarithmic query time?

I am interested in the repeated point in polygon problem, where one is given a polygon in a preprocessing phase and in the online phase, one is asked whether a point is in that polygon. The polygon is not necessarily simple. I am interested in the…
Reinstate Monica
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4
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2 answers

Closest point on a convex hull in log(n)

We are given a convex polygon $C = \{P_1, P_2, \dots, P_n\}$, where the points are ordered either clockwise or counter-clockwise. Additionally, we have a point $P_\text{new} = (x, y)$ that lies outside the convex hull. The goal is to find the point…
amy
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1 answer

Minimum stabbing problem for a set of convex polygons

Let $S = \{P_1, P_2, ..., P_m\}$ be a set of convex polygons in $\mathbb R^2$ with a total of $n$ vertices. Polygons are defined by ordered lists of vertices, and each vertex is represented by a pair $(x,y)$ of its Cartesian coordinates. Polygons…
HEKTO
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4
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1 answer

Check if intersection of several 2D half-planes is empty

I have a large set of half-planes $a_ix+b_iy + c_i \geq 0$. What I need is is the fastest way to determine if they have at least one common point. Currently I build a convex polygon by adding half-planes sequentially, there are $O(n^2)$ checks if a…
Andrey Godyaev
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4
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1 answer

Detecting rotational symmetries of spatial structures

I have a spatial graph-like structure. The structure consists of vertices in the 3D space and connecting edges. Are there any algorithms available that would identify the rotational symmetries of these structures? In particular, I'm interested in…
Botond
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3
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1 answer

How to efficiently find line-segment intersections between two sets?

So I'm building this iterative simulation of a surface (composed of line segments) that cannot self-intersect, which means I have to check intersections at the end of a timestep. The thing is, I know, at the beginning of every timestep, that no…
André Muricy
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