How to find polygons in a given set of points and edges?

How to find polygons in a given set of points and edges?

Sort edges in ever list by polar angle. If it’s degree is 0, remove vertex, if 1, remove vertex and edge. Otherwise get edge E with the smallest angle from this vertex. Repeat moving using left-hand rule until meet vertex A or dead end vertex. In the walk process remove edges outgoing from vertices of degree 2 or mark them as used.

How to find all convex polygons in a plane?

Given N points in plane and M line segments connecting them, find all polygons (convex or concave) that do not contain any other polygons inside. How can I identify these polygons and there corresponding vertices and edges?

How to find outline of two adjacent polygons?

I’m searching for a way to find the outline of two adjacent polygons. The polygons are defined by a list of points ordered by occurrence in the polygon. In my use case, there are no overlapping polygons, there are no gaps between the polygons, and there are no polygons with “holes”.

How to compute the natural combinatorial embedding of edge list?

Compute the natural combinatorial embedding of what’s left as a doubly connected edge list.

When does a point lie inside or outside a polygon?

2) A point is inside the polygon if either count of intersections is odd or point lies on an edge of polygon. If none of the conditions is true, then point lies outside. If none of the conditions is true, then point lies outside.

How to calculate the area of a polygon?

We can compute the area of a polygon using the Shoelace formula . The above formula is derived by following the cross product of the vertices to get the Area of triangles formed in the polygon. Below is an implementation of the above formula.

How to calculate the CW of a polygon?

A much computationally simpler method, if you already know a point inside the polygon: 1 Choose any line segment from the original polygon, points and their coordinates in that order. 2 Add a known “inside” point, and form a triangle. 3 Calculate CW or CCW as suggested here with those three points.

When does a point lie on the interior of a polygon?

If this sum is 2pi then the point is an interior point, if 0 then the point is an exterior point. This also works for polygons with holes given the polygon is defined with a path made up of coincident edges into and out of the hole as is common practice in many CAD packages.