Rotating the jamming case -- parallel coordinate points between polygon (defined)

Returns the directed tangent of the parallel vertex between polygon.

A directed tangent is as stated in its name. It is necessary to distinguish the parallel tangent from the inverse and the same direction.
It is further assumed that the polygon is clockwise (clockwise when the vertices are arranged) and the tangent of the polygon is positive when the polygon is online to the right. On the contrary, when the polygon is on the left of the tangent, the polygon can be given in a counterclockwise order.
Although only agreed, it is necessary to develop some standards to avoid confusion between structures and results. Using this Convention will never affect the results and impose any restrictions.

Note: The tangent definition exports the vertex pair..

Parallel points between Polygon

Given two polygonPAndQ, A pair of vertices (P,Q) (Respectively belongPAndQ), WhenPAndQWhen the (directed) Parallel tangent points to the same direction, they constitute a parallel VertexPAndQ.

Two such tangent always determine at least one parallel vertex. There are three situations based on the intersection of a line and a polygon:

1. "Point-to-point" and vertex-to-point
2. "Vertices-edges" and vertices
3. "Edge-edge" and Vertex

Scenario 1 is generated when the two tangent points and the corresponding polygon are handed over to the unique vertex respectively. In the figure, the two Black Point vertices constitute and the vertex point is hidden.

Case 2 is generated when a tangent and Its polygon are handed over to an edge and the other tangent and Its polygon are handed over to only one vertex. Note that the existence of this tangent must include two different "point-to-point" and vertex-to-vertex.

Case 3 occurs when two polygon have parallel edges. The tangent and Their polygon are handed over to these edges respectively. At this time, the tangent also identifies four different "Point-points" and points between them.

 

Original article address:Http://cgm.cs.mcgill.ca /~ Orm/cpp.html

 

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