从边缘查找内部几何体

Question

First I am not sure which keywords to use for this and I think I am probably using the wrong ones to google about it, so if someone could give me any hint it would be much appreciated.

My problem is the following: I need to find the "rooms" inside a house plan. For example take this geometry:

The desired algorithm would tell me which vertexes bound each of the rooms. So for this example it would be:

• room A: 1, 2, 9, 10, 3, 4, 5, 8 ,1
• room B: 2, 3, 10, 9, 2
• room C: 11, 12, 14, 13, 11
• room D: 5, 6, 7, 8, 5

I have the vertexes and the edges as input data. Edit: The edge data is as follows (edge 8, 1 ,2):

xy

47 196

47 85

258 85

it is in pixel coord.

Answer 1

Graph Theory did not really help me because I have disconnected loops that share information. For example [1 2 9 10 3 4 5 8 1] AND [11 12 14 13 11]. So in the end I ended up doing a image fill, when expanding the boarders of the fill 1 pixel and doing a boolen operation to figure out which vertex are inside the filled image.

Answer 2

One of possible solutions is to triangulate this area so that every input edge is an edge of some triangle. Then split triangles into connected sets and find their border.

There are several algorithms for triangulation: ear-clipping, Delaunay, ...

Answer 3

This is planar graph . It has V vertices, E edges and F = E - V + 2 faces (including outer face). We have to determine the edge list for all the faces. Every edge will be used twice in these lists (in forward and backward direction).

Create main arc list, add all the arcs (ie for 1-2 undirected edge add both 1-2 and 2-1 directed arcs)

Find the lowest vertex point. If there are some such points, choose the leftmost one (7th here). Travel the outer face (contour) in CCW direction (choose the rightmost outgoing arc at every vertex): 7-6-5-4-3-2-1-7. Remove visited arcs from the main list.

Get any arc from the main list, travel the first inner face, follow the right-hand rule (ie 7-8-5-6-7), remove visited arcs.

Repeat until the main list is empty.

Repeat all the procedure for disconnected components (11-12-13-14)