Question

I have several boxes (x,y,width,height) randomly scattered around, and some of them need to be linked from point (x1,y1) in box1 to point (x2,y2) in box2 by drawing a line.

I am trying to figure a way to make such line avoid passing through any other boxes (other than box1 and box2) by drawing several straight interconnected lines to go around any box in the way (if it is not possible to go with one straight line).

The problem is that I don’t know an algorithm for such thing (let alone having a technical/common name for it). Would appreciate any help in the form of algorithm or expressed ideas.

Answer 1

1. Put all (x,y) coords of the corners of the boxes in a set V

2. Add the start- and end coordinates to V.

3. Create a set of edges E connecting each corner that does not cross any box-side (except for the diagonals in the boxes).

   How to check if a line crosses a box side can be done with this algorithm

4. Now use a path-finding algorithm of your choice, to find a path in the graph (V, E).

   If you need a simple algorithm that finds the shortest path, just go with a BFS.

(This will produce a path that goes along the sides of some boxes. If this is undesirable, you could in step 1 put the points at some distance delta from the actual corners.)

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If the edges may not be diagonal:

1. Create a large grid of lines that goes between the boxes.

2. Throw away the grid-edges that cross a box-side.

3. Find a path in the grid using a path-finding algorithm of your choice.