问题
I am trying to find the minimal bounding box of a 2d point cloud, where only a part of the point cloud is visible.
Given a point cloud with a rough rectangular shape, clipped so that only one corner is visible:
The point cloud is clipped at the green border. I know the position of the border in the image, and I know that there will always be exactly one corner of the rectangular shape visible within this border. I also know the size of the rectangular shape.
Now I want to find the minimal bounding box that contains all the points of this shape, even those not visible on-screen. Since I know the dimensions of the box, finding the two sides visible is enough to determine the other two.
(there are actually two possible solutions, since width and height of the shape can be swapped, but let's ignore that for the moment)
I want to find the red box.
I do not need an exact solution, or a fast one. My current attempt uses a simple brute force algorithm that rotates the point cloud in 1° steps and finds the axis-aligned bounding box.
I just need a criterion that tells me which rotation is the best one for this case. Minimal-Area is the usual criterion for a minimal bounding box, but that obviously only works if all points are visible.
There is probably some optimal algorithm involving convex hulls, but I'd rather keep the solution as simple as possible
回答1:
All you really need is the positions of the corners of the intersection between your red and green rectangle. Assuming the points are a decent approximation of the border, this should be a reasonably reliable method to get those:
- Pick the two points A and B most distant from eachother. Those are two corners of the area of intersection.
- Find the points C and D with the greatest perpendicular distance from the line AB (example) on either side. Those are another two corners of the area intersection.
A, B, C & D are some combination of corners of the red rectangle and intersections between the green and the red rectangles. To work out which are which, just check which are within some small tolerance of the green rectangle's border. And with that, you've got enough information to easily work out the position of the red rectangle.
来源：https://stackoverflow.com/questions/20152204/minimal-bounding-box-of-a-clipped-point-cloud