如何确定 3d 点是否位于某个体积内？

Question

I have a set of 3d points in a txt file in the form of (x,y,z) as shown in figure 1. I want to specify the boundaries of these points as in figure 2 such that if any new points were added outside the boundaries they are deleted as the blue points, and if they are inside the boundaries as the green ones they are kept. How can I achieve that in python? I tried convex hull but it only gets the boundary points !

The real data can be found here, I used figures for simplification. https://drive.google.com/file/d/1ei9NaJHN922pYItK2CRIXyLfwqm_xgrt/view?usp=sharing

Figure 1

Figure 2

Answer 1

For 2D points, you can apply the test as described in Wikipedia :

One simple way of finding whether the point is inside or outside a simple polygon is to test how many times a ray, starting from the point and going in any fixed direction, intersects the edges of the polygon. If the point is on the outside of the polygon the ray will intersect its edge an even number of times. If the point is on the inside of the polygon then it will intersect the edge an odd number of times. The status of a point on the edge of the polygon depends on the details of the ray intersection algorithm.

The n-dimensional case involves a convex hull test and requires linear programming techniques as described here .