Boundary enclosing a given set of points

Here is some Python code that computes the alpha-shape (concave hull) and keeps only the outer boundary. This is probably what matlab’s boundary does inside. from scipy.spatial import Delaunay import numpy as np def alpha_shape(points, alpha, only_outer=True): “”” Compute the alpha shape (concave hull) of a set of points. :param points: np.array of shape (n,2) … Read more

Find if a point is inside a convex hull for a set of points without computing the hull itself

The problem can be solved by finding a feasible point of a Linear Program. If you’re interested in the full details, as opposed to just plugging an LP into an existing solver, I’d recommend reading Chapter 11.4 in Boyd and Vandenberghe’s excellent book on convex optimization. Set A = (X[1] X[2] … X[n]), that is, … Read more

Location of highest density on a sphere

There is in fact no real reason to partition the sphere into a regular non-overlapping mesh, try this: partition your sphere into semi-overlapping circles see here for generating uniformly distributed points (your circle centers) Dispersing n points uniformly on a sphere you can identify the points in each circle very fast by a simple dot … Read more

robust algorithm for surface reconstruction from 3D point cloud?

I have been facing this dilemma for some months now, and made exhaustive research. Algorithms Mainly there are 2 categories of algorithms: computation geometry, and implicit surfaces. Computation Geometry They fit the mesh on the existing points. Probably the most famous algorithm of this group is powercrust, because it is theoretically well-established – it guarantees … Read more

Shortest distance between points algorithm The problem can be solved in O(n log n) time using the recursive divide and conquer approach, e.g., as follows: Sort points along the x-coordinate Split the set of points into two equal-sized subsets by a vertical line x = xmid Solve the problem recursively in the left and right subsets. This will give … Read more