convex-hull

I have a 3D surface given as a set of triples (x_i, y_i, z_i), where x_i and y_i are roughly on a grid, and each (x_i, y_i) has a single associated z_i value. The typical grid is 20x20 I need to find which points belong to the convex hull of the surface, within a given tolerance. I'm looking for an efficient algorithm to perform the computation (my customer has provided an O(n³) version, which takes ~10s on a 400 point dataset...) There's quite a lot out there, didn't you search? Here are a couple with O( n log h ) runtime, where n is number of input points and h is number of vertices of the

Suppose I have a point cloud given in 6-dimensional space, which I can make as dense as needed. These points turn out to lie on the surface of a lower-dimensional polytope (i.e. the point vectors (x1, x2, ... x6) appear to be coplanar). I would like to find the vertices of this unknown polytope and my current attempt makes use of the qhull algorithm, via the scipy interface in Python. In the beginning I would only get error messages, apparently caused by the lower dimensional input and/or the many degenerate points. I have tried a couple of brute-force methods to eliminate the degenerate

Given n points on the plane. No 3 are collinear. Given the number k. Find the subset of k points, such that the convex hull of the k points has minimum perimeter out of any convex hull of a subset of k points. I can think of a naive method runs in O(n^k k log k). (Find the convex hull of every subset of size k and output the minimum). I think this is a NP problem, but I can't find anything suitable for reduction to. Anyone have ideas on this problem? An example, the set of n=4 points {(0,0), (0,1), (1,0), (2,2)} and k=3 Result: {(0,0),(0,1),(1,0)} Since this set contains 3 points the convex

I succesfully implemented a Delaunay triangulation of a contour in OpenCV 2.3.1. With cvPointPolygonTest I can get all the triangles in the convex hull, then I tried to perform another cvPointPolygonTest on triangles centroid to know if they are in the main contour or not , so I can have the constrained triangulation of the contour. But, it doesn't work well, as some triangles are (eg. with a walking man who has his two legs distant) 'over' a hole . Does anyone know a way to perform a constrained triangulation. I thought about convexityDefects, but can't manage to understand how to begin with

The qhull library ( qhull.org) has several examples to start in his website, but all the information regarding to the C++ is not very useful to me. I am trying to make a simple convex Hull of 3D points that I read from a file, I can´t use the technique that is suggested in the website of calling the qhull.exe as an external application because I need to make several convex hull from some modifications that I made in the data points. I can´t find a simple example for doing this, can someone give me some help in this task? Any information would be useful. Thanks Since I had a hard time using

I'm looking for an algorithm for finding largest subset of points (by largest i mean in number) that form a convex polygon from the given set of point. I think this might be solvable using DP but i'm not sure. Is it possible to do this in O(n^3) ? Actually i just need the size of the largest subset, so it doesn't need to have unique solution Edit : just to keep this simple, Given input : a set of points in 2D Desired output : maximum number of points that form a convex polygon, like in the example the output is 5 (ABHCD is one of the possible convex polygon) There's a similar problem spoj.com