computational-geometry

I was recently asked this question in an interview. Even though I was able to come up the O ( n ²) solution, the interviewer was obsessed with an O ( n ) solution. I also checked few other solutions of O ( n log n ) which I understood, but O ( n ) solution is still not my cup of tea which assumes appointments sorted by start-time. Can anyone explain this? Problem Statement: You are given n appointments. Each appointment contains a start time and an end time. You have to retun all conflicting appointments efficiently. Person: 1,2, 3, 4, 5 App Start: 2, 4, 29, 10, 22 App End: 5, 7, 34, 11, 36

I'm looking for a simple (if exists) algorithm to find the Voronoi diagram for a set of points on the surface of a sphere. Source code would be great. I'm a Delphi man (yes, I know...), but I eat C-code too. Jason S Here's a paper on spherical Voronoi diagrams . Or if you grok Fortran (bleah!) there's this site . Update in July 2016: Thanks to a number of volunteers (especially Nikolai Nowaczyk and I), there is now far more robust / correct code for handling Voronoi diagrams on the surface of a sphere in Python. This is officially available as scipy.spatial.SphericalVoronoi from version 0.18

SHORT DESCRIPTION OF MY PROBLEM I need to implement GCODE autorefactoring from G1 instructions to G2 and G3 ( http://www.cnccookbook.com/CCCNCGCodeArcsG02G03.htm ) for 3D Printing. G1 is a movement in straight line with printing (path is describe by vector). I'm searching for algorytm to aproxymate circle/arc (specialy it's midpoint) based on given vectors path. Note that G2 and G3 can't print curves that are not part of a circle - so not every vectors path can be approximate this way. LONG DESCRIPTION OF MY PROBLEM I'm searching way to approximate part (or all) of vectors path (can be regular

I have an issue in graham scan algorithm when my list have a lot of points, but works every time fine with low amount of points. I made some screenshots : working : (300 points) not working (5000 points) angle calculation: public static double angle(MyVector3D vec1, MyVector3D vec2) { return Math.Atan2(vec2.Y - vec1.Y, vec2.X - vec1.X) * 180 / Math.PI; } sorting points by polar angle depend on max Y point : //bubblesort private void sortList() { double temp = 0.0; MyVector3D tempVector = new MyVector3D(); for (int i = 1; i < points.Count; i++) { for (int j = 1; j < points.Count - 1; j++) { if

Greetings, We have a set of points which represent an intersection of a 3d body and a horizontal plane. We would like to detect the 2D shapes that represent the cross sections of the body. There can be one or more such shapes. We found articles that discuss how to operate on images using Hough Transform, but we may have thousands of such points, so converting to an image is very wasteful. Is there a simpler way to do this? Thank you In converting your 3D model to a set of points, you have thrown away the information required to find the intersection shapes. Walk the edge-face connectivity

For the purposes of implementing a high-performance dynamic pathfinding algorithm on a sphere (in C++), I'm interested in performing an incremental constrained delaunay triangulation on the surface of a sphere. Existing libraries do not seem to be sufficient - the closest that I've been able to find so far is CGAL, which has the topological space right but the metric space wrong. The library should have: Reasonable performance (I have about 100k points to put into it) Spherical topological and metric space (honestly, this overrules #1 by a wide margin) Incremental point insertion and deletion

I'm making an image processing project and I have stuck in one the project's steps. Here is the situation; This is my mask: and I want to detect the maximum-sized rectangle that can fit into this mask like this. I'm using MATLAB for my project. Do you know any fast way to accomplish this aim. Any code sample, approach or technique would be great. EDIT 1 : The two algorithms below are works with lot's of the cases. But both of them give wrong results in some difficult cases. I'am using both of them in my project. This approach starts with the entire image and shrinks each border in turn pixel