computational-geometry

Im looking for some fairly easy (I know polygon union is NOT an easy operation but maybe someone could point me in the right direction with a relativly easy one) algorithm on merging two intersecting polygons. Polygons could be concave without holes and also output polygon should not have holes in it. Polygons are represented in counter-clockwise manner. What I mean is presented on a picture. As you can see even if there is a hole in union of polygons I dont need it in the output. Input polygons are for sure without holes. I think without holes it should be easier to do but still I dont have

A classic algorithm question in 2D version is typically described as Given n non-negative integers representing an elevation map where the width of each bar is 1, compute how much water it is able to trap after raining. For example, Given the input [0,1,0,2,1,0,1,3,2,1,2,1] the return value would be 6 The algorithm that I used to solve the above 2D problem is int trapWaterVolume2D(vector<int> A) { int n = A.size(); vector<int> leftmost(n, 0), rightmost(n, 0); //left exclusive scan, O(n), the highest bar to the left each point int leftMaxSoFar = 0; for (int i = 0; i < n; i++){ leftmost[i] =

I'm not sure how to approach this problem. I'm not sure how complex a task it is. My aim is to have an algorithm that generates any polygon. My only requirement is that the polygon is not complex (i.e. sides do not intersect). I'm using Matlab for doing the maths but anything abstract is welcome. Any aid/direction? EDIT: I was thinking more of code that could generate any polygon even things like this: There's a neat way to do what you want by taking advantage of the MATLAB classes DelaunayTri and TriRep and the various methods they employ for handling triangular meshes. The code below follows

For any shape how can I create a spiral inside it of a similar shape. This would be a similar idea to bounding (using Minkowski sum). Rather than creating the same shape inside the shape though it would be a spiral of same shape. I found this - http://www.cis.upenn.edu/~cis110/13su/lectures/Spiral.java It creates a spiral based on the parameters passed so it can be for any regular shape. I want the above for all shapes i.e. irregular polygons too. I am not hugely familiar with geometric terminology but I have looked up Involutes and an Internal Spiral Search Algorithm too but haven't been

I am trying to find the destination point, given a starting point lat/long, bearing & distance. The calculator from this website below gives me the desired results. http://www.movable-type.co.uk/scripts/latlong.html When I try to implement the same through code, I don't get the right results. Below is my code - private GLatLng pointRadialDistance(double lat1, double lon1, double radianBearing, double radialDistance) { double rEarth = 6371.01; lat1 = DegreeToRadian(lat1); lon1 = DegreeToRadian(lon1); radianBearing = DegreeToRadian(radianBearing); radialDistance = radialDistance / rEarth; double

Given a set of points in the plane, a notion of alpha-shape, for a given positive number alpha, is defined by finding the Delaunay triangulation and deleting any triangles for which at least one edge exceeds alpha in length. Here's an example using d3: http://bl.ocks.org/gka/1552725 The problem is that, when there are thousands of points, simply drawing all the interior triangles is too slow for an interactive visualization, so I'd like to just find the bounding polygons. This isn't so simple, because as you can see from that example sometimes there might be two such polygons. As a

I am trying to get a global pose estimate from an image of four fiducials with known global positions using my webcam. I have checked many stackexchange questions and a few papers and I cannot seem to get a a correct solution. The position numbers I do get out are repeatable but in no way linearly proportional to camera movement. FYI I am using C++ OpenCV 2.1. At this link is pictured my coordinate systems and the test data used below. % Input to solvePnP(): imagePoints = [ 481, 831; % [x, y] format 520, 504; 1114, 828; 1106, 507] objectPoints = [0.11, 1.15, 0; % [x, y, z] format 0.11, 1.37, 0