computational-geometry

Show that the convex hull of n points in the plane can be computed in O(n) time if each coordinate of each point is a rational number of the form p/q , with bounded values for p and q. Note: This is a homework problem. I can just think of using Jarvis March by somehow avoiding the scan of all points. Maybe this can be done by throwing rays in fixed directions (using the rational condition) to check where the next point exists . Don't use Jarvis March since it has time complexity of O(nh) . In the worst case, h may be as large as n . Note that h is the number of points on the hull. Instead, you

I'm trying to code the Ritter's bounding sphere algorithm in arbitrary dimensions, and I'm stuck on the part of creating a sphere which would have 3 given points on it's edge, or in other words, a sphere which would be defined by 3 points in N-dimensional space. That sphere's center would be the minimal-distance equidistant point from the (defining) 3 points. I know how to solve it in 2-D (circumcenter of a triangle defined by 3 points), and I've seen some vector calculations for 3D, but I don't know what the best method would be for N-D, and if it's even possible. (I'd also appreciate any

I need a way to characterize the size of sets of 2-D points, so I can determine whether to render them as individual points in a space or as representative polygons, dependent on the scale of the viewport. I already have an algorithm to calculate the convex hull of the set to produce the representative polygon, but I need a way to characterize its size. One obvious measure is the maximum distance between points on the convex hull, which is the diameter of the set. But I'm really more interested in the size of its cross-section perpendicular to its diameter, to figure out how narrow the

Having fun with D3 geo orthographic projection to build an interactive globe, based on all the great examples I found. You can see my simple mockup at http://bl.ocks.org/patricksurry/5721459 I want the user to manipulate the globe like a trackball ( http://www.opengl.org/wiki/Trackball ). I started with one of Mike's examples ( http://mbostock.github.io/d3/talk/20111018/azimuthal.html ), and improved slightly to use canvas coordinates and express the mouse locations in 'trackball coordinates' (i.e. rotation around canvas horizontal and vertical axes) so that a fixed mouse movement gives more

I have a polar plane relative to a base point (colored green in the diagram below). The points and segments are represented thus: class Node { int theta; double radius; } class Segment { //each segment must have node that is northern relative to other Node northern; Node southern; } I want to figure out if the red line going from the base point to each segment node intersects any other segment. In this example, the red line does intersect. What algorithmic approach should I apply? Computational complexity is less important than simplicity of implementation. If you are striving for simplicity