computational-geometry

Consider a large set of floating-point intervals in 1-dimension, e.g. [1.0, 2.5], 1.0 |---------------|2.5 [1.5, 3.6], 1.5|---------------------|3.6 ..... It is desired to find all intervals that contain a given point. For example given point = 1.2, algorithm should return the first interval, and if given point = 2.0, it should return the first two interval in the above example. In the problem I am dealing, this operation needs to be repeated for a large number of times for a large number of intervals. Therefore a brute-force search is not desired and performance is an important factor. After

I'm trying to understand the paper "Clipping of Arbitrary Polygons with Degeneracies" by E. L Foster and J. R. Overfelt [1], which claims to extend the classic Greiner-Hormann polygon clipping algorithm by handling of degeneracies. However, I ran into some difficulties with the procedure they describe. Consider the situation depicted on Figure 6(c) and suppose the polygons are oriented in the same way. Start the labeling phase from the I5 (as opposed from I1, as they do): for both subject polygon S and clipping polygon C, I5 has previous and next labels (on, on). Therefore, according to Table

The problem I have to solve is the 4D version of the 1D problem of stabbing queries : find which intervals a number belongs to. I am looking for a multi-dimensional implementation of segment trees . Ideally, it will be in Java and it will use fractional cascading . Multi-dimensional implementations exist for kd-trees (k-NN searches) and range trees (given a bounding box, find all points in it) but for segment trees I've only found 1D implementations. I'd be happy to consider other data structures with similar space/time complexity to address the same problem. To expand on my comment, the

I would like to compute the mean and standard deviation of the areas of a set of Voronoi regions in 2D (if the region extends to infinity, I'll just clip it to the unit square). However if possible I would like to do this computation from the Delaunay Triangulation without explicitly computing the Voronoi regions? Is this even possible, or is it better to just compute the Voronoi diagram explicitly? In order to calculate the voronoi region of a vertex you need to iterate the 1-ring around it. Then the area of the region is defined as: A = 1/8 * (sum for every adjacent vertex p_i) { (cot alpha

Given the center point and radius of a circle, how do I know if a certain point (x,y) is in the circle? Anyone knows it? Thanks. Originally you asked for Objective-C. CGFloat DistanceBetweenTwoPoints(CGPoint point1,CGPoint point2) { CGFloat dx = point2.x - point1.x; CGFloat dy = point2.y - point1.y; return sqrt(dx*dx + dy*dy ); }; -(void)touchesEnded:(NSSet *)touches withEvent:(UIEvent *)event { CGPoint point = [[touches anyObject] locationInView:self]; CGFloat distance = DistanceBetweenTwoPoints(self.circleCenter, point); if(distance < self.radius){ //inside the circle } } This code assumes,