computational-geometry

I have SVG abirtrary paths which i need to pack as efficiently as possible within a given rectangle(as less waste of space as possible). After some research i found the bin packing algorithms which seems to be dealing with boxes and not curved random shapes(my SVG shapes are quite complex and include beziers etc.). AFAIK, there is no deterministic algorithm for actually packing abstract shapes. I wish to be proven wrong here which would be ideal(having a mathematical deterministic method for packing them). In case I am right however and there is not, what would be the best approach to this

I'm using Java AWT to draw lines on a panel ( Line2D and Graphics2D.drawLine() ) and I'm wondering how I can draw a line with tick marks, similar to: |----|----|----|----|----| I know the positions I'd like to draw the ticks at in advance. The lines could be in any position, so the ticks must be drawn at an angle releative to the line itself. My basic geometry & ability to apply it in Java is failing me. :) I suggest you implement a ruler-drawing-method that draws a simple horizontal ruler from left to right Figure out the desired angle using Math.atan2 . Apply an AffineTransform with

let's say I have a huge set of non-overlapping rectangle with integer coordinates, who are fixed once and for all I have another rectangle A with integer coordinates whose coordinates are moving (but you can assume that its size is constant) What is the most efficient way to find which rectangles are intersecting (or inside) A? I cannot simply loop through my set as it is too big. Thanks edit : the rectangles are all parallel to the axis Personally, I would solve this with a KD-Tree or a BIH-Tree. They are both adaptive spatial data structures that have a log(n) search time. I have an

I've successfully implemented a way to generate Voronoi diagrams in 2 dimensions using Fortune's method. But now I'm trying to use it for nearest neighbor queries for a point (which is not one of the original points used to generate the diagram). I keep seeing people saying that it can be done in O(lg n) time (and I believe them), but I can't find a description of how it's actually done. I'm familiar with binary searches, but I can't figure out a good criteria to guarantee that upper bound. I also figured maybe it could have to do with inserting the point into the diagram and updating

I'm working on a data mining algorithm where i want to pick a random direction from a particular point in the feature space. If I pick a random number for each of the n dimensions from [-1,1] and then normalize the vector to a length of 1 will I get an even distribution across all possible directions? I'm speaking only theoretically here since computer generated random numbers are not actually random. Bram Cohen One simple trick is to select each dimension from a gaussian distribution, then normalize: from random import gauss def make_rand_vector(dims): vec = [gauss(0, 1) for i in range(dims)]

I'm looking for a library or a paper that describes how to determine if one triangular mesh intersects another. Interestingly I am coming up empty. If there is some way to do it in CGAL, it is eluding me. It seems like it clearly should be possible, because triangle intersection is possible and because each mesh contains a finite number of triangles. But I assume there must be a better way to do it than the obvious O(n*m) approach where one mesh has n triangles and the other has m triangles. The way we usually do it using CGAL is with CGAL::box_intersection_d . You can make it by mixing this