computational-geometry

I'm trying to understand the section 5. of this paper about LSH, in particular how to bucket the generated hashes. Quoting the linked paper: Given bit vectors consisting of d bits each, we choose N = O(n 1/(1+epsilon) ) random permutations of the bits. For each random permutation σ, we maintain a sorted order O σ of the bit vectors, in lexicographic order of the bits permuted by σ. Given a query bit vector q, we find the approximate nearest neighbor by doing the following: For each permu- tation σ, we perform a binary search on O σ to locate the two bit vectors closest to q (in the

I need to plot a group of points based on distances. I have three unknown points X, Y, and Z. I then get another unknown point (A) and its distances from the originals (AX, AY, AZ). I will continue getting points and distances (B, BX, BY, BZ; C, CX, CY, CZ) etc. My question is whether its possible to plot all of the points. If so, how many points would I need for an exact plot map? What about an approximate map? This is similar to this question but I get a different set of distances and am not limited to the original number of points. Also, if it would help I could add more points to the X, Y,

Is there any algorithm that would allow to approximate a path on the x-y plane (i.e. an ordered suite of points defined by x and y) with a limited number of line segments and arcs of circles (constant curvature)? The resulting curve needs to be C1 (continuity of slope). The maximum number or segments and arcs could be a parameter. An additional interesting constraint would be to prevent two consecutive circles of arcs without an intermediate line segment joining them. I do not see any way to do this, and I do not think that there exists a method for it, but any hint towards this objective is

I have a 3D surface, (think about the xy plane). The plane can be slanted. (think about a slope road). Given a list of 3D coordinates that define the surface( Point3D1X , Point3D1Y , Point3D1Z , Point3D12X , Point3D2Y , Point3D2Z , Point3D3X , Point3D3Y , Point3D3Z , and so on), how to calculate the area of the surface? Note that my question here is analogous to finding area in 2D plane. In 2D plane we have a list of points that defines a polygon, and using this list of points we can find the area of the polygon. Now assuming that all these points have z values in such a way that they are

This is a question similar to the one here , but I figure that it would be helpful if I can recast it in a more general terms. I have a set of polygons, these polygons can touch one another, overlap and can take on any shape. My question is, given a list of points, how to devise an efficient algorithm that find which polygons are the points located? One of the interesting restriction of the location of the points is that, all the points are located at the edges of the polygons, if this helps. I understand that r-trees can help , but given that I am doing a series of points, is there a more

As of early 2014, SVG spec does not have any built-in support for Boolean Operations Boolean operations are methods for altering the inherent geometry of mostly overlapping paths. They allow the construction of complicated shapes by performing operations on simpler shapes and are somehow similar to Constructive Solid Geometry(CSG) . However this question refers to 2D vector paths. The popular path operations are: Union, Substraction,Intersection, XOR(Exclusive Or). Are there any libraries floating around that would help me out in this? There's Javascript Clipper , which allows for all the sets