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• Given an even number of vertices, how to find an optimum set of pairs based on proximity?

  - by Alex Z

  The problem: We have a set of n vertices in 3D euclidean space, and there is an even number of these vertices. We want to pair them up based on their proximity. In other words, we'd like to be able to find a set of vertex pairs, where the vertices in each pair are as close as possible together. We want to minimise sacrificing the proximity between the vertices of any other pairs as much as possible in doing this. I am not looking for the most optimal solution (if it even strictly exists/can be done), just a reasonable one that can be computed relatively quickly. A relatively awful brute force approach involves choosing a vertex and looping through the rest to find its nearest neighbor and then repeating until there are none left. Of course as we near the end of the list the closest vertex could be very far away, but it is the only choice, therefore this can fail badly on the third point above.

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• Why does C++ mandate that complex only be instantiated for float, double, or long double?

  - by templatetypedef

  According to the C++ ISO spec, §26.2/2: The effect of instantiating the template complex for any type other than float, double or long double is unspecified. Why would the standard authors explicitly add this restriction? This makes it unspecified, for example, what happens if you make complex<int> or a complex<MyCustomFixedPointType> and seems like an artificial restriction. Is there a reason for this limitation? Is there a workaround if you want to instantiate complex with your own custom type? I'm primarily asking this question because of this earlier question, in which the OP was confused as to why abs was giving bizarre outputs for complex<int>. That said, this still doesn't quite make sense given that we also might want to make complex numbers out of fixed-points types, higher-precision real numbers, etc. Thanks!

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• Express highest floating point quantity that is less than 1

  - by edA-qa mort-ora-y

  I was doing some rounding calculations and happened upon a question. How can I express the highest quantity less than 1 for a given floating point type? That is, how I write/represent value x such that x < 1, x + y >= 1 for any y > 0. In fractions this would be x = (q-1)/q where q is the precision of the type. For example, if you are counting in 1/999 increments then x = 998/999. For a given type (float, double, long double), how could one express the value x in code? I also wonder if such a value actually exists for all values of y. That is, as y's exponent gets smaller perhaps the relation doesn't hold anymore. So an answer with some range restriction on y is also acceptable. (The value of x I want still does exist, the relationship may just not properly express it.)

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• Determining polygon intersection and containment

  - by Victor Liu

  I have a set of simple (no holes, no self-intersections) polygons, and I need to check that they don't intersect each other (one can be entirely contained in another; that is okay). I can check this by simply checking the per-vertex inside-ness of one polygon versus other polygons. I also need to determine the containment tree, which is the set of relationships that say which polygon contains any given polygon. Since no polygon can intersect any other, then any contained polygon has a unique container; the "next-bigger" one. In other words, if A contains B contains C, then A is the parent of B, and B is the parent of C, and we don't consider A the parent of C. The question: How do I efficiently determine the containment relationships and check the non-intersection criterion? I ask this as one question because maybe a combined algorithm is more efficient than solving each problem separately. The algorithm should take as input a list of polygons, given by a list of their vertices. It should produce a boolean B indicating if none of the polygons intersect any other polygon, and also if B = true, a list of pairs (P, C) where polygon P is the parent of child C. This is not homework. This is for a hobby project I am working on.

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• How would I find all sets of N single-digit, non-repeating numbers that add up to a given sum in PHP

  - by TerranRich

  Let's say I want to find all sets of 5 single-digit, non-repeating numbers that add up to 30... I'd end up with [9,8,7,5,1], [9,8,7,4,2], [9,8,6,4,3], [9,8,6,5,2], [9,7,6,5,3], and [8,7,6,5,4]. Each of those sets contains 5 non-repeating digits that add up to 30, the given sum. Any help would be greatly appreciated. Even just a starting point for me to use would be awesome. I came up with one method, which seems like a long way of going about it: get all unique 5-digit numbers (12345, 12346, 12347, etc.), add up the digits, and see if it equals the given sum (e.g. 30). If it does, add it to the list of possible matching sets. I'm doing this for a personal project, which will help me in solving Kakuro puzzles without actually solving the whole thing at once. Yeah, it may be cheating, but it's... it's not THAT bad... :P

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• Moving a Ball on iPhone

  - by Chandan Shetty SP

  I am using below formula to move the ball circular, where accelX and accelY are the values from accelerometer, it is working fine. But the problem in this code is mRadius(I fixed its value to 50), i need to change mRadius according to accelerometer values and also i need bouncing effect when it touches other circles please send your answers ASAP... I am waiting. float degrees = -atan2(accelX, accelY) * 180 / 3.14159; int x = cCentrePoint.x + mRadius * cos(degreesToRadians(degrees)); int y = cCentrePoint.y + mRadius * sin(degreesToRadians(degrees)); Here is the snap of the game i want to develop. http://iphront.com/wp-content/uploads/2009/12/bdece528ea334033.jpg.jpg

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• Algorithm for assigning a unique series of bits for each user?

  - by Mark

  The problem seems simple at first: just assign an id and represent that in binary. The issue arises because the user is capable of changing as many 0 bits to a 1 bit. To clarify, the hash could go from 0011 to 0111 or 1111 but never 1010. Each bit has an equal chance of being changed and is independent of other changes. What would you have to store in order to go from hash - user assuming a low percentage of bit tampering by the user? I also assume failure in some cases so the correct solution should have an acceptable error rate. I would an estimate the maximum number of bits tampered with would be about 30% of the total set. I guess the acceptable error rate would depend on the number of hashes needed and the number of bits being set per hash. I'm worried with enough manipulation the id can not be reconstructed from the hash. The question I am asking I guess is what safe guards or unique positioning systems can I use to ensure this happens.

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• Ruby BigDecimal sanity check (floating point newb)

  - by Andy

  Hello, Hoping to get some feedback from someone more experienced here. I haven't dealt with the dreaded floating-point calculation before... Is my understanding correct that with Ruby BigDecimal types (even with varying precision and scale lengths) should calculate accurately or should I anticipate floating point shenanigans? All my values within a Rails application are BigDecimal type and I'm seeing some errors (they do have different decimal lengths), hoping it's just my methods and not my object types... Thanks!

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• Solving simultaneous equations

  - by Milo

  Here is my problem: Given x, y, z and ratio where z is known and ratio is known and is a float representing a relative value, I need to find x and y. I know that: x / y == ratio y - x == z What I'm trying to do is make my own scroll pane and I'm figuring out the scrollbar parameters. So for example, If the scrollbar must be able to scroll 100 values (z) and the thumb must consume 80% of the bar (ratio = 0.8) then x would be 400 and y would be 500. Thanks

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• How to maintain decimal percision in calculations

  - by Blankman

  I need to sum 2 decimal values together, then divide by 2 and convert to string. My calculation currently is trimming to 2 decimal places, but I want to keep as many decimals as I can. city.Latitude = ( (lat.North + lat.South) / 2 ).ToString(); the values for lat.North and lat.Souch are like: 55.32342322

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• What is SVD(singular value decomposition)

  - by shiva

  How does it actually reduce noise..can you suggest some nice tutorials?

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• Real life usage of the projective plane theory

  - by Elazar Leibovich

  I'm learning about the theory of the projective plane. Very generally speaking, it is an extension of the plane, which includes additional points which are defined as the intersection points of two parallel lines. In the projective plane, every two lines have an interesection point. Whether they're parallel or not. Every point in the projective plane can be represented by three numbers (you actually need less than that, but nevemind now). Is there any real life application which uses the projective plane? I can think that, for instance, a software which needs to find the intersections of a line, can benefit from always having an intersection point which might lead to simpler code, but is it really used?

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• Are there any example of Mutual recursion?

  - by Yassir

  Are there any example for a recursive function that call an other one which calls the first one too ? example function1() { //do something f2(); //do something } function2() { //do something f1(); //do something }

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• Learning Basic Mathematics

  - by NeedsToKnow

  I'm going to just come out and say it. I'm 20 and can't do maths. Two years ago I passed the end-of-high-school mathematics exam (but not at school), and did pretty well. Since then, I haven't done a scrap of mathematics. I wondered just how bad I had gotten, so I was looking at some simple algebra problems. You know, the kind you learn halfway through highschool. 5(-3x - 2) - (x - 3) = -4(4x + 5) + 13 Couldn't do them. I've got half a year left until I start a Computer Science undergraduate degree. I love designing and creating programs, and I remember I loved mathematics back when I did it. Basically, I've had a pretty bad education, but I want to be knowledgable in these areas. I was thinking of buying some high school textbooks and reading them, but I'm not sure this is the right way to go. I need to start off at some basic level and work towards a greater understanding. My question is: What should I study, how should I study, and what books can you recommend? Thanks!

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• Need some help understanding this problem

  - by Legend

  I was wondering if someone could help me understand this problem. I prepared a small diagram because it is much easier to explain it visually. Problem I am trying to solve: 1. Constructing the dependency graph Given the connectivity of the graph and a metric that determines how well a node depends on the other, order the dependencies. For instance, I could put in a few rules saying that node 3 depends on node 4 node 2 depends on node 3 node 3 depends on node 5 But because the final rule is not "valuable" (again based on the same metric), I will not add the rule to my system. 2. Execute the request order Once I built a dependency graph, execute the list in an order that maximizes the final connectivity. First and foremost, I am wondering if I constructed the problem correctly and if I should be aware of any corner cases. Secondly, is there a closely related algorithm that I can look at? Currently, I am thinking of something like Feedback Arc Set or the Secretary Problem but I am a little confused at the moment. Any suggestions? PS: I am a little confused about the problem myself so please don't flame on me for that. If any clarifications are needed, I will try to update the question.

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• Does anyone know how to do an "inverse" trilinear interpolation?

  - by Kaladze

  Trilinear interpolation approximates the value of a point (x, y, z) inside a cube using the values at the cube vertices. I´m trying to do an "inverse" trilinear interpolation. Knowing the values at the cube vertices and the value attached to a point how can I find (x, y, z)? Any help would be highly appreciated. Thank you!

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• Affine transformation algorithm.

  - by thehawk90

  Does anyone know of any standard algorithms to determine an affine transformation matrix based upon a set of known points in two co-ordinate systems?

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• Fast dot product for a very special case

  - by psihodelia

  Given a vector X of size L, where every scalar element of X is from a binary set {0,1}, it is to find a dot product z=dot(X,Y) if vector Y of size L consists of the integer-valued elements. I suggest, there must exist a very fast way to do it. Let's say we have L=4; X[L]={1, 0, 0, 1}; Y[L]={-4, 2, 1, 0} and we have to find z=X[0]*Y[0] + X[1]*Y[1] + X[2]*Y[2] + X[3]*Y[3] (which in this case will give us -4). It is obvious that X can be represented using binary digits, e.g. an integer type int32 for L=32. Then, all what we have to do is to find a dot product of this integer with an array of 32 integers. Do you have any idea or suggestions how to do it very fast?

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• Extend and Overload MS and Point Types

  - by dr d b karron

  Do I have make my own Point and Vector types to overload them ? Why does this not work ? namespace System . windows { public partial struct Point : IFormattable { public static Point operator * ( Point P , double D ) { Point Po = new Point ( ); return Po; } } } namespace SilverlightApplication36 { public partial class MainPage : UserControl { public static void ShrinkingRectangle ( WriteableBitmap wBM , int x1 , int y1 , int x2 , int y2 , Color C ) { wBM . DrawRectangle ( x1 , y1 , x2 , y2 , Colors . Red ); Point Center = Mean ( x1 , y1 , x2 , y2 ); wBM . SetPixel ( Center , Colors.Blue , 3 ); Point P1 = new Point ( x1 , y1 ); Point P2 = new Point ( x1 , y2 ); Point P3 = new Point ( x1 , y2 ); Point P4 = new Point ( x2 , y1 ); const int Steps = 10; for ( int i = 0 ; i < Steps ; i++ ) { double iF = (double)(i+1) / (double)Steps; double jF = ( 1.0 - iF ); Point P11 = **P1 * jF;** } }

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• Distance between hyperplanes

  - by michael dillard

  I'm trying to teach myself some machine learning, and have been using the MNIST database (http://yann.lecun.com/exdb/mnist/) do so. The author of that site wrote a paper in '98 on all different kinds of handwriting recognition techniques, available at http://yann.lecun.com/exdb/publis/pdf/lecun-98.pdf. The 10th method mentioned is a "Tangent Distance Classifier". The idea being that if you place each image in a (NxM)-dimensional vector space, you can compute the distance between two images as the distance between the hyperplanes formed by each where the hyperplane is given by taking the point, and rotating the image, rescaling the image, translating the image, etc. I can't figure out enough to fill in the missing details. I understand that most of these are indeed linear operators, so how does one use that fact to then create the hyperplane? And once we have a hyperplane, how do we take its distance with other hyperplanes?

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• How to write an intersects for Shapes in android

  - by Rafael T

  I have an written an Object called Shape which has a Point representing the topLeftCorner and a Dimension with represents its width and height. To get the topRightCorner I can simply add the width to the topLeftPoint.x. I use to rotate them on a certain degree around their center. The problem after the rotation is, that my intersects(Shape) method fails, because it does not honor the rotation of the Shapes. The rotation will be the same for each Shape. My current implementation looks like this inside my Shape Object: public boolean intersects(Shape s){ // functions returning a Point of shape s return intersects(s.topLeft()) || intersects(s.topRight()) || intersects(s.bottomLeft()) || intersects(s.bottomRight()) || intersects(s.leftCenter()) || intersects(s.rightCenter()) || intersects(s.center()); } public boolean intersects(Point p){ return p.x >= leftX() && p.x <= rightX() && p.y >= topY() && p.y <= bottomY(); } Basically I need functions like rotatedLeftX() or rotatedTopRight() to work properly. Also for that calculation I think it doesn't matter when the topLeft point before a rotation of ie 90 will turn into topRight... I already read this and this Question here, but do not understand it fully.

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• Position elements without overlap

  - by eWolf

  I have a number of rectangular elements that I want to position in a 2D space. I calculate an ideal position for each element. Now my problem is that many elements overlap as very often the ideal positions are concentrated in one region. I want to avoid overlap as much as possible (doesn't have to be perfect, though). How can I do this? I've heard physics simulations are suitable for this - is that correct? And can anyone provide an example/tutorial? By the way: I'm using XNA, if you know any .NET library that does exactly this job - tell me!

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• An efficient way to compute mathematical constant e

  - by Cinnamon

  Hello, The standard representation of constant e as the sum of the infinite series is very inefficient for computation, because of many division operations. So are there any alternative ways to compute the constant efficiently? Thanks!

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• How to maintain decimal precision in calculations

  - by Blankman

  I need to sum 2 decimal values together, then divide by 2 and convert to string. My calculation currently is trimming to 2 decimal places, but I want to keep as many decimals as I can. city.Latitude = ( (lat.North + lat.South) / 2 ).ToString(); the values for lat.North and lat.Souch are like: 55.32342322

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• Fixing VB6 inaccurate mathmetical results due to rounding

  - by jay

  Try running this in a .VBS file MsgBox(545.14-544.94) You get a neat little answer of 0.199999999999932! This rounding issue also occurs unfortunately in Sin(2 * pi) since VB can only ever see the (user defined) variable pi as accurate as 3.14159265358979. Is rounding it manually (and loosing accuracy) the only way to improve the result? What is the most effective way of dealing with this kind of problem?

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