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• 3D World to Local transformation

  - by Bill Kotsias

  Hello. I am having a real headache trying to set a node's local position to match a given world position. I was given a solution but, AFAICS, it only takes into account orientation and position but NOT scaling : node_new_local_position = node_parent.derivedOrientation().Inverse() * ( world_position_to_match - node_parent.derivedPosition() ); The node in question is a child of node_parent; node_parent local and derived properties (orientation, position and scaling) are known, as well as its full matrix transform. All the positions are 3d vectors; the orientation is a quaternion; the full transform is a 4x4 matrix. Could someone please help me to modify the solution to support scaling in the node hierarchy? Many thanks in advance, Bill

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• How to detect if an ellipse intersects(collides with) a circle

  - by php html

  I want to improve a collision system. Right now I detect if 2 irregular objects collide if their bounding rectangles collide. I want to obtain the for rectangle the corresponding ellipse while for the other one to use a circle. I found a method to obtain the ellipse coordinates but I have a problem when I try to detect if it intersects the circle. Do you know a algorithm to test if a circle intersects an ellipse?

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• How to make ARGB transparency using bitwise operators.

  - by Smejda

  I need to make transparency, having 2 pixels: pixel1: {A, R, G, B} - foreground pixel pixel2: {A, R, G, B} - background pixel A,R,G,B are Byte values each color is represented by byte value now I'm calculating transparency as: newR = pixel2_R * alpha / 255 + pixel1_R * (255 - alpha) / 255 newG = pixel2_G * alpha / 255 + pixel1_G * (255 - alpha) / 255 newB = pixel2_B * alpha / 255 + pixel1_B * (255 - alpha) / 255 but it is too slow I need to do it with bitwise operators (AND,OR,XOR, NEGATION, BIT MOVE)

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• Detecting Asymptotes in a Graph

  - by nasufara

  I am creating a graphing calculator in Java as a project for my programming class. There are two main components to this calculator: the graph itself, which draws the line(s), and the equation evaluator, which takes in an equation as a String and... well, evaluates it. To create the line, I create a Path2D.Double instance, and loop through the points on the line. To do this, I calculate as many points as the graph is wide (e.g. if the graph itself is 500px wide, I calculate 500 points), and then scale it to the window of the graph. Now, this works perfectly for most any line. However, it does not when dealing with asymptotes. If, when calculating points, the graph encounters a domain error (such as 1/0), the graph closes the shape in the Path2D.Double instance and starts a new line, so that the line looks mathematically correct. Example: However, because of the way it scales, sometimes it is rendered correctly, sometimes it isn't. When it isn't, the actual asymptotic line is shown, because within those 500 points, it skipped over x = 2.0 in the equation 1 / (x-2), and only did x = 1.98 and x = 2.04, which are perfectly valid in that equation. Example: In that case, I increased the window on the left and right one unit each. My question is: Is there a way to deal with asymptotes using this method of scaling so that the resulting line looks mathematically correct? I myself have thought of implementing a binary search-esque method, where, if it finds that it calculates one point, and then the next point is wildly far away from the last point, it searches in between those points for a domain error. I had trouble figuring out how to make it work in practice, however. Thank you for any help you may give!

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• Can you explain(mathematical calculations) gesture example (Levenshtein )?

  - by androidbase Praveen

  I got the example in this link. I can't understand the addmove, costLeven and meatureGesture methods. Can you explain it step by step?

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• Laplacian of Gaussian

  - by Don

  I am having trouble implementing a LoG kernel. I am trying to implement 9x9 kernal with theta = 1.4 as shown in this link http://homepages.inf.ed.ac.uk/rbf/HIPR2/log.htm. However, I am having difficulty with the formula itself.For whatever values I input into the formula, I don't get any of the values in a 9x9 LoG kernel with theta = 1. 4. If someone can provide an example of how they got one of the big values ie -40 or -23, or the code to implement it, It'd be greatly appreciated. Thank you

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• How to find a binary logarithm very fast? (O(1) at best)

  - by psihodelia

  Is there any very fast method to find a binary logarithm of an integer number? For example, given a number x=52656145834278593348959013841835216159447547700274555627155488768 such algorithm must find y=log(x,2) which is 215. x is always a power of 2. The problem seems to be really simple. All what is required is to find the position of the most significant 1 bit. There is a well-known method FloorLog, but it is not very fast especially for the very long multi-words integers. What is the fastest method?

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• probability and relative frequency

  - by Alexandru

  If I use relative frequency to estimate the probability of an event, how good is my estimate based on the number of experiments? Is standard deviation a good measure? A paper/link/online book would be perfect. http://en.wikipedia.org/wiki/Frequentist

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• Pool Billiard AI

  - by Sebi

  Im implementing a pool billiard game in Java and it all works fine. It is a multiplayer game, but nevertheless, it should also be possible to play it alone. For this purpose I'm trying to implement a simple KI. At the moment, the KI choose just randomly a direction and a random intensity of the impulse (don't know the correct english word for that). Of course this AI is very poor and unlikely to ever challenge a player. So i thought about improving the KI, but there are several hard to solve problems. First I thought of just choosing the nearest ball and to try to put it directly into the nearest hole. This isn't that bad, but if there other balls in the line between, it isn't really working anymore. Additionally this dosn't solve te problem of calculating the intensity of the impulse. So are there any general advice? Or any ideas? Best practices?

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• An implementation of Sharir's or Aurenhammer's deterministic algorithm for calculating the intersect

  - by RGrey

  The problem of finding the intersection/union of 'N' discs/circles on a flat plane was first proposed by M. I. Shamos in his 1978 thesis: Shamos, M. I. “Computational Geometry” Ph.D. thesis, Yale Univ., New Haven, CT 1978. Since then, in 1985, Micha Sharir presented an O(n log2n) time and O(n) space deterministic algorithm for the disc intersection/union problem (based on modified Voronoi diagrams): Sharir, M. Intersection and closest-pair problems for a set of planar discs. SIAM .J Comput. 14 (1985), pp. 448-468. In 1988, Franz Aurenhammer presented a more efficient O(n log n) time and O(n) space algorithm for circle intersection/union using power diagrams (generalizations of Voronoi diagrams): Aurenhammer, F. Improved algorithms for discs and balls using power diagrams. Journal of Algorithms 9 (1985), pp. 151-161. Earlier in 1983, Paul G. Spirakis also presented an O(n^2) time deterministic algorithm, and an O(n) probabilistic algorithm: Spirakis, P.G. Very Fast Algorithms for the Area of the Union of Many Circles. Rep. 98, Dept. Comput. Sci., Courant Institute, New York University, 1983. I've been searching for any implementations of the algorithms above, focusing on computational geometry packages, and I haven't found anything yet. As neither appear trivial to put into practice, it would be really neat if someone could point me in the right direction!

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• Algorithm for dividing very large numbers

  - by pocoa

  I need to write an algorithm(I cannot use any 3rd party library, because this is an assignment) to divide(integer division, floating parts are not important) very large numbers like 100 - 1000 digits. I found http://en.wikipedia.org/wiki/Fourier_division algorithm but I don't know if it's the right way to go. Do you have any suggestions?

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• Curve fitting: Find the smoothest function that satisfies a list of constraints.

  - by dreeves

  Consider the set of non-decreasing surjective (onto) functions from (-inf,inf) to [0,1]. (Typical CDFs satisfy this property.) In other words, for any real number x, 0 <= f(x) <= 1. The logistic function is perhaps the most well-known example. We are now given some constraints in the form of a list of x-values and for each x-value, a pair of y-values that the function must lie between. We can represent that as a list of {x,ymin,ymax} triples such as constraints = {{0, 0, 0}, {1, 0.00311936, 0.00416369}, {2, 0.0847077, 0.109064}, {3, 0.272142, 0.354692}, {4, 0.53198, 0.646113}, {5, 0.623413, 0.743102}, {6, 0.744714, 0.905966}} Graphically that looks like this: We now seek a curve that respects those constraints. For example: Let's first try a simple interpolation through the midpoints of the constraints: mids = ({#1, Mean[{#2,#3}]}&) @@@ constraints f = Interpolation[mids, InterpolationOrder->0] Plotted, f looks like this: That function is not surjective. Also, we'd like it to be smoother. We can increase the interpolation order but now it violates the constraint that its range is [0,1]: The goal, then, is to find the smoothest function that satisfies the constraints: Non-decreasing. Tends to 0 as x approaches negative infinity and tends to 1 as x approaches infinity. Passes through a given list of y-error-bars. The first example I plotted above seems to be a good candidate but I did that with Mathematica's FindFit function assuming a lognormal CDF. That works well in this specific example but in general there need not be a lognormal CDF that satisfies the constraints.

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• Fastest algorithm for primality test

  - by dada

  I need to test primality on intervals between numbers which are really big (in the range of long long), so i need some fast algorithm for checking if a number is prime or not. Please suggest your ideas.

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• Sparse constrained linear least-squares solver

  - by Jacob

  This great SO answer points to a good sparse solver, but I've got constraints on x (for Ax = b) such that each element in x is >=0 an <=N. The first thing which comes to mind is an QP solver for large sparse matrices. Also, A is huge (around 2e6x2e6) but very sparse with <=4 elements per row. Any ideas/recommendations? I'm looking for something like MATLAB's lsqlin but with huge sparse matrices.

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• Averaging initial values for rolling series

  - by Dave Jarvis

  Question Given a maximum sliding window size of 40 (i.e., the set of numbers in the list cannot exceed 40), what is the calculation to ensure a smooth averaging transition as the set size grows from 1 to 40? Problem Description Creating a trend line for a set of data has skewed initial values. The complete set of values is unknown at runtime: they are provided one at a time. It seems like a reverse-weighted average is required so that the initial values are averaged differently. In the image below the leftmost data for the trend line are incorrectly averaged. Current Solution Created a new type of ArrayList subclass that calculates the appropriate values and ensures its size never goes beyond the bounds of the sliding window: /** * A list of Double values that has a maximum capacity enforced by a sliding * window. Can calculate the average of its values. */ public class AveragingList extends ArrayList<Double> { private float slidingWindowSize = 0.0f; /** * The initial capacity is used for the sliding window size. * @param slidingWindowSize */ public AveragingList( int slidingWindowSize ) { super( slidingWindowSize ); setSlidingWindowSize( ( float )slidingWindowSize ); } public boolean add( Double d ) { boolean result = super.add( d ); // Prevent the list from exceeding the maximum sliding window size. // if( size() > getSlidingWindowSize() ) { remove( 0 ); } return result; } /** * Calculate the average. * * @return The average of the values stored in this list. */ public double average() { double result = 0.0; int size = size(); for( Double d: this ) { result += d.doubleValue(); } return (double)result / (double)size; } /** * Changes the maximum number of numbers stored in this list. * * @param slidingWindowSize New maximum number of values to remember. */ public void setSlidingWindowSize( float slidingWindowSize ) { this.slidingWindowSize = slidingWindowSize; } /** * Returns the number used to determine the maximum values this list can * store before it removes the first entry upon adding another value. * @return The maximum number of numbers stored in this list. */ public float getSlidingWindowSize() { return slidingWindowSize; } } Resulting Image Example Input The data comes into the function one value at a time. For example, data points (Data) and calculated averages (Avg) typically look as follows: Data: 17.0 Avg : 17.0 Data: 17.0 Avg : 17.0 Data: 5.0 Avg : 13.0 Data: 5.0 Avg : 11.0  Related Sites The following pages describe moving averages, but typically when all (or sufficient) data is known: http://www.cs.princeton.edu/introcs/15inout/MovingAverage.java.html http://stackoverflow.com/questions/2161815/r-zoo-series-sliding-window-calculation http://taragana.blogspot.com/ http://www.dreamincode.net/forums/index.php?showtopic=92508 http://blogs.sun.com/nickstephen/entry/dtrace_and_moving_rolling_averages

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• formula for best approximation for center of 2D rotation with small angles

  - by RocketSurgeon

  This is not a homework. I am asking to see if problem is classical (trivial) or non-trivial. It looks simple on a surface, and I hope it is truly a simple problem. Have N points (N = 2) with coordinates Xn, Yn on a surface of 2D solid body. Solid body has some small rotation (below Pi/180) combined with small shifts (below 1% of distance between any 2 points of N). Possibly some small deformation too (<<0.001%) Same N points have new coordinates named XXn, YYn Calculate with best approximation the location of center of rotation as point C with coordinates XXX, YYY. Thank you

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• Automatic camera calibration

  - by srand

  From Wikipedia, camera resectioning is the process of finding the true parameters of the camera that produced a given photograph or video. Camera resectioning is also known as geometric camera calibration. Currently I am using Camera Calibration Toolbox for Matlab for my camera calibration. The toolbox returns calibration parameters such as focal length, principle point, skew, and distortion. However, the issue with this method is that it requires an extra step in calibrating the camera by using a special calibration object like a checkerboard. Additionally, it only works for one focus of the camera. How can I get the calibration parameters without manually calibrating? For example, how does Microsoft's Photosynth perform camera calibration on its images?

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• Best way to do powerOf(int x, int n)?

  - by Mike

  So given x, and power, n, solve for X^n. There's the easy way that's O(n)... I can get it down to O(n/2), by doing numSquares = n/2; numOnes = n%2; return (numSquares * x * x + numOnes * x); Now there's a log(n) solution, does anyone know how to do it? It can be done recursively.

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• Clustering [assessment] algorithm with distance matrix as an input

  - by Max

  Can anyone suggest some clustering algorithm which can work with distance matrix as an input? Or the algorithm which can assess the "goodness" of the clustering also based on the distance matrix? At this moment I'm using a modification of Kruskal's algorithm (http://en.wikipedia.org/wiki/Kruskal%27s_algorithm) to split data into two clusters. It has a problem though. When the data has no distinct clusters the algorithm will still create two clusters with one cluster containing one element and the other containing all the rest. In this case I would rather have one cluster containing all the elements and another one which is empty. Are there any algorithms which are capable of doing this type of clustering? Are there any algorithms which can estimate how well the clustering was done or even better how many clusters are there in the data? The algorithms should work only with distance(similarity) matrices as an input.

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• Algorithm to fill slots

  - by Peter Lang

  I am searching for an algorithm to fill several slots, which are already filled to some level. The current levels and the available quantity to fill are known Resulting levels should be as equal as possible, but existing level cannot be reduced Slots are filled from left to right, so left slots get higher level if equal level is impossible       The image above shows six examples, each column represents a slot. The grey area is already filled, the blue are is the expected position of the new elements. I could iterate through my slots and increase the quantity on the lowest slot by 1 until the available quantity is consumed, but I wonder about how to actually calculate the new filling levels. I am going to implement this with SQL/PL/SQL, other code is just as welcome though :)

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• Why is Java not telling me when I can't use Integer?

  - by Sebi

  For a small project (Problem 10 Project Euler) i tried to sum up all prime numbers below 2 millions. So I used a brute force method and iterated from 0 to 2'000'000 and checked if the number is a prime. If it is I added it to the sum: private int sum = 0; private void calculate() { for (int i = 0; i < 2000000; i++) { if (i.isPrime()) { sum = sum + i; } } sysout(sum) } The result of this calculation is 1179908154, but this is incorrect. So i changed int to BigInteger and now i get the correct sum 142913828922. Obviously the range of int was overflowed. But why can't Java tell my that? (e.g. by an exception)

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• Finding the string length of a integer in .NET

  - by James Newton-King

  In .NET what is the best way to find the length of an integer in characters if it was represented as a string? e.g. 1 = 1 character 10 = 2 characters 99 = 2 characters 100 = 3 characters 1000 = 4 characters The obvious answer is to convert the int to a string and get its length but I want the best performance possible without the overhead of creating a new string.

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• Finding an element in a cyclic group of prime order

  - by Martin Andersson

  Greetings! How do I check if an element a belongs to a specific cyclic group G of prime order, given the generator? Right now i simply generate all the elements in the group, save them into a container and check if the element is in it.

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• How to get first derivative function for multiple dimensions

  - by nancy

  Hi If I have a constraint with a slope function f(h) = 1, h is the unknown value. I am trying to get the first derivative function for multiple dimensions. Please help. Thanks Nancy

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• Finding subsets that can be completed to tuples without duplicates

  - by Jules

  We have a collection of sets A_1,..,A_n. The goal is to find new sets for each of the old sets. newA_i = {a_i in A_i such that there exist (a_1,..,a_n) in (A1,..,An) with no a_k = a_j for all k and j} So in words this says that we remove all the elements from A_i that can't be used to form a tuple (a_1,..a_n) from the sets (A_1,..,A_n) such that the tuple doesn't contain duplicates. My question is how to compute these new sets quickly. If you just implement this definition by generating all possible v's this will take exponential time. Do you know a better algorithm? Edit: here's an example. Take A_1 = {1,2,3,4} A_2 = {2}. Now the new sets look like this: newA_1 = {1,3,4} newA_2 = {2} The 2 has been removed from A_1 because if you choose it the tuple will always be (2,2) which is invalid because it contains duplicates. On the other hand 1,3,4 are valid because (1,2), (3,2) and (4,2) are valid tuples. Another example: A_1 = {1,2,3} A_2 = {1,4,5} A_3 = {2,4,5} A_4 = {1,2,3} A_5 = {1,2,3} Now the new sets are: newA_1 = {1,2,3} newA_2 = {4,5} newA_3 = {4,5} newA_4 = {1,2,3} newA_5 = {1,2,3} The 1 and 2 are removed from sets 2 and 3 because if you choose the 1 or 2 from these sets you'll only have 2 values left for sets 1, 4 and 5, so you will always have duplicates in tuples that look like (_,1,_,_,_) or like (_,_,2,_,_).

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