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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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  • 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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  • 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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  • 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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  • 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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  • Rotate array clockwise

    - by user69514
    I have a two dimensional array that I need to rotate 90 degrees clockwise, however I keep getting arrayindexoutofbounds... public int[][] rorateArray(int[][] arr){ //first change the dimensions vertical length for horizontal length //and viceversa int[][] newArray = new int[arr[0].length][arr.length]; //invert values 90 degrees clockwise by starting from button of //array to top and from left to right int ii = 0; int jj = 0; for(int i=0; i<arr[0].length; i++){ for(int j=arr.length-1; j>=0; j--){ newArray[ii][jj] = arr[i][j]; jj++; } ii++; } return newArray; }

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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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  • Multiple outliers for two variable linear regression

    - by Dave Jarvis
    Problem Building on my previous question, the "extreme" outliers in the following graph are somewhat obvious: Question Given: T - Set of all temperatures Y - Set of all years ST - Sum of temperatures. SY - Sum of years. N - Number of elements T(n) - Temperature of the nth element in the temperature set How would you implement an efficient MySQL stored procedure or user-defined function (UDF) to determine if T(n) is an outlier? (If such an implementation already exists, that would be good to know as well.) Related Sites I am slowly working through these sites to get a better understanding of the problem: Multiple Outliers Detection Procedures in Linear Regression M-estimator Measure of Surprise for Outlier Detection Ordinary Least Squares Linear Regression Many thanks!

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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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  • 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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  • 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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  • 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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  • WPF Coordinates of intersection from two Line objects

    - by Becky Franklin
    I have two Line objects in C# WPF, and I'm trying to construct a method to work out the coordinates at which the lines intersect (if at all). After giving myself a headache reminding myself of high school maths to do this, I can't work out how to map it into programming format - anyone know how to do this? Thanks very much, Becky

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  • PHP Calculating future date by adding days to a variable date

    - by OneNerd
    I was looking at this post, and it is close to what I need: http://stackoverflow.com/questions/1669165/php-how-to-count-60-days-from-the-add-date However, in that post, the calculation is performed by adding 60 days to the current date. What I need to do is calculate the date based on a variable date (and not the current date). Something like this: $my_date = $some_row_from_a_database; $date_plus_10_days = ???; Anyone know how to do that? Thanks

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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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  • 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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  • Fastest way to list all primes below N in python

    - by jbochi
    This is the best algorithm I could come up with after struggling with a couple of Project Euler's questions. def get_primes(n): numbers = set(range(n, 1, -1)) primes = [] while numbers: p = numbers.pop() primes.append(p) numbers.difference_update(set(range(p*2, n+1, p))) return primes >>> timeit.Timer(stmt='get_primes.get_primes(1000000)', setup='import get_primes').timeit(1) 1.1499958793645562 Can it be made even faster? EDIT: This code has a flaw: Since numbers is an unordered set, there is no guarantee that numbers.pop() will remove the lowest number from the set. Nevertheless, it works (at least for me) for some input numbers: >>> sum(get_primes(2000000)) 142913828922L #That's the correct sum of all numbers below 2 million >>> 529 in get_primes(1000) False >>> 529 in get_primes(530) True EDIT: The rank so far (pure python, no external sources, all primes below 1 million): Sundaram's Sieve implementation by myself: 327ms Daniel's Sieve: 435ms Alex's recipe from Cookbok: 710ms EDIT: ~unutbu is leading the race.

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  • How to calculate both positive and negative angle between two lines?

    - by Jaanus
    There is a very handy set of 2d geometry utilities here. The angleBetweenLines has a problem, though. The result is always positive. I need to detect both positive and negative angles, so if one line is 15 degrees "above" or "below" the other line, the shape obviously looks different. The configuration I have is that one line remains stationary, while the other line rotates, and I need to understand what direction it is rotating in, by comparing it with the stationary line. EDIT: in response to swestrup's comment below, the situation is actually that I have a single line, and I record its starting position. The line then rotates from its starting position, and I need to calculate the angle from its starting position to current position. E.g if it has rotated clockwise, it is positive rotation; if counterclockwise, then negative. (Or vice versa.) How to improve the algorithm so it returns the angle as both positive or negative depending on how the lines are positioned?

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