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• How to interpolate rotations?

  - by uhuu

  I have two vectors describing rotations; a start rotation A and a target rotation B. How would I best go about interpolating A by a factor F to approach B? Using a simple lerp on the vectors fails to work when more than one dimension needs to be interpolated (i.e. produces undesirable rotations). Maybe building quaternions from the rotation vectors and using slerp is the way to go. But how, then, could I extract a vector describing the new rotation from the resulting quaternion? Thanks in advance.

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• I know my Before Tax Pay and my After Tax Pay, how can I work out how much I get taxed?

  - by Pete

  I've been entering some data into an Excel spreadsheet to work out my monthly earnings, etc. and was wondering how I can I find out how much I'm getting taxed? Say this is my current spreadsheet: Hours Worked 37.5 39.5 37.5 30 Hourly Rate $25 $25 $25 $25 Before Tax 937.50 987.50 937.50 750.00 After Tax 260.00 276.00 260.00 ??? How can I use this known data to work out my After Tax pay for the 4th column? :/

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• How to approximate double ?

  - by Andrei Ciobanu

  How to I write a function that approximates a double in the following manner, returning an int: function (2.3) -> 2 function (2.7) -> 3 function (-1.2) -> -1 function (-1.7) -> -2

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• How can I evaluate the connectedness of my nodes?

  - by Travis Leleu

  I've got a space that has nodes that are all interconnected, based on a "similarity score". I would like to determine how "connected" a node is with the others. My purpose is to find nodes that are poorly connected to make sure that the backlink from the other node is prioritized. Perhaps an example would help. I've got a web page that links to my other pages based on a similarity score. Suppose I have the pages: A, B, C, ... A has a backlink from every other page, so it's very well connected. It also has links to all my other pages (each line in the graph is essentially bidirectional). B only has 1 backlink, from A. C has a link from A and D. I would like to make sure that the A-B link is prioritized over the A-C link (even if the similarity score between C and A is higher than B and A). In short, I would like to evaluate which nodes are least and best connected, so that I can mangle the results to my means. I believe this is Graph Connectedness, but I'm at a loss to develop a (simple) algorithm that will help me here. Simply counting the backlinks to a node may be a starting point -- but then how do I take the next step, which is to properly weight the links on the original node (A, in the example above)?

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• Rotating a straight line about a point (2D)

  - by Arijit

  What is the method of rotating a straight line about a point and compute the new equation of the rotated line ? Say we have to rotate ax+by+c =0 through the angle Theta about the point P(x,y). And then find the Equation of the line after rotation.

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• How do i know if this is random enough?

  - by David

  I wrote a program in java that rolls a die and records the total number of times each value 1-6 is rolled. I rolled 6 Million times. Here's the distribution: #of 0's: 0 #of 1's: 1000068 #of 2's: 999375 #of 3's: 999525 #of 4's: 1001486 #of 5's: 1000059 #of 6's: 999487 (0 wasn't an option.) Is this distribution consistant with random dice rolls? What objective statistical tests might confirm that the dice rolls are indeed random enough?

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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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• How can I accelerate the generation of the an MD5 Checksum within vb.net?

  - by Richard

  I'm working with some very large files residing on P2 (Panasonic) cards. Part of the process we employ is to first generate a checksum of the file we are going to copy, then copy the file, then run a checksum on the file to confirm that it copied OK. The problem is, is that files are large (70 GB+) and take a long time to complete. It's an issue since we will eventually be dealing with thousands of these files. I would like to find a faster way to generate the checksum other than using the System.Security.Cryptography.MD5CryptoServiceProvider I don't care if this means using a specialized hardware card, provided it works and is not to ungodly expensive. I would prefer to have a method of encoding that provided some feedback as to how far the process has gone along so I can display it like I do now. The application is written in vb.net. I would prefer to be able to use it as component, library, reference within my application, but I'm willing to call an outside application if there is enough improvement in the speed of generating the checksum. Needless to say, the checksum must be consistent and correct. :-) Thank you in advance for your time and efforts, Richard

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• Calculating intraday candlesticks by time intervals

  - by Sam

  This maybe an over asked question, but my mind draws blank at this moment. I know what a candlestick chart is and how to draw it daily. But how to draw it intraday at asked time periods. I have this server, written in Java, that gives me trade depth (each trade done since the start of the day). Its just a stream of raw data: price, shares, timestamp. How does one go about calculating candlestick data from that? Lets say, they want to have 5 min candlestick or 1min candlestick. Or is there a library that will do that for me if I feed it data? Any help is appreciated!

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• Implementing a hilbert map of the internet

  - by Martin

  In the XKCD comic 195 a design for a map of the internet address space is suggested using a hilbert curve so that items from a similar IPs will be clustered together. Given an IP address, how would I calculate the 2D coordinates (in the range zero to one) that this IP is located on such a map?

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• Built in raytracing?

  - by acidzombie24

  Relating to this question i was wondering if .NET has any libs (or a function) i can use to detect if one point collides with another. I am not sure what angles i should use but is there some function like this func(point src, rect target, angle, distanceOfVision, listPointOrRectOfWalls) Pretty unlikely but i dont know a formula or how to start. Its a quick and dirty prototype. I am thinking of writing the func about but dropping angle and just make line of sight a rectangle and check if any points is between src and target.

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• Efficiency of manually written loops vs operator overloads (C++)

  - by Sagekilla

  Hi all, in the program I'm working on I have 3-element arrays, which I use as mathematical vectors for all intents and purposes. Through the course of writing my code, I was tempted to just roll my own Vector class with simple +, -, *, /, etc overloads so I can simplify statements like: for (int i = 0; i < 3; i++) r[i] = r1[i] - r2[i]; // becomes: r = r1 - r2; Which should be more or less identical in generated code. But when it comes to more complicated things, could this really impact my performance heavily? One example that I have in my code is this: Manually written version: for (int j = 0; j < 3; j++) { p.vel[j] = p.oldVel[j] + (p.oldAcc[j] + p.acc[j]) * dt2 + (p.oldJerk[j] - p.jerk[j]) * dt12; p.pos[j] = p.oldPos[j] + (p.oldVel[j] + p.vel[j]) * dt2 + (p.oldAcc[j] - p.acc[j]) * dt12; } Using a Vector class with operator overloads: p.vel = p.oldVel + (p.oldAcc + p.acc) * dt2 + (p.oldJerk - p.jerk) * dt12; p.pos = p.oldPos + (p.oldVel + p.vel) * dt2 + (p.oldAcc - p.acc) * dt12; I am compiling my code for maximum possible speed, as it's extremely important that this code runs quickly and calculates accurately. So will me relying on my Vector's for these sorts of things really affect me? For those curious, this is part of some numerical integration code which is not trivial to run in my program. Any insight would be appreciated, as would any idioms or tricks I'm unaware of.

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• XNA Track rotated pixel positions

  - by jonny adams

  Hi, Im making a game in xna where a tank has to move over a landscape. I need to be able find the bottom of the tank when it is rotated so I can make it move up and down as the player goes over the landscape. for example if i have a sprite at with its top left corner at 400,300 and i rotate it around its center by 45 degrees around its center, how do i find the new locations of the bottom track. Thanks

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• How to generate correlated binary variables

  - by jonalm

  Dear All I need to generate a series of N random binary variables with a given correlation function. Let x = {x_i} be a series of binary variables (taking the value 0 or 1, i running form 1 to N). The marginal probability is given Pr(x_i = 1) = p, and the values should be correlated in the following way E[ x_i x_j ] = const * |i-j|^-alfa where alfa is a positive number. Is it possible to generate a series like this? preferably in python.

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• Looking for interesting formula

  - by Thinker

  I'm creating a game where players can make an alloy. To make it less predictable and more interesting, I thought that the durability and hardness of an alloy should not be calculated by a simple formula, because it will be extremely easy to find extrema, where alloy have best statistics. So the questions is, is there any formula for a function where extrema can be found only by investigating all points? Input values will be in percents: 0.0%-100.0%. I think it should look like this: half sound wave

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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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• What is the minimal set of coins you should carry to always make exact change?

  - by ??iu

  US coin values: .01, .05, .10, .25 (*) What configuration(s) of US coins can be used to match every value from .01-.99 using the fewest coins possible? How can you find an answer? * note: there is actually a .50 coin but it is very rarely seen

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• syntax to express mathematical formula concisely in your language of choice

  - by aaa

  hello. I am developing functional domain specific embedded language within C++ to translate formulas into working code as concisely and accurately as possible. Right now my language looks something like this: // implies two nested loops j=0:N, i=0,j (range(i) < j < N)[T(i,j) = (T(i,j) - T(j,i))/e(i+j)]; // implies summation over above expression sum(range(i) < j < N))[(T(i,j) - T(j,i))/e(i+j)]; I am looking for possible syntax improvements/extensions or just different ideas about expressing mathematical formulas as clearly and precisely as possible. Can you give me some syntax examples relating to my question which can be accomplished in your language of choice which consider useful. In particular, if you have some ideas about how to translate the above code segments, I would be happy to hear them Thank you

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• How are a session identifiers generated?

  - by Asaf R

  Most web applications depend on some kind of session with the user (for instance, to retain login status). The session id is kept as a cookie in the user's browser and sent with every request. To make it hard to guess the next user's session these session-ids need to be sparse and somewhat random. The also have to be unique. The question is - how to efficiently generate session ids that are sparse and unique? This question has a good answer for unique random numbers, but it seems not scalable for a large range of numbers, simply because the array will end up taking a lot of memory.

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• Arbitrary-precision arithmetic Explanation

  - by TT

  I'm trying to learn C and have come across the inability to work with REALLY big numbers (i.e., 100 digits, 1000 digits, etc.). I am aware that there exist libraries to do this, but I want to attempt to implement it myself. I just want to know if anyone has or can provide a very detailed, dumbed down explanation of arbitrary-precision arithmetic. Thanks!

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• What is the fastest way to compute sin and cos together?

  - by Danvil

  I would like to compute both the sine and co-sine of a value together (for example to create a rotation matrix). Of course I could compute them separately one after another like a = cos(x); b = sin(x);, but I wonder if there is a faster way when needing both values.

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• Rock Paper Scissors for arbitrary odd number of elements

  - by Barry Carter

  How do I efficiently create a rock-scissors-paper game for n elements, where n is any odd number =3. In other words, I want a non-transitive complete ordering of n elements such that each element is greater than (n-1)/2 other elements and each element is lesser than (n-1)/2 other elements.

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• PHP given a series of arbitrary numbers, how can I choose a logical max value on a line graph?

  - by stormist

  I am constructing a line graph in PHP. I was setting the max value of the line graph to the max value of my collection of items, but this ended up making the graph less readable you are unable to view the highest line on the graph as it intersects with the top of it. So what I need is basically a formula to take a set of numbers and calculate what the logical max value of on the line graph should be.. so some examples 3500 250 10049 45394 434 312 Max value on line graph should probably be 50000 493 412 194 783 457 344 max value on line graph would ideally be 1000 545 649 6854 5485 11545 In this case, 12000 makes sense as max value So something as simple as rounding upward to the nearest thousandth might work but I'd need it to progressively increase as the numbers got bigger. (50000 instead of 46,000 in first example) The maximum these numbers will ever be is about a million. Any recommendations would be greatly appreciated, thank you.

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• C++: how can I test if a number is power of ten?

  - by Helltone

  I want to test if a number double x is a power of 10. I could perhaps use cmath's log10 and then test if x == (int) x?

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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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