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  • Howto project a planar polygon on a plane in 3d-space

    - by sum1stolemyname
    I want to project my Polygon along a vector to a plane in 3d Space. I would preferably use a single transformation matrix to do this, but I don't know how to build a matrix of this kind. Given the plane's parameters (ax+by+cz+d), the world coordinates of my Polygon. As stated in the the headline, all vertices of my polygon lie in another plane. the direction vector along which to project my Polygon (currently the polygon's plane's normal vector) goal -a 4x4 transformation matrix which performs the required projection, or some insight on how to construct one myself

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  • Number Algorithm

    - by James
    I've been struggling to wrap my head around this for some reason. I have 15 bits that represent a number. The bits must match a pattern. The pattern is defined in the way the bits start out: they are in the most flush-right representation of that pattern. So say the pattern is 1 4 1. The bits will be: 000000010111101 So the general rule is, take each number in the pattern, create that many bits (1, 4 or 1 in this case) and then have at least one space separating them. So if it's 1 2 6 1 (it will be random): 001011011111101 Starting with the flush-right version, I want to generate every single possible number that meets that pattern. The # of bits will be stored in a variable. So for a simple case, assume it's 5 bits and the initial bit pattern is: 00101. I want to generate: 00101 01001 01010 10001 10010 10100 I'm trying to do this in Objective-C, but anything resembling C would be fine. I just can't seem to come up with a good recursive algorithm for this. It makes sense in the above example, but when I start getting into 12431 and having to keep track of everything it breaks down.

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  • Infix to Postfix and unary/binary operators

    - by Jaapjan
    I have a piece of code that converts an infix expression to an expression tree in memory. This works just fine. There's just one small trouble. I just connect work out how to involve the unary operators correctly (the right associative ones). With the following infix expression : +1 + +2 - -3 - -4 I would expect an RPN of: 1+2++3-4-- Yet, none of the online infix-post converters I can find handle this example in the way I would expect. Does anyone have a clear explanation of handling right associative operators, specifically the binary ones that can be mistaken for the unary ones?

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  • Mathematics for Computer Science Students

    - by Ender
    To cut a long story short, I am a CS student that has received no formal Post-16 Maths education for years. Right now even my Algebra is extremely rusty and I have a couple of months to shape up my skills. I've got a couple of video lectures in my bookmarks, consisting of: Pre-Calculus Algebra Calculus Probability Introduction to Statistics Differential Equations Linear Algebra My aim as of today is to be able to read the CLRS book Introduction to Algorithms and be able to follow the Mathematical notation in that, as well as being able to confidently read and back-up any arguments written in Mathematical notation. Aside from these video lectures, can anyone recommend any good books to help teach someone wishing to go from a low-foundation level to a more advanced level of Mathematics? Just as a note, I've taken a first-year module in Analytical Modelling, so I understand some of the basic concepts of Discrete Mathematics. EDIT: Just a note to those that are looking to learn Linear Algebra using the Video Lectures I have posted up. Peteris Krumins' Blog contains a run-through of these lecture notes as well as his own commentary and lecture notes, an invaluable resource for those looking to follow the lectures too.

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  • What's the best way to normalize scores for ranking things?

    - by beagleguy
    hi all, I'm curious how to do normalizing of numbers for a ranking algorithm let's say I want to rank a link based on importance and I have two columns to work with so a table would look like url | comments | views now I want to rank comments higher than views so I would first think to do comments*3 or something to weight it, however if there is a large view number like 40,000 and only 4 comments then the comments weight gets dropped out. So I'm thinking I have to normalize those scores down to a more equal playing field before I can weight them. Any ideas or pointers to how that's usually done? thanks

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  • Calculating negative fractions in Objective C

    - by Mark Reid
    I've been coding my way through Steve Kochan's Programming in Objective-C 2.0 book. I'm up to an exercise in chapter 7, ex 4, in case anyone has the book. The question posed by the exercise it will the Fraction class written work with negative fractions such as -1/2 + -2/3? Here's the implementation code in question - @implementation Fraction @synthesize numerator, denominator; -(void) print { NSLog(@"%i/%i", numerator, denominator); } -(void) setTo: (int) n over: (int) d { numerator = n; denominator = d; } -(double) convertToNum { if (denominator != 0) return (double) numerator / denominator; else return 1.0; } -(Fraction *) add: (Fraction *) f { // To add two fractions: // a/b + c/d = ((a * d) + (b * c)) / (b * d) // result will store the result of the addition Fraction *result = [[Fraction alloc] init]; int resultNum, resultDenom; resultNum = (numerator * f.denominator) + (denominator * f.numerator); resultDenom = denominator * f.denominator; [result setTo: resultNum over: resultDenom]; [result reduce]; return result; } -(Fraction *) subtract: (Fraction *) f { // To subtract two fractions: // a/b - c/d = ((a * d) - (b * c)) / (b * d) // result will store the result of the addition Fraction *result = [[Fraction alloc] init]; int resultNum, resultDenom; resultNum = numerator * f.denominator - denominator * f.numerator; resultDenom = denominator * f.denominator; [result setTo: resultNum over: resultDenom]; [result reduce]; return result; } -(Fraction *) multiply: (Fraction *) f { // To multiply two fractions // a/b * c/d = (a*c) / (b*d) // result will store the result of the addition Fraction *result = [[Fraction alloc] init]; int resultNum, resultDenom; resultNum = numerator * f.numerator; resultDenom = denominator * f.denominator; [result setTo: resultNum over: resultDenom]; [result reduce]; return result; } -(Fraction *) divide: (Fraction *) f { // To divide two fractions // a/b / c/d = (a*d) / (b*c) // result will store the result of the addition Fraction *result = [[Fraction alloc] init]; int resultNum, resultDenom; resultNum = numerator * f.denominator; resultDenom = denominator * f.numerator; [result setTo: resultNum over: resultDenom]; [result reduce]; return result; } -(void) reduce { int u = numerator; int v = denominator; int temp; while (v != 0) { temp = u % v; u = v; v = temp; } numerator /= u; denominator /= u; } @end My question to you is will it work with negative fractions and can you explain how you know? Part of the issue is I don't know how to calculate negative fractions myself so I'm not too sure how to know. Many thanks.

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  • Derivative Calculator

    - by burki
    Hi! I'm interested in building a derivative calculator. I've racked my brains over solving the problem, but I haven't found a right solution at all. May you have a hint how to start? Thanks

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  • NSDecimalNumber subtraction

    - by happyCoding25
    Hello, I need to subtract 0.5 from number a and set the answer to number b. My code looks like it would work but I'm not sure what I'm doing wrong. The error I get Is on the subtraction line, the error says incompatible type for argument 1 of 'decimalNumberBySubtracting:'. Heres my header: (Note: I only showed the numbers because the header is large) NSDecimalNumber *a; NSDecimalNumber *b; Heres the rest: (Assume this is in an IBAction) b = [a decimalNumberBySubtracting:0.5]; If anyone knows how to properly subtract any help would be appreciated.

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  • Rot13 for numbers.

    - by dreeves
    EDIT: Now a Major Motion Blog Post at http://messymatters.com/sealedbids The idea of rot13 is to obscure text, for example to prevent spoilers. It's not meant to be cryptographically secure but to simply make sure that only people who are sure they want to read it will read it. I'd like to do something similar for numbers, for an application involving sealed bids. Roughly I want to send someone my number and trust them to pick their own number, uninfluenced by mine, but then they should be able to reveal mine (purely client-side) when they're ready. They should not require further input from me or any third party. (Added: Note the assumption that the recipient is being trusted not to cheat.) It's not as simple as rot13 because certain numbers, like 1 and 2, will recur often enough that you might remember that, say, 34.2 is really 1. Here's what I'm looking for specifically: A function seal() that maps a real number to a real number (or a string). It should not be deterministic -- seal(7) should not map to the same thing every time. But the corresponding function unseal() should be deterministic -- unseal(seal(x)) should equal x for all x. I don't want seal or unseal to call any webservices or even get the system time (because I don't want to assume synchronized clocks). (Added: It's fine to assume that all bids will be less than some maximum, known to everyone, say a million.) Sanity check: > seal(7) 482.2382 # some random-seeming number or string. > seal(7) 71.9217 # a completely different random-seeming number or string. > unseal(seal(7)) 7 # we always recover the original number by unsealing.

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  • correcting fisheye distortion programmatically

    - by Will
    I have some points that describe positions in a picture taken with a fisheye lens. I've found this description of how to generate a fisheye effect, but not how to reverse it. How do you calculate the radial distance from the centre to go from fisheye to rectilinear? My function stub looks like this: Point correct_fisheye(const Point& p,const Size& img) { // to polar const Point centre = {img.width/2,img.height/2}; const Point rel = {p.x-centre.x,p.y-centre.y}; const double theta = atan2(rel.y,rel.x); double R = sqrt((rel.x*rel.x)+(rel.y*rel.y)); // fisheye undistortion in here please //... change R ... // back to rectangular const Point ret = Point(centre.x+R*cos(theta),centre.y+R*sin(theta)); fprintf(stderr,"(%d,%d) in (%d,%d) = %f,%f = (%d,%d)\n",p.x,p.y,img.width,img.height,theta,R,ret.x,ret.y); return ret; } Alternatively, I could somehow convert the image from fisheye to rectilinear before finding the points, but I'm completely befuddled by the OpenCV documentation. Is there a straightforward way to do it in OpenCV, and does it perform well enough to do it to a live video feed?

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  • Draw Lines Over a Circle

    - by VOX
    There's a line A-B and C at the center between A and B. It forms a circle as in the figure. If we assume A-B line as a diameter of the circle and then C is it's center. My problem is I have no idea how to draw another three lines (in blue) each 45 degree away from AC or AB. No, this is not a homework, it's part of my complex geometry in a rendering. http://www.freeimagehosting.net/image.php?befcd84d8c.png

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  • Power Law distribution for a given exponent in C# using MathNet

    - by Eric Tobias
    Hello! I am currently working on a project where I need to generate multiple values (floats or doubles preferably) that follow a power law distribution with a given exponent! I was advised to use the MathNet.Iridium library to help me. The problem I have is that the documentation is not as explicit as it should be if there is any! I see multiple distributions that fit the general idea of the power law distribution but I cannot pinpoint a good distribution to use with a certain exponent as a parameter. Does anybody have more experience in that matter and could give me some hints or advice?

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  • DSA signature verification input

    - by calccrypto
    What is the data inputted into DSA when PGP signs a message? From RFC4880, i found A Signature packet describes a binding between some public key and some data. The most common signatures are a signature of a file or a block of text, and a signature that is a certification of a User ID. im not sure if it is the entire public key, just the public key packet, or some other derivative of a pgp key packet. whatever it is, i cannot get the DSA signature to verify here is a sample im testing my program on: -----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1 abcd -----BEGIN PGP SIGNATURE----- Version: BCPG v1.39 iFkEARECABkFAk0z65ESHGFiYyAodGVzdCBrZXkpIDw+AAoJEC3Jkh8+bnkusO0A oKG+HPF2Qrsth2zS9pK+eSCBSypOAKDBgC2Z0vf2EgLiiNMk8Bxpq68NkQ== =gq0e -----END PGP SIGNATURE----- Dumped from pgpdump.net Old: Signature Packet(tag 2)(89 bytes) Ver 4 - new Sig type - Signature of a canonical text document(0x01). Pub alg - DSA Digital Signature Algorithm(pub 17) Hash alg - SHA1(hash 2) Hashed Sub: signature creation time(sub 2)(4 bytes) Time - Mon Jan 17 07:11:13 UTC 2011 Hashed Sub: signer's User ID(sub 28)(17 bytes) User ID - abc (test key) <> Sub: issuer key ID(sub 16)(8 bytes) Key ID - 0x2DC9921F3E6E792E Hash left 2 bytes - b0 ed DSA r(160 bits) - a1 be 1c f1 76 42 bb 2d 87 6c d2 f6 92 be 79 20 81 4b 2a 4e DSA s(160 bits) - c1 80 2d 99 d2 f7 f6 12 02 e2 88 d3 24 f0 1c 69 ab af 0d 91 -> hash(DSA q bits) and the public key for it is: -----BEGIN PGP PUBLIC KEY BLOCK----- Version: BCPG v1.39 mOIETTPqeBECALx+i9PIc4MB2DYXeqsWUav2cUtMU1N0inmFHSF/2x0d9IWEpVzE kRc30PvmEHI1faQit7NepnHkkphrXLAoZukAoNP3PB8NRQ6lRF6/6e8siUgJtmPL Af9IZOv4PI51gg6ICLKzNO9i3bcUx4yeG2vjMOUAvsLkhSTWob0RxWppo6Pn6MOg dMQHIM5sDH0xGN0dOezzt/imAf9St2B0HQXVfAAbveXBeRoO7jj/qcGx6hWmsKUr BVzdQhBk7Sku6C2KlMtkbtzd1fj8DtnrT8XOPKGp7/Y7ASzRtBFhYmMgKHRlc3Qg a2V5KSA8PohGBBMRAgAGBQJNM+p5AAoJEC3Jkh8+bnkuNEoAnj2QnqGtdlTgUXCQ Fyvwk5wiLGPfAJ4jTGTL62nWzsgrCDIMIfEG2shm8bjMBE0z6ngQAgCUlP7AlfO4 XuKGVCs4NvyBpd0KA0m0wjndOHRNSIz44x24vLfTO0GrueWjPMqRRLHO8zLJS/BX O/BHo6ypjN87Af0VPV1hcq20MEW2iujh3hBwthNwBWhtKdPXOndJGZaB7lshLJuW v9z6WyDNXj/SBEiV1gnPm0ELeg8Syhy5pCjMAgCFEc+NkCzcUOJkVpgLpk+VLwrJ /Wi9q+yCihaJ4EEFt/7vzqmrooXWz2vMugD1C+llN6HkCHTnuMH07/E/2dzciEYE GBECAAYFAk0z6nkACgkQLcmSHz5ueS7NTwCdED1P9NhgR2LqwyS+AEyqlQ0d5joA oK9xPUzjg4FlB+1QTHoOhuokxxyN =CTgL -----END PGP PUBLIC KEY BLOCK----- the public key packet of the key is mOIETTPqeBECALx+i9PIc4MB2DYXeqsWUav2cUtMU1N0inmFHSF/2x0d9IWEpVzEkRc30PvmEHI1faQi t7NepnHkkphrXLAoZukAoNP3PB8NRQ6lRF6/6e8siUgJtmPLAf9IZOv4PI51gg6ICLKzNO9i3bcUx4ye G2vjMOUAvsLkhSTWob0RxWppo6Pn6MOgdMQHIM5sDH0xGN0dOezzt/imAf9St2B0HQXVfAAbveXBeRoO 7jj/qcGx6hWmsKUrBVzdQhBk7Sku6C2KlMtkbtzd1fj8DtnrT8XOPKGp7/Y7ASzR in radix 64 i have tried many different combinations of sha1(< some data + 'abcd'),but the calculated value v never equals r, of the signature i know that the pgp implementation i used to create the key and signature is correct. i also know that my DSA implementation and PGP key data extraction program are correct. thus, the only thing left is the data to hash. what is the correct data to be hashed?

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  • Is there a Java library with 3D spline functions?

    - by Liam
    In particular, I need a way to represent a curve/spline that passes through a set of known 3D points, and a way of finding other points on the curve/spline, by subdivision/interpolation. For example, if I have a set of points P0 to PN, I want to find 100 points between P0 and P1 that are on a spline that passes through P0 and P1. I see that Java3D's KBRotPosScaleSplinePathInterpolator performs such a calculation, but it is tied to that API's scenegraph model and I do not see how to return the values I need.

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  • How to generate a lower frequency version of a signal in Matlab?

    - by estourodepilha.com
    With a sine input, I tried to modify it's frequency cutting some lower frequencies in the spectrum, shifting the main frequency towards zero. As the signal is not fftshifted I tried to do that by eliminating some samples at the begin and at the end of the fft vector: interval = 1; samplingFrequency = 44100; signalFrequency = 440; sampleDuration = 1 / samplingFrequency; timespan = 1 : sampleDuration : (1 + interval); original = sin(2 * pi * signalFrequency * timespan); fourierTransform = fft(original); frequencyCut = 10; %% Hertz frequencyCut = floor(frequencyCut * (length(pattern) / samplingFrequency) / 4); %% Samples maxFrequency = length(fourierTransform) - (2 * frequencyCut); signal = ifft(fourierTransform(frequencyCut + 1:maxFrequency), 'symmetric'); But it didn't work as expected. I also tried to remove the center part of the spectrum, but it wielded a higher frequency sine wave too. How to make it right?

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  • How to perform spatial partitioning in n-dimensions?

    - by kevin42
    I'm trying to design an implementation of Vector Quantization as a c++ template class that can handle different types and dimensions of vectors (e.g. 16 dimension vectors of bytes, or 4d vectors of doubles, etc). I've been reading up on the algorithms, and I understand most of it: here and here I want to implement the Linde-Buzo-Gray (LBG) Algorithm, but I'm having difficulty figuring out the general algorithm for partitioning the clusters. I think I need to define a plane (hyperplane?) that splits the vectors in a cluster so there is an equal number on each side of the plane. [edit to add more info] This is an iterative process, but I think I start by finding the centroid of all the vectors, then use that centroid to define the splitting plane, get the centroid of each of the sides of the plane, continuing until I have the number of clusters needed for the VQ algorithm (iterating to optimize for less distortion along the way). The animation in the first link above shows it nicely. My questions are: What is an algorithm to find the plane once I have the centroid? How can I test a vector to see if it is on either side of that plane?

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