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• Find if a user is facing a certain Location using Digital Compass by constructing a triangle and usi

  - by Aidan

  Hi Guys, I'm constructing a geolocation based application and I'm trying to figure out a way to make my application realise when a user is facing the direction of the given location (a particular long / lat co-ord). I've done some Googling and checked the SDK but can't really find anything for such a thing. Does anyone know of a way? To clarify Android knows my location, the second location and my orientation. What I want is a way for Android to recognise when my orientation is "facing" the second location (e.g within 90 Degrees or so). We're also assuming that the user is stationary and needs updates every second or so therefore getBearing(); is useless. Alright so we get it has to be math, there appears to be no simple SDK stuff we can use. I did some searching of my own and found Barycentric Co-ords http://www.blackpawn.com/texts/pointinpoly/default.html . So what I'm trying to do now is map the camera's field of view. For Example if the person is facing a certain direction the program should construct a triangle around that field of view, e.g it should make one vertices the phone's position and then go out either side for a set distance making the 2 end points vertices constructing a triangle. If I had this I could then apply Barycentric co-ords to see if the point lay within the newly constructed triangle. Idea's anyone? Example. I could get my current orientation, add 45 to it and go up X distance one side and subtact 45 and go up X distance the other side to find my 2 other points. Though, how would I make android know which way it should go "up" I guess? It would know its baring as this stage so I need it to recognise it's bearing and go out that direction.

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• Calculating distance between two X,Y coordinates

  - by Umopepisdn

  I am writing a tool for a game that involves calculating the distance between two coordinates on a spherical plane 500 units across. That is, [0,0] through [499,499] are valid coordinates, and [0,0] and [499,499] are also right next to each other. Currently, in my application, I am comparing the distance between a city with an [X,Y] location respective to the user's own [X,Y] location, which they have configured in advance. To do this, I found this algorithm, which kind of works: Math.sqrt ( dx * dx + dy * dy ); Because sorting a paged list by distance is a useful thing to be able to do, I implemented this algorithm in a MySQL query and have made it available to my application using the following part of my SELECT statement: SQRT( POW( ( ".strval($sourceX)." - cityX ) , 2 ) + POW( ( ".strval($sourceY)." - cityY ) , 2 ) ) AS distance This works fine for many calculations, but does not take into account the fact that [0,0] and [499,499] are kitty-corner to one another. Is there any way I can tweak this algorithm to generate an accurate distance, given that 0 and 499 are adjacent? Thanks, -Umo

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• Interview question : What is the fastest way to generate prime number recursively ?

  - by hilal

  Generation of prime number is simple but what is the fastest way to find it and generate( prime numbers) it recursively ? Here is my solution. However, it is not the best way. I think it is O(N*sqrt(N)). Please correct me, if I am wrong. public static boolean isPrime(int n) { if (n < 2) { return false; } else if (n % 2 == 0 & n != 2) { return false; } else { return isPrime(n, (int) Math.sqrt(n)); } } private static boolean isPrime(int n, int i) { if (i < 2) { return true; } else if (n % i == 0) { return false; } else { return isPrime(n, --i); } } public static void generatePrimes(int n){ if(n < 2) { return ; } else if(isPrime(n)) { System.out.println(n); } generatePrimes(--n); } public static void main(String[] args) { generatePrimes(200); }

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• How to parse mathematical expressions involving parentheses

  - by Rob P.

  Please forgive my title, I really don't know how to phrase it better. This isn't a school assignment or anything, but I realize it's a mostly academic question. But, what I've been struggling to do is parse 'math' text and come up with an answer. For Example - I can figure out how to parse '5 + 5' or '3 * 5' - but I fail when I try to correctly chain operations together. (5 + 5) * 3 It's mostly just bugging me that I can't figure it out. If anyone can point me in a direction, I'd really appreciate it. EDIT Thanks for all of the quick responses. I'm sorry I didn't do a better job of explaining. First - I'm not using regular expressions. I also know there are already libraries available that will take, as a string, a mathematical expression and return the correct value. So, I'm mostly looking at this because, sadly, I don't "get it". Second - What I've tried doing (is probably misguided) but I was counting '(' and ')' and evaluating the deepest items first. In simple examples, this worked; but my code is not pretty and more complicated stuff crashes. When I 'calculated' the lowest level, I was modifying the string. So... (5 + 5) * 3 Would turn into 10 * 3 Which would then evaluate to 30 But it just felt 'wrong'. I hope that helps clarify things. I'll certainly check out the links provided.

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• how to reverse an angle

  - by MissHalberd

  I am no mathematician, but I somehow got into game development as a hobby. Having never studied anything beyond basic math, I have a lot of trouble figuring out how to reverse the angle of something, facing to the opposite direction, among the X axis. One image says more than 1000 words though (specially uneducated words): http://img156.imageshack.us/i/wihwin.png/ I basically want to reverse the direction of cannon objects adhered to a robot. When the robot changes from facing right to facing left, I do (180 - angle) as everyone suggested me, but it reverses the angle...literally, making the cannons aim up when they are aiming down. So, I need to do something else, but it escapes my knowledge. Anyone would be so kind to help me with this? Oh, I use regular C by the way, in case there's something built-in specific to it. To put it in other words, I work in 2D, so I want an angle that is facing right to face left. 0 being "totally to the right", 180 "left", 90 "up" and 270 "down". I want something that is aiming with an angle of 91 to turn into 89 when reversed, literally. There's no Z axis present. EDIT: Thanks for the answers! Trying them out now. I'll post which one worked in a minute!

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• Beginner Question ; About Prime Generation in "C" - What is wrong with my code ? -

  - by alorsoncode

  I'm a third year irregular CS student and ,i just realized that i have to start coding. I passed my coding classes with lower bound grades so that i haven't a good background in coding&programming. I'm trying to write a code that generates prime numbers between given upper and lower bounds. Not knowing C well, enforce me to write a rough code then go over it to solve. I can easily set up the logic for intended function but i probably create a wrong algorithm through several different ways. Here I share my last code, i intend to calculate that when a number gives remainder Zero , it should be it self and 1 , so that count==2; What is wrong with my implementation and with my solution generating style? I hope you will warm me up to programming world, i couldn't find enough motivation and courage to get deep into programming. Thanks in Advance :) Stdio and Math.h is Included int primegen(int down,int up) { int divisor,candidate,count=0,k; for(candidate=down;candidate<=up;candidate++) { for(divisor=1;divisor<=candidate;divisor++) { k=(candidate%divisor); } if (k==0) count++; if(count==2) { printf("%d\n", candidate); count=0; } else { continue; } } } int main() { primegen(3,15); return 0; }

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• Value types of variable size

  - by YellPika

  I'm trying to code a small math library in C#. I wanted to create a generic vector structure where the user could define the element type (int, long, float, double, etc.) and dimensions. My first attempt was something like this... public struct Vector<T> { public readonly int Dimensions; public readonly T[] Elements; // etc... } Unfortunately, Elements, being an array, is also a reference type. Thus, doing this, Vector<int> a = ...; Vector<int> b = a; a[0] = 1; b[0] = 2; would result in both a[0] and b[0] equaling 2. My second attempt was to define an interface IVector<T>, and then use Reflection.Emit to automatically generate the appropriate type at runtime. The resulting classes would look roughly like this: public struct Int32Vector3 : IVector<T> { public int Element0; public int Element1; public int Element2; public int Dimensions { get { return 3; } } // etc... } This seemed fine until I found out that interfaces seem to act like references to the underlying object. If I passed an IVector to a function, and changes to the elements in the function would be reflected in the original vector. What I think is my problem here is that I need to be able to create classes that have a user specified number of fields. I can't use arrays, and I can't use inheritance. Does anyone have a solution? EDIT: This library is going to be used in performance critical situations, so reference types are not an option.

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• How much of slow and fast flash memory a "flash memory" have?

  - by gsc-frank

  Trying to know what is the best of my flash memories to use ReadyBoost I realize that I don't know how much of fast flash memory each of my flash drives have. One can read: In some situations, you might not be able to use all of the memory on your device to speed up your computer. For example, some flash memory devices contain both slow and fast flash memory, but ReadyBoost can only use fast flash memory to speed up your computer. From http://windows.microsoft.com/is-IS/windows7/Using-memory-in-your-storage-device-to-speed-up-your-computer

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• How much of slow and fast flash memory a "flash memory" have? [migrated]

  - by gsc-frank

  Trying to know what is the best of my flash memories to use ReadyBoost I realize that I don't know how much of fast flash memory each of my flash drives have. One can read: In some situations, you might not be able to use all of the memory on your device to speed up your computer. For example, some flash memory devices contain both slow and fast flash memory, but ReadyBoost can only use fast flash memory to speed up your computer. From http://windows.microsoft.com/is-IS/windows7/Using-memory-in-your-storage-device-to-speed-up-your-computer

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• Why is writing to my external hard drive slow, while benchmarks show fast writing?

  - by matix2267

  I have an iOmega eGo 320GB portable drive connected through USB2.0 to my laptop running Windows Vista. It's been working fine for quite some time until recently it became very slow when writing e.g. when copying ~300MB movie over to the drive at first it is extremely fast but it actually doesn't write it only puts in cache and then hangs on last 10-20MBs for about a minute. When copying larger files it's the same story: starts fast but then slows down to ~5MB/s (sometimes even slower down to 2MB/s). Strange thing is that I have always had caching disabled for this drive (it was disabled by default and I never bothered changing it). At first I thought that the disk is dying so I checked S.M.A.R.T. values and everything is fine there. I also run chkdsk and it seemed to fix the problem - it worked fast for a few minutes but then it slowed down again. I also tried plugging it into another USB port - no difference. Additionally I noticed that reading under certain circumstances is sometimes slower e.g. loading times for some games are ~10 times longer, whereas simple copying files from this drive to my internal HDD is fast. I ran a speed benchmark using CrystalDiskMark with a 5x100MB run and strangely got these results: read write (MB/s) Seq 33.05 28.25 512k 17.30 15.27 4k 0.267 0.372 4kQD32 0.510 0.260 This is different from what most other people have (I've found many threads about slow disk write while googling but all of them were slow on benchmarks too) which is why I decided to post this problem here. BTW most of the time when writing (or sometimes reading) the activity led is mostly idle (blinks a while and then stops for longer, sometimes has slower blinks ~1 sek, sometimes goes off for a few seconds - extremely long blink :) ) but when benchmarking, defragmenting or just reading (copying from this drive, installing apps from installers there, watching HD videos) it is blinking really fast (like it should) and there are no slowdowns. It shouldn't be driver issue unless stock Windows drivers have some issues I'm not aware of.

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• How to increase fast-forward/rewind on Vista Media Center recorded TV shows?

  - by jtimberman

  How do I granularly increase the various fast-forward/rewind speed/rate for each of the speed settings for skipping through commercials? The current defaults go from barely faster than playback, too fast for unexpectedly short commercials, to omfg its so fast I can't see what is happening. Do people suffer with these defaults, or is there some better setting in the registry, or elsewhere?

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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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• Small-o(n^2) implementation of Polynomial Multiplication

  - by AlanTuring

  I'm having a little trouble with this problem that is listed at the back of my book, i'm currently in the middle of test prep but i can't seem to locate anything regarding this in the book. Anyone got an idea? A real polynomial of degree n is a function of the form f(x)=a(n)x^n+?+a1x+a0, where an,…,a1,a0 are real numbers. In computational situations, such a polynomial is represented by a sequence of its coefficients (a0,a1,…,an). Assuming that any two real numbers can be added/multiplied in O(1) time, design an o(n^2)-time algorithm to compute, given two real polynomials f(x) and g(x) both of degree n, the product h(x)=f(x)g(x). Your algorithm should **not** be based on the Fast Fourier Transform (FFT) technique. Please note it needs to be small-o(n^2), which means it complexity must be sub-quadratic. The obvious solution that i have been finding is indeed the FFT, but of course i can't use that. There is another method that i have found called convolution, where if you take polynomial A to be a signal and polynomial B to be a filter. A passed through B yields a shifted signal that has been "smoothed" by A and the resultant is A*B. This is supposed to work in O(n log n) time. Of course i am completely unsure of implementation. If anyone has any ideas of how to achieve a small-o(n^2) implementation please do share, thanks.

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• Is there an algorithm for converting quaternion rotations to Euler angle rotations?

  - by Will Baker

  Is there an existing algorithm for converting a quaternion representation of a rotation to an Euler angle representation? The rotation order for the Euler representation is known and can be any of the six permutations (i.e. xyz, xzy, yxz, yzx, zxy, zyx). I've seen algorithms for a fixed rotation order (usually the NASA heading, bank, roll convention) but not for arbitrary rotation order. Furthermore, because there are multiple Euler angle representations of a single orientation, this result is going to be ambiguous. This is acceptable (because the orientation is still valid, it just may not be the one the user is expecting to see), however it would be even better if there was an algorithm which took rotation limits (i.e. the number of degrees of freedom and the limits on each degree of freedom) into account and yielded the 'most sensible' Euler representation given those constraints. I have a feeling this problem (or something similar) may exist in the IK or rigid body dynamics domains. Solved: I just realised that it might not be clear that I solved this problem by following Ken Shoemake's algorithms from Graphics Gems. I did answer my own question at the time, but it occurs to me it may not be clear that I did so. See the answer, below, for more detail. Just to clarify - I know how to convert from a quaternion to the so-called 'Tait-Bryan' representation - what I was calling the 'NASA' convention. This is a rotation order (assuming the convention that the 'Z' axis is up) of zxy. I need an algorithm for all rotation orders. Possibly the solution, then, is to take the zxy order conversion and derive from it five other conversions for the other rotation orders. I guess I was hoping there was a more 'overarching' solution. In any case, I am surprised that I haven't been able to find existing solutions out there. In addition, and this perhaps should be a separate question altogether, any conversion (assuming a known rotation order, of course) is going to select one Euler representation, but there are in fact many. For example, given a rotation order of yxz, the two representations (0,0,180) and (180,180,0) are equivalent (and would yield the same quaternion). Is there a way to constrain the solution using limits on the degrees of freedom? Like you do in IK and rigid body dynamics? i.e. in the example above if there were only one degree of freedom about the Z axis then the second representation can be disregarded. I have tracked down one paper which could be an algorithm in this pdf but I must confess I find the logic and math a little hard to follow. Surely there are other solutions out there? Is arbitrary rotation order really so rare? Surely every major 3D package that allows skeletal animation together with quaternion interpolation (i.e. Maya, Max, Blender, etc) must have solved exactly this problem?

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• difference equations in MATLAB - why the need to switch signs?

  - by jefflovejapan

  Perhaps this is more of a math question than a MATLAB one, not really sure. I'm using MATLAB to compute an economic model - the New Hybrid ISLM model - and there's a confusing step where the author switches the sign of the solution. First, the author declares symbolic variables and sets up a system of difference equations. Note that the suffixes "a" and "2t" both mean "time t+1", "2a" means "time t+2" and "t" means "time t": %% --------------------------[2] MODEL proc-----------------------------%% % Define endogenous vars ('a' denotes t+1 values) syms y2a pi2a ya pia va y2t pi2t yt pit vt ; % Monetary policy rule ia = q1*ya+q2*pia; % ia = q1*(ya-yt)+q2*pia; %%option speed limit policy % Model equations IS = rho*y2a+(1-rho)yt-sigma(ia-pi2a)-ya; AS = beta*pi2a+(1-beta)*pit+alpha*ya-pia+va; dum1 = ya-y2t; dum2 = pia-pi2t; MPs = phi*vt-va; optcon = [IS ; AS ; dum1 ; dum2; MPs]; He then computes the matrix A: %% ------------------ [3] Linearization proc ------------------------%% % Differentiation xx = [y2a pi2a ya pia va y2t pi2t yt pit vt] ; % define vars jopt = jacobian(optcon,xx); % Define Linear Coefficients coef = eval(jopt); B = [ -coef(:,1:5) ] ; C = [ coef(:,6:10) ] ; % B[c(t+1) l(t+1) k(t+1) z(t+1)] = C[c(t) l(t) k(t) z(t)] A = inv(C)*B ; %(Linearized reduced form ) As far as I understand, this A is the solution to the system. It's the matrix that turns time t+1 and t+2 variables into t and t+1 variables (it's a forward-looking model). My question is essentially why is it necessary to reverse the signs of all the partial derivatives in B in order to get this solution? I'm talking about this step: B = [ -coef(:,1:5) ] ; Reversing the sign here obviously reverses the sign of every component of A, but I don't have a clear understanding of why it's necessary. My apologies if the question is unclear or if this isn't the best place to ask.

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• JavaScript + Maths: Image zoom with CSS3 Transforms, How to set Origin? (with example)

  - by Sunday Ironfoot

  My Math skills really suck! I'm trying to implement an image zoom effect, a bit like how the Zoom works with Google Maps, but with a grid of fix position images. I've uploaded an example of what I have so far here: http://www.dominicpettifer.co.uk/Files/MosaicZoom.html (uses CSS3 transforms so only works with Firefox, Opera, Chrome or Safari) Use your mouse wheel to zoom in/out. The HTML source is basically an outer div with an inner-div, and that inner-div contains 16 images arranged using absolute position. It's going to be a Photo Mosaic basically. I've got the zoom bit working using CSS3 transforms: $(this).find('div').css('-moz-transform', 'scale(' + scale + ')'); ...however, I'm relying on the mouse X/Y position on the outer div to zoom in on where the mouse cursor is, similar to how Google Maps functions. The problem is that if you zoom right in on an image, move the cursor to the bottom/left corner and zoom again, instead of zooming to the bottom/left corner of the image, it zooms to the bottom/left of the entire mosaic. This has the effect of appearing to jump about the mosaic as you zoom in closer while moving the mouse around, even slightly. That's basically the problem, I want the zoom to work exactly like Google Maps where it zooms exactly to where your mouse cursor position is, but I can't get my head around the Maths to calculate the transform-origin: X/Y values correctly. Please help, been stuck on this for 3 days now. Here is the full code listing for the mouse wheel event: var scale = 1; $("#mosaicContainer").mousewheel(function(e, delta) { if (delta > 0) { scale += 1; } else { scale -= 1; } scale = scale < 1 ? 1 : (scale > 40 ? 40 : scale); var x = e.pageX - $(this).offset().left; var y = e.pageY - $(this).offset().top; $(this).find('div').css('-moz-transform', 'scale(' + scale + ')') .css('-moz-transform-origin', x + 'px ' + y + 'px'); return false; });

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• Collision point of 2 curves in a 3d-room

  - by Frank

  Hello, i am programming a small game for quite some time. We started coding a small FPS-Shooter inside of a project at school to get a bit experience using directX. I dont know why, but i couldnt stop the project and started programming at home aswell. At the moment i am trying to create some small AI. Of cause thats definatlly not easy, but thats my personal goal anyways. The topic could prolly fill multiple books hehe. I've got the walking part of my bots done so far. They walk along a scriped path. I am not working on the "aiming" of the bots. While programming that i hit on some math problem i couldnt solve yet. I hope of your input on this to help me get further. Concepts, ideas and everything else are highly appreciated. Problem: Calculate the position (D3DXVECTOR3) where the curve of the projectile (depends on gravity, speed), hit the curved of the enemys walking path (depends on speed). We assume that the enemy walks in a constant line. Known variables: float projectilSpeed = 2000 m/s //speed of the projectile per second float gravitation = 9.81 m/s^2 //of cause the gravity lol D3DXVECTOR3 targetPosition //position of the target stored in a vector (x,y,z) D3DXVECTOR3 projectilePosition //position of the projectile D3DXVECTOR3 targetSpeed //stores the change of the targets position in the last second Variabledefinition ProjectilePosition at time of collision = ProjectilePos_t TargetPosition at time of collision = TargetPos_t ProjectilePosition at time 0, now = ProjectilePos_0 TargetPosition at time 0, now = TargetPos_0 Time to impact = t Aim-angle = theta My try: Found a formular to calculate "drop" (Drop of the projectile based on the gravity) on Wikipedia: float drop = 0.5f * gravity * t * t The speed of the projectile has a horizontal and a vertical part.. Found a formular for that on wikipedia aswell: ProjectilVelocity.x = projectilSpeed * cos(theta) ProjectilVelocity.y = projectilSpeed * sin(theta) So i would assume this is true for the projectile curve: ProjectilePos_t.x = ProjectilePos_0.x + ProjectileSpeed * t ProjectilePos_t.y = ProjectilePos_0.y + ProjectileSpeed * t + 0.5f * gravity * t * t ProjectilePos_t.z = ProjectilePos_0.z + ProjectileSpeed * t The target walk with a constant speed, so we can determine his curve by this: TargetPos_t = TargetPos_0 + TargetSpeed * D3DXVECTOR3(t, t, t) Now i dont know how to continue. I have to solve it somehow to get a hold on the time to impact somehow. As a basic formular i could use: float time = distanz / projectileSpeed But that wouldnt be truly correct as it would assume a linear "Trajectory". We just find this behaivor when using a rocket. I hope i was able to explain the problem as much as possible. If there are questions left, feel free to ask me! Greets from germany, Frank

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• Make the Web Fast: Automagic site optimization with mod_pagespeed 1.0!

  Make the Web Fast: Automagic site optimization with mod_pagespeed 1.0! Ask and vote for questions at: bit.ly mod_pagespeed is an open-source Apache module that automatically optimizes web pages and resources on them: images, CSS, JavaScript, and much more. In this episode, we'll catch up with Joshua Marantz, the tech lead of the project at Google and talk about the history of mod_pagespeed, its fast growing adoption (130K+ sites!), technical architecture and how it works under the hood. Finally, we'll talk about the upcoming 1.0 release milestone for the project. If you're curious about mod_pagespeed, then this is definitely the show you won't want to miss! From: GoogleDevelopers Views: 0 0 ratings Time: 00:00 More in Science & Technology

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• Make the Web Fast: Automagic site optimization with mod_pagespeed 1.0!

  Make the Web Fast: Automagic site optimization with mod_pagespeed 1.0! mod_pagespeed is an open-source Apache module that automatically optimizes web pages and resources on them: images, CSS, JavaScript, and much more. In this episode, we'll catch up with Joshua Marantz, the tech lead of the project at Google and talk about the history of mod_pagespeed, its fast growing adoption (130K+ sites!), technical architecture and how it works under the hood. Finally, we'll talk about the upcoming 1.0 release milestone for the project. If you're curious about mod_pagespeed, then this is definitely the show you won't want to miss! From: GoogleDevelopers Views: 2 0 ratings Time: 01:05:06 More in Science & Technology

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• What factors help in getting a site indexed by Google fast?

  - by ekaj

  What should I do to get a site indexed on Google, fast? Taking example of Super User I just did a quick Google for a question that was 20 minutes old, to look for an answer, and it was already on Google Search - how is this possible? I glanced over this article which seems to suggest that SU has added RSS feeds (which SU has, but when I opened the feed the article says last posted 6 minutes ago, but when Googled it is 11 hours old) - which leads me to think (Based on that article, I don't know much about search indexing but I am reading at the moment) that most of this indexing is done thanks to the sitemap. is there anything else I am unaware of that helps SU questions get on Google so fast?

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• Checking for Repeated Strings in 2d list

  - by Zach Santiago

  i have a program where i have a list of names and classes. i have the list in alphabetical order. now im trying to check if names repeat, add the classes to one single name. im trying to write some code like go through names if name is already in list, add the class to the one name. so an example would be, instead of having 'Anita ','phys 1443', and 'Anita','IE 3312' i would just have 'Anita','PHYS 1443','IE 3312'. How would i go about doing this in a logival way, WITHOUT using any sort of built in functions? i tried comparing indexe's like if list[i][0] == list[i+1][0], append list[i+1][1] to an emptylist. while that almost worked, it would screw up at some points along the way. here is my attempt size = len(c) i = 0 c = [['Anita', 'PHYS 1443'], ['Anita', 'IE 3312'], ['Beihuang', 'PHYS 1443'], ['Chiao-Lin', 'MATH 1426'], ['Chiao-Lin', 'IE 3312'], ['Christopher', 'CSE 1310'], ['Dylan', 'CSE 1320'], ['Edmund', 'PHYS 1443'], ['Ian', 'IE 3301'], ['Ian', 'CSE 1320'], ['Ian', 'PHYS 1443'], ['Isis', 'PHYS 1443'], ['Jonathan', 'MATH 2325'], ['Krishna', 'MATH 2325'], ['Michael', 'IE 3301'], ['Nang', 'MATH 2325'], ['Ram', 'CSE 1320'], ['Taesu', 'CSE 1320'], ["Tre'Shaun", 'IE 3312'], ["Tre'Shaun", 'MATH 2325'], ["Tre'Shaun", 'CSE 1310']] ## Check if any names repeat d.append(c[0][0]) while i < size - 1 : if c[i][0] == c[i+1][0] : d.append(c[i][1]) d.append(c[i+1][1]) else : d.append(c[i+1][0]) d.append(c[i+1][1]) i = i + 1 print d output was. ['Anita', 'PHYS 1443', 'IE 3312', 'Beihuang', 'PHYS 1443', 'Chiao-Lin', 'MATH 1426', 'MATH 1426', 'IE 3312', 'Christopher', 'CSE 1310', 'Dylan', 'CSE 1320', 'Edmund', 'PHYS 1443', 'Ian', 'IE 3301', 'IE 3301', 'CSE 1320', 'CSE 1320', 'PHYS 1443', 'Isis', 'PHYS 1443', 'Jonathan', 'MATH 2325', 'Krishna', 'MATH 2325', 'Michael', 'IE 3301', 'Nang', 'MATH 2325', 'Ram', 'CSE 1320', 'Taesu', 'CSE 1320', "Tre'Shaun", 'IE 3312', 'IE 3312', 'MATH 2325', 'MATH 2325', 'CSE 1310']

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• approximating log10[x^k0 + k1]

  - by Yale Zhang

  Greetings. I'm trying to approximate the function Log10[x^k0 + k1], where .21 < k0 < 21, 0 < k1 < ~2000, and x is integer < 2^14. k0 & k1 are constant. For practical purposes, you can assume k0 = 2.12, k1 = 2660. The desired accuracy is 5*10^-4 relative error. This function is virtually identical to Log[x], except near 0, where it differs a lot. I already have came up with a SIMD implementation that is ~1.15x faster than a simple lookup table, but would like to improve it if possible, which I think is very hard due to lack of efficient instructions. My SIMD implementation uses 16bit fixed point arithmetic to evaluate a 3rd degree polynomial (I use least squares fit). The polynomial uses different coefficients for different input ranges. There are 8 ranges, and range i spans (64)2^i to (64)2^(i + 1). The rational behind this is the derivatives of Log[x] drop rapidly with x, meaning a polynomial will fit it more accurately since polynomials are an exact fit for functions that have a derivative of 0 beyond a certain order. SIMD table lookups are done very efficiently with a single _mm_shuffle_epi8(). I use SSE's float to int conversion to get the exponent and significand used for the fixed point approximation. I also software pipelined the loop to get ~1.25x speedup, so further code optimizations are probably unlikely. What I'm asking is if there's a more efficient approximation at a higher level? For example: Can this function be decomposed into functions with a limited domain like log2((2^x) * significand) = x + log2(significand) hence eliminating the need to deal with different ranges (table lookups). The main problem I think is adding the k1 term kills all those nice log properties that we know and love, making it not possible. Or is it? Iterative method? don't think so because the Newton method for log[x] is already a complicated expression Exploiting locality of neighboring pixels? - if the range of the 8 inputs fall in the same approximation range, then I can look up a single coefficient, instead of looking up separate coefficients for each element. Thus, I can use this as a fast common case, and use a slower, general code path when it isn't. But for my data, the range needs to be ~2000 before this property hold 70% of the time, which doesn't seem to make this method competitive. Please, give me some opinion, especially if you're an applied mathematician, even if you say it can't be done. Thanks.

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• Counting point size based on chart area during zooming/unzoomin

  - by Gacek

  Hi folks. I heave a quite simple task. I know (I suppose) it should be easy, but from the reasons I cannot understand, I try to solve it since 2 days and I don't know where I'm making the mistake. So, the problem is as follows: - we have a chart with some points - The chart starts with some known area and points have known size - we would like to "emulate" the zooming effect. So when we zoom to some part of the chart, the size of points is getting proportionally bigger. In other words, the smaller part of the chart we select, the bigger the point should get. So, we have something like that. We know this two parameters: initialArea; // Initial area - area of the whole chart, counted as width*height initialSize; // initial size of the points Now lets assume we are handling some kind of OnZoom event. We selected some part of the chart and would like to count the current size of the points float CountSizeOnZoom() { float currentArea = CountArea(...); // the area is counted for us. float currentSize = initialSize * initialArea / currentArea; return currentSize; } And it works. But the rate of change is too fast. In other words, the points are getting really big too soon. So I would like the currentSize to be invertly proportional to currentArea, but with some scaling coefficient. So I created the second function: float CountSizeOnZoom() { float currentArea = CountArea(...); % the area is counted for us. // Lets assume we want the size of points to change ten times slower, than area of the chart changed. float currentSize = initialSize + 0.1f* initialSize * ((initialArea / currentArea) -1); return currentSize; } Lets do some calculations in mind. if currentArea is smaller than initialArea, initialArea/currentArea > 1 and then we add "something" small and postive to initialSize. Checked, it works. Lets check what happens if we would un-zoom. currentArea will be equal to initialArea, so we would have 0 at the right side (1-1), so new size should be equal to initialSize. Right? Yeah. So lets check it... and it doesn't work. My question is: where is the mistake? Or maybe you have any ideas how to count this scaled size depending on current area in some other way?

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• mapping rect in small image to larger image (in order to do a copyPixels operation)

  - by skinnyTOD

  Hi all - this is (I think) a relatively simple math question but I've spent a day banging my head against it and have only the dents and no solution... I'm coding in actionscript 3 - the functionality is: large image loaded at runtime. The bitmapData is stored and a smaller version is created to display on the available screen area (I may end up just scaling the large image since it is in memory anyway). The user can create a rectangle hotspot on the smaller image (the functionality will be more complex: multiple rects with transparency: example a donut shape with hole, etc) 3 When the user clicks on the hotspot, the rect of the hotspot is mapped to the larger image and a new bitmap "callout" is created, using the larger bitmap data. The reason for this is so the "callout" will be better quality than just scaling up the area of the hotspot. The image below shows where I am at so far- the blue rect is the clicked hotspot. In the upper left is the "callout" - copied from the larger image. I have the aspect ratio right but I am not mapping to the larger image correctly. Ugly code below... Sorry this post is so long - I just figured I ought to provide as much info as possible. Thanks for any tips! --trace of my data values *source BitmapDada 1152 864 scaled to rect 800 600 scaled BitmapData 800 600 selection BitmapData 58 56 scaled selection 83 80 ratio 1.44 before (x=544, y=237, w=58, h=56) (x=544, y=237, w=225.04, h=217.28) * Image here: http://i795.photobucket.com/albums/yy237/skinnyTOD/exampleST.jpg public function onExpandCallout(event:MouseEvent):void{ if (maskBitmapData.getPixel32(event.localX, event.localY) != 0){ var maskClone:BitmapData = maskBitmapData.clone(); //amount to scale callout - this will vary/can be changed by user var scale:Number =150 //scale percentage var normalizedScale :Number = scale/=100; var w:Number = maskBitmapData.width*normalizedScale; var h:Number = maskBitmapData.height*normalizedScale; var ratio:Number = (sourceBD.width /targetRect.width); //creat bmpd of the scaled size to copy source into var scaledBitmapData:BitmapData = new BitmapData(maskBitmapData.width * ratio, maskBitmapData.height * ratio, true, 0xFFFFFFFF); trace("source BitmapDada " + sourceBD.width, sourceBD.height); trace("scaled to rect " + targetRect.width, targetRect.height); trace("scaled BitmapData", bkgnImageSprite.width, bkgnImageSprite.height); trace("selection BitmapData", maskBitmapData.width, maskBitmapData.height); trace("scaled selection", scaledBitmapData.width, scaledBitmapData.height); trace("ratio", ratio); var scaledBitmap:Bitmap = new Bitmap(scaledBitmapData); var scaleW:Number = sourceBD.width / scaledBitmapData.width; var scaleH:Number = sourceBD.height / scaledBitmapData.height; var scaleMatrix:Matrix = new Matrix(); scaleMatrix.scale(ratio,ratio); var sRect:Rectangle = maskSprite.getBounds(bkgnImageSprite); var sR:Rectangle = sRect.clone(); var ss:Sprite = new Sprite(); ss.graphics.lineStyle(8, 0x0000FF); //ss.graphics.beginFill(0x000000, 1); ss.graphics.drawRect(sRect.x, sRect.y, sRect.width, sRect.height); //ss.graphics.endFill(); this.addChild(ss); trace("before " + sRect); w = uint(sRect.width * scaleW); h = uint(sRect.height * scaleH); sRect.inflate(maskBitmapData.width * ratio, maskBitmapData.height * ratio); sRect.offset(maskBitmapData.width * ratio, maskBitmapData.height * ratio); trace(sRect); scaledBitmapData.copyPixels(sourceBD, sRect, new Point()); addChild(scaledBitmap); scaledBitmap.x = offsetPt.x; scaledBitmap.y = offsetPt.y; } }

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• Have you been stuck with the math in a Flash project?

  - by VideoDnd

  Have you been stuck with the math in a Flash project? It's a loose design pattern my director formulated. My goal is to keep the project object oriented, and get 'non Flash obstacles' off my plate. XML values going to AS3, updating a changing acceleration formula. I don't hate math, but it just doesn't seem OOP or good project planning to have the math stuck in Flash. Your comments are welcome.

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