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• Continuous vs Discrete artificial neural networks

  - by gmatt

  I realize that this is probably a very niche question, but has anyone had experience with working with continuous neural networks? I'm specifically interested in what a continuous neural network may be useful for vs what you normally use discrete neural networks for.

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• Is OOP based on any branch of mathematics?

  - by ektrules

  I know relational databases are based on set-theory, functional programming is based on lambda calculus, logic programming is based on logic (of course :)), and now that I think of it; I'm not sure if imperative and generic programming is based on any particular branch of mathematics either.

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• help with matlab and Discrete Fourier transform

  - by user504363

  Hi all I have previous experience with Matlab, but the problem that I face some problems in apply a problem in (DSP : Digital signal processing) which is not my study field, but I must finish that problems in days to complete my project. all i want is help me with method and steps of solving this problem in matlab and then I can write the code with myself. the problem is about the signal x(t) = exp(-a*t); 1) what's the Discrete Fourier transform of the sampled signal with sample rate fs 2) if a=1 and fs =1 , plot the amplitude spectrum of sampled signal 3) fix the sampling frequency at fs = 1(hz) [what's it mean ?] and plot the magnitude of the Fourier Transform of the sampled signal at various values of a thanks

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• Mathematics for AI/Machine learning ?

  - by Ankur Gupta

  I intend to build a simple recommendation systems for fun. I read a little on the net and figured being good at math would enable on to build a good recommendation system. My math skills are not good. I am willing to put considerable efforts and time in learning maths. Can you please tell me what mathematics topics should I cover? Also if any of you folks can point me to some online material to learn from it would be great. I am aware of MIT OCW, book like collective intelligence. Math Topics to cover and from where to read would really help.

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• Discrete event simulation framework for .NET

  - by Kuba

  Does anyone have an experience with some discrete event simulation library that could be used in .NET (C#)? Despite the basic functionality for queing events and dispatching them, it would be fine to have some non-deterministic behavior (e.g. failures simulation). I have some tips and I am even considering to write my own, but first, I would like to collect some recomendations. Thanks. Additional info: i'm not looking explicitly for free product, however, the prize matters :) Just to precise the field i need to map, here is the example of a product: http://www.holushko.com/index.html

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• How much does game development mathematics change over time?

  - by FlightOfGrey

  This question is mainly aimed at this book, Essential Mathematics for Games and Interactive Applications, Second Edition which I have seen highly recommended all around the internet, so I'm sure there are people on here who own a copy. What I want to know specifically is if any of the information would be out dated since the book was released on June 2, 2008? Also interested to see how the mathematics behind game development has changed over time.

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• Simple in-place discrete fourier transform ( DFT )

  - by Adam

  I'm writing a very simple in-place DFT. I am using the formula shown here: http://en.wikipedia.org/wiki/Discrete_Fourier_transform#Definition along with Euler's formula to avoid having to use a complex number class just for this. So far I have this: private void fft(double[] data) { double[] real = new double[256]; double[] imag = new double[256]; double pi_div_128 = -1 * Math.PI / 128; for (int k = 0; k < 256; k++) { for (int n = 0; n < 256; n++) { real[k] += data[k] * Math.Cos(pi_div_128 * k * n); imag[k] += data[k] * Math.Sin(pi_div_128 * k * n); } data[k] = Math.Sqrt(real[k] * real[k] + imag[k] * imag[k]); } } But the Math.Cos and Math.Sin terms eventually go both positive and negative, so as I'm adding those terms multiplied with data[k], they cancel out and I just get some obscenely small value. I see how it is happening, but I can't make sense of how my code is perhaps mis-representing the mathematics. Any help is appreciated. FYI, I do have to write my own, I realize I can get off-the shelf FFT's.

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• Generic applet style system for publishing mathematics demonstrations?

  - by Alex

  Anyone who's tried to study mathematics using online resources will have come across these Java applets that demonstrate a particular mathematical idea. Examples: http://www.math.ucla.edu/~tao/java/Mobius.html http://www.mathcs.org/java/programs/FFT/index.html I love the idea of this interactive approach because I believe it is very helpful in conveying mathematical principles. I'd like to create a system for visually designing and publishing these 'mathlets' such that they can be created by teachers with little programming experience. So in order to create this app, i'll need a GUI and a 'math engine'. I'll probably be working with .NET because thats what I know best and i'd like to start experimenting with F#. Silverlight appeals to me as a presentation framework for this project (im not worried about interoperability right now). So my questions are: does anything like this exist already in full form? are there any GUI frameworks for displaying mathematical objects such as graphs & equations? are there decent open source libraries that exposes a mathematical framework (Math.NET looks good, just wondering if there is anything else out there) is there any existing work on taking mathematical models/demos built with maple/matlab/octave/mathematica etc and publishing them to the web?

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• The Numerical ‘Magic’ of Cyclic Numbers

  - by Akemi Iwaya

  If you love crunching numbers or are just a fan of awesome number ‘tricks’ to impress your friends with, then you will definitely want to have a look at cyclic numbers. Dr Tony Padilla from the University of Nottingham shows how these awesome numbers work in Numberphile’s latest video. Cyclic Numbers – Numberphile [YouTube] Want to learn more about cyclic numbers? Then make sure to visit the Wikipedia page linked below! Cyclic number [Wikipedia]     

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• How Big Is a Billion? [Video]

  - by Jason Fitzpatrick

  A billion is a billion except, when it isn’t. Depending on where and when you were raised and educated, the world “billion” is some magnitudes different–read on to see the difference between a billion in long and short number systems. [via Geeks Are Sexy] Here’s How to Download Windows 8 Release Preview Right Now HTG Explains: Why Linux Doesn’t Need Defragmenting How to Convert News Feeds to Ebooks with Calibre

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• Rapid Planning: Next Generation MRP

  - by john.bermudez

  MRP has been a mainstay of manufacturing systems for 40 years. MRP evolved from simple inventory planning systems to become the heart of the MRPII systems which eventually became ERP. While the applications surrounding it have become broader, more sophisticated and web-based, MRP continues to operate in the loneliness of the Saturday night batch window quietly exploding bills of materials and logging exceptions for hours. During this same 40 years, manufacturing business processes have seen countless changes and improvements including JIT, TQM, Six Sigma, Flow Manufacturing, Lean Manufacturing and Supply Chain Management. Although much logic has been added to MRP to deal with new manufacturing processes, it has not been able to keep up with the real-time pace of today's supply chain. As a result, planners have devised ingenious ways to trick MRP to handle new processes but often need to dump the output into spreadsheets of their own design in the hope of wrestling thousands of exceptions to ground. Oracle's new Rapid Planning application is just what companies still running MRP have been waiting for! The newest member of the Value Chain Planning product line, Rapid Planning is designed to empower planners with comprehensive supply planning that runs online in minutes, not hours. It enables a planner simulate the incremental impact of a new order or re-run an entire plan in a separate sandbox. Rapid Planning does a complete multi-level bill of material explosion like MRP but plans orders considering material and capacity constraints. Considering material and capacity constraints in planning can help you quickly reduce inventory and improve on-time shipments. Rapid Planning is an APS application that leverages years of Oracle development experience and customer feedback. Rather than rely exclusively on black-box heuristics, Rapid Planning is designed to give planners the computing power to use their industry experience and business knowledge to improve MRP. For example, Rapid Planning has a powerful worksheet user interface with built-in query capability that allows the planner to locate the orders she is interested in and use a mass update function to make quick work of large changes. The planner can save these queries and unique user interface to personalize their planning environment. Most importantly, Rapid Planning is designed to do supply planning in today's dynamic supply chain environment. It can be used to supplement MRP or replace MRP entirely. It generates plans that provide order-by-order details with aggregate key performance indicators that enable planners to quickly assess the overall business impact of a plan. To find out more about how Rapid Planning can help improve your MRP, please contact me at [email protected] or your Oracle Account Manager.

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• Parabolic throw with set Height and range (libgdx)

  - by Tauboga

  Currently i'm working on a minigame for android where you have a rotating ball in the center of the display which jumps when touched in the direction of his current angle. I'm simply using a gravity vector and a velocity vector in this way: positionBall = positionBall.add(velocity); velocity = velocity.add(gravity); and velocity.x = (float) Math.cos(angle) * 12; /* 12 to amplify the velocity */ velocity.y = (float) Math.sin(angle) * 15; /* 15 to amplify the velocity */ That works fine. Here comes the problem: I want to make the jump look the same on all possible resolutions. The velocity needs to be scaled in a way that when the ball is thrown straight upwards it will touch the upper display border. When thrown directly left or right the range shall be exactly long enough to touch the left/right display border. Which formula(s) do I need to use and how to implement them correctly? Thanks in advance!

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• Convert vector interpolation to quaternion interpolation? (Catmull-Rom)

  - by edA-qa mort-ora-y

  I have some existing code which does catmull-rom interpolation on two vectors (facing and up). I'm converting this to use quaternions instead (to replace the two vectors). Is there a general way to convert the vector based interpolation to a quaternion one? The approach I'm using now is to exact the axis and angle from the quanternion. I then interpolate each of those independently and convert back to a quaternion. Is there a more direct method?

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• How can I test if an oriented rectangle contains another oriented rectangle?

  - by gronzzz

  I have the following situation: To detect whether is the red rectangle is inside orange area I use this function: - (BOOL)isTile:(CGPoint)tile insideCustomAreaMin:(CGPoint)min max:(CGPoint)max { if ((tile.x < min.x) || (tile.x > max.x) || (tile.y < min.y) || (tile.y > max.y)) { NSLog(@" Object is out of custom area! "); return NO; } return YES; } But what if I need to detect whether the red tile is inside of the blue rectangle? I wrote this function which uses the world position: - (BOOL)isTileInsidePlayableArea:(CGPoint)tile { // get world positions from tiles CGPoint rt = [[CoordinateFunctions shared] worldFromTile:ccp(24, 0)]; CGPoint lb = [[CoordinateFunctions shared] worldFromTile:ccp(24, 48)]; CGPoint worldTile = [[CoordinateFunctions shared] worldFromTile:tile]; return [self isTile:worldTile insideCustomAreaMin:ccp(lb.x, lb.y) max:ccp(rt.x, rt.y)]; } How could I do this without converting to the global position of the tiles?

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• Kepler orbit : get position on the orbit over time

  - by Artefact2

  I'm developing a space-simulation related game, and I am having some trouble implementing the movement of binary stars, like this: The two stars orbit their centroid, and their trajectories are ellipses. I basically know how to determine the angular velocity at any position, but not the angular velocity over time. So, for a given angle, I can very easily compute the stars position (cf. http://en.wikipedia.org/wiki/Orbit_equation). I'd want to get the stars position over time. The parametric equations of the ellipse works but doesn't give the correct speed : { X(t) = a×cos(t) ; Y(t) = b×sin(t) }. Is it possible, and how can it be done?

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• Isometric Movement in Javascript In the DOM

  - by deep

  I am creating a game using Javascript. I am not using the HTML5 Canvas Element. The game requires both side view controlles, and Isometric controls, hence the movementMode variable. I have got the specific angles, but I am stuck on an aspect of this. https://chillibyte.makes.org/thimble/movement function draw() { if (keyPressed) { if (whichKey == keys.left) { move(-1,0) } if (whichKey == keys.right) { move(1,0) } if (whichKey == keys.up) { move(0,-1) } if (whichKey == keys.down) { move(0,1) } } } This gives normal up, down , left, and right. i want to refactor this so that i can plugin two variables into the move() function, which will give the movement wanted. Now for the trig. /| / | / | y / | /a___| x Take This Right angled Triangle. given that x is 1, y must be equal to tan(a) That Seems right. However, when I do Math.tan(45), i get a number similar to 1.601. Why? To Sum up this question. I have a function, and i need a function which will converts an angle to a value, which will tell me the number of pixels that i need to go up by, if i only go across 1. Is it Math.tan that i want? or is it something else?

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• Twitter Storm VS. Google's MapReduce

  - by Edward J. Yoon

  IMO, the era of Information Retrieval is dead with the advent of SNS. And the question type is changed from "How many backlinks your site has?" to "How many people have clicked URL you've shared on SNS?". So many people who newbie in Big Data Analytics often asks me "How can I analyze stream data time-series pattern mining methods using Map/Reduce?", "How can I mining the valuable insights using Map/Reduce?", "blah~ blah~ using Map/Reduce?". The answer is No Map/Reduce.

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• Integration error in high velocity

  - by Elektito

  I've implemented a simple simulation of two planets (simple 2D disks really) in which the only force is gravity and there is also collision detection/response (collisions are completely elastic). I can launch one planet into orbit of the other just fine. The collision detection code though does not work so well. I noticed that when one planet hits the other in a free fall it speeds backward and goes much higher than its original position. Some poking around convinced me that the simplistic Euler integration is causing the error. Consider this case. One object has a mass of 1kg and the other has a mass equal to earth. Say the object is 10 meters above ground. Assume that our dt (delta t) is 1 second. The object goes to the height of 9 meters at the end of the first iteration, 7 at the end of the second, 4 at the end of the third and 0 at the end of the fourth iteration. At this points it hits the ground and bounces back with the speed of 10 meters per second. The problem is with dt=1, on the first iteration it bounces back to a height of 10. It takes several more steps to make the object change its course. So my question is, what integration method can I use which fixes this problem. Should I split dt to smaller pieces when velocity is high? Or should I use another method altogether? What method do you suggest? EDIT: You can see the source code here at github:https://github.com/elektito/diskworld/

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• Most efficient way to implement delta time

  - by Starkers

  Here's one way to implement delta time: /// init /// var duration = 5000, currentTime = Date.now(); // and create cube, scene, camera ect ////// function animate() { /// determine delta /// var now = Date.now(), deltat = now - currentTime, currentTime = now, scalar = deltat / duration, angle = (Math.PI * 2) * scalar; ////// /// animate /// cube.rotation.y += angle; ////// /// update /// requestAnimationFrame(render); ////// } Could someone confirm I know how it works? Here what I think is going on: Firstly, we set duration at 5000, which how long the loop will take to complete in an ideal world. With a computer that is slow/busy, let's say the animation loop takes twice as long as it should, so 10000: When this happens, the scalar is set to 2.0: scalar = deltat / duration scalar = 10000 / 5000 scalar = 2.0 We now times all animation by twice as much: angle = (Math.PI * 2) * scalar; angle = (Math.PI * 2) * 2.0; angle = (Math.PI * 4) // which is 2 rotations When we do this, the cube rotation will appear to 'jump', but this is good because the animation remains real-time. With a computer that is going too quickly, let's say the animation loop takes half as long as it should, so 2500: When this happens, the scalar is set to 0.5: scalar = deltat / duration scalar = 2500 / 5000 scalar = 0.5 We now times all animation by a half: angle = (Math.PI * 2) * scalar; angle = (Math.PI * 2) * 0.5; angle = (Math.PI * 1) // which is half a rotation When we do this, the cube won't jump at all, and the animation remains real time, and doesn't speed up. However, would I be right in thinking this doesn't alter how hard the computer is working? I mean it still goes through the loop as fast as it can, and it still has render the whole scene, just with different smaller angles! So this a bad way to implement delta time, right? Now let's pretend the computer is taking exactly as long as it should, so 5000: When this happens, the scalar is set to 1.0: angle = (Math.PI * 2) * scalar; angle = (Math.PI * 2) * 1; angle = (Math.PI * 2) // which is 1 rotation When we do this, everything is timsed by 1, so nothing is changed. We'd get the same result if we weren't using delta time at all! My questions are as follows Mostly importantly, have I got the right end of the stick here? How do we know to set the duration to 5000 ? Or can it be any number? I'm a bit vague about the "computer going too quickly". Is there a way loop less often rather than reduce the animation steps? Seems like a better idea. Using this method, do all of our animations need to be timesed by the scalar? Do we have to hunt down every last one and times it? Is this the best way to implement delta time? I think not, due to the fact the computer can go nuts and all we do is divide each animation step and because we need to hunt down every step and times it by the scalar. Not a very nice DSL, as it were. So what is the best way to implement delta time? Below is one way that I do not really get but may be a better way to implement delta time. Could someone explain please? // Globals INV_MAX_FPS = 1 / 60; frameDelta = 0; clock = new THREE.Clock(); // In the animation loop (the requestAnimationFrame callback)… frameDelta += clock.getDelta(); // API: "Get the seconds passed since the last call to this method." while (frameDelta >= INV_MAX_FPS) { update(INV_MAX_FPS); // calculate physics frameDelta -= INV_MAX_FPS; } How I think this works: Firstly we set INV_MAX_FPS to 0.01666666666 How we will use this number number does not jump out at me. We then intialize a frameDelta which stores how long the last loop took to run. Come the first loop frameDelta is not greater than INV_MAX_FPS so the loop is not run (0 = 0.01666666666). So nothing happens. Now I really don't know what would cause this to happen, but let's pretend that the loop we just went through took 2 seconds to complete: We set frameDelta to 2: frameDelta += clock.getDelta(); frameDelta += 2.00 Now we run an animation thanks to update(0.01666666666). Again what is relevance of 0.01666666666?? And then we take away 0.01666666666 from the frameDelta: frameDelta -= INV_MAX_FPS; frameDelta = frameDelta - INV_MAX_FPS; frameDelta = 2 - 0.01666666666 frameDelta = 1.98333333334 So let's go into the second loop. Let's say it took 2(? Why not 2? Or 12? I am a bit confused): frameDelta += clock.getDelta(); frameDelta = frameDelta + clock.getDelta(); frameDelta = 1.98333333334 + 2 frameDelta = 3.98333333334 This time we enter the while loop because 3.98333333334 = 0.01666666666 We run update We take away 0.01666666666 from frameDelta again: frameDelta -= INV_MAX_FPS; frameDelta = frameDelta - INV_MAX_FPS; frameDelta = 3.98333333334 - 0.01666666666 frameDelta = 3.96666666668 Now let's pretend the loop is super quick and runs in just 0.1 seconds and continues to do this. (Because the computer isn't busy any more). Basically, the update function will be run, and every loop we take away 0.01666666666 from the frameDelta untill the frameDelta is less than 0.01666666666. And then nothing happens until the computer runs slowly again? Could someone shed some light please? Does the update() update the scalar or something like that and we still have to times everything by the scalar like in the first example?

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• Why do we use Pythagoras in game physics?

  - by Starkers

  I've recently learned that we use Pythagoras a lot in our physics calculations and I'm afraid I don't really get the point. Here's an example from a book to make sure an object doesn't travel faster than a MAXIMUM_VELOCITY constant in the horizontal plane: MAXIMUM_VELOCITY = <any number>; SQUARED_MAXIMUM_VELOCITY = MAXIMUM_VELOCITY * MAXIMUM_VELOCITY; function animate(){ var squared_horizontal_velocity = (x_velocity * x_velocity) + (z_velocity * z_velocity); if( squared_horizontal_velocity <= SQUARED_MAXIMUM_VELOCITY ){ scalar = squared_horizontal_velocity / SQUARED_MAXIMUM_VELOCITY; x_velocity = x_velocity / scalar; z_velocity = x_velocity / scalar; } } Let's try this with some numbers: An object is attempting to move 5 units in x and 5 units in z. It should only be able to move 5 units horizontally in total! MAXIMUM_VELOCITY = 5; SQUARED_MAXIMUM_VELOCITY = 5 * 5; SQUARED_MAXIMUM_VELOCITY = 25; function animate(){ var x_velocity = 5; var z_velocity = 5; var squared_horizontal_velocity = (x_velocity * x_velocity) + (z_velocity * z_velocity); var squared_horizontal_velocity = 5 * 5 + 5 * 5; var squared_horizontal_velocity = 25 + 25; var squared_horizontal_velocity = 50; // if( squared_horizontal_velocity <= SQUARED_MAXIMUM_VELOCITY ){ if( 50 <= 25 ){ scalar = squared_horizontal_velocity / SQUARED_MAXIMUM_VELOCITY; scalar = 50 / 25; scalar = 2.0; x_velocity = x_velocity / scalar; x_velocity = 5 / 2.0; x_velocity = 2.5; z_velocity = z_velocity / scalar; z_velocity = 5 / 2.0; z_velocity = 2.5; // new_horizontal_velocity = x_velocity + z_velocity // new_horizontal_velocity = 2.5 + 2.5 // new_horizontal_velocity = 5 } } Now this works well, but we can do the same thing without Pythagoras: MAXIMUM_VELOCITY = 5; function animate(){ var x_velocity = 5; var z_velocity = 5; var horizontal_velocity = x_velocity + z_velocity; var horizontal_velocity = 5 + 5; var horizontal_velocity = 10; // if( horizontal_velocity >= MAXIMUM_VELOCITY ){ if( 10 >= 5 ){ scalar = horizontal_velocity / MAXIMUM_VELOCITY; scalar = 10 / 5; scalar = 2.0; x_velocity = x_velocity / scalar; x_velocity = 5 / 2.0; x_velocity = 2.5; z_velocity = z_velocity / scalar; z_velocity = 5 / 2.0; z_velocity = 2.5; // new_horizontal_velocity = x_velocity + z_velocity // new_horizontal_velocity = 2.5 + 2.5 // new_horizontal_velocity = 5 } } Benefits of doing it without Pythagoras: Less lines Within those lines, it's easier to read what's going on ...and it takes less time to compute, as there are less multiplications Seems to me like computers and humans get a better deal without Pythagoras! However, I'm sure I'm wrong as I've seen Pythagoras' theorem in a number of reputable places, so I'd like someone to explain me the benefit of using Pythagoras to a maths newbie. Does this have anything to do with unit vectors? To me a unit vector is when we normalize a vector and turn it into a fraction. We do this by dividing the vector by a larger constant. I'm not sure what constant it is. The total size of the graph? Anyway, because it's a fraction, I take it, a unit vector is basically a graph that can fit inside a 3D grid with the x-axis running from -1 to 1, z-axis running from -1 to 1, and the y-axis running from -1 to 1. That's literally everything I know about unit vectors... not much :P And I fail to see their usefulness. Also, we're not really creating a unit vector in the above examples. Should I be determining the scalar like this: // a mathematical work-around of my own invention. There may be a cleverer way to do this! I've also made up my own terms such as 'divisive_scalar' so don't bother googling var divisive_scalar = (squared_horizontal_velocity / SQUARED_MAXIMUM_VELOCITY); var divisive_scalar = ( 50 / 25 ); var divisive_scalar = 2; var multiplicative_scalar = (divisive_scalar / (2*divisive_scalar)); var multiplicative_scalar = (2 / (2*2)); var multiplicative_scalar = (2 / 4); var multiplicative_scalar = 0.5; x_velocity = x_velocity * multiplicative_scalar x_velocity = 5 * 0.5 x_velocity = 2.5 Again, I can't see why this is better, but it's more "unit-vector-y" because the multiplicative_scalar is a unit_vector? As you can see, I use words such as "unit-vector-y" so I'm really not a maths whiz! Also aware that unit vectors might have nothing to do with Pythagoras so ignore all of this if I'm barking up the wrong tree. I'm a very visual person (3D modeller and concept artist by trade!) and I find diagrams and graphs really, really helpful so as many as humanely possible please!

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• Isometric layer moving inside map

  - by gronzzz

  i'm created isometric map and now trying to limit layer moving. Main idea, that i have left bottom, right bottom, left top, right top points, that camera can not move outside, so player will not see map out of bounds. But i can not understand algorithm of how to do that. It's my layer scale/moving code. - (void)touchBegan:(UITouch *)touch withEvent:(UIEvent *)event { _isTouchBegin = YES; } - (void)touchMoved:(UITouch *)touch withEvent:(UIEvent *)event { NSArray *allTouches = [[event allTouches] allObjects]; UITouch *touchOne = [allTouches objectAtIndex:0]; CGPoint touchLocationOne = [touchOne locationInView: [touchOne view]]; CGPoint previousLocationOne = [touchOne previousLocationInView: [touchOne view]]; // Scaling if ([allTouches count] == 2) { _isDragging = NO; UITouch *touchTwo = [allTouches objectAtIndex:1]; CGPoint touchLocationTwo = [touchTwo locationInView: [touchTwo view]]; CGPoint previousLocationTwo = [touchTwo previousLocationInView: [touchTwo view]]; CGFloat currentDistance = sqrt( pow(touchLocationOne.x - touchLocationTwo.x, 2.0f) + pow(touchLocationOne.y - touchLocationTwo.y, 2.0f)); CGFloat previousDistance = sqrt( pow(previousLocationOne.x - previousLocationTwo.x, 2.0f) + pow(previousLocationOne.y - previousLocationTwo.y, 2.0f)); CGFloat distanceDelta = currentDistance - previousDistance; CGPoint pinchCenter = ccpMidpoint(touchLocationOne, touchLocationTwo); pinchCenter = [self convertToNodeSpace:pinchCenter]; CGFloat predictionScale = self.scale + (distanceDelta * PINCH_ZOOM_MULTIPLIER); if([self predictionScaleInBounds:predictionScale]) { [self scale:predictionScale scaleCenter:pinchCenter]; } } else { // Dragging _isDragging = YES; CGPoint previous = [[CCDirector sharedDirector] convertToGL:previousLocationOne]; CGPoint current = [[CCDirector sharedDirector] convertToGL:touchLocationOne]; CGPoint delta = ccpSub(current, previous); self.position = ccpAdd(self.position, delta); } } - (void)touchEnded:(UITouch *)touch withEvent:(UIEvent *)event { _isDragging = NO; _isTouchBegin = NO; // Check if i need to bounce _touchLoc = [touch locationInNode:self]; } #pragma mark - Update - (void)update:(CCTime)delta { CGPoint position = self.position; float scale = self.scale; static float friction = 0.92f; //0.96f; if(_isDragging && !_isScaleBounce) { _velocity = ccp((position.x - _lastPos.x)/2, (position.y - _lastPos.y)/2); _lastPos = position; } else { _velocity = ccp(_velocity.x * friction, _velocity.y *friction); position = ccpAdd(position, _velocity); self.position = position; } if (_isScaleBounce && !_isTouchBegin) { float min = fabsf(self.scale - MIN_SCALE); float max = fabsf(self.scale - MAX_SCALE); int dif = max > min ? 1 : -1; if ((scale > MAX_SCALE - SCALE_BOUNCE_AREA) || (scale < MIN_SCALE + SCALE_BOUNCE_AREA)) { CGFloat newSscale = scale + dif * (delta * friction); [self scale:newSscale scaleCenter:_touchLoc]; } else { _isScaleBounce = NO; } } }

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• Sun & Moon Movement

  - by Thomas Mosey

  I'm creating a 2D HTML5 Canvas Game and am stuck on how to go about animating my Sun & Moon. The current setup is basically setting the moon at -1024 on the X-axis and the sun at 0 and animating them at 1 pixel a second. My canvas width is 1024 pixels and whenever the sun/moons X position crosses over the width of the canvas, it's X position is then set to -1024 to repeat the animation. What I am trying to do is get it to sync up with my day/night cycles. Each day is 10000 ticks long (A tick being added every frame) with Day/Night being 50% each (5000 ticks each). What I am trying to calculate is what I'll need to add to the X position of each per frame to get the sun from an X of 0 to 1024 after 5000 ticks/frames. Any help is appreciated.

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• Bridge made out of blocks at an angle

  - by Pozzuh

  I'm having a bit of trouble with the math behind my project. I want the player to be able to select 2 points (vectors). With these 2 points a floor should be created. When these points are parallel to the x-axis it's easy, just calculate the amount of blocks needed by a simple division, loop through that amount (in x and y) and keep increasing the coordinate by the size of that block. The trouble starts when the 2 vectors aren't parallel to an axis, for example at an angle of 45 degrees. How do I handle the math behind this? If I wasn't completely clear, I made this awesome drawing in paint to demonstrate what I want to achieve. The 2 red dots would be the player selected locations. (The blocks indeed aren't square.) http://i.imgur.com/pzhFMEs.png.

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• Why do we use the Pythagorean theorem in game physics?

  - by Starkers

  I've recently learned that we use Pythagorean theorem a lot in our physics calculations and I'm afraid I don't really get the point. Here's an example from a book to make sure an object doesn't travel faster than a MAXIMUM_VELOCITY constant in the horizontal plane: MAXIMUM_VELOCITY = <any number>; SQUARED_MAXIMUM_VELOCITY = MAXIMUM_VELOCITY * MAXIMUM_VELOCITY; function animate(){ var squared_horizontal_velocity = (x_velocity * x_velocity) + (z_velocity * z_velocity); if( squared_horizontal_velocity <= SQUARED_MAXIMUM_VELOCITY ){ scalar = squared_horizontal_velocity / SQUARED_MAXIMUM_VELOCITY; x_velocity = x_velocity / scalar; z_velocity = x_velocity / scalar; } } Let's try this with some numbers: An object is attempting to move 5 units in x and 5 units in z. It should only be able to move 5 units horizontally in total! MAXIMUM_VELOCITY = 5; SQUARED_MAXIMUM_VELOCITY = 5 * 5; SQUARED_MAXIMUM_VELOCITY = 25; function animate(){ var x_velocity = 5; var z_velocity = 5; var squared_horizontal_velocity = (x_velocity * x_velocity) + (z_velocity * z_velocity); var squared_horizontal_velocity = 5 * 5 + 5 * 5; var squared_horizontal_velocity = 25 + 25; var squared_horizontal_velocity = 50; // if( squared_horizontal_velocity <= SQUARED_MAXIMUM_VELOCITY ){ if( 50 <= 25 ){ scalar = squared_horizontal_velocity / SQUARED_MAXIMUM_VELOCITY; scalar = 50 / 25; scalar = 2.0; x_velocity = x_velocity / scalar; x_velocity = 5 / 2.0; x_velocity = 2.5; z_velocity = z_velocity / scalar; z_velocity = 5 / 2.0; z_velocity = 2.5; // new_horizontal_velocity = x_velocity + z_velocity // new_horizontal_velocity = 2.5 + 2.5 // new_horizontal_velocity = 5 } } Now this works well, but we can do the same thing without Pythagoras: MAXIMUM_VELOCITY = 5; function animate(){ var x_velocity = 5; var z_velocity = 5; var horizontal_velocity = x_velocity + z_velocity; var horizontal_velocity = 5 + 5; var horizontal_velocity = 10; // if( horizontal_velocity >= MAXIMUM_VELOCITY ){ if( 10 >= 5 ){ scalar = horizontal_velocity / MAXIMUM_VELOCITY; scalar = 10 / 5; scalar = 2.0; x_velocity = x_velocity / scalar; x_velocity = 5 / 2.0; x_velocity = 2.5; z_velocity = z_velocity / scalar; z_velocity = 5 / 2.0; z_velocity = 2.5; // new_horizontal_velocity = x_velocity + z_velocity // new_horizontal_velocity = 2.5 + 2.5 // new_horizontal_velocity = 5 } } Benefits of doing it without Pythagoras: Less lines Within those lines, it's easier to read what's going on ...and it takes less time to compute, as there are less multiplications Seems to me like computers and humans get a better deal without Pythagorean theorem! However, I'm sure I'm wrong as I've seen Pythagoras' theorem in a number of reputable places, so I'd like someone to explain me the benefit of using Pythagorean theorem to a maths newbie. Does this have anything to do with unit vectors? To me a unit vector is when we normalize a vector and turn it into a fraction. We do this by dividing the vector by a larger constant. I'm not sure what constant it is. The total size of the graph? Anyway, because it's a fraction, I take it, a unit vector is basically a graph that can fit inside a 3D grid with the x-axis running from -1 to 1, z-axis running from -1 to 1, and the y-axis running from -1 to 1. That's literally everything I know about unit vectors... not much :P And I fail to see their usefulness. Also, we're not really creating a unit vector in the above examples. Should I be determining the scalar like this: // a mathematical work-around of my own invention. There may be a cleverer way to do this! I've also made up my own terms such as 'divisive_scalar' so don't bother googling var divisive_scalar = (squared_horizontal_velocity / SQUARED_MAXIMUM_VELOCITY); var divisive_scalar = ( 50 / 25 ); var divisive_scalar = 2; var multiplicative_scalar = (divisive_scalar / (2*divisive_scalar)); var multiplicative_scalar = (2 / (2*2)); var multiplicative_scalar = (2 / 4); var multiplicative_scalar = 0.5; x_velocity = x_velocity * multiplicative_scalar x_velocity = 5 * 0.5 x_velocity = 2.5 Again, I can't see why this is better, but it's more "unit-vector-y" because the multiplicative_scalar is a unit_vector? As you can see, I use words such as "unit-vector-y" so I'm really not a maths whiz! Also aware that unit vectors might have nothing to do with Pythagorean theorem so ignore all of this if I'm barking up the wrong tree. I'm a very visual person (3D modeller and concept artist by trade!) and I find diagrams and graphs really, really helpful so as many as humanely possible please!

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• Calculate vector direction

  - by Starkers

  Is the direction angle always measured from the plus x axis? Does a vector in the +,+ quadrant always have a direction between 0 and 90, and in -,+ between 90 and 180 and in -,- between 180 and 270 and in -,+ between 270 and 360 ? Also, how should we calculate the direction using tan? Would that mean nested if statements to find out what quadrant we're in, and then applying the appropriate "work arounds"? E.g. If we were in the -,+ (like in the diagram) would we find the angle from the + axis would be 90 + tan^-1(y/x), the 90 + only used because we're in the -,+ quadrant. Also, that's just a quick solution, may be off, I just want to know if we use nested if statements to get the angle from the + x axis. Finally, should we find the distance in degrees or radians?

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