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  • Literature for Inverse Kinematics: Joint Limits and beyond

    - by Jeff
    Recently I've been playing around with Inverse Kinematics and have been pretty impressed with the results. Naturally I want to take it further, but have no clue where to start. In particular, I would like to introduce joint limits (ie for a prismatic joint how far it can move, hinge joint what angles it has to be between, etc etc). Currently I understand how to produce the Jacobian matrix for the various joint types. I am particularly looking for literature (preferably free, and preferably easy to understand) on various ways to implement joint limits. Also I would like to find out different ideas on how inverse kinematics can be used.

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  • Introducing Programming To a Mathematician

    - by ell
    I currently am a programmer, I'm almost 16 years of age and have pretty much narrowed my careers down to something involving a Computer Science degree or Electrical Engineering degree (I know they are quite different but this question is about my friend) but my friend isn't so sure. He is very interested in maths and is very good at it and I think he would enjoy programming but he isn't willing to try it (edit he is willing to try but has never done before). Can anyone give me an suggestions for a language or tool that he could dabble in programming (at a reasonably basic level I assume) to solve maths problems or involve some kind of maths. As I say he enjoys maths a lot but I think he would enjoy programming, the problem is I don't want him to be put off by the stuff that isn't relevant at introductory levels such as memory allocation et al. I know that is very important but the point is that I want him to learn a bit of programming with maths then hopefully if he is interested enough he can start learning programming as programming. Thanks in advance, ell. Edit: Its not that he's completely uninterested - more that he hasn't actively explored the area before, maybe because he isn't informed about it. I wouldn't want to force him to do something he doesn't want to, I see this as more of a little push so that he can learn about programming. If he doesn't like it - fair enough, I can't control that and don't want to but if he turns out to enjoy it - this push will have been the right thing.

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  • For normal mapping, why can we not simply add the tangent normal to the surface normal?

    - by sebf
    I am looking at implementing bump mapping (which in all implementations I have seen is really normal mapping), and so far all I have read says that to do this, we create a matrix to convert from world-space to tangent-space, in order to transform the lights and eye direction vectors into tangent space, so that the vectors from the normal map may be used directly in place of those passed through from the vertex shader. What I do not understand though, is why we cannot just use the normalised sum of the sampled-normal vector, and the surface-normal? (assuming we already transform and pass through the surface normal for the existing lighting functions) Take the diagram below; the normal is simply the deviation from the 'reference normal' for any given coordinate system, correct? And transforming the surface normal of a mapped surface from world space to tangent space makes it equivalent to the tangent space 'reference normal', no? If so, why do we transform all lighting vectors into tangent space, instead of simply transforming the sampled tangent once in the pixel shader?

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  • how to programtically build a grid of interlocking but random sized squares

    - by Mrwolfy
    I want to create a two dimensional layout of rectangular shapes, a grid made up of random sized cubes. The cubed should fit together and have equal padding or margin (space between). Kind of like a comic book layout, or more like the image attached. How could I do this procedurally? Practically, I would probably be using Python and some graphic software to render an image, but I don't know the type of algorithm (or whatnot) I would need to use to generate the randomized grid.

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  • LaTeX-like display programming environment

    - by Gage
    I used to be a hobbyist programmer, but now I'm also a fairly experienced physicist and find myself programming to solve certain problems quite a lot. In physics, we use variables with superscripts, subscripts, italics, underlines, etc etc. To bridge this gap to the computer we usually use LaTeX. Now, I generally use MATLAB for handling any data and such, and find it very irritating that I can't basically use LaTeX for variable names. Something as simple as sy has to be named either sigma_y or some descriptive name like peak_height_error. I don't necessarily want full on workable LaTeX in my code, but I do want to be able to use greek letters and super/sub-scripts at the very least. Does this exist?

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  • How can I generate a navigation mesh for a tile grid?

    - by Roflha
    I haven't actually started programming for this one yet, but I wanted to see how I would go about doing this anyway. Say I have a grid of tiles, all of the same size, some traversable and some not. How would I go about creating a navigation mesh of polygons from this grid? My idea was to take the non-traversable tiles out and extend lines from there edges to make polygons... that's all I have got so far. Any advice?

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  • Implementing 2D CSG (for collision shapes)?

    - by bluescrn
    Are there any simple (or well documented) algorithms for basic CSG operations on 2D polygons? I'm looking for a way to 'add' a number of overlapping 2D collision shapes. These may be convex or concave, but will be closed shapes, defined as a set of line segments, with no self-intersections. The use of this would be to construct a clean set of collision edges, for use with a 2D physics engine, from a scene consisting of many arbitrarily placed (and frequently overlapping) objects, each with their own collision shape. To begin with, I only need to 'add' shapes, but the ability to 'subtract', to create holes, may also be useful.

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  • How can a large, Fortran-based number crunching codebase be modernized?

    - by Dave Mateer
    A friend in academia asked me for advice (I'm a C# business application developer). He has a legacy codebase which he wrote in Fortran in the medical imaging field. It does a huge amount of number crunching using vectors. He uses a cluster (30ish cores) and has now gone towards a single workstation with 500ish GPUS in it. However where to go next with the codebase so: Other people can maintain it over next 10 year cycle Get faster at tweaking the software Can run on different infrastructures without recompiles After some research from me (this is a super interesting area) some options are: Use Python and CUDA from Nvidia Rewrite in a functional language. For example, F# or Haskell Go cloud based and use something like Hadoop and Java Learn C What has been your experience with this? What should my friend be looking at to modernize his codebase? UPDATE: Thanks @Mark and everyone who has answered. The reasons my friend is asking this question is that it's a perfect time in the projects lifecycle to do a review. Bringing research assistants up to speed in Fortran takes time (I like C#, and especially the tooling and can't imagine going back to older languages!!) I liked the suggestion of keeping the pure number crunching in Fortran, but wrapping it in something newer. Perhaps Python as that seems to be getting a stronghold in academia as a general-purpose programming language that is fairly easy to pick up. See Medical Imaging and a guy who has written a Fortran wrapper for CUDA, Can I legally publish my Fortran 90 wrappers to Nvidias' CUFFT library (from the CUDA SDK)?.

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  • Basic tutorial/introduction for 3d matrices, idealy in c++, without openGl or directX

    - by René Nyffenegger
    I am wondering if there is a simple tutorial that covers the basics of how to initialize rotation, translation and projection matrices, and how to multiply them, and how to get the screen coordinates afterwards for a 3d point. Idealy, the tutorial comes with compilable code and is not dependent on any 3rd party library. Searching the internet, I found lots of tutorials, so this is not the problem. Yet, it seemed all of these either covered openGl or directX, or they were theoretical in nature.

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  • Why does multiplying texture coordinates scale the texture?

    - by manning18
    I'm having trouble visualizing this geometrically - why is it that multiplying the U,V coordinates of a texture coordinate has the effect of scaling that texture by that factor? eg if you scaled the texture coordinates by a factor of 3 ..then doesn't this mean that if you had texture coordinates 0,1 and 0,2 ...you'd be sampling 0,3 and 0,6 in the U,V texture space of 0..1? How does that make it bigger eg HLSL: tex2D(textureSampler, TexCoords*3) Integers make it smaller, decimals make it bigger I mean I understand intuitively if you added to the U,V coordinates, as that is simply an offset into the sampling range, but what's the case with multiplication? I have a feeling when someone explains this to me I'm going to be feeling mighty stupid

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  • Rotate sphere in Javascript / three.js while moving on x/z axes

    - by kaipr
    I have a sphere/ball in three.js which I want to "roll" arround on a x/z axis. For the z axe I could simply do this no matter what the current x and y rotation is: sphere.roll_z = function(distance) { sphere.position.z += distance; sphere.rotation.x += distance > 0 ? 0.05 : -0.05; } But how can I roll it along the x axe? And how could I properly do the roll_z? I've found a lot about quateration and matrixes, but I can't figure out how to use them properly to achieve my (rather simple) goal. I'm aware that I have to update multiple rotations and that I have to calculate how far to rotate the sphere to match the distance, but the "how" is the question. It's probably just lack of mathematical skills which I should train, but a working example/short explanation would help alot to start with.

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  • Inverting matrix then decomposing gives different quaternion than decomposing then inverting the quat

    - by Fraser
    I'm getting different signs when I convert a matrix to quaternion and invert that, versus when I invert a matrix and then get the quaternion from it: Quaternion a = Quaternion.Invert(getRotation(m)); Quaternion b = getRotation(Matrix.Invert(m)); I would expect a and b to be identical (or inverses of each other). However, it looks like q1 = (x, y, -z, -w) while q2 = (-x, -y, w, z). In other words, the Z and W components have been switched for some reason. Note: getRotation() decomposes the transform matrix and returns just the rotation part of it (I've tried normalizing the result; it does nothing). The matrix m is a complete transform matrix and contains a translation (and possibly a scale) as well as a rotation. I'm using D3DXMatrixDecompose to do the actual decomposition.

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  • Matrix multiplication - Scene Graphs

    - by bgarate
    I wrote a MatrixStack class in C# to use in a SceneGraph. So, to get the world matrix for an object I am suposed to use: WorldMatrix = ParentWorld * LocalTransform But, in fact, it only works as expected when I do the other way: WorldMatrix = LocalTransform * ParentWorld Mi code is: public class MatrixStack { Stack<Matrix> stack = new Stack<Matrix>(); Matrix result = Matrix.Identity; public void PushMatrix(Matrix matrix) { stack.Push(matrix); result = matrix * result; } public Matrix PopMatrix() { result = Matrix.Invert(stack.Peek()) * result; return stack.Pop(); } public Matrix Result { get { return result; } } public void Clear() { stack.Clear(); result = Matrix.Identity; } } Why it works this way and not the other? Thanks!

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  • Missing z-axis rotation for transforming between two vectors

    - by Steve Baughman
    I'm trying to rotate a cube so that it's facing up, but am getting hung up on the final implementation details. It now reliably will rotate the x,y axis to the correct side, but the z-axis is never rotating (See photos of before and after rotation). When I'm using the code below I always get '0' for my rotationVector.z. What am I missing here? // Define lookAt vector lookAtVector = GLKVector3Make(0,0,1); // Define axes vectors axes[0] = GLKVector3Make(0,0,1); axes[1] = GLKVector3Make(-1,0,0); axes[2] = GLKVector3Make(0,1,0); axes[3] = GLKVector3Make(1,0,0); axes[4] = GLKVector3Make(0,-1,0); axes[5] = GLKVector3Make(0,0,-1); CGFloat highest_dot = -1.0; GLKVector3 closest_axis; for(int i = 0; i < 6; i++) { // multiply cube's axes by existing matrix GLKVector3 axis = GLKMatrix4MultiplyVector3(matrix, axes[i]); CGFloat dot = GLKVector3DotProduct(axis, lookAtVector); if(dot > highest_dot) { closest_axis = axis; highest_dot = dot; } } GLKVector3 rotationVector = GLKVector3CrossProduct(closest_axis, lookAtVector); // Get angle between vectors CGFloat angle = atan2(GLKVector3Length(rotationVector), GLKVector3DotProduct(closest_axis, lookAtVector)); // normalize the rotation vector rotationVector = GLKVector3Normalize(rotationVector); // Create transform CATransform3D rotationTransform = CATransform3DMakeRotation(angle, rotationVector.x, rotationVector.y, rotationVector.z); // add rotation transform to existing transformation baseTransform = CATransform3DConcat(baseTransform, rotationTransform); return baseTransform; Before 3d Rotation After 3d Rotation Implementation based on this post

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  • Rotate around the centre of the screen

    - by Dan Scott
    I want my camera to rotate around the centre of screen and I'm not sure how to achieve that. I have a rotation in the camera but I'm not sure what its rotating around. (I think it might be rotating around the position.X of camera, not sure) If you look at these two images: http://imgur.com/E9qoAM7,5qzyhGD#0 http://imgur.com/E9qoAM7,5qzyhGD#1 The first one shows how the camera is normally, and the second shows how I want the level to look when I would rotate the camera 90 degrees left or right. My camera: public class Camera { private Matrix transform; public Matrix Transform { get { return transform; } } private Vector2 position; public Vector2 Position { get { return position; } set { position = value; } } private float rotation; public float Rotation { get { return rotation; } set { rotation = value; } } private Viewport viewPort; public Camera(Viewport newView) { viewPort = newView; } public void Update(Player player) { position.X = player.PlayerPos.X + (player.PlayerRect.Width / 2) - viewPort.Width / 4; if (position.X < 0) position.X = 0; transform = Matrix.CreateTranslation(new Vector3(-position, 0)) * Matrix.CreateRotationZ(Rotation); if (Keyboard.GetState().IsKeyDown(Keys.D)) { rotation += 0.01f; } if (Keyboard.GetState().IsKeyDown(Keys.A)) { rotation -= 0.01f; } } } (I'm assuming you would need to rotate around the centre of the screen to achieve this)

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  • Large sparse (stiff) ODE system needed for testing

    - by macydanim
    I hope this is the right place for this question. I have been working on a sparse stiff implicit ODE solver and have finished the code so far. I now tested the solver with the Van der Pol equation, and another stiff problem, which is of dimension 4. But to perform better tests I am searching for a bigger system. I'm thinking of the order N = 100...1000, if possible stiff and sparse. Does anybody have an example I could use? I really don't know where to search.

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  • Typical Applications of Linear System Solver in Game Developemnt

    - by craftsman.don
    I am going to write a custom solver for linear system. I would like to survey the typical problems involved the linear system solving in games. So that I can custom optimization on these problems based on the shape of the matrix. currently I am focus on these problems: B-Spline editing (I use a linear solve to resolve the C0, C1, C2 continuity) Constraint in Simulation (especially Position-Constraint, cloth) Both of them are Banded Matrix. I want to hear about some other applications of a linear system in games. Thank you.

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  • Logarithmic spacing of FFT bins

    - by Mykel Stone
    I'm trying to do the examples within the GameDev.net Beat Detection article ( http://archive.gamedev.net/archive/reference/programming/features/beatdetection/index.html ) I have no issue with performing a FFT and getting the frequency data and doing most of the article. I'm running into trouble though in the section 2.B, Enhancements and beat decision factors. in this section the author gives 3 equations numbered R10-R12 to be used to determine how many bins go into each subband: R10 - Linear increase of the width of the subband with its index R11 - We can choose for example the width of the first subband R12 - The sum of all the widths must not exceed 1024 He says the following in the article: "Once you have equations (R11) and (R12) it is fairly easy to extract 'a' and 'b', and thus to find the law of the 'wi'. This calculus of 'a' and 'b' must be made manually and 'a' and 'b' defined as constants in the source; indeed they do not vary during the song." However, I cannot seem to understand how these values are calculated...I'm probably missing something simple, but learning fourier analysis in a couple of weeks has left me Decimated-in-Mind and I cannot seem to see it.

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  • Languages/Methods to Learn for Scientific Computing?:

    - by Zéychin
    I'm a second-semester Junior working towards a Computer Science degree with a Scientific Computing concentration and a Mathematics degree with a concentration on Applied Discrete Mathematics. So, number crunching and such rather than a bunch of regular expressions, interface design, and networking. I've found that I'm not learning new relevant languages from my coursework and am interested in what the community would recommend me to learn. I know as far as programming methods go, I need to learn more about parallelizing programs, but if there's anything else you can recommend, I would appreciate it. Here's a list of the languages with which I am very experienced (web technologies omitted as they barely apply here). Any recommendations for additional languages I should learn would be very much appreciated!: Java C C++ Fortran77/90/95 Haskell Python MATLAB

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  • What are the maths behind 'Raiden 2' purple laser?

    - by Aybe
    The path of the laser is affected by user input and enemies present on the screen. Here is a video, at 5:00 minutes the laser in question is shown : Raiden II (PS) - 1 Loop Clear - Part 2 UPDATE Here is a test using Inkscape, ship is at bottom, the first 4 enemies are targeted by the plasma. There seems to be a sort of pattern. I moved the ship first, then the handle from it to form a 45° angle, then while trying to fit the curve I found a pattern of parallel handles and continued so until I reached the last enemy. Update, 5/26/2012 : I started an XNA project using beziers, there is still some work needed, will update the question next week. Stay tuned ! Update : 5/30/2012 : It really seems that they are using Bézier curves, I think I will be able to replicate/imitate a plasma of such grade. There are two new topics I discovered since last time : Arc length, Runge's phenomenon, first one should help in having a linear movement possible over a Bézier curve, second should help in optimizing the number of vertices. Next time I will put a video so you can see the progress 8-)

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  • Are there any formalized/mathematical theories of software testing?

    - by Erik Allik
    Googling "software testing theory" only seems to give theories in the soft sense of the word; I have not been able to find anything that would classify as a theory in the mathematical, information theoretical or some other scientific field's sense. What I'm looking for is something that formalizes what testing is, the notions used, what a test case is, the feasibility of testing something, the practicality of testing something, the extent to which something should be tested, formal definition/explanation of code coverage, etc. UPDATE: Also, I'm not sure, intuitively, about the connection between formal verification and what I asked, but there's clearly some sort of connection.

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  • How can I make sense of the word "Functor" from a semantic standpoint?

    - by guillaume31
    When facing new programming jargon words, I first try to reason about them from an semantic and etymological standpoint when possible (that is, when they aren't obscure acronyms). For instance, you can get the beginning of a hint of what things like Polymorphism or even Monad are about with the help of a little Greek/Latin. At the very least, once you've learned the concept, the word itself appears to go along with it well. I guess that's part of why we name things names, to make mental representations and associations more fluent. I found Functor to be a tougher nut to crack. Not so much the C++ meaning -- an object that acts (-or) as a function (funct-), but the various functional meanings (in ML, Haskell) definitely left me puzzled. From the (mathematics) Functor Wikipedia article, it seems the word was borrowed from linguistics. I think I get what a "function word" or "functor" means in that context - a word that "makes function" as opposed to a word that "makes sense". But I can't really relate that to the notion of Functor in category theory, let alone functional programming. I imagined a Functor to be something that creates functions, or behaves like a function, or short for "functional constructor", but none of those seems to fit... How do experienced functional programmers reason about this ? Do they just need any label to put in front of a concept and be fine with it ? Generally speaking, isn't it partly why advanced functional programming is hard to grasp for mere mortals compared to, say, OO -- very abstract in that you can't relate it to anything familiar ? Note that I don't need a definition of Functor, only an explanation that would allow me to relate it to something more tangible, if there is any.

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  • Determining explosion radius damage - Circle to Rectangle 2D

    - by Paul Renton
    One of the Cocos2D games I am working on has circular explosion effects. These explosion effects need to deal a percentage of their set maximum damage to all game characters (represented by rectangular bounding boxes as the objects in question are tanks) within the explosion radius. So this boils down to circle to rectangle collision and how far away the circle's radius is from the closest rectangle edge. I took a stab at figuring this out last night, but I believe there may be a better way. In particular, I don't know the best way to determine what percentage of damage to apply based on the distance calculated. Note : All tank objects have an anchor point of (0,0) so position is according to bottom left corner of bounding box. Explosion point is the center point of the circular explosion. TankObject * tank = (TankObject*) gameSprite; float distanceFromExplosionCenter; // IMPORTANT :: All GameCharacter have an assumed (0,0) anchor if (explosionPoint.x < tank.position.x) { // Explosion to WEST of tank if (explosionPoint.y <= tank.position.y) { //Explosion SOUTHWEST distanceFromExplosionCenter = ccpDistance(explosionPoint, tank.position); } else if (explosionPoint.y >= (tank.position.y + tank.contentSize.height)) { // Explosion NORTHWEST distanceFromExplosionCenter = ccpDistance(explosionPoint, ccp(tank.position.x, tank.position.y + tank.contentSize.height)); } else { // Exp center's y is between bottom and top corner of rect distanceFromExplosionCenter = tank.position.x - explosionPoint.x; } // end if } else if (explosionPoint.x > (tank.position.x + tank.contentSize.width)) { // Explosion to EAST of tank if (explosionPoint.y <= tank.position.y) { //Explosion SOUTHEAST distanceFromExplosionCenter = ccpDistance(explosionPoint, ccp(tank.position.x + tank.contentSize.width, tank.position.y)); } else if (explosionPoint.y >= (tank.position.y + tank.contentSize.height)) { // Explosion NORTHEAST distanceFromExplosionCenter = ccpDistance(explosionPoint, ccp(tank.position.x + tank.contentSize.width, tank.position.y + tank.contentSize.height)); } else { // Exp center's y is between bottom and top corner of rect distanceFromExplosionCenter = explosionPoint.x - (tank.position.x + tank.contentSize.width); } // end if } else { // Tank is either north or south and is inbetween left and right corner of rect if (explosionPoint.y < tank.position.y) { // Explosion is South distanceFromExplosionCenter = tank.position.y - explosionPoint.y; } else { // Explosion is North distanceFromExplosionCenter = explosionPoint.y - (tank.position.y + tank.contentSize.height); } // end if } // end outer if if (distanceFromExplosionCenter < explosionRadius) { /* Collision :: Smaller distance larger the damage */ int damageToApply; if (self.directHit) { damageToApply = self.explosionMaxDamage + self.directHitBonusDamage; [tank takeDamageAndAdjustHealthBar:damageToApply]; CCLOG(@"Explsoion-> DIRECT HIT with total damage %d", damageToApply); } else { // TODO adjust this... turning out negative for some reason... damageToApply = (1 - (distanceFromExplosionCenter/explosionRadius) * explosionMaxDamage); [tank takeDamageAndAdjustHealthBar:damageToApply]; CCLOG(@"Explosion-> Non direct hit collision with tank"); CCLOG(@"Damage to apply is %d", damageToApply); } // end if } else { CCLOG(@"Explosion-> Explosion distance is larger than explosion radius"); } // end if } // end if Questions: 1) Can this circle to rect collision algorithm be done better? Do I have too many checks? 2) How to calculate the percentage based damage? My current method generates negative numbers occasionally and I don't understand why (Maybe I need more sleep!). But, in my if statement, I ask if distance < explosion radius. When control goes through, distance/radius must be < 1 right? So 1 - that intermediate calculation should not be negative. Appreciate any help/advice!

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  • Physics timestep questions

    - by SSL
    I've got a projectile working perfectly using the code below: //initialised in loading screen 60 is the FPS - projectilEposition and velocity are Vector3 types gravity = new Vector3(0, -(float)9.81 / 60, 0); //called every frame projectilePosition += projectileVelocity; This seems to work fine but I've noticed in various projectile examples I've seen that the elapsedtime per update is taken into account. What's the difference between the two and how can I convert the above to take into account the elapsedtime? (I'm using XNA - do I use ElapsedTime.TotalSeconds or TotalMilliseconds)? Edit: Forgot to add my attempt at using elapsedtime, which seemed to break the physics: projectileVelocity.Y += -(float)((9.81 * gameTime.ElapsedGameTime.TotalSeconds * gameTime.ElapsedGameTime.TotalSeconds) * 0.5f); Thanks for the help

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  • building a game for different resoulution phones

    - by Jason
    Hi, I am starting some tests for building a game on the android program. So far everything is working and seems nice. However I do not understand how to make sure my game looks correct on all phones as the all will have slightly different screen ratios (and even very different on some odd phones) What I am doing right now is making a view frustrum ( could also be ortho ) which I set to go from -ratio to +ratio ( as I have seen on many examples) however this causes my test shape to be stretched and sometimes cut off by the edge of the screen. I am tilting my phone to landscape to do my tests ( a bit extreame) but it should still render correctly if I have dome things right. Should I be scaling by some ratio before drawing or something? An example would be greatly apriciated PS I am doing a 2d game

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