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• Estimate angle to launch missile, maths question

  - by Jonathan

  I've been working on this for an hour or two now and my maths really isn't my strong suit which is definitely not a good thing for a game programmer but that shouldn't stop me enjoying a hobby surely? After a few failed attempts I was hoping someone else out there could help so here's the situation. I'm trying to implement a bit of faked intelligence when the A.I fires it's missiles at a target in a 2D game world. By predicting the likely position the target will be in given it's current velocity and the time it will take the missile to reach it's target. I created an image to demonstrate my thinking: http://i.imgur.com/SFmU3.png which also contains the logic I use for accelerating the missile after launch. The ship that fires the missile can fire within a total of 40 degree angle, 20 either side of itself, but this could likely become variable. My current attempt was to break the space between the two lines into segments which match the targets width. Then calculate the time it would take the missile to get to that location using the formula. So for each iteration of this we total up the values and that tells us the distance travelled, ad it would then just need compared to distance to the segment. startVelocity * ((startVelocity * acceleration)^(currentframe-1) So for example. If we start at a velocity of 1f/frame with an acceleration of 0.1f the formula, at frame 4, would be 1 * (1.1^3) = 1.331 But I quickly realized I was getting lost when trying to put this into practice. Does this seem like a correct starting point or am I going completely the wrong way about it? Any pointers would help me greatly. Maths really isn't my strong suit so I get easily lost in these matters and don't even really know a good phrase to search for with this. So I guess in summary my question is more about the correct way to approach this problem and any additional code samples on top of that would be great but I'm not averse to working out the complete code from helpful pointers.

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• Better way to go up/down slope based on yaw?

  - by CyanPrime

  Alright, so I got a bit of movement code and I'm thinking I'm going to need to manually input when to go up/down a slope. All I got to work with is the slope's normal, and vector, and My current and previous position, and my yaw. Is there a better way to rotate whether I go up or down the slope based on my yaw? Vector3f move = new Vector3f(0,0,0); move.x = (float)-Math.toDegrees(Math.cos(Math.toRadians(yaw))); move.z = (float)-Math.toDegrees(Math.sin(Math.toRadians(yaw))); move.normalise(); if(move.z < 0 && slopeNormal.z > 0 || move.z > 0 && slopeNormal.z < 0){ if(move.x < 0 && slopeNormal.x > 0 || move.x > 0 && slopeNormal.x < 0){ move.y += slopeVec.y; } } if(move.z > 0 && slopeNormal.z > 0 || move.z < 0 && slopeNormal.z < 0){ if(move.x > 0 && slopeNormal.x > 0 || move.x < 0 && slopeNormal.x < 0){ move.y -= slopeVec.y; } } move.scale(movementSpeed * delta); Vector3f.add(pos, move, pos);

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• Ray Picking Problems

  - by A Name I Haven't Decided On

  I've read so many answers on here about how to do Ray Picking, that I thought I had the idea of it down. But when I try to implement it in my game, I get garbage. I'm working with LWJGL. Here's the code: public static Ray getPick(int mouseX, int mouseY){ glPushMatrix(); //Setting up the Mouse Clip Vector4f mouseClip = new Vector4f((float)mouseX * 2 / 960f - 1, 1 - (float)mouseY * 2 / 640f ,0 ,1); //Loading Matrices FloatBuffer modMatrix = BufferUtils.createFloatBuffer(16); FloatBuffer projMatrix = BufferUtils.createFloatBuffer(16); glGetFloat(GL_MODELVIEW_MATRIX, modMatrix); glGetFloat(GL_PROJECTION_MATRIX, projMatrix); //Assigning Matrices Matrix4f proj = new Matrix4f(); Matrix4f model = new Matrix4f(); model.load(modMatrix); proj.load(projMatrix); //Multiplying the Projection Matrix by the Model View Matrix Matrix4f tempView = new Matrix4f(); Matrix4f.mul(proj, model, tempView); tempView.invert(); //Getting the Camera Position in World Space. The 4th Column of the Model View Matrix. model.invert(); Point cameraPos = new Point(model.m30, model.m31, model.m32); //Theoretically getting the vector the Picking Ray goes Vector4f rayVector = new Vector4f(); Matrix4f.transform(tempView, mouseClip, rayVector); rayVector.translate((float)-cameraPos.getX(),(float) -cameraPos.getY(),(float) -cameraPos.getZ(), 0f); rayVector.normalise(); glPopMatrix(); //This Basically Spits out a value that changes as the Camera moves. //When the Mouse moves, the values change around 0.001 points from screen edge to edge. System.out.format("Vector: %f %f %f%n", rayVector.x, rayVector.y, rayVector.z); //return new Ray(cameraPos, rayVector); return null; } I don't really know why this isn't working. I was hoping some more experienced eyes might be able to help me out. I can get the camera position like a champ, it's the vector the rays going in that I can't seem to get right. Thanks.

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• How to Effectively Create Bullet Patterns

  - by SoulBeaver

  I'm currently creating a top-down shooter like Touhou. The most important factor of the game is that there are many diverse patterns and ways at which bullets are generated and shot at the player, see this video: http://www.youtube.com/watch?v=4Nb5Ohbt1Sg#start=0:60;end=9:53; At the moment, I'm using a class "Pattern" which has a series of steps on moving and shooting. However, I feel this method is quite laborous as I have to create a new Pattern for each attack and perhaps new Bullet classes that will implement a certain behavior. This question received a comment suggesting I should look into BulletML for easy creation and storage of bullets with a specific pattern. It looks decent, but it led me to wonder, what other solutions do you have that I should take into consideration? Update My current design is as follows: An example of an implemented pattern: My GigasPattern first executes a teleport which moves Alice to a certain point (X, Y) on the screen. After this is completed, the pattern starts using the Mover to move the sprite around (whereas teleporting has separate effects and animation). These are of no concern, really, as they are quite simple. The Shooter also creates various Attacks, which are classes again that the Shooter can use to create various patterns of bullets, much like the one in the question I posted. Once the Mover has reached it's destination, both it and the shooter stop and return to an inactive state. The pattern completes, is removed by the AI and a new one gets chosen.

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• Wired : "Japanese despise western games" - how much is it true?

  - by user712092

  Wired has article that western games are seen as "bad games". Why is that? If that is true, than what do they see as bad? This article, i think, is biased towards western games: “The other day,” says Q Entertainment’s Mielke, “I was having lunch with a friend and I said, ‘Have you ever played StarCraft?’ And he said, ‘What’s StarCraft?’ Sometimes it’s just really shocking that their gaming vocabulary isn’t as extensive as it could be. I think Japanese game developers need to start playing other people’s games to open their minds, just like a writer might want to read classic literature to be inspired.” Rather than trusting such articles, I rather ask here.

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• Implement Fast Inverse Square Root in Javascript?

  - by BBz

  The Fast Inverse Square Root from Quake III seems to use a floating-point trick. As I understand, floating-point representation can have some different implementations. So is it possible to implement the Fast Inverse Square Root in Javascript? Would it return the same result? float Q_rsqrt(float number) { long i; float x2, y; const float threehalfs = 1.5F; x2 = number * 0.5F; y = number; i = * ( long * ) &y; i = 0x5f3759df - ( i >> 1 ); y = * ( float * ) &i; y = y * ( threehalfs - ( x2 * y * y ) ); return y; }

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• Game maps with "counties" that are split along lines that aren't necessarily straight

  - by pm_2

  I want to create a game environment that supports a 2D map. This is a really basic map, but must be split along lines that are not necessarily straight. So imagine a country with county boundaries. I then want to be able to detect drag / drop events within these counties. What I'm really looking for here is a pointer to where to start on this (how it has been done before - any existing libraries out there), as I'm sure that what I'm trying to do is not new - although I can't find a beginners guide for this anywhere.

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• The most efficent ways for drawing lines all day long with OpenGL

  - by nkint

  I'd like to put a computer screen that is running an OpenGL programs in a room. It has to run all day long (not in the night). I'd like to draw lines that are slowly fading in the background. The setting is simple: a uniform color background (say, black) and colored lines (say, white) that are slowly fading out. With slowly I mean.. hours. Say that the first line I draw is with alpha 255 (fully visible), after one hours is 240. After 10 hours is 105. One line could have 250 points and there will be like 300 line in one day. For now I have done a prototype with very rudimentary method like: glBegin( GL_LINE_STRIP ); iterator = point_list.begin(); for (++iterator, end = point_list.end(); iterator != end; ++iterator) { const Vec3D &v = *iterator; glVertex2f(v.x(), v.y()); } glEnd(); More efficient method?

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• Getting a texture from a renderbuffer in OpenGL?

  - by Rushyo

  I've got a renderbuffer (DepthStencil) in an FBO and I need to get a texture from it. I can't have both a DepthComponent texture and a DepthStencil renderbuffer in the FBO, it seems, so I need some way to convert the renderbuffer to a DepthComponent texture after I'm done with it for use later down the pipeline. I've tried plenty of techniques to grab the depth component from the renderbuffer for weeks but I always come out with junk. All I want at the end is the same texture I'd get from an FBO if I wasn't using a renderbuffer. Can anyone post some comprehensive instructions or code that covers this seemingly simple operation? EDIT: Linky to an extract version of the code http://dl.dropbox.com/u/9279501/fbo.cs Screeny of the Depth of Field effect + FBO - without depth(!) http://i.stack.imgur.com/Hj9Oe.jpg Screeny without Depth of Field effect + FBO - depth working fine http://i.stack.imgur.com/boOm1.jpg

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• Do I need "cube subclasses" to represent the blocks in a Minecraft-like world?

  - by stighy

  I would like to try to develop a very simple game like Minecraft for my own education. My main problem at the moment is figuring out how to model classes that represent the world, which will be made of blocks of various types (such as dirt, stone and sand). I am thinking of creating the following class structure: Cube (with proprerties like color, strength, flammable, gravity) with subclasses: Dirt Stone Sand et cetera My question is, do I need the Cube subclasses or a single class Cube sufficient?

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• HTML5-Canvas: worth using ImpactJS or other framework?

  - by John

  I've been making an HTML5 game without any type of external framework. I haven't found a reason to use one so far. However, there is one thing I'm wondering about. On my Galaxy Nexus, I get about ~40fps. While that would usually be a decent framerate, my game is a rather fast paced game with a gamepad. Because of this, it feels very unsatisfying to play when not capped at 60fps. Are there frameworks out there that can improve performance without toning down on graphics? Or is there something I could do myself without necessarily having to use a framework? I've looked over the basic things such as sticking to integer coordinates, but I didn't see an increase in performance whatsoever? I did some testing with jsperf and results were virtually identical. Does this depend more on the browser?

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• Is it possible to use 3G internet for a TCP/IP game server?

  - by Amit Ofer

  I'm working on a turned based multiplayer android game with a friend. I started working on the game server and client using socket programming. I found a few tutorials on how to implement a basic chat on android and I started extending that example to suit my needs. Basically the game is really simple and the communication only include sending a few string from the client to the server every turn and sending the calculated scores back to all the clients after each turn. the idea is that one of the players creates the game and thus initialize the server, and each player connects to this client using ip. I tried this solution and it seems to work great when all the players are using the same wifi connection or by using router port forwarding. The problem is when trying to use 3G internet for the server, I guess the problem is that 3G ip address isn't global and you can't use port forwarding there, correct me if I'm wrong here. Is there a way to overcome this issue? or the only solution is to limit my game to wifi only or think of a different solution than the standard socket programming solution? I.E web server etc. what do you think would be the best approach here? Thanks.

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• Grid based collision - How many cells?

  - by Fibericon

  The game I'm creating is a bullet hell game, so there can be quite a few objects on the screen at any given time. It probably maxes out at about 40 enemies and 200 or so bullets. That being said, I'm splitting up the playing field into a grid for my collision checking. Right now, it's only 8 cells. How many would be optimal? I'm worried that if I use too many, I'll be wasting CPU power. My main concern is processing power, to make the game run smoothly. RAM is not a big concern for me.

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• String Conversion to Char for Java Game

  - by Jen

  Is there someone who could help me achieve the following points on this problems? I can't seem to get it. I tried using toCharArray and Scanner to achieve this, but it doesn't work, nor do I know how to make this things possible for my word game. :( · Get a popular name of person, place, verse, saying or event from the user. This may have a single or multiple words in it. · Create a copy of this string to an array where each letter is replaced with a hyphen (-) and each space is replaced with an underscore (_). Symbols and numbers will remain shown. · The program then asks a letter from the user. If the letter is in the inputted string, then it should be shown on the array at the same position it is shown in the string. Meaning, the letter replaces the hyphen (-) at the correct position of the array. · The program again prompts for a letter from the user and replaces the hyphen (-) of the array if it exists on the inputted string. This will be repeatedly done until such time each hyphen (-) is replaced with the correct letter. · If the user inputs an invalid letter, that is, a letter that does not exist on the inputted string, then the program should inform the user. If this happens 3 times while there is still at least one hyphen on the array, then the program should inform the user that he lost the game and showing him the whole correct string. · If the user completes the game, meaning, all hyphens have been replaced with the correct letters; then the program should congratulate the user for a job well done.

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• How do I clip an image in OpenGL ES on Android?

  - by Maxim Shoustin

  My game involves "wiping off" an image by touch: After moving a finger over it, it looks like this: At the moment, I'm implementing it with Canvas, like this: 9Paint pTouch; 9int X = 100; 9int Y = 100; 9Bitmap overlay; 9Canvas c2; 9Rect dest; pTouch = new Paint(Paint.ANTI_ALIAS_FLAG); pTouch.setXfermode(new PorterDuffXfermode(Mode.SRC_OUT)); pTouch.setColor(Color.TRANSPARENT); pTouch.setMaskFilter(new BlurMaskFilter(15, Blur.NORMAL)); overlay = BitmapFactory.decodeResource(getResources(),R.drawable.wraith_spell).copy(Config.ARGB_8888, true); c2 = new Canvas(overlay); dest = new Rect(0, 0, getWidth(), getHeight()); Paint paint = new Paint();9 paint.setFilterBitmap(true); ... @Override protected void onDraw(Canvas canvas) { ... c2.drawCircle(X, Y, 80, pTouch); canvas.drawBitmap(overlay, 0, 0, null); ... } @Override 9public boolean onTouchEvent(MotionEvent event) { switch (event.getAction()) { case MotionEvent.ACTION_DOWN: case MotionEvent.ACTION_MOVE: { X = (int) event.getX(); Y = (int) event.getY();9 invalidate(); c2.drawCircle(X, Y, 80, pTouch);9 break; } } return true; ... What I'm essentially doing is drawing transparency onto the canvas, over the red ball image. Canvas and Bitmap feel old... Surely there is a way to do something similar with OpenGL ES. What is it called? How do I use it? [EDIT] I found that if I draw an image and above new image with alpha 0, it goes to be transparent, maybe that direction? Something like: gl.glColor4f(0.0f, 0.0f, 0.0f, 0.01f);

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• Detecting tile with height in isometric game

  - by Carlos Navarro

  I'm trying to create an isometric tile-based game (for iPhone) and I'm having trouble with height in tiles. What I currently do (without heights) is apply some mathematic transformations to my 2D-matrix (which represent the tiles) so that I know where in the screen (x,y) should I place the isometric tile. Then, when the user clicks somewhere in the screen, I take that values and pass them through a function (kind of f^-1) to get which tile it belongs to. This works perfectly. My problem is: imagine that I want some tiles to have a different height from others. In order to draw the tile itself its pretty simple, since the z-coordinate has no transformation in the isometric approach used in games (z'=z). BUT what if I want to calculate the tile coordinate (defined by X-tile and Y-tile) from the touch coordinates (x,y)? Any guess?

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• How can I make Maya export a mesh as double-sided?

  - by bobobobo

  I'm exporting from Maya 2009 to OBJ. The mesh I'm exporting has in it's Render Stats "Double Sided" checked, but when the polygon is exported, only a single side is actually exported. What really needs to happen is for each polygon that is double sided, two polygons need to be exported, facing in opposite directions.. I can do this manually, but is there a way to make the OBJ exporter do it for me?

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• Ouya / Android : button mapping biwise

  - by scorvi

  I am programming a game with the Gameplay3d Engine. But the Android site has no gamepad support and that is what I need to port my game to Ouya. So I implemented a simple gamepad support and it supports 2 gamepads. So my problem is that I put the button stats in a float array for every gamepad. But the Gameplay3d engine saves their stats in a unsigned int _buttons variable. It is set with bitwise operations and I have no clue how to translate my array to this.

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• Adding root bone in 3DS Max?

  - by carlturtle

  my animation artist has made me a nice first person pair of arms, animated it, textured it, and given it to me. Then he went on vacation. I am programming my animations, and I am trying to test the model he has given me. Building my project gives me a warning: Multiple skeletons were found in the file. The first skeleton, named "frame l upperarm" has been moved to be a child of the scene root. The other, "frame r upperarm", will be ignored. Fragment identifier "frame r upperarm". Then an error: "Vertex is bound to bone "frame l forearm", but this bone is not present in the skeleton." I realize this means that there are two skeletons, as said in this problem: Importing 3d model with multiple skeletons I have 3DS Max, but I have no idea how to use it, and Google/CGTalk/Plycount turn up nothing relevant on how to add a root bone or combine skeletons. If anyone knows how, it would help me out greatly. Thanks.

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• Particle trajectory smoothing: where to do the simulation?

  - by nkint

  I have a particle system in which I have particles that are moving to a target and the new targets are received via network. The list of new target are some noisy coordinates of a moving target stored in the server that I want to smooth in the client. For doing the smoothing and the particle I wrote a simple particle engine with standard euler integration model. So, my pseudo code is something like that: # pseudo code class Particle: def update(): # do euler motion model integration: # if the distance to the target is more than a limit # add a new force to the accelleration # seeking the target, # and add the accelleration to velocity # and velocity to the position positionHistory.push_back(position); if history.length > historySize : history.pop_front() class ParticleEngine: particleById = dict() # an associative array # where the keys are the id # and particle istances are sotred as values # this method is called each time a new tcp packet is received and parsed def setNetTarget(int id, Vec2D new_target): particleById[id].setNewTarget(new_target) # this method is called each new frame def draw(): for p in particleById.values: p.update() beginVertex(LINE_STRIP) for v in p.positionHistory: vertex(v.x, v.y) endVertex() The new target that are arriving are noisy but setting some accelleration/velocity parameters let the particle to have a smoothed trajectories. But if a particle trajectory is a circle after a while the particle position converge to the center (a normal behaviour of euler integration model). So I decided to change the simulation and use some other interpolation (spline?) or smooth method (kalman filter?) between the targets. Something like: switch( INTERPOLATION_MODEL ): case EULER_MOTION: ... case HERMITE_INTERPOLATION: ... case SPLINE_INTERPOLATION: ... case KALMAN_FILTER_SMOOTHING: ... Now my question: where to write the motion simulation / trajectory interpolation? In the Particle? So I will have some Particle subclass like ParticleEuler, ParticleSpline, ParticleKalman, etc..? Or in the particle engine?

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• Creating new games on Android and/or iPhone

  - by James Clifton

  I have a succesfull facebook poker game that is running very nicely, now some people have asked if I can port this to other platforms - mainly mobile devices (and I have been asked to make a tablet version, do I really need a seperate version?) I am currently a PHP programmer (and game designer) and I simply dont' have the time to learn Android and other languages - so I have decided to pay third parties to program them (if viable). The information I need to know is what programming language is needed for the following four devices - Android mobile phone, iPhone, iPad and tablets? Can they all run off a central sql database? If they can't then i'm not interested :( Do any of these run FLASH? Have I covered all my main bases here? For example if a person programs for a ANDROID mobile phone is that to much differant to an ANDROID tablet? They will have slightly differant graphics (because the tablet has a greater screen area might as well use it) but do they need to be started from scratch? Same goes for iPhone/iPad, do they really need to be programmed differantly if the only differance is the graphics?

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• Library For Opengl 1.4?

  - by Robinson Joaquin

  My netbook only supports openGL version 1.4, my GPU is intel gma 3150, so for you what is the best library/tools to use or somewhat great move to make/advice, there are no wrong answers, (I am trying to create a game) PS: I already check the net for resources but, opengl (redbook) 4th edition is scarce (and redbook for v1.1 is already deprecated and is very OLD than what I'm looking for), besides I don't have money to buy a new laptop or a opengl book from online shop because international delivery is very expensive, I'm from outside US.

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• Problem with boundary collision

  - by James Century

  The problem: When the player hits the left boundary he stops (this is exactly what I want), when he hits the right boundary. He continues until his rectangle's left boundary meets with the right boundary. Outcome: https://www.youtube.com/watch?v=yuJfIWZ_LL0&feature=youtu.be My Code public class Player extends GameObject{ BufferedImageLoader loader; Texture tex = Game.getInstance(); BufferedImage image; Animation playerWalkLeft; private HealthBarManager healthBar; private String username; private int width; private ManaBarManager manaBar; public Player(float x, float y, ObjectID ID) { super(x, y, ID, null); loader = new BufferedImageLoader(); playerWalkLeft = new Animation(5,tex.player[10],tex.player[11],tex.player[12],tex.player[13],tex.player[14],tex.player[15],tex.player[17],tex.player[18]); } public void tick(LinkedList<GameObject> object) { setX(getX()+velX); setY(getY()+velY); playerWalkLeft.runAnimation(); } public void render(Graphics g) { g.setColor(Color.BLACK); FontMetrics fm = g.getFontMetrics(g.getFont()); if(username != null) width = fm.stringWidth(username); if(username != null){ g.drawString(username,(int) x-width/2+15,(int) y); } if(velX != 0){ playerWalkLeft.drawAnimation(g, (int)x, (int)y); }else{ g.drawImage(tex.player[16], (int)x, (int)y, null); } g.setColor(Color.PINK); g.drawRect((int)x,(int)y,33,48); g.drawRect(0,0,(int)Game.getWalkableBounds().getWidth(), (int)Game.getWalkableBounds().getHeight()); } @SuppressWarnings("unused") private Image getCurrentImage() { return image; } public float getX() { return x; } public float getY() { return y; } public void setX(float x) { Rectangle gameBoundry = Game.getWalkableBounds(); if(x >= gameBoundry.getMinX() && x <= gameBoundry.getMaxX()){ this.x = x; } } public void setY(float y) { //IGNORE THE SetY please. this.y = y; } public float getVelX() { return velX; } public void setHealthBar(HealthBarManager healthBar){ this.healthBar = healthBar; } public HealthBarManager getHealthBar(){ return healthBar; } public float getVelY() { return velY; } public void setVelX(float velX) { this.velX = velX; } public void setVelY(float velY) { this.velY = velY; } public ObjectID getID() { return ID; } public void setUsername(String playerName) { this.username = playerName; } public String getUsername(){ return this.username; } public void setManaBar(ManaBarManager manaBar) { this.manaBar = manaBar; } public ManaBarManager getManaBar(){ return manaBar; } public int getLevel(){ return 1; } public boolean isPlayerInsideBoundry(float x, float y){ Rectangle boundry = Game.getWalkableBounds(); if(boundry.contains(x,y)){ return true; } return false; } } What I've tried: - Using a method that checks if the game boundary contains player boundary rectangle. This gave me the same result as what the check statement in my setX did.

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• Previewing a Demo Level in Mobile for UDK?

  - by Reno Yeo

  I've already clicked on "Emulate Mobile Features" and everything has been compiled. I've also set the mobile previewer settings to iPhone 4's dimensions and features. However, when i click on the mobile previewer, a new window pops up but it goes into a "Not Responding" mode after a while. Is there anything I'm doing wrong? To be honest, I'm afraid of the difficulty curve required in learning UDK, but I am interested in developing a game for it.

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• Understanding dot notation

  - by Starkers

  Here's my interpretation of dot notation: a = [2,6] b = [1,4] c = [0,8] a . b . c = (2*6)+(1*4)+(0*8) = 12 + 4 + 0 = 16 What is the significance of 16? Apparently it's a scalar. Am I right in thinking that a scalar is the number we times a unit vector by to get a vector that has a scaled up magnitude but the same direction as the unit vector? So again, what is the relevance of 16? When is it used? It's not the magnitude of all the vectors added up. The magnitude of all of them is calculated as follows: sqrt( ax * ax + ay * ay ) + sqrt( bx * bx + by * by ) + sqrt( cx * cx + cy * cy) sqrt( 2 * 2 + 6 * 6 ) + sqrt( 1 * 1 + 4 * 4 ) + sqrt( 0 * 0 + 8 * 8) sqrt( 4 + 36 ) + sqrt( 1 + 16 ) + sqrt( 0 + 64) sqrt( 40 ) + sqrt( 17 ) + sqrt( 64) 6.3 + 4.1 + 8 10.4 + 8 18.4 So I don't really get this diagram: Attempting with sensible numbers: a = [1,0] b = [4,3] a . b = (1*0) + (4*3) = 0 + 12 = 12 So what exactly is a . b describing here? The magnitude of that vector? Because that isn't right: the 'a.b' vector = [4,0] sqrt( x*x + y*y ) sqrt( 4*4 + 0*0 ) sqrt( 16 + 0 ) 4 So what is 12 describing?

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