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• Arbitrary projection matrix from 6 arbitrary frustum planes

  - by Doub

  A projection matrix represent a tranformation from the camera view space to the rendering system clip space. In other words, it defines the transormation between a 6-sided frustum to the clip cube. The glOrtho and glFrustum use only 6 parameter to define such a projection, but impose several constraints on the frustum that will get projected to the clip cube: the near and far planes are parallel, the left and right planes intersect on a vertical line, and the top and bottom planes intersect on a horizontal lines, both lines being parallel to the near and far planes. I'd like to lift these restrictions. So, from the definition of the 6 frustum side planes (in whatever representation you see fit), how can I compute a general projection matrix?

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• Can't remove JPanel from JFrame while adding new class into it

  - by A.K.

  Basically, I have my Frame class, which instantiates all the properties for the JFrame, and draws a JLabel with an image (my title screen). Then I made a separate JPanel with a start button on it, and made a mouse listener that will allow me to remove these objects while adding in a new Board() class (Which paints the main game). *Note: The JLabel is SEPARATE from the JPanel, but it still gets moved to the side by it. Problem: Whenever I click the button though, it only shows a little square of what I presume is my board class trying to run. Code below for the Frame Class: package OurPackage; //Made By A.K. 5/24/12 //Contains Frame. import java.awt.BorderLayout; import java.awt.Color; import java.awt.Container; import java.awt.Dimension; import java.awt.Graphics; import java.awt.Graphics2D; import java.awt.GridBagLayout; import java.awt.GridLayout; import java.awt.Image; import java.awt.Rectangle; import java.awt.event.ActionEvent; import java.awt.event.ActionListener; import java.awt.event.KeyEvent; import java.awt.event.MouseAdapter; import java.awt.event.MouseEvent; import java.awt.event.MouseListener; import javax.swing.*; import javax.swing.plaf.basic.BasicOptionPaneUI.ButtonActionListener; public class Frame implements MouseListener { public static boolean StartGame = false; ImageIcon img = new ImageIcon(getClass().getResource("/Images/ActionJackTitle.png")); ImageIcon StartImg = new ImageIcon(getClass().getResource("/Images/JackStart.png")); public Image Title; JLabel TitleL = new JLabel(img); public JPanel panel = new JPanel(); JButton StartB = new JButton(StartImg); JFrame frm = new JFrame("Action-Packed Jack"); public Frame() { TitleL.setPreferredSize(new Dimension(1200, 420)); frm.add(TitleL); frm.setLayout(new GridBagLayout()); frm.add(panel); panel.setSize(new Dimension(220, 45)); panel.setLayout(new GridBagLayout ()); panel.add(StartB); StartB.addMouseListener(this); StartB.setPreferredSize(new Dimension(220, 45)); frm.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE); frm.setSize(1200, 420); frm.setVisible(true); frm.setResizable(false); frm.setLocationRelativeTo(null); } public static void main(String[] args) { new Frame(); } public void mouseClicked(MouseEvent e) { StartB.setContentAreaFilled(false); panel.remove(StartB); frm.remove(panel); frm.remove(TitleL); //frm.setLayout(null); frm.add(new Board()); //Add Game "Tiles" Or Content. x = 1200 frm.validate(); System.out.println("Hit!"); } @Override public void mouseEntered(MouseEvent arg0) { // TODO Auto-generated method stub } @Override public void mouseExited(MouseEvent arg0) { // TODO Auto-generated method stub } @Override public void mousePressed(MouseEvent arg0) { // TODO Auto-generated method stub } @Override public void mouseReleased(MouseEvent arg0) { // TODO Auto-generated method stub } }

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• Collision Detection for a 2D RPG

  - by PHMitrious

  First of all, I have done some research on this topic before asking, and I'm asking this question as a mean to get some opinions on this topic, so I don't make a decision only on my own, but taking into account other people's experience as well. I'm starting a 2D online RPG project. I am using SFML for graphics and input and I'm creating a basic game structure and all for the game, creating modules for each part of the game. Well, let me get to the point I just wanted to give you guys some context. I want to decide on how I'm going to work with collision detection. Well I'm kinda going to work on maps with a tile map divided in layers (as usual) and add an extra 2 layers - not exactly in the map - for objects. So I'll have collisions between objects and agents (players - npcs - monsters - spells etc) and agents and tiles. The seconds one can be easily solved the first one need a little bit of work. I considered both creating a basic collision test engine using polygons and a quadtree to diminish tests since I'm going to be working with big maps with lots of objects - creating both a physical and graphical world representation. And I also considered using a physics engine like Box2D for collision tests. I think the first approach would take more work on my part but the second one would have the overhead of using a whole physics engine for just collision detection and no physics. What do you guys think ?

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• Point[] and Tri not "could not be found"

  - by Craig Dannehl

  Hi I'm trying to learn how to load a .obj file using OpenTK in windows Forms. I have seen a lot of examples out there, but I do see almost everyone uses List, and Point[]. Code example show these highlighted like there IDE know what these are; for example List<Tri> tris = new List<Tri>(); but mine just returns "The type or namespace name 'Tri' could not be found" is there an include I need to add or a using I am missing. Currently have this using System; using System.Collections.Generic; using System.Linq; using System.Text; using System.IO; using System.Drawing; using OpenTK; using OpenTK.Graphics; using OpenTK.Graphics.OpenGL;

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• Input Handling and Game loop

  - by Bob Coder

  So, I intercept the WM_KEYDOWN and other messages. Thing is, my game can't/shouldn't react to these messages just yet, since my game might be currently drawing to the screen or in the middle of updating my game entities. So the idea is to keep a keyboardstate and mousestate, which is updated by the part of my code that intercepts the windows messages. These states just keep track of which keys/buttons are currently pressed. Then, at the start of my game's update function, I access these keyboard and mouse states and my game reacts to the user input. Now, which is the best way to access these states? I assume that windows messages can be sent whenever, so the keyboard/mouse states are constantly being edited. Accessing say a list of currently pressed keys in the keyboard state the same time another part of the code is editing the list would cause problems. Should I make a deep copy of a state and act on that? How would I deal with the garbage generated though, this would take place every frame.

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• XNA C# Rectangle Intersect Ball on a Square

  - by user2436057

  I made a Game like Peggle Deluxe using C# and XNA for lerning. I have 2 rectangles a ball and a square field. The ball gets shoot out with a cannon and if the Ball hits the Square the Square disapears and the Ball flys away.But the Ball doesent spring of realistically, it sometimes flys away in a different direction or gets stuck on the edge. Thads my Code at the moment: public void Update(Ball b, Deadline dl) { ArrayList listToDelete = new ArrayList(); foreach (Field aField in allFields) { if (aField.square.Intersects(b.ballhere)) { listToDelete.Add(aField); Punkte = Punkte + 100; float distanceX = Math.Abs(b.ballhere.X - aField.square.X); float distanceY = Math.Abs(b.ballhere.Y - aField.square.Y); if (distanceX < distanceY) { b.myMovement.X = -b.myMovement.X; } else { b.myMovement.Y = -b.myMovement.Y; } } } It changes the X or Y axis depending on how the ball hits the Square but not everytimes. What could cause the problem? Thanks for your answer. Greetings from Switzerland.

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• Automatically zoom out the camera to show all players (XNA)

  - by user36159

  I am building a game in XNA that takes place in a rectangular arena. The game is multiplayer and each player may go where they like within the arena. The camera is a persepective camera that looks directly downwards. The camera should be automatically repositioned based on the game state. Currently, the xy position is a weighted sum of the xy positions of important entities. I would like the camera's z position to be calculated from the xy coordinates so that it zooms out to the point where all important entities are visible. My current approach is to: hw = the greatest x distance from the camera to an important entity hh = the greatest y distance from the camera to an important entity Calculate z = max(hw / tan(FoVx), hh / tan(FoVy)) My code seems to almost work as it should, but the resulting z values are always too low by a factor of about 4. Any ideas?

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• OpenGL ES 2 on Android: native window

  - by ThreaderSlash

  According to OGLES specification, we have the following definition: EGLSurface eglCreateWindowSurface(EGLDisplay display, EGLConfig config, NativeWindowType native_window, EGLint const * attrib_list) More details, here: http://www.khronos.org/opengles/documentation/opengles1_0/html/eglCreateWindowSurface.html And also by definition: int32_t ANativeWindow_setBuffersGeometry(ANativeWindow* window, int32_t width, int32_t height, int32_t format); More details, here: http://mobilepearls.com/labs/native-android-api I am running Android Native App on OGLES 2 and debugging it in a Samsung Nexus device. For setting up the 3D scene graph environment, the following variables are defined: struct android_app { ... ANativeWindow* window; }; android_app* mApplication; ... mApplication=&pApplication; And to initialize the App, we run the commands in the code: ANativeWindow_setBuffersGeometry(mApplication->window, 0, 0, lFormat); mSurface = eglCreateWindowSurface(mDisplay, lConfig, mApplication->window, NULL); Funny to say is that, the command ANativeWindow_setBuffersGeometry behaves as expected and works fine according to its definition, accepting all the parameters sent to it. But the eglCreateWindowSurface does no accept the parameter mApplication-window, as it should accept according to its definition. Instead, it looks for the following input: EGLNativeWindowType hWnd; mSurface = eglCreateWindowSurface(mDisplay,lConfig,hWnd,NULL); As an alternative, I considered to use instead: NativeWindowType hWnd=android_createDisplaySurface(); But debugger says: Function 'android_createDisplaySurface' could not be resolved Is 'android_createDisplaySurface' compatible only for OGLES 1 and not for OGLES 2? Can someone tell if there is a way to convert mApplication-window? In a way that the data from the android_app get accepted to the window surface?

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• How to effectively gather info about how players play my HTML5 game?

  - by Bane

  I'm finishing another HTML5 game, and this time I'd like to do some spying business on the players... Mostly just basic stuff: when they are playing, for how long, what upgrades they are buying the most and so on. Now, my first idea was just to collect this information during the gameplay, and then have a Javascript function fire when they close the tab/browser, and said function would send it to my server via Socket.io. This, of course, wouldn't work, because anyone who takes a look at the code would realize it and could start sending a tonne of false info which would mess up my statistics. Questions: Is there a way to effectively do this? If yes, what kind of info should I be looking for, aside from stuff I already mentioned?

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• getting bone base and tip positions from a transform matrix?

  - by ddos

  I need this for a Blender3d script, but you don't really need to know Blender to answer this. I need to get bone head and tip positions from a transform matrix read from a file. The position of base is the location part of the matrix, length of the bone (distance from base to tip) is the scale, position of the tip is calculated from the scale (distance from bone base) and rotation part of the matrix. So how to calculate these? bone.base([x,y,z]) # x,y,z - floats bone.tip([x,y,z])

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• Interactive Fiction engine and Tech Support - has anyone done this? [on hold]

  - by Larry G. Wapnitsky

  I've always been a big fan of Interactive Fiction and have been wanting to try my hand at it for a while. I have a need to create a decision tree for my tech support group (L1-L3) and feel as though presenting a decision tree in the form of an IF game would be rather interesting and helpful. I plan on using Inform7, but am curious if anyone has done anything like this in the past. If so, can you present examples, links to examples, opinions? Thanks, Larry

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• Direct2D Transform

  - by James

  I have a beginner question about Direct2D transforms. I have a 20 x 10 bitmap that I would like to draw in different orientations. To start, I would like to draw it vertically with a destination rectangle of say: (left, top, right, bottom) (300, 300, 310, 320) The bitmap is wider than it is tall (20 x 10), but when I draw it vertically, it will be appear taller than it is wide (10 x 20). I know that I can use a rotation matrix like so: m_pRenderTarget->SetTransform( D2D1::Matrix3x2F::Rotation( 90.0f, D2D1::Point2F(<center of shape>)) ); But when I use this method to rotate my shape, the destination rectangle is still wider than it is tall. Maybe it would look something like this: (left, top, right, bottom) (280, 290, 300, 300) The destination rectangle is 20 x 10 but the bitmap appears on the screen as 10 x 20. I can't look at the destination rectangle in the debugger and compare it to: (left, top, right, bottom) (300, 300, 310, 320) Is there any simple way to say "I want to rotate it so that the image is rendered to exactly this destination rectangle after the rotation?" In this case, I would like to say "Please rotate the bitmap so that it appears on the screen at this location:" (left, top, right, bottom) (300, 300, 310, 320) If I can't do that, is there any way to find out the 10 x 20 destination rectangle where the bitmap is actually being rendered to the screen?

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• Procedural world generation oriented on gameplay features

  - by Richard Fabian

  In large procedural landscape games, the land seems dull, but that's probably because the real world is largely dull, with only limited places where the scenery is dramatic or tactical. Looking at world generation from this point of view, a landscape generator for a game (that is, not for the sake of scenery, but for the sake of gameplay) needs to not follow the rules of landscaping, but instead some rules married to the expectations of the gamer. For example, there could be a choke point / route generator that creates hills ravines, rivers and mountains between cities, rather than the natural way cities arise, scattered on the land based on resources or conditions generated by the mountains and rainfall patterns. Is there any existing work being done like this? Start with cities or population centres and then add in terrain afterwards? The reason I'm asking is that I'd previously pondered taking existing maps from fantasy fiction (my own and others), putting the information into the system as a base point, and then generating a good world to play in from it. This seems covered by existing technology, that is, where the designer puts in all the necessary information such as the city populations, resources, biomes, road networks and rivers, then allows the PCG fill in the gaps. But now I'm wondering if it may be possible to have a content generator generate also the overall design. Generate the cities and population centres, balancing them so that there is a natural seeming need of commerce, then generate the positions and connectivity, then from the type of city produce the list of necessary resources that must be nearby, and only then, maybe given some rules on how to make the journey between cities both believable and interesting, generate the final content including the roads, the choke points, the bridges and tunnels, ferries and the terrain including the biomes and coastline necessary. If this has been done before, I'd like to know, and would like to know what went wrong, and what went right.

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• Calculate gears rotation for a realtime simulation

  - by nkint

  Hi I'm trying to do a game with real time simulations of gears. There is a big Gear with inside a smaller gear. I managed to draw gears with different diameters but equal size teeth, but if i try to move the smaller one inside the bigger one the movement is odd. see the animated gif. the biggest gear is in center C1 and the small in the center C2. I calculate C2 position in this way: C2.x = C1.x + C1_RADIUS-C2_RADIUS) * cos(t); C2.y = C1.y - C1_RADIUS-C2_RADIUS) * sin(t); for t that goes from 0 to TWO_PI in n steps. I apply as rotation the angle t, but maybe it is wrong and i have to calculate another rotation for get a perfect joint

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• How to Align Gun with Bullets

  - by Shane

  I have a top-down 2D shooter. I have an image of a player holding a gun, that rotates to face the mouse. Please note that the gun isn't a separate image tethered to the player, but rather part of the player. Right now, bullets are created at the player's x and y. This works when the player is facing the right way, but not when they rotate. The bullets move in the right direction, but don't come from the gun. How can I fix this? TL;DR: When the player rotates, bullets don't come from gun. public void fire() { angle = sprite.getRotation(); System.out.println(angle); x = sprite.getX(); y = sprite.getY(); Bullet b = new Bullet(x, y, angle); Utils.world.addBullet(b); }

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• Running multiple box2D world objects on a server

  - by CharbelAbdo

  I'm creating a multiplayer game using LibGdx (with Box2d) and Kryonet. Since this is the first time I work on multiplayer games, I read a bit about server - client implementations, and it turns out that the server should handle important tasks like collision detection, hits, characters dying etc... Based on some articles (like the excellent Gabriel Gambetta Fast paced multiplayer series), I also know that the client should work in parallel to avoid the lag while the server responds to commands. Physics wise, each game will have 2 players, and any projectiles fired. What I'm thinking of doing is the following: Create a physics world on the client When the game is signaled to start, I create the same physics world on the server (without any rendering obviously). Whenever the player issues a command (move or fire), I send the command to the server and immediately start processing it on the client. When the server receives the command, it applies it on the server's world (set velocity etc...) Each 100ms, the server sends the new state to the client which corrects what was calculated locally. Any critical action (hit, death, level up) is calculated only on the server and sent to the client. Essentially, I would have a Box2d World object running on the server for each game in progress, in sync with the worlds running on the clients. The alternative would be to do my own calculations on the server instead of relying on Box2D to do them for me, but I'm trying to avoid that. My question is: Is it wise to have, for example, 1000 instances of the World object running and executing steps on the server? Tomcat used around 750 MBytes of memory when trying it without any object added to the world. Anybody tried that before? If not, is there any alternative? Google did not help me, are there any guidelines to use when you want to have physics on both the client and the server? Thanks for any help.

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• Good 3D Game Engine for the Horror Genre [on hold]

  - by James Wassall

  I am starting to think about and design (pencil drawings) a simple, horror game. I'm in need of a good engine which supports features like Dynamic Lighting (for a characters flashlight) and dynamic shadows. My first choice was obviously Unity3D, as its free and is (supposedly) the easiest to use. However, I believe that a lot of features are locked for the Pro version (a $1500 investment). Is there any good, free engines that support dynamic events? I have read a lot of posts recommending the Source engine but I don't want to make a mod, I would like to make a fully featured standalone game. I'm not looking for opinions on "Which engine you prefer" or "Which engine do you use", all I would like is to be presented with the facts. -James

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• 2D Grid based game - how should I draw grid lines?

  - by Adam K Dean

  I'm playing around with a 2D grid based game idea, and I am using sprites for the grid cells. Let's say there is a 10 x 10 grid and each cell is 48x48, which will have sprites drawn there. That is fine. But in design mode, I'd like to have a grid overlay the screen. I can do this either with sprites (2x600 pixel image etc) or with primitives, but which is best? Should I really be switching between sprites and 3d/2d rendering? Like so: Thanks!

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• Is there a way to export all the images of my tweening effect in Flash?

  - by Paul

  i'm using Flash to create the animation of my character in 2D (i'm just beginning). Is it possible to make a tween effect of a character, and then automatically export all the images/frames? So far, it's a bit fastidious : i create my tweening effect, then i put a keyframe for each frame i want to copy and paste, then i select the movieclips and shapes and copy and paste them into another flash document, i position those clips at the exact same location as the previous image, then i erase the previous image and export the image... For 30 frames! Is there any faster way? Thanks

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• How do I have to take into account the direction in which the camera is facing when creating a first person strafe (left/right) movement

  - by Chris

  This is the code I am currently using, and it works great, except for the strafe always causes the camera to move along the X axis which is not relative to the direction in which the camera is actually facing. As you can see currently only the x location is updated: [delta * -1, 0, 0] How should I take into account the direction in which the camera is facing (I have the camera's target x,y,z) when creating a first person strafe (left/right) movement? case 'a': var eyeOriginal = g_eye; var targetOriginal = g_target; var viewEye = g_math.subVector(g_eye, g_target); var viewTarget = g_math.subVector(g_target, g_eye); viewEye = g_math.addVector([delta * -1, 0, 0], viewEye); viewTarget = g_math.addVector([delta * -1, 0, 0], viewTarget); g_eye = g_math.addVector(viewEye, targetOriginal); g_target = g_math.addVector(viewTarget, eyeOriginal); break; case 'd': var eyeOriginal = g_eye; var targetOriginal = g_target; var viewEye = g_math.subVector(g_eye, g_target); var viewTarget = g_math.subVector(g_target, g_eye); viewEye = g_math.addVector([delta, 0, 0], viewEye); viewTarget = g_math.addVector([delta, 0, 0], viewTarget); g_eye = g_math.addVector(viewEye, targetOriginal); g_target = g_math.addVector(viewTarget, eyeOriginal); break;

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• How do I cap rendering of tiles in a 2D game with SDL?

  - by farmdve

  I have some boilerplate code working, I basically have a tile based map composed of just 3 colors, and some walls and render with SDL. The tiles are in a bmp file, but each tile inside it corresponds to an internal number of the type of tile(color, or wall). I have pretty basic collision detection and it works, I can also detetc continuous presses, which allows me to move pretty much anywhere I want. I also have a moving camera, which follows the object. The problem is that, the tile based map is bigger than the resolution, thus not all of the map can be displayed on the screen, but it's still rendered. I would like to cap it, but since this is new to me, I pretty much have no idea. Although I cannot post all the code, as even though I am a newbie and the code pretty basic, it's already quite a few lines, I can post what I tried to do void set_camera() { //Center the camera over the dot camera.x = ( player.box.x + DOT_WIDTH / 2 ) - SCREEN_WIDTH / 2; camera.y = ( player.box.y + DOT_HEIGHT / 2 ) - SCREEN_HEIGHT / 2; //Keep the camera in bounds. if(camera.x < 0 ) { camera.x = 0; } if(camera.y < 0 ) { camera.y = 0; } if(camera.x > LEVEL_WIDTH - camera.w ) { camera.x = LEVEL_WIDTH - camera.w; } if(camera.y > LEVEL_HEIGHT - camera.h ) { camera.y = LEVEL_HEIGHT - camera.h; } } set_camera() is the function which calculates the camera position based on the player's positions. I won't pretend I know much about it. Rectangle box = {0,0,0,0}; for(int t = 0; t < TOTAL_TILES; t++) { if(box.x < (camera.x - TILE_WIDTH) || box.y > (camera.y - TILE_HEIGHT)) apply_surface(box.x - camera.x, box.y - camera.y, surface, screen, &clips[tiles[t]]); box.x += TILE_WIDTH; //If we've gone too far if(box.x >= LEVEL_WIDTH) { //Move back box.x = 0; //Move to the next row box.y += TILE_HEIGHT; } } This is basically my render code. The for loop loops over 192 tiles stored in an int array, each with their own unique value describing the tile type(wall or one of three possible colored tiles). box is an SDL_Rect containing the current position of the tile, which is calculated on render. TILE_HEIGHT and TILE_WIDTH are of value 80. So the cap is determined by if(box.x < (camera.x - TILE_WIDTH) || box.y > (camera.y - TILE_HEIGHT)) However, this is just me playing with the values and see what doesn't break it. I pretty much have no idea how to calculate it. My screen resolution is 1024/768, and the tile map is of size 1280/960.

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• Can't get sprite to rotate correctly?

  - by rphello101

  I'm attempting to play with graphics using Java/Slick 2d. I'm trying to get my sprite to rotate to wherever the mouse is on the screen and then move accordingly. I figured the best way to do this was to keep track of the angle the sprite is at since I have to multiply the cosine/sine of the angle by the move speed in order to get the sprite to go "forwards" even if it is, say, facing 45 degrees in quadrant 3. However, before I even worry about that, I'm having trouble even getting my sprite to rotate in the first place. Preliminary console tests showed that this code worked, but when applied to the sprite, it just kind twitches. Anyone know what's wrong? int mX = Mouse.getX(); int mY = HEIGHT - Mouse.getY(); int pX = sprite.x; int pY = sprite.y; int tempY, tempX; double mAng, pAng = sprite.angle; double angRotate=0; if(mX!=pX){ tempY=pY-mY; tempX=mX-pX; mAng = Math.toDegrees(Math.atan2(Math.abs((tempY)),Math.abs((tempX)))); if(mAng==0 && mX<=pX) mAng=180; } else{ if(mY>pY) mAng=270; else mAng=90; } //Calculations if(mX<pX&&mY<pY){ //If in Q2 mAng = 180-mAng; } if(mX<pX&&mY>pY){ //If in Q3 mAng = 180+mAng; } if(mX>pX&&mY>pY){ //If in Q4 mAng = 360-mAng; } angRotate = mAng-pAng; sprite.angle = mAng; sprite.image.setRotation((float)angRotate);

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• How do I tackle top down RPG movement?

  - by WarmWaffles

  I have a game that I am writing in Java. It is a top down RPG and I am trying to handle movement in the world. The world is largely procedural and I am having a difficult time tackling how to handle character movement around the world and render the changes to the screen. I have the world loaded in blocks which contains all the tiles. How do I tackle the character movement? I am stumped and can't figure out where I should go with it. EDIT: Well I was abstract with the issue at hand. Right now I can only think of rigidly sticking everything into a 2D array and saving the block ID and the player offset in the Block or I could just "float" everything and move about between tiles so to speak.

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• Fast software color interpolating triangle rasterization technique

  - by Belgin

  I'm implementing a software renderer with this rasterization method, however, I was wondering if there is a possibility to improve it, or if there exists an alternative technique that is much faster. I'm specifically interested in rendering small triangles, like the ones from this 100k poly dragon: As you can see, the method I'm using is not perfect either, as it leaves small gaps from time to time (at least I think that's what's happening). I don't mind using assembly optimizations. Pseudocode or actual code (C/C++ or similar) is appreciated. Thanks in advance.

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• 2D shader to draw representation of rotating sphere.

  - by TheBigO

  I want to display a 3D textured sphere, and then rotate it in one direction. The direction will never change, and the camera will never move. One way is to actually create a spherical mesh, map a texture to it, rotate the sphere, and render in 3D. My question is, is there a way to display a 2D circle, that looks like a rotating sphere, with just a 2D shader. In other words, can someone think of a trick, like mapping a texture to the circle in a particular way, to give the appearance of an in-place rotating sphere, that is always viewed from the side? I don't need exact shader code, I'm just looking for the right idea.

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