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  • GLSL billboard move center of rotation

    - by Jacob Kofoed
    I have successfully set up a billboard shader that works, it can take in a quad and rotate it so it always points toward the screen. I am using this vertex-shader: void main(){ vec4 tmpPos = (MVP * bufferMatrix * vec4(0.0, 0.0, 0.0, 1.0)) + (MV * vec4( vertexPosition.x * 1.0 * bufferMatrix[0][0], vertexPosition.y * 1.0 * bufferMatrix[1][1], vertexPosition.z * 1.0 * bufferMatrix[2][2], 0.0) ); UV = UVOffset + vertexUV * UVScale; gl_Position = tmpPos; BufferMatrix is the model-matrix, it is an attribute to support Instance-drawing. The problem is best explained through pictures: This is the start position of the camera: And this is the position, looking in from 45 degree to the right: Obviously, as each character is it's own quad, the shader rotates each one around their own center towards the camera. What I in fact want is for them to rotate around a shared center, how would I do this? What I have been trying to do this far is: mat4 translation = mat4(1.0); translation = glm::translate(translation, vec3(pos)*1.f * 2.f); translation = glm::scale(translation, vec3(scale, 1.f)); translation = glm::translate(translation, vec3(anchorPoint - pos) / vec3(scale, 1.f)); Where the translation is the bufferMatrix sent to the shader. What I am trying to do is offset the center, but this might not be possible with a single matrix..? I am interested in a solution that doesn't require CPU calculations each frame, but rather set it up once and then let the shader do the billboard rotation. I realize there's many different solutions, like merging all the quads together, but I would first like to know if the approach with offsetting the center is possible. If it all seems a bit confusing, it's because I'm a little confused myself.

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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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  • Masking OpenGL texture by a pattern

    - by user1304844
    Tiled terrain. User wants to build a structure. He presses build and for each tile there is an "allow" or "disallow" tile sprite added to the scene. FPS drops right away, since there are 600+ tiles added to the screen. Since map equals screen, there is no scrolling. I came to an idea to make an allow grid covering the whole map and mask the disallow fields. Approach 1: Create allow and disallow grid textures. Draw a polygon on screen. Pass both textures to the fragment shader. Determine the position inside the polygon and use color from allowTexture if the fragment belongs to the allow field, disallow otherwise Problem: How do I know if I'm on the field that isn't allowed if I cannot pass the matrix representing the map (enum FieldStatus[][] (Allow / Disallow)) to the shader? Therefore, inside the shader I don't know which fragments should be masked. Approach 2: Create allow texture. Create an empty texture buffer same size as the allow texture Memset the pixels of the empty texture to desired color for each pixel that doesn't allow building. Draw a polygon on screen. Pass both textures to the fragment shader. Use texture2 color if alpha 0, texture1 color otherwise. Problem: I'm not sure what is the right way to manipulate pixels on a texture. Do I just make a buffer with width*height*4 size and memcpy the color[] to desired coordinates or is there anything else to it? Would I have to call glTexImage2D after every change to the texture? Another problem with this approach is that it takes a lot more work to get a prettier effect since I'm manipulating the color pixels instead of just masking two textures. varying vec2 TexCoordOut; uniform sampler2D Texture1; uniform sampler2D Texture2; void main(void){ vec4 allowColor = texture2D(Texture1, TexCoordOut); vec4 disallowColor = texture2D(Texture2, TexCoordOut); if(disallowColor.a > 0){ gl_FragColor= disallowColor; }else{ gl_FragColor= allowColor; }} I'm working with OpenGL on Windows. Any other suggestion is welcome.

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  • Everything turning black when pitching down

    - by Gordon
    Just a quick questions about something that's occurring in my world. Every time I pitch my camera downward, everything starts turning black, and if I pitch upward, everything sort of intensifies. I'm multiplying my normals by the normal matrix in the shader, and I'm multiplying my lights direction by the model view matrix. If I leave the normal and light dir in world space everything ends up fine. I thought putting them both in view space would not cause those weird things to happen?

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  • Kinect Hand tracking in xna

    - by N0xus
    I'm trying to create an application using the Kinect to simulate the following project: Kinect Hand Tracking I want my project to have similar usability with the Kinect tracking hand and finger positions for use in a menu system, or to navigate another system. What I would like to know is; is it possible for the exact same to be accomplished in XNA using Kinect? I know that it can be done in Winform / C#, but I know XNA / C# a lot better and would (ideally) prefer to use that.

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  • OpenGLES GLSL Shader attributes always bound to 0

    - by codemonkey
    So I have a very simple vertex shader as follows #version 120 attribute vec3 position; attribute vec3 inColor; uniform mat4 mvp; varying vec3 fragColor; void main(void){ fragColor = inColor; gl_Position = mvp * vec4(position, 1.0); } Which I load, as well as the fragment shader: #version 120 varying vec3 fragColor; void main(void) { gl_FragColor = vec4(fragColor,1.0); } Which I then load, compile, and link to my shader program. I check for link status using glGetProgramiv(shaderProgram, GL_LINK_STATUS, &shaderSuccess); which returns GL_TRUE so I think its ok. However, when I query the active attributes and uniforms using #ifdef DEBUG int totalAttributes = -1; glGetProgramiv(shaderProgram, GL_ACTIVE_ATTRIBUTES, &totalAttributes); for(int i=0; i<totalAttributes; ++i) { int name_len=-1, num=-1; GLenum type = GL_ZERO; char name[100]; glGetActiveAttrib(shaderProgram, GLuint(i), sizeof(name)-1, &name_len, &num, &type, name ); name[name_len] = 0; GLuint location = glGetAttribLocation(shaderProgram, name); fprintf(stderr, "Attribute %s is bound at %d\n", name, location); } int totalUniforms = -1; glGetProgramiv(shaderProgram, GL_ACTIVE_UNIFORMS, &totalUniforms); for(int i=0; i<totalUniforms; ++i) { int name_len=-1, num=-1; GLenum type = GL_ZERO; char name[100]; glGetActiveUniform(shaderProgram, GLuint(i), sizeof(name)-1, &name_len, &num, &type, name ); name[name_len] = 0; GLuint location = glGetUniformLocation(shaderProgram, name); fprintf(stderr, "Uniform %s is bound at %d\n", name, location); } #endif I get: Attribute inColor is bound at 0 Attribute position is bound at 1 Uniform mvp is bound at 0 Which leads to failure when trying to use the shader to render the objects. I have tried switching the order of declaration of position & inColor, but still, only position is bound with the other two giving 0 Can someone please explain why this is happening? Thanks

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  • How do I render only part of a texture to a point sprite in OpenGL ES for Android?

    - by nbolton
    Using the libgdx framework, I've figured out how to render a texture to a point sprite. The problem is, it renders the entire texture to the point sprite, where I only want a small part of it (since it's an isometric tile image). Here's a snippet from some demo code I wrote... create() { renderer = new ImmediateModeRenderer(); tiles = Gdx.graphics.newTexture( Gdx.files.internal("data/tiles2.png"), TextureFilter.MipMap, TextureFilter.Linear, TextureWrap.ClampToEdge, TextureWrap.ClampToEdge); Gdx.gl.glClearColor(0.6f, 0.7f, 0.9f, 1); Gdx.gl.glEnable(GL10.GL_TEXTURE_2D); Gdx.gl.glEnable(GL11.GL_POINT_SPRITE_OES); Gdx.gl11.glTexEnvi( GL11.GL_POINT_SPRITE_OES, GL11.GL_COORD_REPLACE_OES, GL11.GL_TRUE); Gdx.gl10.glPointSize(s); tiles.bind(); } render() { Gdx.gl.glClear(GL10.GL_COLOR_BUFFER_BIT); renderer.begin(GL10.GL_POINTS); // render 3 point sprites at various 3d points renderer.vertex(-.1f, 0, -.1f); renderer.vertex(0, 0, 0); renderer.vertex(.1f, 0, .1f); // ... more vertices here if needed (one for each sprite) ... renderer.end(); }

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  • OUYA and Unity set up problems

    - by Atkobeau
    I'm having trouble with the Unity / OUYA plugin. I'm using Unity 4 with the latest update on a Windows 7 machine. When I open the starter kit and try to compile the plugin I get the following error: Picked up _JAVA_OPTIONS: -Xmx512M And if I try to Build and Run I get this error: Error building Player: ArgumentException: Illegal characters in path. I'm stumped, I've gone through lots of forum posts here and on stackoverflow and I can't seem to resolve it. My environment variables look like this: PATH - C:\Users\dave\Documents\adt-bundle-windows-x86_64-20130219\sdk\tools; C:\Users\dave\Documents\adt-bundle-windows-x86_64-20130219\sdk\platform-tools\ JAVA_HOME - C:\Program Files (x86)\Java\jdk1.6.0_45\ Everything in the OUYA Panel is white Any ideas?

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  • A* Start path finding in HTML5 Canvas

    - by gyhgowvi
    I'm trying implement A* Start path finding in my games(which are written with JavaScript, HTML5 Canvas). Library for A* Start found this - http://46dogs.blogspot.com/2009/10/star-pathroute-finding-javascript-code.html and now I'm using this library for path finding. And with this library, I'm trying write a simple test, but stuck with one problem. I'm now done when in HTML5 canvas screen click with mouse show path until my mouse.x and mouse.y. Here is a screenshot - http://oi46.tinypic.com/14qxrl.jpg (Pink square: Player, Orange squares: path until my mouse.x/mouse.y) Code how I'm drawing the orange squares until my mouse.x/mouse.y is: 'http://pastebin.com/bfq74ybc (Sorry I do not understand how upload code in my post) My problem is I do not understand how to move my player until path goal. I've tried: 'http://pastebin.com/nVW3mhUM But with this code my player is not beung drawn.(When I run the code, player.x and player.y are equals to 0 and when I click with the mouse I get the path player blink and disappear) Maybe anyone know how to solve this problem? And I'm very very very sorry for my bad English language. :)

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  • Box2d world width and height ratio with screen width and height

    - by Sujith
    I have view, for example GameView which extends SurfaceView . I have integrated Box2D physics in GameView. I have two widths , GameView width, height and Box2D physics world width ,height. I need to get the position of box2d world with the GameView co-ordinates. For example, Total width of screen = 240 Total height of screen = 320 Screen points needed to be mapped onto box2d co-ordinates (x,y) = 127, 139 For this i need to get the max width and height of the Box2d physics world. Is there is any way to get the max width and height of Box2d world. or Can i limit the width and height of box2d world within the screen resolution.

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  • Why can't I create direct3d objects?

    - by quakkels
    I've been programming professionally for years using languages like VBScript, JavaScript, and C#. As a hobby, I'm getting into some c/c++ and games programming with DirectX. I am running into an issue where I cannot create direct3d objects. I am using Visual C++ 2010 Express. After I installed vc++2010express I then installed the June 2010 release of DirectX. I am trying to include DirectX via #pragma statements. This is the code I have so far in my winmain.cpp source file: #include <Windows.h> #include <d3d11.h> #include <time.h> #include <iostream> using namespace std; #pragma comment(lib, "d3d11.lib") #pragma comment(lib, "d3dx11.lib") // program settings const string AppTitle = "Direct3D in a Window"; const int ScreenWidth = 1024; const int ScreenHeight = 768; // direct3d objects LPDIRECT3D11 d3d = NULL; // this line is showing an error The type LPDIRECT3D11 is showing an error: Error: Identifier "LPDIRECT3D11" is undefined Am I missing something here to get VC++2010Express to recognize and load the DirectX libs? Thanks for any help.

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  • Comparing angles and working out the difference

    - by Thomas O
    I want to compare angles and get an idea of the distance between them. For this application, I'm working in degrees, but it would also work for radians and grads. The problem with angles is that they depend on modular arithmetic, i.e. 0-360 degrees. Say one angle is at 15 degrees and one is at 45. The difference is 30 degrees, and the 45 degree angle is greater than the 15 degree one. But, this breaks down when you have, say, 345 degrees and 30 degrees. Although they compare properly, the difference between them is 315 degrees instead of the correct 45 degrees. How can I solve this? I could write algorithmic code: if(angle1 > angle2) delta_theta = 360 - angle2 - angle1; else delta_theta = angle2 - angle1; But I'd prefer a solution that avoids compares/branches, and relies entirely on arithmetic.

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  • How does a BSP tree work for Z sorting?

    - by Jenko
    I'm developing a 3D engine in software, and so I must compute Z sorting manually. I'm currently using the painters algorithm to sort triangles and then drawing them back-to-front. This causes artifacts that I'm trying to correct. Would using a dynamic BSP-tree ensure "correct Z sorting" of triangles? Why? Because the bounding volumes of triangles would be similar? Since I would have a single "world" BSP tree, would I have to remove and re-add any moved/scaled/rotated object into the tree? Is it possible to add triangles into a BSP tree without the expensive cutting process? Why do you need to cut triangles on the axis planes anyway? Is it faster to traverse a BSP tree from any angle, than to sort all tris each draw like the painters algorithm?

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  • OpenGL Learning Material (that's up to date)

    - by Sauron
    So im sure there are topics on this, but alot of them list older material. And the last book: http://www.amazon.com/OpenGL-SuperBible-Comprehensive-Tutorial-Reference/dp/0321712617/ref=sr_1_1?ie=UTF8&qid=1346116133&sr=8-1&keywords=opengl REALLY REALLY disappointed me. I DO NOT want to use someone else's library to learn this stuff, that bothers me SOOO much. So I was hoping there was a newer book that goes into detail, and doesn't use some sort of library "Hiding" everything from you. Or should I just look at older material? If so....anything thats not "too" out of date. Terrain tutorials are a plus (that's kinda my "goal"). Thanks

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  • Circle to Circle collision, checking each circle against all others

    - by user14861
    I'm currently coding a little circle to circle collision demo but I've got a little stuck. I think I currently have the code to detect collision but I'm not sure how to loop through my list of circles and check them off against one another. Collision check code: public static Vector2 GetIntersectionDepth(Circle a, Circle b) { float xValue = a.Center.X - b.Center.X; float yValue = a.Center.Y - b.Center.Y; Vector2 depth = Vector2.Zero; float distance = Vector2.Distance(a.Center, b.Center); if (a.Radius + b.Radius > distance) { float result = (a.Radius + b.Radius) - distance; depth.X = (float)Math.Cos(result); depth.Y = (float)Math.Sin(result); } return depth; } Loop through code: Vector2 depth = Vector2.Zero; for (int i = 0; i < bounds.Count; i++) for (int j = i+1; j < bounds.Count; j++) { depth = CircleToCircleIntersection.GetIntersectionDepth(bounds[i], bounds[j]); } Clearly I'm a complete newbie, wondering if anyone can give any suggestions or point out my errors, thanks in advance. :)

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  • Is it normal to these Xcode prompts/errors when you deploy to IOS Simulator from Unity?

    - by Greg
    Just trying out the IOS build process.... Is it normal to see: Q1 - "upgrade to latest project format - project currently in Xcode 3.1 format, this will upgrade to 3.2" - just click OK and let Xcode do it's stuff? Q2 - same as Q1 but this time for the message "Remove obsolete build settings - will remove the build setting PREBINDING" Q3 - also when deploying to "Lastest IOS Simulator" you get the Simulator target produced, but also a non-simulator target which has lots of errors. So I assume you just ignore this target and not use it in Xcode correct? (i.e. just use the simulator target that is produced) Q4 - get a lot of warning after the simulator target is built? program works ok however.... Images For Q1 and Q2: For Q4: Settings used in Unity: Errors I see in XCode:

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  • How can I generate a texture that looks like left-over tea leaves?

    - by Jedidja
    We are working on a project for iPhone and Windows Phone 7 where we'd like to be able to generate tea leaves at the bottom of a cup. It doesn't have to look photo-realistic, and actually cartoon-y is ok. What sort of techniques should we research to accomplish this? Are there any libraries (preferably in C, but we can translate) that would be helpful? Here are some samples pulled from a Google Image search

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  • Starting out with OpenGL when most tutorials are out of date

    - by AUTO
    I'm sure there are already a bunch of questions like this asked, but the constant updating of the OpenGL library throws them all away, and in a month or two, the answers here will be worthless again. I am ready to start programming in OpenGL using C++. I've got a working compiler (DevCpp; do NOT ask me to switch to VC++, and don't ask me why). Now I'm just looking for a solid tutorial on how to program with OpenGL. My assistant found the tutorial provided by NeHe Productions, but as I've come to find out, it's WAY OUT OF DATE! (although I did pull together a basic window to support an OpenGL canvas) Then I went online, and found the OpenGL SuperBible, which apparently uses freeglut? But what I'd like to know is whether or not SuperBible 5th edition is up to date any longer. The suggestion to freeglut I found said the latest version was 2.6.0 but now it's 2.8.0! Is the OpenGL SuperBible still a good, and fairly up-to-date place to start? Is there a better place to go to learn OpenGL? Am I allowed to simply store freeglut in the DevCpp include directory (maybe in GL), or is there some important procedure? Are there any comments or suggestions that I didn't think to ask since I'm only just beginning? @dreta cleared some things up for me, so now I have a better idea of what to ask: I think I'd like to start out with OpenGL using a wrapper library instead of directly accessing OpenGL.I just think that, for a beginner, it would be easier for me to program and get good results, while I don't yet have to understand all the grimy details (as @stephelton mentioned). The problem is, I can't find any library that doesn't have undefined references to no longer supported functions. Freeglut sounds operational, but it still uses GLU.Does anyone know what I can do?Also, I tried compiling the first SuperBible's source, but I got errors since GLAPI is not being defined as a type, the error originating in the GLU library. I'd like to use the SuperBible, but I don't know how to fix this.

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  • vector rotations for branches of a 3d tree

    - by freefallr
    I'm attempting to create a 3d tree procedurally. I'm hoping that someone can check my vector rotation maths, as I'm a bit confused. I'm using an l-system (a recursive algorithm for generating branches). The trunk of the tree is the root node. It's orientation is aligned to the y axis. In the next iteration of the tree (e.g. the first branches), I might create a branch that is oriented say by +10 degrees in the X axis and a similar amount in the Z axis, relative to the trunk. I know that I should keep a rotation matrix at each branch, so that it can be applied to child branches, along with any modifications to the child branch. My questions then: for the trunk, the rotation matrix - is that just the identity matrix * initial orientation vector ? for the first branch (and subsequent branches) - I'll "inherit" the rotation matrix of the parent branch, and apply x and z rotations to that also. e.g. using glm::normalize; using glm::rotateX; using glm::vec4; using glm::mat4; using glm::rotate; vec4 vYAxis = vec4(0.0f, 1.0f, 0.0f, 0.0f); vec4 vInitial = normalize( rotateX( vYAxis, 10.0f ) ); mat4 mRotation = mat4(1.0); // trunk rotation matrix = identity * initial orientation vector mRotation *= vInitial; // first branch = parent rotation matrix * this branches rotations mRotation *= rotate( 10.0f, 1.0f, 0.0f, 0.0f ); // x rotation mRotation *= rotate( 10.0f, 0.0f, 0.0f, 1.0f ); // z rotation Are my maths and approach correct, or am I completely wrong? Finally, I'm using the glm library with OpenGL / C++ for this. Is the order of x rotation and z rotation important?

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  • Is it safe StringToHash() to use in Unity?

    - by Sebastian Krysmanski
    I'm currently browsing through the Unity tutorials and saw that they're recommending to use Animator.StringToHash("some string") to created unique ids for animation properties (see here). Since I'm a programmer, to me the word "hash" doesn't represents something unique. Like the Java documentation for hashValue() states: It is not required that if two objects are unequal [...], then calling the hashCode method on each of the two objects must produce distinct integer results. So, according to this (and my definition of "hash"), two strings may have the same hash value. (You can also argue that there are an infinite number of possible strings but only 2^32 possible int values.) So, is there a possibility that StringToHash() will give me an id that actually belongs to another property (than the one I requested the hash for)?

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  • Impact of variable-length loops on GPU shaders

    - by Will
    Its popular to render procedural content inside the GPU e.g. in the demoscene (drawing a single quad to fill the screen and letting the GPU compute the pixels). Ray marching is popular: This means the GPU is executing some unknown number of loop iterations per pixel (although you can have an upper bound like maxIterations). How does having a variable-length loop affect shader performance? Imagine the simple ray-marching psuedocode: t = 0.f; while(t < maxDist) { p = rayStart + rayDir * t; d = DistanceFunc(p); t += d; if(d < epsilon) { ... emit p return; } } How are the various mainstream GPU families (Nvidia, ATI, PowerVR, Mali, Intel, etc) affected? Vertex shaders, but particularly fragment shaders? How can it be optimised?

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  • Collision with CCSprite

    - by Coder404
    I'm making an iOS app based off the code from here In the .m file of the tutorial is this: -(void)update:(ccTime)dt { NSMutableArray *projectilesToDelete = [[NSMutableArray alloc] init]; for (CCSprite *projectile in _projectiles) { CGRect projectileRect = CGRectMake( projectile.position.x - (projectile.contentSize.width/2), projectile.position.y - (projectile.contentSize.height/2), projectile.contentSize.width, projectile.contentSize.height); NSMutableArray *targetsToDelete = [[NSMutableArray alloc] init]; for (CCSprite *target in _targets) { CGRect targetRect = CGRectMake( target.position.x - (target.contentSize.width/2), target.position.y - (target.contentSize.height/2), target.contentSize.width, target.contentSize.height); if (CGRectIntersectsRect(projectileRect, targetRect)) { [targetsToDelete addObject:target]; } } for (CCSprite *target in targetsToDelete) { [_targets removeObject:target]; [self removeChild:target cleanup:YES]; } if (targetsToDelete.count > 0) { [projectilesToDelete addObject:projectile]; } [targetsToDelete release]; } for (CCSprite *projectile in projectilesToDelete) { [_projectiles removeObject:projectile]; [self removeChild:projectile cleanup:YES]; } [projectilesToDelete release]; } I am trying to take away the projectiles and have the app know when the CCSprite "Player" and the targets collide. Could someone help me with this? Thanks

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  • Sharing VBO with multiple objects and fixed size buffer data

    - by Mark Ingram
    I'm just messing around with OpenGL and getting some basic structures in place and my first attempt resulted in each SceneObject class (just contains vertex information right now) having it's own VBO inside it, however I've read that it might be better to share VBOs across multiple objects. Also, I read that you should avoid resizing a VBO (repeated calls to glBufferData with different size parameters), and instead choose a fixed size for a VBO, and just try a range from the buffer. I don't think changing the size of the buffer data would happen too often, but surely it would be better to only allocate the data you need? Choosing an arbitrary value seems risky. I'm looking for some advice on working with individual objects in a scene and their associated buffer data.

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  • strange behavior in Box2D+LibGDX when applying impulse

    - by Z0lenDer
    I have been playing around with Box2D and LibGDX and have been using a sample code from DecisionTreeGames as the testing ground. Now I have a screen with four walls and a rectangle shape, lets call it a brick. When I use applyLinearImpulse to the brick, it starts bouncing right and left without any pattern and won't stop! I tried adding friction and increasing the density, but the behavior still remains the same. Here are some of the code that might be useful: method for applying the impulse: center = brick.getWorldCenter(); brick.applyLinearImpulse(20, 0, center.x, center.y); Defining the brick: brick_bodyDef.type = BodyType.DynamicBody; brick_bodyDef.position.set(pos); // brick is initially on the ground brick_bodyDef.angle = 0; brick_body = world.createBody(brick_bodyDef); brick_body.setBullet(true); brick_bodyShape.setAsBox(w,h); brick_fixtureDef.density = 0.9f; brick_fixtureDef.restitution = 1; brick_fixtureDef.shape = brick_bodyShape; brick_fixtureDef.friction=1; brick_body.createFixture(fixtureDef); Walls are defined the same only their bullet value is set to false I would really appreciate it if you could help me have a change this code to have a realistic behavior (i.e. when I apply impulse to the brick it should trip a few times and then stop completely).

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  • Logic that can traverse all possible layouts, but not checking every combination of identical pieces?

    - by George Bailey
    Suppose we have a grid of arbitrary size, which is filled by blocks of various widths and heights. There are many 2x2 blocks (meaning they take a total of 4 cells in the grid) and many 3x3 blocks, as well as some 5x4, 4x5, 2x3, etc. I was hoping I could set up a program that would look at all possible layouts, and rank them, and find the best one. Simply it would look at all possible positions of these blocks, and see what setup is the best rank. (the rank based on how many of these can be connected by a roadway system of 1x1 road blocks, and how many squares can be left empty after this is done. - wanting to fit the most blocks as possible with the least roads.) My question, is how should I traverse all the possibilities? I could take all the blocks and try them one at a time, but since all 2x2 blocks are equal, and there are a couple dozen of them, there is no point in trying every combination there, as in the following AA BBB AA BBB CCBBB CCEEE DD EEE DD EEE is exactly the same as CC EEE CC EEE AAEEE AABBB DD BBB DD BBB You notice that there are 2 3x3 blocks and 3 2x2 blocks in my two examples. Based on the model I have now, the computer would try both of these combinations, as well as many others. The problem is that it is going to try every single possible variation of my couple dozen 2x2 blocks. And that is sorely inefficient. Is there a reasonable way to take out this duplicated work, somehow getting the computer program to treat all 2x2 blocks as equal/identical, instead of one requiring rearranging/swapping of these identical blocks? Can this be done?

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