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• How do I implement a Bullet Physics CollisionObject that represents my cube like terrain?

  - by Byte56

  I've successfully integrated the Bullet Physics library into my entity/component system. Entities can collide with each other. Now I need to enable them to collide with the terrain, which is finite and cube-like (think InfiniMiner or it's clone Minecraft). I only started using the Bullet Physics library yesterday, so perhaps I'm missing something obvious. So far I've extended the RigidBody class to override the checkCollisionWith(CollisionObject co) function. At the moment it's just a simple check of the origin, not using the other shape. I'll iterate on that later. For now it looks like this: @Override public boolean checkCollideWith(CollisionObject co) { Transform t = new Transform(); co.getWorldTransform(t); if(COLONY.SolidAtPoint(t.origin.x, t.origin.y,t.origin.z)){ return true; } return false; } This works great, as far as detecting when collisions happen. However, this doesn't handle the collision response. It seems that the default collision response is to move the colliding objects outside of each others shapes, possibly their AABBs. At the moment the shape of the terrain is just a box the size of the world. This means the entities that collide with the terrain just shoot away to outside that world size box. So it's clear that I either need to modify the collision response or I need to create a shape that conforms directly to the shape of the terrain. So which option is best and how do I go about implementing it? It should be noted that the terrain is dynamic and frequently modified by the player.

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• Geometry shader for multiple primitives

  - by Byte56

  How can I create a geometry shader that can handle multiple primitives? For example when creating a geometry shader for triangles, I define a layout like so: layout(triangles) in; layout(triangle_strip, max_vertices=3) out; But if I use this shader then lines or points won't show up. So adding: layout(triangles) in; layout(triangle_strip, max_vertices=3) out; layout(lines) in; layout(line_strip, max_vertices=2) out; The shader will compile and run, but will only render lines (or whatever the last primitive defined is). So how do I define a single geometry shader that will handle multiple types of primitives? Or is that not possible and I need to create multiple shader programs and change shader programs before drawing each type?

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• Calculate an AABB for bone animated model

  - by Byte56

  I have a model that has its initial bounding box calculated by finding the maximum and minimum on the x, y and z axes. Producing a correct result like so: The vertices are then stored in a VBO and only altered with matrices for rotation and bone animation. Currently the bounds are not updated when the model is altered. So the animated and rotated model has bounds like so: (Maybe it's hard to tell, but the bounds are the same as before, and don't accurately represent the rotated/animated model) So my question is, how can I calculate the bounding box using the armature matrices and rotation/translation matrices for each model? Keep in mind the modified vertex data is not available because those calculations are performed on the GPU in the shader. The end result I want is to have an accurate AABB the represents the animated model for picking/basic collision checks.

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• How do I apply skeletal animation from a .x (Direct X) file?

  - by Byte56

  Using the .x format to export a model from Blender, I can load a mesh, armature and animation. I have no problems generating the mesh and viewing models in game. Additionally, I have animations and the armature properly loaded into appropriate data structures. My problem is properly applying the animation to the models. I have the framework for applying the models and the code for selecting animations and stepping through frames. From what I understand, the AnimationKeys inside the AnimationSet supplies the transformations to transform the bind pose to the pose in the animated frame. As small example: Animation { {Armature_001_Bone} AnimationKey { 2; //Position 121; //number of frames 0;3; 0.000000, 0.000000, 0.000000;;, 1;3; 0.000000, 0.000000, 0.005524;;, 2;3; 0.000000, 0.000000, 0.022217;;, ... } AnimationKey { 0; //Quaternion Rotation 121; 0;4; -0.707107, 0.707107, 0.000000, 0.000000;;, 1;4; -0.697332, 0.697332, 0.015710, 0.015710;;, 2;4; -0.684805, 0.684805, 0.035442, 0.035442;;, ... } AnimationKey { 1; //Scale 121; 0;3; 1.000000, 1.000000, 1.000000;;, 1;3; 1.000000, 1.000000, 1.000000;;, 2;3; 1.000000, 1.000000, 1.000000;;, ... } } So, to apply frame 2, I would take the position, rotation and scale from frame 2, create a transformation matrix (call it Transform_A) from them and apply that matrix the vertices controlled by Armature_001_Bone at their weights. So I'd stuff TransformA into my shader and transform the vertex. Something like: vertexPos = vertexPos * bones[ int(bfs_BoneIndices.x) ] * bfs_BoneWeights.x; Where bfs_BoneIndices and bfs_BoneWeights are values specific to the current vertex. When loading in the mesh vertices, I transform them by the rootTransform and the meshTransform. This ensures they're oriented and scaled correctly for viewing the bind pose. The problem is when I create that transformation matrix (using the position, rotation and scale from the animation), it doesn't properly transform the vertex. There's likely more to it than just using the animation data. I also tried applying the bone transform hierarchies, still no dice. Basically I end up with some twisted models. It should also be noted that I'm working in openGL, so any matrix transposes that might need to be applied should be considered. What data do I need and how do I combine it for applying .x animations to models?

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• How do I get a new license for gDEBugger after the 1 free year?

  - by Byte56

  I downloaded the gDEBugger from gremedy over a year ago, with their one year free license. The license has since expired and their site says that I'll be presented with the option for 1 year free license the first time I run it after install. This doesn't happen when re-installing, it just tells me the license has expired. How do I get a new license? I use this regularly for debugging shader problems and performance testing my game.

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• Low CPU/Memory/Memory-bandwith Pathfinding (maybe like in Warcraft 1)

  - by Valmond

  Dijkstra and A* are all nice and popular but what kind of algorithm was used in Warcraft 1 for pathfinding? I remember that the enemy could get trapped in bowl-like caverns which means there were (most probably) no full-path calculations from "start to end". If I recall correctly, the algorithm could be something like this: A) Move towards enemy until success or hitting a wall B) If blocked by a wall, follow the wall until you can move towards the enemy without being blocked and then do A) But I'd like to know, if someone knows :-) [edit] As explained to Byte56, I'm searching for a low cpu/mem/mem-bandwidth algo and wanted to know if Warcraft had some special secrets to deliver (never seen that kind of pathfinding elsewhere), I hope that that is more concordant with the stackexchange rules.

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• Alternatives to voxel-based terrain

  - by Neomex

  Are there any alternatives to voxel based terrains? Such terrain should be fully destructable, allow for arches, overhangs, preserve sharp features where needed and keep consistent topology. Maybe you can explain the problem that makes you ask this question? Voxel based terrain is basically just using a 3D grid of data to store data. There are lots of ways to render that data, but it doesn't get much simpler for storing it. – Byte56 Current isosurface extraction methods aren't most effective/bug-free. Cubical Marching Squares seem to solve most of the issues, however it is a relatively new method and there aren't too many resources about it. (I've found single university paper) Even if we stick to CMS, when we want to add multi-material support, we can either divide surface into multiple meshes, or pass a texture array or texture atlas to shaders, then we are limited to set amount of textures and additionally increase memory-usage alot.

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• Convert OpenGL code to DirectX

  - by Fredrik Boston Westman

  First of all, this is kind of a follow up question on @byte56 excellent anwser on this question concerning picking algorithms. I'm trying to convert one of his code examples to directX 11 however I have run into some problems ( I can pick but the picking is way off), and I wanted to make sure I had done it right before moving on and checking the rest of my code. I am not that familiar with openGl but I can imagine openGl has different coordinations systems, and functions that alters how you must implement to code a bit. The getPickRay function on the answer linked is what I'm trying to convert. This is the part of my code that I think is giving me trouble when converting from openGl to directX Because I'm unsure on how their different coordination systems differs from one another. PRVecX = ((( 2.0f * mouseX) / ClientWidth ) - 1 ) * tan((viewAngle)/2); PRVecY = (1-(( 2.0f * mouseY) / ClientHeight)) * tan((viewAngle)/2); Another thing that I am unsure about is this part: XMVECTOR worldSpaceNear = XMVector3TransformCoord(cameraSpaceNear, invMat); XMVECTOR worldSpaceFar = XMVector3TransformCoord(cameraSpaceFar, invMat); A couple of notes: The mouse coordinates are already converted so that the top left corner of the client window would be (0,0) and the bottom right (800,600) ( or whatever resolution you would have) The viewAngle is the same angle that I used when setting the camera view with XMMatrixPerspectiveFovLH. I removed the variables aspectRatio and zoomFactor because I assumed that they were related to some specific function of his game. To summarize it up to questions : Does the openGL coordination system differ in such a way that this equation in the first of my code examples wouldn't be valid when used in DirectX 11 ( with its respective screen coordination system)? Is the openGL method Matrix4f.transform(a, b, c) equal to the directX method c = XMVector3TransformCoord(b,a)? (where a is a matrix and b,c are vectors). Because I know when it comes to matrices order is important.

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• Implementing features in an Entity System

  - by Bane

  After asking two questions on Entity Systems (1, 2), and reading some articles on them, I think that I understand them much better than before. But, I still have some uncertainties, and mainly they are about building a Particle Emitter, an Input system, and a Camera. I obviously still have some problems understanding Entity Systems, and they might apply to a whole other range of objects, but I chose these three because they are very different concepts and should cover a pretty big ground, and help me understand Entity Systems and how to handle problems like these myself, as they come along. I am building an engine in Javascript, and I've implemented most of the core features, which include: input handling, flexible animation system, particle emitter, math classes and functions, scene handling, a camera and a render, and a whole bunch of other things that engines usually support. Then, I read Byte56's answer that got me interested into making the engine into an Entity System one. It would still remain an HTML5 game engine with the basic Scene philosophy, but it should support dynamic creation of entities from components. These are some of the definitions from the previous questions, updated: An Entity is an identifier. It doesn't have any data, it's not an object, it's a simple id that represents an index in the Scene's list of all entities (which I actually plan to implement as a component matrix). A Component is a data holder, but with methods that can operate on that data. The best example is a Vector2D, or a "Position" component. It has data: x and y, but also some methods that make operating on the data a bit easier: add(), normalize(), and so on. A System is something that can operate on a set of entities that meet the certain requirements, usually they (the entities) need to have a specified (by the system itself) set of components to be operated upon. The system is the "logic" part, the "algorithm" part, all the functionality supplied by components is purely for easier data management. The problem that I have now is fitting my old engine concept into this new programming paradigm. Lets start with the simplest one, a Camera. The camera has a position property (Vector2D), a rotation property and some methods for centering it around a point. Each frame, it is fed to a renderer, along with a scene, and all the objects are translated according to it's position. Then the scene is rendered. How could I represent this kind of an object in an Entity System? Would the camera be an entity or simply a component? A combination (see my answer)? Another issues that is bothering me is implementing a Particle Emitter. For what exactly I mean by that, you can check out my video of it: http://youtu.be/BObargIMQsE. The problem I have with this is, again, what should be what. I'm pretty sure that particles themselves shouldn't be entities, as I want to support 10k+ of them, and creating that much entities would be a heavy blow on my performance, I believe. Or maybe not? Depends on the implementation, but anyone with experience: please, do answer. The last bit I wan't to talk about, which is also bugging me the most, is how input should be handled. In my current version of the engine, there is a class called Input. It's a handler that subscribes to browser's events, such as keypresses, and mouse position changes, and also it maintains an internal state. Then, the player class has a react() method, which accepts an input object as an argument. The advantage of this is that the input object could be serialized into JSON and then shared over the network, allowing for smooth multiplayer simulations. But how does this translate into an Entity System?

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• Converting openGl code to DirectX

  - by Fredrik Boston Westman

  First of all, this is kind of a follow up question on @byte56 excellent anwser on this question concerning picking algorithms. I'm trying to convert one of his code examples to directX 11 however I have run in to some problems ( I can pick but the picking is way off), and I wanted to make sure I had done it rigth before moving on and checking the rest of my code. I am not that familiar with openGl but I can imagine openGl has diffrent coordinations systems, and functions that alters how you must implement to code abit. This is his code example: public Ray GetPickRay() { int mouseX = Mouse.getX(); int mouseY = WORLD.Byte56Game.getHeight() - Mouse.getY(); float windowWidth = WORLD.Byte56Game.getWidth(); float windowHeight = WORLD.Byte56Game.getHeight(); //get the mouse position in screenSpace coords double screenSpaceX = ((float) mouseX / (windowWidth / 2) - 1.0f) * aspectRatio; double screenSpaceY = (1.0f - (float) mouseY / (windowHeight / 2)); double viewRatio = Math.tan(((float) Math.PI / (180.f/ViewAngle) / 2.00f))* zoomFactor; screenSpaceX = screenSpaceX * viewRatio; screenSpaceY = screenSpaceY * viewRatio; //Find the far and near camera spaces Vector4f cameraSpaceNear = new Vector4f((float) (screenSpaceX * NearPlane), (float) (screenSpaceY * NearPlane), (float) (-NearPlane), 1); Vector4f cameraSpaceFar = new Vector4f((float) (screenSpaceX * FarPlane), (float) (screenSpaceY * FarPlane), (float) (-FarPlane), 1); //Unproject the 2D window into 3D to see where in 3D we're actually clicking Matrix4f tmpView = Matrix4f(view); Matrix4f invView = (Matrix4f) tmpView.invert(); Vector4f worldSpaceNear = new Vector4f(); Matrix4f.transform(invView, cameraSpaceNear, worldSpaceNear); Vector4f worldSpaceFar = new Vector4f(); Matrix4f.transform(invView, cameraSpaceFar, worldSpaceFar); //calculate the ray position and direction Vector3f rayPosition = new Vector3f(worldSpaceNear.x, worldSpaceNear.y, worldSpaceNear.z); Vector3f rayDirection = new Vector3f(worldSpaceFar.x - worldSpaceNear.x, worldSpaceFar.y - worldSpaceNear.y, worldSpaceFar.z - worldSpaceNear.z); rayDirection.normalise(); return new Ray(rayPosition, rayDirection); } All rigths reserved to him of course This is my DirectX 11 code : void GraphicEngine::pickRayVector(float mouseX, float mouseY,XMVECTOR& pickRayInWorldSpacePos, XMVECTOR& pickRayInWorldSpaceDir) { float PRVecX, PRVecY; float nearPlane = 0.1f; float farPlane = 200.0f; floar viewAngle = 0.4 * 3.14; PRVecX = ((( 2.0f * mouseX) / ClientWidth ) - 1 ) * tan((viewAngle)/2); PRVecY = (1-(( 2.0f * mouseY) / ClientHeight)) * tan((viewAngle)/2); XMVECTOR cameraSpaceNear = XMVectorSet(PRVecX * nearPlane,PRVecY * nearPlane, -nearPlane, 1.0f); XMVECTOR cameraSpaceFar = XMVectorSet(PRVecX * farPlane,PRVecY * farPlane, -farPlane, 1.0f); // Transform 3D Ray from View space to 3D ray in World space XMMATRIX invMat; XMVECTOR matInvDeter; invMat = XMMatrixInverse(&matInvDeter, cam->getCameraView()); //Inverse of View Space matrix is World space matrix XMVECTOR worldSpaceNear = XMVector3TransformCoord(cameraSpaceNear, invMat); XMVECTOR worldSpaceFar = XMVector3TransformCoord(cameraSpaceFar, invMat); pickRayInWorldSpacePos = worldSpaceNear; pickRayInWorldSpaceDir = worldSpaceFar-worldSpaceNear; pickRayInWorldSpaceDir = XMVector3Normalize(pickRayInWorldSpaceDir); } A couple of notes: The mouse coordinates are already converted so that the top left corner of the client window would be (0,0) and the bottom rigth (800,600) ( or whatever resolution you would have) I hadn't used any far or near plane before, so i just made some arbitrary number up for them. To my understanding it shouldnt matter as long as the object you are trying to pick is in between the range of thoese numbers The viewAngle is the same angle that I used when setting the camera view with XMMatrixPerspectiveFovLH , I just hadn't made it a member variable of my Camera class yet. I removed the variable aspectRation and zoomFactor because I assumed that they where related to some specific function of his game. Now I'm not sure, but I think the problems lies either withing the mouse to viewspace conversion, maby that we use diffrent coordinations systems. Either that or how i transform the matrixes in the the end, because i know order is important when it comes to matrixes. Any help is appriciated! Thanks in advance. Edit: One more note, my code is in c++

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• 3D picking lwjgl

  - by Wirde

  I have written some code to preform 3D picking that for some reason dosn't work entirely correct! (Im using LWJGL just so you know.) I posted this at stackoverflow at first but after researching some more in to my problem i found this neat site and tought that you guys might be more qualified to answer this question. This is how the code looks like: if(Mouse.getEventButton() == 1) { if (!Mouse.getEventButtonState()) { Camera.get().generateViewMatrix(); float screenSpaceX = ((Mouse.getX()/800f/2f)-1.0f)*Camera.get().getAspectRatio(); float screenSpaceY = 1.0f-(2*((600-Mouse.getY())/600f)); float displacementRate = (float)Math.tan(Camera.get().getFovy()/2); screenSpaceX *= displacementRate; screenSpaceY *= displacementRate; Vector4f cameraSpaceNear = new Vector4f((float) (screenSpaceX * Camera.get().getNear()), (float) (screenSpaceY * Camera.get().getNear()), (float) (-Camera.get().getNear()), 1); Vector4f cameraSpaceFar = new Vector4f((float) (screenSpaceX * Camera.get().getFar()), (float) (screenSpaceY * Camera.get().getFar()), (float) (-Camera.get().getFar()), 1); Matrix4f tmpView = new Matrix4f(); Camera.get().getViewMatrix().transpose(tmpView); Matrix4f invertedViewMatrix = (Matrix4f)tmpView.invert(); Vector4f worldSpaceNear = new Vector4f(); Matrix4f.transform(invertedViewMatrix, cameraSpaceNear, worldSpaceNear); Vector4f worldSpaceFar = new Vector4f(); Matrix4f.transform(invertedViewMatrix, cameraSpaceFar, worldSpaceFar); Vector3f rayPosition = new Vector3f(worldSpaceNear.x, worldSpaceNear.y, worldSpaceNear.z); Vector3f rayDirection = new Vector3f(worldSpaceFar.x - worldSpaceNear.x, worldSpaceFar.y - worldSpaceNear.y, worldSpaceFar.z - worldSpaceNear.z); rayDirection.normalise(); Ray clickRay = new Ray(rayPosition, rayDirection); Vector tMin = new Vector(), tMax = new Vector(), tempPoint; float largestEnteringValue, smallestExitingValue, temp, closestEnteringValue = Camera.get().getFar()+0.1f; Drawable closestDrawableHit = null; for(Drawable d : this.worldModel.getDrawableThings()) { // Calcualte AABB for each object... needs to be moved later... firstVertex = true; for(Surface surface : d.getSurfaces()) { for(Vertex v : surface.getVertices()) { worldPosition.x = (v.x+d.getPosition().x)*d.getScale().x; worldPosition.y = (v.y+d.getPosition().y)*d.getScale().y; worldPosition.z = (v.z+d.getPosition().z)*d.getScale().z; worldPosition = worldPosition.rotate(d.getRotation()); if (firstVertex) { maxX = worldPosition.x; maxY = worldPosition.y; maxZ = worldPosition.z; minX = worldPosition.x; minY = worldPosition.y; minZ = worldPosition.z; firstVertex = false; } else { if (worldPosition.x > maxX) { maxX = worldPosition.x; } if (worldPosition.x < minX) { minX = worldPosition.x; } if (worldPosition.y > maxY) { maxY = worldPosition.y; } if (worldPosition.y < minY) { minY = worldPosition.y; } if (worldPosition.z > maxZ) { maxZ = worldPosition.z; } if (worldPosition.z < minZ) { minZ = worldPosition.z; } } } } // ray/slabs intersection test... // clickRay.getOrigin().x + clickRay.getDirection().x * f = minX // clickRay.getOrigin().x - minX = -clickRay.getDirection().x * f // clickRay.getOrigin().x/-clickRay.getDirection().x - minX/-clickRay.getDirection().x = f // -clickRay.getOrigin().x/clickRay.getDirection().x + minX/clickRay.getDirection().x = f largestEnteringValue = -clickRay.getOrigin().x/clickRay.getDirection().x + minX/clickRay.getDirection().x; temp = -clickRay.getOrigin().y/clickRay.getDirection().y + minY/clickRay.getDirection().y; if(largestEnteringValue < temp) { largestEnteringValue = temp; } temp = -clickRay.getOrigin().z/clickRay.getDirection().z + minZ/clickRay.getDirection().z; if(largestEnteringValue < temp) { largestEnteringValue = temp; } smallestExitingValue = -clickRay.getOrigin().x/clickRay.getDirection().x + maxX/clickRay.getDirection().x; temp = -clickRay.getOrigin().y/clickRay.getDirection().y + maxY/clickRay.getDirection().y; if(smallestExitingValue > temp) { smallestExitingValue = temp; } temp = -clickRay.getOrigin().z/clickRay.getDirection().z + maxZ/clickRay.getDirection().z; if(smallestExitingValue < temp) { smallestExitingValue = temp; } if(largestEnteringValue > smallestExitingValue) { //System.out.println("Miss!"); } else { if (largestEnteringValue < closestEnteringValue) { closestEnteringValue = largestEnteringValue; closestDrawableHit = d; } } } if(closestDrawableHit != null) { System.out.println("Hit at: (" + clickRay.setDistance(closestEnteringValue).x + ", " + clickRay.getCurrentPosition().y + ", " + clickRay.getCurrentPosition().z); this.worldModel.removeDrawableThing(closestDrawableHit); } } } I just don't understand what's wrong, the ray are shooting and i do hit stuff that gets removed but the result of the ray are verry strange it sometimes removes the thing im clicking at, sometimes it removes things thats not even close to what im clicking at, and sometimes it removes nothing at all. Edit: Okay so i have continued searching for errors and by debugging the ray (by painting smal dots where it travles) i can now se that there is something oviously wrong with the ray that im sending out... it has its origin near the world center (nearer or further away depending on where on the screen im clicking) and always shots to the same position no matter where I direct my camera... My initial toughts is that there might be some error in the way i calculate my viewMatrix (since it's not possible to get the viewmatrix from the gluLookAt method in lwjgl; I have to build it my self and I guess thats where the problem is at)... Edit2: This is how i calculate it currently: private double[][] viewMatrixDouble = {{0,0,0,0}, {0,0,0,0}, {0,0,0,0}, {0,0,0,1}}; public Vector getCameraDirectionVector() { Vector actualEye = this.getActualEyePosition(); return new Vector(lookAt.x-actualEye.x, lookAt.y-actualEye.y, lookAt.z-actualEye.z); } public Vector getActualEyePosition() { return eye.rotate(this.getRotation()); } public void generateViewMatrix() { Vector cameraDirectionVector = getCameraDirectionVector().normalize(); Vector side = Vector.cross(cameraDirectionVector, this.upVector).normalize(); Vector up = Vector.cross(side, cameraDirectionVector); viewMatrixDouble[0][0] = side.x; viewMatrixDouble[0][1] = up.x; viewMatrixDouble[0][2] = -cameraDirectionVector.x; viewMatrixDouble[1][0] = side.y; viewMatrixDouble[1][1] = up.y; viewMatrixDouble[1][2] = -cameraDirectionVector.y; viewMatrixDouble[2][0] = side.z; viewMatrixDouble[2][1] = up.z; viewMatrixDouble[2][2] = -cameraDirectionVector.z; /* Vector actualEyePosition = this.getActualEyePosition(); Vector zaxis = new Vector(this.lookAt.x - actualEyePosition.x, this.lookAt.y - actualEyePosition.y, this.lookAt.z - actualEyePosition.z).normalize(); Vector xaxis = Vector.cross(upVector, zaxis).normalize(); Vector yaxis = Vector.cross(zaxis, xaxis); viewMatrixDouble[0][0] = xaxis.x; viewMatrixDouble[0][1] = yaxis.x; viewMatrixDouble[0][2] = zaxis.x; viewMatrixDouble[1][0] = xaxis.y; viewMatrixDouble[1][1] = yaxis.y; viewMatrixDouble[1][2] = zaxis.y; viewMatrixDouble[2][0] = xaxis.z; viewMatrixDouble[2][1] = yaxis.z; viewMatrixDouble[2][2] = zaxis.z; viewMatrixDouble[3][0] = -Vector.dot(xaxis, actualEyePosition); viewMatrixDouble[3][1] =-Vector.dot(yaxis, actualEyePosition); viewMatrixDouble[3][2] = -Vector.dot(zaxis, actualEyePosition); */ viewMatrix = new Matrix4f(); viewMatrix.load(getViewMatrixAsFloatBuffer()); } Would be verry greatfull if anyone could verify if this is wrong or right, and if it's wrong; supply me with the right way of doing it... I have read alot of threads and documentations about this but i can't seam to wrapp my head around it... Edit3: Okay with the help of Byte56 (thanks alot for the help) i have now concluded that it's not the viewMatrix that is the problem... I still get the same messedup result; anyone that think that they can find the error in my code, i certenly can't, have bean working on this for 3 days now :(

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