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  • Constructive criticsm on my linear sampling Gaussian blur

    - by Aequitas
    I've been attempting to implement a gaussian blur utilising linear sampling, I've come across a few articles presented on the web and a question posed here which dealt with the topic. I've now attempted to implement my own Gaussian function and pixel shader drawing reference from these articles. This is how I'm currently calculating my weights and offsets: int support = int(sigma * 3.0) weights.push_back(exp(-(0*0)/(2*sigma*sigma))/(sqrt(2*pi)*sigma)); total += weights.back(); offsets.push_back(0); for (int i = 1; i <= support; i++) { float w1 = exp(-(i*i)/(2*sigma*sigma))/(sqrt(2*pi)*sigma); float w2 = exp(-((i+1)*(i+1))/(2*sigma*sigma))/(sqrt(2*pi)*sigma); weights.push_back(w1 + w2); total += 2.0f * weights[i]; offsets.push_back(w1 / weights[i]); } for (int i = 0; i < support; i++) { weights[i] /= total; } Here is an example of my vertical pixel shader: vec3 acc = texture2D(tex_object, v_tex_coord.st).rgb*weights[0]; vec2 pixel_size = vec2(1.0 / tex_size.x, 1.0 / tex_size.y); for (int i = 1; i < NUM_SAMPLES; i++) { acc += texture2D(tex_object, (v_tex_coord.st+(vec2(0.0, offsets[i])*pixel_size))).rgb*weights[i]; acc += texture2D(tex_object, (v_tex_coord.st-(vec2(0.0, offsets[i])*pixel_size))).rgb*weights[i]; } gl_FragColor = vec4(acc, 1.0); Am I taking the correct route with this? Any criticism or potential tips to improving my method would be much appreciated.

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  • Integration error in high velocity

    - by Elektito
    I've implemented a simple simulation of two planets (simple 2D disks really) in which the only force is gravity and there is also collision detection/response (collisions are completely elastic). I can launch one planet into orbit of the other just fine. The collision detection code though does not work so well. I noticed that when one planet hits the other in a free fall it speeds backward and goes much higher than its original position. Some poking around convinced me that the simplistic Euler integration is causing the error. Consider this case. One object has a mass of 1kg and the other has a mass equal to earth. Say the object is 10 meters above ground. Assume that our dt (delta t) is 1 second. The object goes to the height of 9 meters at the end of the first iteration, 7 at the end of the second, 4 at the end of the third and 0 at the end of the fourth iteration. At this points it hits the ground and bounces back with the speed of 10 meters per second. The problem is with dt=1, on the first iteration it bounces back to a height of 10. It takes several more steps to make the object change its course. So my question is, what integration method can I use which fixes this problem. Should I split dt to smaller pieces when velocity is high? Or should I use another method altogether? What method do you suggest? EDIT: You can see the source code here at github:https://github.com/elektito/diskworld/

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  • Wikipedia A* pathfinding algorithm takes a lot of time

    - by Vee
    I've successfully implemented A* pathfinding in C# but it is very slow, and I don't understand why. I even tried not sorting the openNodes list but it's still the same. The map is 80x80, and there are 10-11 nodes. I took the pseudocode from here Wikipedia And this is my implementation: public static List<PGNode> Pathfind(PGMap mMap, PGNode mStart, PGNode mEnd) { mMap.ClearNodes(); mMap.GetTile(mStart.X, mStart.Y).Value = 0; mMap.GetTile(mEnd.X, mEnd.Y).Value = 0; List<PGNode> openNodes = new List<PGNode>(); List<PGNode> closedNodes = new List<PGNode>(); List<PGNode> solutionNodes = new List<PGNode>(); mStart.G = 0; mStart.H = GetManhattanHeuristic(mStart, mEnd); solutionNodes.Add(mStart); solutionNodes.Add(mEnd); openNodes.Add(mStart); // 1) Add the starting square (or node) to the open list. while (openNodes.Count > 0) // 2) Repeat the following: { openNodes.Sort((p1, p2) => p1.F.CompareTo(p2.F)); PGNode current = openNodes[0]; // a) We refer to this as the current square.) if (current == mEnd) { while (current != null) { solutionNodes.Add(current); current = current.Parent; } return solutionNodes; } openNodes.Remove(current); closedNodes.Add(current); // b) Switch it to the closed list. List<PGNode> neighborNodes = current.GetNeighborNodes(); double cost = 0; bool isCostBetter = false; for (int i = 0; i < neighborNodes.Count; i++) { PGNode neighbor = neighborNodes[i]; cost = current.G + 10; isCostBetter = false; if (neighbor.Passable == false || closedNodes.Contains(neighbor)) continue; // If it is not walkable or if it is on the closed list, ignore it. if (openNodes.Contains(neighbor) == false) { openNodes.Add(neighbor); // If it isn’t on the open list, add it to the open list. isCostBetter = true; } else if (cost < neighbor.G) { isCostBetter = true; } if (isCostBetter) { neighbor.Parent = current; // Make the current square the parent of this square. neighbor.G = cost; neighbor.H = GetManhattanHeuristic(current, neighbor); } } } return null; } Here's the heuristic I'm using: private static double GetManhattanHeuristic(PGNode mStart, PGNode mEnd) { return Math.Abs(mStart.X - mEnd.X) + Math.Abs(mStart.Y - mEnd.Y); } What am I doing wrong? It's an entire day I keep looking at the same code.

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  • x axis detection issues platformer starter kit

    - by dbomb101
    I've come across a problem with the collision detection code in the platformer starter kit for xna.It will send up the impassible flag on the x axis despite being nowhere near a wall in either direction on the x axis, could someone could tell me why this happens ? Here is the collision method. /// <summary> /// Detects and resolves all collisions between the player and his neighboring /// tiles. When a collision is detected, the player is pushed away along one /// axis to prevent overlapping. There is some special logic for the Y axis to /// handle platforms which behave differently depending on direction of movement. /// </summary> private void HandleCollisions() { // Get the player's bounding rectangle and find neighboring tiles. Rectangle bounds = BoundingRectangle; int leftTile = (int)Math.Floor((float)bounds.Left / Tile.Width); int rightTile = (int)Math.Ceiling(((float)bounds.Right / Tile.Width)) - 1; int topTile = (int)Math.Floor((float)bounds.Top / Tile.Height); int bottomTile = (int)Math.Ceiling(((float)bounds.Bottom / Tile.Height)) - 1; // Reset flag to search for ground collision. isOnGround = false; // For each potentially colliding tile, for (int y = topTile; y <= bottomTile; ++y) { for (int x = leftTile; x <= rightTile; ++x) { // If this tile is collidable, TileCollision collision = Level.GetCollision(x, y); if (collision != TileCollision.Passable) { // Determine collision depth (with direction) and magnitude. Rectangle tileBounds = Level.GetBounds(x, y); Vector2 depth = RectangleExtensions.GetIntersectionDepth(bounds, tileBounds); if (depth != Vector2.Zero) { float absDepthX = Math.Abs(depth.X); float absDepthY = Math.Abs(depth.Y); // Resolve the collision along the shallow axis. if (absDepthY < absDepthX || collision == TileCollision.Platform) { // If we crossed the top of a tile, we are on the ground. if (previousBottom <= tileBounds.Top) isOnGround = true; // Ignore platforms, unless we are on the ground. if (collision == TileCollision.Impassable || IsOnGround) { // Resolve the collision along the Y axis. Position = new Vector2(Position.X, Position.Y + depth.Y); // Perform further collisions with the new bounds. bounds = BoundingRectangle; } } //This is the section which deals with collision on the x-axis else if (collision == TileCollision.Impassable) // Ignore platforms. { // Resolve the collision along the X axis. Position = new Vector2(Position.X + depth.X, Position.Y); // Perform further collisions with the new bounds. bounds = BoundingRectangle; } } } } } // Save the new bounds bottom. previousBottom = bounds.Bottom; }

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  • 2D Tile Map for Platformer, XML or SQLite?

    - by Stephen Tierney
    I'm developing a 2D platformer with some uni friends. We've based it upon the XNA Platformer Starter Kit which uses .txt files to store the tile map. While this is simple it does not give us enough control and flexibility with level design. I'm doing some research into whether to store level data in an XML file or in a database like SQLite. Which would be the best for this situation? Do either have any drawbacks (performance etc) compared to the other?

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  • matrix 4x4 position data

    - by freefallr
    I understand that a 4x4 matrix holds rotation and position data. The rotation data is held in the 3x3 sub-matrix at the top left of the matrix. The position data is held in the last column of the matrix. e.g. glm::vec3 vParentPos( mParent[3][0], mParent[3][1], mParent[3][2] ); My question is - am I accessing the parent matrix correctly in the example above? I know that opengl uses a different matrix ordering that directx, (row order instead of column order or something), so, should the mParent be accessed as follows instead? glm::vec3 vParentPos( mParent[0][3], mParent[1][3], mParent[2][3] ); thanks!

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  • Need ideas for an algorithm to draw irregular blotchy shapes

    - by Yttermayn
    I'm looking to draw irregular shapes on an x,y grid, and I'd like to come up with a simple, fast method if possible. My only idea so far is to draw a bunch of circles of random sizes very near each other, but at a random distance apart from a more or less central coordinate, then fill in any blank spaces. I realize this is a clunky, inelegant method, hopefully it will give you a rough idea of the kinds of rounded, random blotchy shapesI'm shooting for. Please suggest methods to accomplish this, I'm not so much interested in code. I can noodle that part out myself. Thanks!

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  • Unity: parallel vectors and cross product, how to compare vectors

    - by Heisenbug
    I read this post explaining a method to understand if the angle between 2 given vectors and the normal to the plane described by them, is clockwise or anticlockwise: public static AngleDir GetAngleDirection(Vector3 beginDir, Vector3 endDir, Vector3 upDir) { Vector3 cross = Vector3.Cross(beginDir, endDir); float dot = Vector3.Dot(cross, upDir); if (dot > 0.0f) return AngleDir.CLOCK; else if (dot < 0.0f) return AngleDir.ANTICLOCK; return AngleDir.PARALLEL; } After having used it a little bit, I think it's wrong. If I supply the same vector as input (beginDir equal to endDir), the cross product is zero, but the dot product is a little bit more than zero. I think that to fix that I can simply check if the cross product is zero, means that the 2 vectors are parallel, but my code doesn't work. I tried the following solution: Vector3 cross = Vector3.Cross(beginDir, endDir); if (cross == Vector.zero) return AngleDir.PARALLEL; And it doesn't work because comparison between Vector.zero and cross is always different from zero (even if cross is actually [0.0f, 0.0f, 0.0f]). I tried also this: Vector3 cross = Vector3.Cross(beginDir, endDir); if (cross.magnitude == 0.0f) return AngleDir.PARALLEL; it also fails because magnitude is slightly more than zero. So my question is: given 2 Vector3 in Unity, how to compare them? I need the elegant equivalent version of this: if (beginDir.x == endDir.x && beginDir.y == endDir.y && beginDir.z == endDir.z) return true;

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  • What light attenuation function does UDK use?

    - by ananamas
    I'm a big fan of the light attenuation in UDK. Traditionally I've always used the constant-linear-quadratic falloff function to control how "soft" the falloff is, which gives three values to play with. In UDK you can get similar results, but you only need to tweak one value: FalloffExponent. I'm interested in what the actual mathematical function here is. The UDK lighting reference describes it as follows: FalloffExponent: This allows you to modify the falloff of a light. The default falloff is 2. The smaller the number, the sharper the falloff and the more the brightness is maintained until the radius is reached. Does anyone know what it's doing behind the scenes?

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  • Fitting a rectangle into screen with XNA

    - by alecnash
    I am drawing a rectangle with primitives in XNA. The width is: width = GraphicsDevice.Viewport.Width and the height is height = GraphicsDevice.Viewport.Height I am trying to fit this rectangle in the screen (using different screens and devices) but I am not sure where to put the camera on the Z-axis. Sometimes the camera is too close and sometimes to far. This is what I am using to get the camera distance: //Height of piramid float alpha = 0; float beta = 0; float gamma = 0; alpha = (float)Math.Sqrt((width / 2 * width/2) + (height / 2 * height / 2)); beta = height / ((float)Math.Cos(MathHelper.ToRadians(67.5f)) * 2); gamma = (float)Math.Sqrt(beta*beta - alpha*alpha); position = new Vector3(0, 0, gamma); Any idea where to put the camera on the Z-axis?

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  • OpenGL and gluUnProject, 3d object following mouse

    - by Robert
    i have a 3d object and i want him to "follow" my mouse position, so i use gluUnProject function to convert screen coordinates to 3d world coordinates and i translate this object with the new coordinates. Its working but i have a problem, my object can follow my mouse but he is moving extremely fast, when i move my mouse a little bit(something like 2 pixels), its moving extremly fast in the 3d world. I want something like that : http://www.youtube.com/watch?v=90zS8SVUAIY (red circle following mouse). Thanks for your help.

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  • Modern Shader Book?

    - by Michael Stum
    I'm interested in learning about Shaders: What are they, when/for what would I use them, and how to use them. (Specifically I'm interested in Water and Bloom effects, but I know close to 0 about Shaders, so I need a general introduction). I saw a lot of books that are a couple of years old, so I don't know if they still apply. I'm targeting XNA 4.0 at the moment (which I believe means HLSL Shaders for Shader Model 4.0), but anything that generally targets DirectX 11 and OpenGL 4 is helpful I guess.

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  • Setting Anchor Point

    - by Siddharth
    I want to set anchor point for the sprite like cocos2d has done for their implementation. I do not found any thing like that in andengine so please provide guidance on that. I want to move the sprite on touch so I use following code but that does not work for me. super.setPosition(pX - this.getWidthScaled() / 2, pY - this.getHeightScaled() / 2); Because I touch on the corner of the image but automatically it comes at center of the image because of above code. I want to remain the touch at desire position and drag it. For me the anchor point became useful. But I don't found anything in andengine.

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  • Stop map from scrolling but let player still move?

    - by ChocoMan
    I have a basic method of scrolling around on a map (moving the map instead of the player), but at when the player gets to a certain proximity to the edge, how do you stop the map from scrolling, but still allow the player to move around until it is away from that proximity? I'm not looking for any code. Just a suggestion so that I can implement it myself. I can see it visually (creating 4 boxed intersecting boundaries for the player to enter), but not sure how to come about stopping and resuming the scrolling of the map.

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  • What is the benefit of triple buffering?

    - by user782220
    I read everything written in a previous question. From what I understand in double buffering the program must wait until the finished drawing is copied or swapped before starting the next drawing. In triple buffering the program has two back buffers and can immediately start drawing in the one that is not involved in such copying. But with triple buffering if you're in a situation where you can take advantage of the third buffer doesn't that suggest that you are drawing frames faster than the monitor can refresh. So then you don't actually get a higher frame rate. So what is the benefit of triple buffering then?

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  • OpenGL flickerinng near the edges

    - by Daniel
    I am trying to simulate particles moving around the scene with OpenCL for computation and OpenGL for rendering with GLUT. There is no OpenCL-OpenGL interop yet, so the drawing is done in the older fixed pipeline way. Whenever circles get close to the edges, they start to flicker. The drawing should draw a part of the circle on the top of the scene and a part on the bottom. The effect is the following: The balls you see on the bottom should be one part on the bottom and one part on the top. Wrapping around the scene, so to say, but they constantly flicker. The code for drawing them is: void Scene::drawCircle(GLuint index){ glMatrixMode(GL_MODELVIEW); glLoadIdentity(); glTranslatef(pos.at(2*index),pos.at(2*index+1), 0.0f); glBegin(GL_TRIANGLE_FAN); GLfloat incr = (2.0 * M_PI) / (GLfloat) slices; glColor3f(0.8f, 0.255f, 0.26f); glVertex2f(0.0f, 0.0f); glColor3f(1.0f, 0.0f, 0.0f); for(GLint i = 0; i <=slices; ++i){ GLfloat x = radius * sin((GLfloat) i * incr); GLfloat y = radius * cos((GLfloat) i * incr); glVertex2f(x, y); } glEnd(); } If it helps, this is the reshape method: void Scene::reshape(GLint width, GLint height){ if(0 == height) height = 1; //Prevent division by zero glViewport(0, 0, width, height); glMatrixMode(GL_PROJECTION); glLoadIdentity(); gluOrtho2D(xmin, xmax, ymin, ymax); std::cout << xmin << " " << xmax << " " << ymin << " " << ymax << std::endl; }

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  • OpenGL Tessellation makes point

    - by urza57
    A little problem with my tessellation shader. I try to implement a simple tessellation shader but it only makes points. Here's my vertex shader : out vec4 ecPosition; out vec3 ecNormal; void main( void ) { vec4 position = gl_Vertex; gl_Position = gl_ModelViewProjectionMatrix * position; ecPosition = gl_ModelViewMatrix * position; ecNormal = normalize(gl_NormalMatrix * gl_Normal); } My tessellation control shader : layout(vertices = 3) out; out vec4 ecPosition3[]; in vec3 ecNormal[]; in vec4 ecPosition[]; out vec3 myNormal[]; void main() { gl_out[gl_InvocationID].gl_Position = gl_in[gl_InvocationID].gl_Position; myNormal[gl_InvocationID] = ecNormal[gl_InvocationID]; ecPosition3[gl_InvocationID] = ecPosition[gl_InvocationID]; gl_TessLevelOuter[0] = float(4.0); gl_TessLevelOuter[1] = float(4.0); gl_TessLevelOuter[2] = float(4.0); gl_TessLevelInner[0] = float(4.0); } And my Tessellation Evaluation shader: layout(triangles, equal_spacing, ccw) in; in vec3 myNormal[]; in vec4 ecPosition3[]; out vec3 ecNormal; out vec4 ecPosition; void main() { float u = gl_TessCoord.x; float v = gl_TessCoord.y; float w = gl_TessCoord.z; vec3 position = vec4(gl_in[0].gl_Position.xyz * u + gl_in[1].gl_Position.xyz * v + gl_in[2].gl_Position.xyz * w ); vec3 position2 = vec4(ecPosition3[0].xyz * u + ecPosition3[1].xyz * v + ecPosition3[2].xyz * w ); vec3 normal = myNormal[0] * u + myNormal[1] * v + myNormal[2] * w ); ecNormal = normal; gl_Position = vec4(position, 1.0); ecPosition = vec4(position2, 1.0); } Thank you !

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  • Calculating the position of an object with regards to current position using OpenGL like matrices

    - by spartan2417
    i have a 1st person camera that collides with walls, i also have a small sphere in front of my camera denoted by the camera position plus the distance ahead. I cannot get the postion of the sphere but i have the position of my camera. e.g. i need to find the position of the point or at the very least find away of calculating the position using the camera positions. code: static Float P_z = 0; P_z = -15; PushMatrix(); LoadMatrix(&Inv); Material(SCEGU_AMBIENT, 0x00000066); TranslateXYZ(0,0,P_z); ScaleXYZ(0.1f,0.1f,0.1f); pointer.Render(); PopMatrix(); where Inv is the camera positions (Inv.w.x,Inv.w.z), pointer is the sphere.

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  • Looking for a good actionscript 3 book

    - by Jari Komppa
    I've been looking for a book on actionscript3 development, but while there's tons of books out there, nobody seems to want to recommend any specific one. One book I've been pointed towards is the cookbook by o'reilly, but it, like most books out there, seems to be based on the assumption that I'm using flexbuilder or flash. Instead, I'm "just" using flashdevelop, or the free SDK directly. I've also been told to just go with the api reference and live with it. I could do that, I suppose, but I'd rather have a book that gives me the big picture. Kind of like with cocoa, there's the hillegrass' book, or the red book of OpenGL. So, what would be the actionscript3 book out there?

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  • How do I draw a point sprite using OpenGL ES on Android?

    - by nbolton
    Edit: I'm using the GL enum, which is incorrect since it's not part of OpenGL ES (see my answer). I should have used GL10, GL11 or GL20 instead. Here's a few snippets of what I have so far... void create() { renderer = new ImmediateModeRenderer(); tiles = Gdx.graphics.newTexture( Gdx.files.getFileHandle("res/tiles2.png", FileType.Internal), TextureFilter.MipMap, TextureFilter.Linear, TextureWrap.ClampToEdge, TextureWrap.ClampToEdge); } void render() { Gdx.gl.glClear(GL10.GL_COLOR_BUFFER_BIT | GL10.GL_DEPTH_BUFFER_BIT); Gdx.gl.glClearColor(0.6f, 0.7f, 0.9f, 1); } void renderSprite() { int handle = tiles.getTextureObjectHandle(); Gdx.gl.glBindTexture(GL.GL_TEXTURE_2D, handle); Gdx.gl.glEnable(GL.GL_POINT_SPRITE); Gdx.gl11.glTexEnvi(GL.GL_POINT_SPRITE, GL.GL_COORD_REPLACE, GL.GL_TRUE); renderer.begin(GL.GL_POINTS); renderer.vertex(pos.x, pos.y, pos.z); renderer.end(); } create() is called once when the program starts, and renderSprites() is called for each sprite (so, pos is unique to each sprite) where the sprites are arranged in a sort-of 3D cube. Unfortunately though, this just renders a few white dots... I suppose that the texture isn't being bound which is why I'm getting white dots. Also, when I draw my sprites on anything other than 0 z-axis, they do not appear -- I read that I need to crease my zfar and znear, but I have no idea how to do this using libgdx (perhaps it's because I'm using ortho projection? What do I use instead?). I know that the texture is usable, since I was able to render it using a SpriteBatch, but I guess I'm not using it properly with OpenGL.

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  • how to link a c++ object to a local variable in Lua

    - by MahanGM
    I'm completing my scripting interface with Lua, but recently I've stuck at some point. I have several functions for my Entitiy events like Update(). I have a function called create_entitiy() which instantiate a new entity from a given entity index: function Update() local bullet = create_entity(0, 0, "obj_bullet") end create_entity returns a table which is the properties of the created entity. Now how can I make a connection between bullet variable and my newly created object? Right now for previously added objects to the scene, I simply set a global table for each of them and then after every call to Update(), I go through registered names to find object tables and perform new changes. Like the one below: function Update() if keyboard_key_press(vk_right) then obj_player.x += 3 end I can get obj_player table because I know its name from C++, plus I can get it as a global table and simply reach for the first instance named obj_player. Is there any solution for me to make bullet variable act like this? I was thinking to get all local variables in Update() function and check for every one to see if is it table and it has an unique field attached to it like id, this way I can determine that this is an object table and do the rest of the process. By the way, is this interface going to work easier with luaBind if I implement it? Bottom line: How can I make a local variable in Lua that receives a table from create_entity function and track that local variable to capture it from C++. e. g. function Update() local bullet = create_entity(0, 0, "obj_bullet") bullet.x = 10 <== Commit a change in table end Now I want to get variable bullet from C++. And it's not just this variable, there might be a ton of these local variables with different names.

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  • What does SetTextureStage(0, D3DTSS_COLORARG2, 0) in DirectX mean?

    - by Vite Falcon
    I'm trying to convert some DirectX code to Ogre3D and was wondering what the following translates to: pDev->SetTextureStage(0, D3DTSS_TEXCOORDINDEX, 0) pDev->SetTextureStage(0, D3DTSS_COLORARG1, D3DTA_TEXTURE) pDev->SetTextureStage(0, D3DTSS_COLOROP, D3DTOP_MODULATE) pDev->SetTextureStage(0, D3DTSS_COLORARG2, 0) What is the modulation operation happening here? Is the texture getting modulated with the background? Or is it getting zeroed? I've tried searching for what this means and unfortunately I haven't come across anything meaningful. Any help to shed light on this matter will be much appreciated.

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  • 3D BSP rendering for maps made in 2d platform style

    - by Dev Joy
    I wish to render a 3D map which is always seen from top, camera is in sky and always looking at earth. Sample of a floor layout: I don't think I need complex structures like BSP trees to render them. I mean I can divide the map in grids and render them like done in 2D platform games. I just want to know if this is a good idea and what may go wrong if I don't choose a BSP tree rendering here. Please also mention is any better known rendering techniques are available for such situations.

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  • GLSL Shader Effects: How to do motion blur, etc?

    - by DevilWithin
    I am not sure how right it is to ask this question, but still here it goes. I have a full 2D environment, with sprites going around as landscape, characters, etc And to make it more state-of-art looking, i want to implement a motion blur effect, similar to modern FPS's (i.e. crysis) blur when moving fast the camera. In a sidescroller, the desired effect is having this slight blur appearing to give the idea of fast movement, when the camera is moving. If anyone could give me some tips on doing this, im assuming in a pixel shader, i'd be grate. Also, if anyone has other good tips on cool pixel shader effects for 2D games it would be awesome, like some stylizing post fx, such as previous Prince of Persia illustrative style. Thanks

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  • Is there any hueristic to polygonize a closed 2d-raster shape with n triangles?

    - by Arthur Wulf White
    Lets say we have a 2d image black on white that shows a closed geometric shape. Is there any (not naive brute force) algorithm that approximates that shape as closely as possible with n triangles? If you want a formal definition for as closely as possible: Approximate the shape with a polygon that when rendered into a new 2d image will match the largest number of pixels possible with the original image.

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