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  • Must all AI states be able to react to any event?

    - by Prog
    FSMs implemented with the State design pattern are a common way to design AI agents. I am familiar with the State design pattern and know how to implement it. How is this used in games to design AI agents? Consider a simplified class Monster, representing an AI agent: class Monster { State state; // other fields omitted public void update(){ // called every game-loop cycle state.execute(this); } public void setState(State state){ this.state = state; } // irrelevant stuff omitted } There are several State subclasses implementing execute() differently. So far, classic State pattern. AI agents are subject to environmental effects and other objects communicating with them. For example, an AI agent might tell another AI agent to attack (i.e. agent.attack()). Or a fireball might tell an AI agent to fall down. This means that the agent must have methods such as attack() and fallDown(), or commonly some message receiving mechanism to understand such messages. With an FSM, the current State of the agent should be the one taking care of such method calls - i.e. the agent delegates to the current state upon every event. Is this correct? If correct, how is this done? Are all states obligated by their superclass to implement methods such as attack(), fallDown() etc., so the agent can always delegate to them on almost every event? Or is it done in some other way?

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  • most efficient AABB vs Ray collision algorithms

    - by Asher Einhorn
    Is there a known 'most efficient' algorithm for AABB vs Ray collision detection? I recently stumbled accross Arvo's AABB vs Sphere collision algorithm, and I am wondering if there is a similarly noteworthy algorithm for this. One must have condition for this algorithm is that I need to have the option of querying the result for the distance from the ray's origin to the point of collision. having said this, if there is another, faster algorithm which does not return distance, then in addition to posting one that does, also posting that algorithm would be very helpful indeed. Please also state what the function's return argument is, and how you use it to return distance or a 'no-collision' case. For example, does it have an out parameter for the distance as well as a bool return value? or does it simply return a float with the distance, vs a value of -1 for no collision? (For those that don't know: AABB = Axis Aligned Bounding Box)

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  • Fast determination of whether objects are onscreen in 2D

    - by Ben Ezard
    So currently, I have this in each object's renderer's update method: float a = transform.position.x * Main.scale; float b = transform.position.y * Main.scale; float c = Camera.main.transform.position.x * Main.scale; float d = Camera.main.transform.position.y * Main.scale; onscreen = a + width - c > 0 && a - c < GameView.width && b + height - d > 0 && b - d < GameView.height; transform.position is a 2D vector containing the game engine's definition of where the object is - this is then multiplied by Main.scale to translate that coordinate into actual screen space Similarly, Camera.main.transform.position is the in-engine representation of where the main camera is, and this is also multiplied by Main.scale The problem is, as my game is tile-based, thousands of these updates get called every frame, just to determine whether or not each object should be drawn - how can I improve this please?

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  • Changing direction after collision

    - by Balint
    In the first tutorial for GameMaker (catch the clown), I want to set the direction of the clown after the collision with the wall. I want to do it by pressing the wall object with the mouse (before the collision, to set the angle parameter). For example by pressing only once the wall object it would change the clown's direction after collision by 45 degrees, twice by 90 degrees, and so on. How can I do that?

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  • Handling buildings in isometric tile based games

    - by MustSeeMelons
    A simple question, to which i couldn't find a definitive answer - how to manage buildings on a tiled map? Should the building be sliced in to tiles or one big image? EDIT: The game is being built from scratch using C++/SDL 2.0, it will be a turn based strategy, something like Fallout 1 & 2 without the hex grid, a simple square grid, where the Y axis is squished by 50%. Buildings can span multiple tiles, the characters move tile by tile. For now, the terrain is completely flat. Some basic functionality is in place, so I'm aiming to advancing the terrain and levels them selves - adding buildings, gates, cliffs, not sure about the elevation.

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  • Correct way to use Farseer Physics in XNA

    - by user1640602
    I am using Farseer Physics for my 2D sidescroller game and I'm not sure how to proceed with it. I currently have a Sprite class (handles nothing but graphics), a GameObject class (contains specific object info like hit points), a World object which contains the list of Bodies, and a Level object which contains all of these objects. Originally I was trying to keep track of the Sprites, GameObjects, and Bodies separately because I felt that would provide loose coupling but it quickly became a headache. So my new idea was to add a Sprite member to the GameObject class but I'm still not sure how to maintain the Bodies because they have to communicate with GameObject. Specifically, my issue is this: The position of the Body is used to draw the Sprite inside of the Level. In order to do that I would have to maintain a link between GameObjects and Bodies. Is this correct or is there a better way to architect my game? If any of this is unclear please ask and I'll try to clarify. Thank you in advance for any help.

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  • Very slow direct3D texture sampling

    - by __dominic
    Hi, So I'm writing a small game using Direct3D 9 and I'm using multitexturing for the terrain. All I'm doing is sampling 3 textures and a blend map and getting the overall color from the three textures based on the color channels from the blend map. Anyway, I am getting a massive frame rate drop when I sample more than 1 texture, I'm going from 120+ fps to just under 50. This is the HLSL code responsible for the slow down: float3 ground = tex2D(GroundTex, multiTex).rgb; float3 stone = tex2D(StoneTex, multiTex).rgb; float3 grass = tex2D(GrassTex, multiTex).rgb; float3 blend = tex2D(BlendMapTex, blendMap).rgb; Am I doing it wrong ? If anyone has any info or tips about texture sampling or anything, that would be nice. Thanks.

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  • Need some help implementing VBO's with Frustum Culling

    - by Isracg
    i'm currently developing my first 3D game for a school project, the game world is completely inspired by minecraft (world completely made out of cubes). I'm currently seeking to improve the performance trying to implement vertex buffer objects but i'm stuck, i already have this methods implemented: Frustum culling, only drawing exposed faces and distance culling but i have the following doubts: I currently have about 2^24 cubes in my world, divided in 1024 chunks of 16*16*64 cubes, right now i'm doing immediate mode rendering, which works well with frustum culling, if i implement one VBO per chunk, do i have to update that VBO each time i move the camera (to update the frustum)? is there a performance hit with this? Can i dynamically change the size of each VBO? of do i have to make each one the biggest possible size (the chunk completely filled with objects)?. Would i have to keep each visited chunk in memory or could i efficiently remove that VBO and recreated it when needed?.

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  • Best way to mask 2D sprites in XNA?

    - by electroflame
    I currently am trying to mask some sprites. Rather than explaining it in words, I've made up some example pictures: The area to mask (in white) Now, the red sprite that needs to be cropped. The final result. Now, I'm aware that in XNA you can do two things to accomplish this: Use the Stencil Buffer. Use a Pixel Shader. I have tried to do a pixel shader, which essentially did this: float4 main(float2 texCoord : TEXCOORD0) : COLOR0 { float4 tex = tex2D(BaseTexture, texCoord); float4 bitMask = tex2D(MaskTexture, texCoord); if (bitMask.a > 0) { return float4(tex.r, tex.g, tex.b, tex.a); } else { return float4(0, 0, 0, 0); } } This seems to crop the images (albeit, not correct once the image starts to move), but my problem is that the images are constantly moving (they aren't static), so this cropping needs to be dynamic. Is there a way I could alter the shader code to take into account it's position? Alternatively, I've read about using the Stencil Buffer, but most of the samples seem to hinge on using a rendertarget, which I really don't want to do. (I'm already using 3 or 4 for the rest of the game, and adding another one on top of it seems overkill) The only tutorial I've found that doesn't use Rendertargets is one from Shawn Hargreaves' blog over here. The issue with that one, though is that it's for XNA 3.1, and doesn't seem to translate well to XNA 4.0. It seems to me that the pixel shader is the way to go, but I'm unsure of how to get the positioning correct. I believe I would have to change my onscreen coordinates (something like 500, 500) to be between 0 and 1 for the shader coordinates. My only problem is trying to work out how to correctly use the transformed coordinates. Thanks in advance for any help!

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  • 3D Collision help

    - by Taylor
    I'm having difficulties with my project. I'm quite new in XNA. Anyway, I'm trying to make 3D game and I'm already stuck on one basic thing. I have terrain made from a heightmap, and an avatar model. I want to set up some collisions for game so the player won't go through the ground. But I just don't know how to detect collisions for so complex an object. I could just make a simple box collision for my avatar, but what about the ground? I already implemented the JigLibX physics engine in my project and I know that I can make a collision map with heightmap, but I can't find any tutorials or help with this. So how can I set proper collision for complex objects? How can I detect heightmap collisions in JigLibX? Just some links to tutorials would be enough. Thanks in advance!

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  • HLSL What you get when you subtract world position from InvertViewProjection.Transform?

    - by cubrman
    In one of NVIDIA's Vertex shaders (the metal one) I found the following code: // transform object normals, tangents, & binormals to world-space: float4x4 WorldITXf : WorldInverseTranspose < string UIWidget="None"; >; // provide tranform from "view" or "eye" coords back to world-space: float4x4 ViewIXf : ViewInverse < string UIWidget="None"; >; ... float4 Po = float4(IN.Position.xyz,1); // homogeneous location coordinates float4 Pw = mul(Po,WorldXf); // convert to "world" space OUT.WorldView = normalize(ViewIXf[3].xyz - Pw.xyz); The term OUT.WorldView is subsequently used in a Pixel Shader to compute lighting: float3 Ln = normalize(IN.LightVec.xyz); float3 Nn = normalize(IN.WorldNormal); float3 Vn = normalize(IN.WorldView); float3 Hn = normalize(Vn + Ln); float4 litV = lit(dot(Ln,Nn),dot(Hn,Nn),SpecExpon); DiffuseContrib = litV.y * Kd * LightColor + AmbiColor; SpecularContrib = litV.z * LightColor; Can anyone tell me what exactly is WorldView here? And why do they add it to the normal?

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  • A* how make natural look path?

    - by user11177
    I've been reading this: http://theory.stanford.edu/~amitp/GameProgramming/Heuristics.html But there are some things I don't understand, for example the article says to use something like this for pathfinding with diagonal movement: function heuristic(node) = dx = abs(node.x - goal.x) dy = abs(node.y - goal.y) return D * max(dx, dy) I don't know how do set D to get a natural looking path like in the article, I set D to the lowest cost between adjacent squares like it said, and I don't know what they meant by the stuff about the heuristic should be 4*D, that does not seem to change any thing. This is my heuristic function and move function: def heuristic(self, node, goal): D = 10 dx = abs(node.x - goal.x) dy = abs(node.y - goal.y) return D * max(dx, dy) def move_cost(self, current, node): cross = abs(current.x - node.x) == 1 and abs(current.y - node.y) == 1 return 19 if cross else 10 Result: The smooth sailing path we want to happen: The rest of my code: http://pastebin.com/TL2cEkeX

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  • Rendering Texture Quad to Screen or FBO (OpenGL ES)

    - by Usman.3D
    I need to render the texture on the iOS device's screen or a render-to-texture frame buffer object. But it does not show any texture. It's all black. (I am loading texture with image myself for testing purpose) //Load texture data UIImage *image=[UIImage imageNamed:@"textureImage.png"]; GLuint width = FRAME_WIDTH; GLuint height = FRAME_HEIGHT; //Create context void *imageData = malloc(height * width * 4); CGColorSpaceRef colorSpace = CGColorSpaceCreateDeviceRGB(); CGContextRef context = CGBitmapContextCreate(imageData, width, height, 8, 4 * width, colorSpace, kCGImageAlphaPremultipliedLast | kCGBitmapByteOrder32Big); CGColorSpaceRelease(colorSpace); //Prepare image CGContextClearRect(context, CGRectMake(0, 0, width, height)); CGContextDrawImage(context, CGRectMake(0, 0, width, height), image.CGImage); glGenTextures(1, &texture); glBindTexture(GL_TEXTURE_2D, texture); glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_NEAREST); glTexImage2D(GL_TEXTURE_2D, 0, GL_RGBA, width, height, 0, GL_RGBA, GL_UNSIGNED_BYTE, imageData); glTexParameterf(GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, GL_CLAMP_TO_EDGE); glTexParameterf(GL_TEXTURE_2D, GL_TEXTURE_WRAP_T, GL_CLAMP_TO_EDGE); Simple Texture Quad drawing code mentioned here //Bind Texture, Bind render-to-texture FBO and then draw the quad const float quadPositions[] = { 1.0, 1.0, 0.0, -1.0, 1.0, 0.0, -1.0, -1.0, 0.0, -1.0, -1.0, 0.0, 1.0, -1.0, 0.0, 1.0, 1.0, 0.0 }; const float quadTexcoords[] = { 1.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 1.0, 1.0 }; // stop using VBO glBindBuffer(GL_ARRAY_BUFFER, 0); // setup buffer offsets glVertexAttribPointer(ATTRIB_VERTEX, 3, GL_FLOAT, GL_FALSE, 3*sizeof(float), quadPositions); glVertexAttribPointer(ATTRIB_TEXCOORD0, 2, GL_FLOAT, GL_FALSE, 2*sizeof(float), quadTexcoords); // ensure the proper arrays are enabled glEnableVertexAttribArray(ATTRIB_VERTEX); glEnableVertexAttribArray(ATTRIB_TEXCOORD0); //Bind Texture and render-to-texture FBO. glBindTexture(GL_TEXTURE_2D, GLid); //Actually wanted to render it to render-to-texture FBO, but now testing directly on default FBO. //glBindFramebuffer(GL_FRAMEBUFFER, textureFBO[pixelBuffernum]); // draw glDrawArrays(GL_TRIANGLES, 0, 2*3); What am I doing wrong in this code? P.S. I'm not familiar with shaders yet, so it is difficult for me to make use of them right now.

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  • GestureListener's fling method doesn't get called

    - by nosferat
    I'm using SimpleGestureDetector from the libgdx-users Wiki as my InputProcessor. I set it in the created() method: Gdx.input.setInputProcess(new SimpleDirectionGestureDetector(charController)); charController is my class which implements the DirectionListener interface defined in the SimpleDirectionGestureDetector class and it is responsible for moving the player character. However the character doesn't change direction when I'm performing a fling action in any direction. I've checked and the fling() method in the SimpleDirectionGesture class doesn't get called and I have no idea why, since everything seems good. What am I doing wrong?

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  • Most suited technology for browser games?

    - by Tingle
    I was thinking about making a 2D MMO which I would in the long run support on various plattforms like desktop, mac, browser, android and ios. The server will be c++/linux based and the first client would go in the browser. So I have done some research and found that webgl and flash 11 support hardware accelerated rendering, I saw some other things like normal HTML5 painting. So my question is, which technology should I use for such a project? My main goal would be that the users have a hassle free experience using what there hardware can give them with hardware acceleration. And the client should work on the most basic out-of-the-box pc's that any casual pc or mac user has. And another criteria would be that it should be developer friendly. I've messed with webgl abit for example and that would require writing a engine from scratch - which is acceptable but not preferred. Also, in case of non-actionscript, which kind language is most prefered in terms of speed and flexability. I'm not to fond of javascript due to the garbage collector but have learned to work around it. Thank you for you time.

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  • Buffer System For Items

    - by Ohmages
    I am going to reference this image of what I want to accomplish in JavaScript. This is the Diablo buffer system. This question may be a bit advanced (or possibly not even allowed). But I was wondering how you might go about implementing this type of system in a JavaScript game. Currently to implement such a system in JavaScript escapes me, and I am turning to SO to get some suggestions, ideas, and hopefully some insight in how I could accomplish this without being to costly on the CPU. Some thoughts of mine for implementing such a system would be to: Create DIVS within a DIV that hold each position of the inventory Go through each item you own in a container and see which DIV it belongs to Make said item images the DIVs image This type of system might possibly work if ALL items were 1x1, but for this example its not going to work out. I am at a complete lost of ideas how to even accomplish this. Although, maybe rendering directly to the canvas and checking mouse cords could work, there would more than likely be A HUGE annoyance when checking if other items are overlapping each other (meaning you cant place the item down, and possibly switching item with the cursor item ). That said, what am I left with? Do I need to makeshift my own hack system with messy code, or is there some source out there (that I don't know about) that has replicated this type of system in their own game. I would be very grateful to get some replies on how you might go about doing this, and will accept answers that can logically explain how you might implement such a system (code is not required). P.S. Id like to use pure JavaScript, and nothing else (even though it might be "reinventing the wheel", I also like to learn).

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  • Optimal way to learn DirectX?

    - by BluePhase
    I am finding it very difficult to learn DirectX 11. The MSDN website is just full of unorganized information that doesn't seem to help at all. I am particularly looking for something that explains many if not all aspects of developing with DirectX 11. I have been searching for weeks and still come up empty. I have found some books but they don't really explain the fundamentals of the language at all. Thanks in advanced.

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  • 2D XNA Game Engine with a Good Wiki [closed]

    - by gcx
    I'm a newbie game developer. I'm planning to develop a XBOX (with a Kinect to double the fun) game. I've researched some 2D game engines that i can use in my project. After some research I've found IceCream engine and it looks delicious with its Milkshake editor. But I can't seem to find "working" game source examples for that engine and its own website's tutorial is not very sufficent. (If you are familiar with this engine) do you know any community that has helpful resources for this particular engine? If not, which engines do you recommend (that has a great wiki) for a XNA based XBOX - Kinect game?

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  • How do you maintain content size vs. content quality in a mobile application?

    - by PeterK
    I am developing my first Cocos2d iPhone/iPad game that includes quite a few sprites, I would need approximately 80 different. As this is for both normal and HD displays I have 2x of each sprite. I am using TexturePacker to optimize the thing. I would like to ask if there are any rules-of-thumb, tricks, ideas etc. to adjust to in regards to size of content, quality and how you maintain high-quality HD-based graphics due to its size vs. the device memory sizes? Also, is it a good idea to only have one copy of the sprites and scale it using code?

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  • what knowledge would I need to make a good simulation games

    - by Skeith
    I have an idea for a game like theme park but don't know how simulation games are made. I am not some noob on his first game so I appreciated constructive answers instead of "its hard, don't do it". What I want is to know how simulation game mechanics are put together. I figure it would be heaver on the AI than normal games and not knowing much about AI would like to know some programming techniques I should look into for this style game. specific techniques please not just a book on ai. what sort of architecture would be used? I guess it would have some sort of probability engine with pre designed events that are triggered based on the AI state. Would it use a FSM or be purely event driven ? Any information on how a sims game functions would be cool.

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  • How do you maintain content size vs. content quality in an application?

    - by PeterK
    I am developing my first Cocos2d iPhone/iPad game that includes quite a few sprites, I would need approximately 80 different. As this is for both normal and HD displays I have 2x of each sprite. I am using TexturePacker to optimize the thing. I would like to ask if there are any rules-of-thumb, tricks, ideas etc. to adjust to in regards to size of content, quality and how you maintain high-quality HD-based graphics due to its size vs. the device memory sizes? Also, is it a good idea to only have one copy of the sprites and scale it using code?

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  • Simple 2 player server

    - by Sourabh Lal
    I have recently started learning javascript and html and have developed simple 2 player games such as tick-tack-toe, battleship, and dots&boxes. However these 2 player games can only be played on one computer (i.e. the 2 players must sit together) However, I want to modify this so that one can play with a friend on a different computer. Any suggestions on how this is possible? Also since I am a beginner please do not assume that I know all the jargon.

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  • Why is this 8 puzzle unsolvable?

    - by Ashwin
    I am developing a 8 puzzle game. I went through the rules in this (see Detecting Unsolvable Puzzles) link, which tell you how to detect if an initial state is unsolvable. It says that if the number of inversions is odd, then the goal state cannot be reached and if even the goal state can be reached. Inversion is defined as Given a board, an inversion is any pair of blocks i and j where i < j but i appears after j when considering the board in row-major order (row 0, followed by row 1, and so forth). There is a 8-puzzle solver(applet) here. Choose 8-puzzle from the options. 1,0,3,2,4,5,6,7,8 and 7,0,2,8,5,3,6,4,1 As you can see both of them contain an even number of inversions. Still the program says that the puzzle is unsolvable. So is the Princeton link wrong?

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  • HLSL Shader not working right?

    - by dvds414
    Okay so I have this shader for ambient occlusion. It loads to world correctly, but it just shows all the models as being white. I do not know why. I am just running the shader while the model is rendering, is that correct? or do I need to make a render target or something? if so then how? I'm using C++. Here is my shader. float sampleRadius; float distanceScale; float4x4 xProjection; float4x4 xView; float4x4 xWorld; float3 cornerFustrum; struct VS_OUTPUT { float4 pos : POSITION; float2 TexCoord : TEXCOORD0; float3 viewDirection : TEXCOORD1; }; VS_OUTPUT VertexShaderFunction( float4 Position : POSITION, float2 TexCoord : TEXCOORD0) { VS_OUTPUT Out = (VS_OUTPUT)0; float4 WorldPosition = mul(Position, xWorld); float4 ViewPosition = mul(WorldPosition, xView); Out.pos = mul(ViewPosition, xProjection); Position.xy = sign(Position.xy); Out.TexCoord = (float2(Position.x, -Position.y) + float2( 1.0f, 1.0f ) ) * 0.5f; float3 corner = float3(-cornerFustrum.x * Position.x, cornerFustrum.y * Position.y, cornerFustrum.z); Out.viewDirection = corner; return Out; } texture depthTexture; texture randomTexture; sampler2D depthSampler = sampler_state { Texture = <depthTexture>; ADDRESSU = CLAMP; ADDRESSV = CLAMP; MAGFILTER = LINEAR; MINFILTER = LINEAR; }; sampler2D RandNormal = sampler_state { Texture = <randomTexture>; ADDRESSU = WRAP; ADDRESSV = WRAP; MAGFILTER = LINEAR; MINFILTER = LINEAR; }; float4 PixelShaderFunction(VS_OUTPUT IN) : COLOR0 { float4 samples[16] = { float4(0.355512, -0.709318, -0.102371, 0.0 ), float4(0.534186, 0.71511, -0.115167, 0.0 ), float4(-0.87866, 0.157139, -0.115167, 0.0 ), float4(0.140679, -0.475516, -0.0639818, 0.0 ), float4(-0.0796121, 0.158842, -0.677075, 0.0 ), float4(-0.0759516, -0.101676, -0.483625, 0.0 ), float4(0.12493, -0.0223423, -0.483625, 0.0 ), float4(-0.0720074, 0.243395, -0.967251, 0.0 ), float4(-0.207641, 0.414286, 0.187755, 0.0 ), float4(-0.277332, -0.371262, 0.187755, 0.0 ), float4(0.63864, -0.114214, 0.262857, 0.0 ), float4(-0.184051, 0.622119, 0.262857, 0.0 ), float4(0.110007, -0.219486, 0.435574, 0.0 ), float4(0.235085, 0.314707, 0.696918, 0.0 ), float4(-0.290012, 0.0518654, 0.522688, 0.0 ), float4(0.0975089, -0.329594, 0.609803, 0.0 ) }; IN.TexCoord.x += 1.0/1600.0; IN.TexCoord.y += 1.0/1200.0; normalize (IN.viewDirection); float depth = tex2D(depthSampler, IN.TexCoord).a; float3 se = depth * IN.viewDirection; float3 randNormal = tex2D( RandNormal, IN.TexCoord * 200.0 ).rgb; float3 normal = tex2D(depthSampler, IN.TexCoord).rgb; float finalColor = 0.0f; for (int i = 0; i < 16; i++) { float3 ray = reflect(samples[i].xyz,randNormal) * sampleRadius; //if (dot(ray, normal) < 0) // ray += normal * sampleRadius; float4 sample = float4(se + ray, 1.0f); float4 ss = mul(sample, xProjection); float2 sampleTexCoord = 0.5f * ss.xy/ss.w + float2(0.5f, 0.5f); sampleTexCoord.x += 1.0/1600.0; sampleTexCoord.y += 1.0/1200.0; float sampleDepth = tex2D(depthSampler, sampleTexCoord).a; if (sampleDepth == 1.0) { finalColor ++; } else { float occlusion = distanceScale* max(sampleDepth - depth, 0.0f); finalColor += 1.0f / (1.0f + occlusion * occlusion * 0.1); } } return float4(finalColor/16, finalColor/16, finalColor/16, 1.0f); } technique SSAO { pass P0 { VertexShader = compile vs_3_0 VertexShaderFunction(); PixelShader = compile ps_3_0 PixelShaderFunction(); } }

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  • Understanding dot notation

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

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