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• Obtain rectangle indicating 2D world space camera can see

  - by Gareth

  I have a 2D tile based game in XNA, with a moveable camera that can scroll around and zoom. I'm trying to obtain a rectangle which indicates the area, in world space, that my camera is looking at, so I can render anything this rectangle intersects with (currently, everything is rendered). So, I'm drawing the world like this: _SpriteBatch.Begin( SpriteSortMode.FrontToBack, null, SamplerState.PointClamp, // Don't smooth null, null, null, _Camera.GetTransformation()); The GetTransformation() method on my Camera object does this: public Matrix GetTransformation() { _transform = Matrix.CreateTranslation(new Vector3(-_pos.X, -_pos.Y, 0)) * Matrix.CreateRotationZ(Rotation) * Matrix.CreateScale(new Vector3(Zoom, Zoom, 1)) * Matrix.CreateTranslation(new Vector3(_viewportWidth * 0.5f, _viewportHeight * 0.5f, 0)); return _transform; } The camera properties in the method above should be self explanatory. How can I get a rectangle indicating what the camera is looking at in world space?

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• Drawing an outline around an arbitrary group of hexagons

  - by Perky

  Is there an algorithm for drawing an outline around around an arbitrary group of hexagons? The polygon outline drawn may be concave. See the images below, the green line is what I am trying to achieve. The hexagons are stored as vertices and drawn as polygons. Edit: I've uploaded images that should explain more. I want to favour convex hulls because it's conveys an area of control more quickly. Each hexagon is stored in a multidimensional array so they all have x and y coordinates, I can easily find adjacent hexagons and the opposite vertex, i.e. adjacentHexagon = getAdjacentHexagon( someHexagon, NORTHWEST ) if there isn't a hexagon immediately adjacent it will continue to search in that direction until it finds one or hits the map edges.

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• 3D rotation matrices deform object while rotating

  - by Kevin

  I'm writing a small 3D renderer (using an orthographic projection right now). I've run into some trouble with my 3D rotation matrices. They seem to squeeze my 3D object (a box primitive) at certain angles. Here's a live demo (only tested in Google Chrome): http://dl.dropbox.com/u/109400107/3D/index.html The box is viewed from the top along the Y axis and is rotating around the X and Z axis. These are my 3 rotation matrices (Only rX and rZ are being used): var rX = new Matrix([ [1, 0, 0], [0, Math.cos(radiants), -Math.sin(radiants)], [0, Math.sin(radiants), Math.cos(radiants)] ]); var rY = new Matrix([ [Math.cos(radiants), 0, Math.sin(radiants)], [0, 1, 0], [-Math.sin(radiants), 0, Math.cos(radiants)] ]); var rZ = new Matrix([ [Math.cos(radiants), -Math.sin(radiants), 0], [Math.sin(radiants), Math.cos(radiants), 0], [0, 0, 1] ]); Before projecting the verticies I multiply them by rZ and rX like so: vert1.multiply(rZ); vert1.multiply(rX); vert2.multiply(rZ); vert2.multiply(rX); vert3.multiply(rZ); vert3.multiply(rX); The projection itself looks like this: bX = (pos.x + (vert1.x*scale)); bY = (pos.y + (vert1.z*scale)); Where "pos.x" and "pos.y" is an offset for centering the box on the screen. I just can't seem to find a solution to this and I'm still relativly new to working with Matricies. You can view the source-code of the demo page if you want to see the whole thing.

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• How to manage drawing loop when changing render targets

  - by George Duckett

  I'm managing my game state by having a base GameScreen class with a Draw method. I then have (basically) a stack of GameScreens that I render. I render the bottom one first, as screens above might not completely cover the ones below. I now have a problem where one GameScreen changes render targets while doing its rendering. Anything the previous screens have drawn to the backbuffer is lost (as XNA emulates what happens on the xbox). I don't want to just set the backbuffer to preserve its contents as I want this to work on the xbox as well as PC. How should I manage this problem? A few ideas I've had: Render every GameScreen to its own render target, then render them all to the backbuffer. Create some kind of RenderAction queue where a game screen (and anything else I guess) could queue something to be rendered to the back buffer. They'd render whatever they wanted to any render target as normal, but if they wanted to render to the backbuffer they'd stick that in a queue which would get processed once all rendertarget rendering was done. Abstract away from render targets and backbuffers and have some way of representing the way graphics flows and transforms between render targets and have something manage/work out the correct rendering order (and render targets) given what rendering process needs as input and what it produces as output. I think each of my ideas have pros and cons and there are probably several other ways of approaching this general problem so I'm interested in finding out what solutions are out there.

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• Drawing a random x,y grid of objects within a prespective

  - by T Reddy

  I'm wrapping my head around OpenGL ES 2.0 and I think I'm trying to do something very simple, but I think the math may be eluding me. I created a simple, flat-ish cylinder in Blender that is 2 units in diameter. I want to create an arbitrary grid of these edge to edge (think of a checker board). I'm using a 3D perspective with GLKit: CGSize size = [[self view] bounds].size; _projectionMatrix = GLKMatrix4MakePerspective(GLKMathDegreesToRadians(45.0f), size.width/size.height, 0.1f, 100.0f); So, I managed to manually get all of these cylinders drawn on the screen just fine. However, I would like to understand how I can programmatically "fit" all of these cylinders on the screen at the same time given the camera location, screen size, cylinder diameter, and the number of rows/columns. So the net effect is that for small grids (i.e., 5x5) the objects are closer to the camera, but for large grids (i.e., 30x30) the objects are farther away. In either case, all of the cylinders are visible.

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• Best way to do large XNA animations?

  - by Harold

  What's the best way to have large animations in XNA 4.0? I have created a spritesheet with the sprite being 250x400 (more of an image than a sprite but hey ho) and there are approximately 45 frames in the animation. This causes problems for XNA as it says that the maximum filesize for Reach is 2048. I'd rather not change to hidef as I heard that means that your game is less compatible with some computers and systems so does anyone have any idea what the best thing I could do is? The only thing I could come up with is to have a list of textures to flick through but that's not ideal.

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• Facebook Game database design

  - by facebook-100000781341887

  Hi, I'm currently develop a facebook mafia like PHP game(of course, a light weight version), here is a simplify database(MySQL) of the game id-a <int3> <for index> uid <chr15> <facebook uid> HP <int3> <health point> exp <int3> <experience> money <int3> <money> list_inventory <chr5> <the inventory user hold...some special here, talk next> ... and 20 other fields just like reputation, num of combat... *the number next to the type is the size(byte) of the type For the list_inventory, there have 40 inventorys in my game, (actually, I have 5 these kind of list in my database), and each user can only contain 1 qty of each inventory, therefore, I assign 5 char for this field and each bit of char as 1 item(5 char * 8 bit = 40 slot), and I will do some manipulation by PHP to extract the data from this 5 byte. OK, I was thinking on this, if this game contains 100,000 user, and only 10% are active, therefore, if use my method, for the space use, 5 byte * 100,000 = 500 KB if I use another method, create a table user_hold_inventory, if the user have the inventory, then insert a record into this table, so, for 10,000 active user, I assume they got all item, but for other, I assume they got no item, here is the fields of the new table id-b <int3> <for index> id-a <int3> <id of the user table> inv_no <int1> <inventory that user hold> for the space use, ([id] (3+3) byte + [inv_no] 1 byte ) * [active user] 10,000 * [all inventory] * 40 = 2.8 MB seems method 2 have use more space, but it consume less CPU power. Please comment these 2 method or please correct me if there have another better method rather than what I think. Another question is, my database contain 26 fields, but I counted 5 of them are not change frquently, should I need to separate it on the other table or not? So many words, thanks for reading :)

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• Understanding Box2d Restitution & Bouncing

  - by layzrr

  I'm currently trying to implement basketball bouncing into my game using Box2d (jBox2d technically), but I'm a bit confused about restitution. While trying to create the ball in the testbed first, I've run into infinite bouncing, as described in this question, however obviously not using my own implementation. The Box2d manual describes restitution as follows: Restitution is used to make objects bounce. The restitution value is usually set to be between 0 and 1. Consider dropping a ball on a table. A value of zero means the ball won't bounce. This is called an inelastic collision. A value of one means the ball's velocity will be exactly reflected. This is called a perfectly elastic collision. My confusion lies in that I am still getting infinite bouncing with restitution values at 0.75/0.8. The same behavior can be seen in the testbed under Collision Watching - Varying Restitution, on the 6th and 7th balls. I believe the last one has restitution of 1, which makes sense, but I don't understand why the second to last ball bounces infinitely (as is happening with my working basketball I've created). I am looking to understand the restitution concept more fully, as well as look for a solution to infinite bouncing with the Box2d framework. My instinct was to sleep objects that appeared to be moving in very small increments, but this seems like a misuse of the engine. Should I just work with lower restitution values altogether?

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• D3D9 Alpha Blending on the surfaces

  - by Indeera

  I have a surface (OffScreenPlain or RenderTarget with D3DFMT_A8R8G8B8) which I copy pixels (ARGB) to, from a third party function. Before pixel copying, Bits are accessed by LockRect. This surface is then StretchRect to the Backbuffer which is (D3DFMT_A8R8G8B8). Surface and Backbuffer are different dimensions. Filtering is set to D3DTEXF_NONE. Just after creating the d3d device I've set following RenderState settings D3DRS_ALPHABLENDENABLE -> TRUE D3DRS_BLENDOP -> D3DBLENDOP_ADD D3DRS_SRCBLEND -> D3DBLEND_SRCALPHA D3DRS_DESTBLEND -> D3DBLEND_INVSRCALPHA But I see no alpha blending happening. I've verified that alpha is specified in pixels. I've done a simple test by creating a vertex buffer and drawing a triangle (DrawPrimitive) which displays with alpha blending. In this test surface was StretchRect first and then DrawPrimitive, and the surface content displays without alpha blending and the triangle displays with alpha blending. What am I missing here? Thanks

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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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• Register Game Object Components in Game Subsystems? (Component-based Game Object design)

  - by topright

  I'm creating a component-based game object system. Some tips: GameObject is simply a list of Components. There are GameSubsystems. For example, rendering, physics etc. Each GameSubsystem contains pointers to some of Components. GameSubsystem is a very powerful and flexible abstraction: it represents any slice (or aspect) of the game world. There is a need in a mechanism of registering Components in GameSubsystems (when GameObject is created and composed). There are 4 approaches: 1: Chain of responsibility pattern. Every Component is offered to every GameSubsystem. GameSubsystem makes a decision which Components to register (and how to organize them). For example, GameSubsystemRender can register Renderable Components. pro. Components know nothing about how they are used. Low coupling. A. We can add new GameSubsystem. For example, let's add GameSubsystemTitles that registers all ComponentTitle and guarantees that every title is unique and provides interface to quering objects by title. Of course, ComponentTitle should not be rewrited or inherited in this case. B. We can reorganize existing GameSubsystems. For example, GameSubsystemAudio, GameSubsystemRender, GameSubsystemParticleEmmiter can be merged into GameSubsystemSpatial (to place all audio, emmiter, render Components in the same hierarchy and use parent-relative transforms). con. Every-to-every check. Very innefficient. con. Subsystems know about Components. 2: Each Subsystem searches for Components of specific types. pro. Better performance than in Approach 1. con. Subsystems still know about Components. 3: Component registers itself in GameSubsystem(s). We know at compile-time that there is a GameSubsystemRenderer, so let's ComponentImageRender will call something like GameSubsystemRenderer::register(ComponentRenderBase*). pro. Performance. No unnecessary checks as in Approach 1. con. Components are badly coupled with GameSubsystems. 4: Mediator pattern. GameState (that contains GameSubsystems) can implement registerComponent(Component*). pro. Components and GameSubystems know nothing about each other. con. In C++ it would look like ugly and slow typeid-switch. Questions: Which approach is better and mostly used in component-based design? What Practice says? Any suggestions about implementation of Approach 4? Thank you.

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• Understanding math used to determine if vector is clockwise / counterclockwise from your vector

  - by MTLPhil

  I'm reading Programming Game AI by Example by Mat Buckland. In the Math & Physics primer chapter there's a listing of the declaration of a class used to represent 2D vectors. This class contains a method called Sign. It's implementation is as follows //------------------------ Sign ------------------------------------------ // // returns positive if v2 is clockwise of this vector, // minus if anticlockwise (Y axis pointing down, X axis to right) //------------------------------------------------------------------------ enum {clockwise = 1, anticlockwise = -1}; inline int Vector2D::Sign(const Vector2D& v2)const { if (y*v2.x > x*v2.y) { return anticlockwise; } else { return clockwise; } } Can someone explain the vector rules that make this hold true? What do the values of y*v2.x and x*v2.y that are being compared actually represent? I'd like to have a solid understanding of why this works rather than just accepting that it does without figuring it out. I feel like it's something really obvious that I'm just not catching on to. Thanks for your help.

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• Efficiency concerning thread granularity

  - by MaelmDev

  Lately, I've been thinking of ways to use multithreading to improve the speed of different parts of a game engine. What confuses me is the appropriate granularity of threads, especially when dealing with single-instruction-multiple-data (SIMD) tasks. Let's use line-of-sight detection as an example. Each AI actor must be able to detect objects of interest around them and mark them. There are three basic ways to go about this with multithreading: Don't use threading at all. Create a thread for each actor. Create a thread for each actor-object combination. Option 1 is obviously going to be the least efficient method. However, choosing between the next two options is more difficult. Only using one thread per actor is still running through every object in series instead of in parallel. However, are CPU's able to create and join threads in the granularity posed in Option 3 efficiently? It seems like that many calls to the OS could be really slow, and varying enormously between different hardware.

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• Blender to 3ds max to cal3d format

  - by Kaliber64

  There are quite a few questions on cal3d but they are old and don't apply anymore. In Blender(must be 2.49a for python script to work!!!): I have a scene with 7 meshes, 1 armature, 10 bones. I tried going to one mesh to simplify it but doesn't change anything. I found a small blend file that was used for cal3d and it exported just fine. So I tried to copy it's setup with no success. EDIT*8/13/2012 In the last week here is what I have found so far. I made the mesh in the newest blender(2.62?) and exported it to import it in the old one(2.49a). Did an animation in the old one because importing new blend files to old blenders, its just said it would lose keyframe data and all was good. And then you get the last problem of it not exporting meshes. BUT I found that meshes made in the old one export regardless. I can't find any that won't export. So if I used the old blender to remake my model I could get it to export :) At this point I found a modified release of cal3d (because the most core model variable would not initiate as I made a really small test subject in old blender instead of remaking my big one which took 4 hours.) which fixes the morph objects and adds what cal3d left off with. Under their license they have to release the modification but it has no documentation so I have to figure it out on my own. Its mostly the same. But with this lib it came with a 3ds max exporter. My question now is how do I transfer armature and mesh information from blender to 3ds max in order to export into cal3d format. Every time I try the models are see through and small and there are no bones. The formats I have tried to import are .3ds .obj(mesh only) and COLLADA. In all of them the mesh is invisible and no bones. It says the default texture is on so I should be able to see it. All the vertices are present I found a vertex highlighter so I can see those. If any of this is confusing let me know so I can clear it up. Its late .<=sleep.

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• glColor3f Setting colour

  - by Aaron

  This draws a white vertical line from 640 to 768 at x512: glDisable(GL_TEXTURE_2D); glBegin(GL_LINES); glColor3f((double)R/255,(double)G/255,(double)B/255); glVertex3f(SX, -SPosY, 0); // origin of the line glVertex3f(SX, -EPosY, 0); // ending point of the line glEnd(); glEnable(GL_TEXTURE_2D); This works, but after having a problem where it wouldn't draw it white (Or to any colour passed) I discovered that disabling GL_TEXTURE_2D Before drawing the line, and the re-enabling it afterwards for other things, fixed it. I want to know, is this a normal step a programmer might take? Or is it highly inefficient? I don't want to be causing any slow downs due to a mistake =) Thanks

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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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• Deterministic Multiplayer RTS game questions?

  - by Martin K

  I am working on a cross-platform multiplayer RTS game where the different clients and a server(flash and C#), all need to stay deterministically synchronised. To deal with Floatpoint inconsistencies, I've come across this method: http://joshblog.net/2007/01/30/flash-floating-point-number-errors/#comment-49912 which basically truncates off the nondeterministic part: return Math.round(1000 * float) / 1000; Howewer my concern is that every time there is a division, there is further chance of creating additional floatpoint errors, in essence making it worse? . So it occured to me, how about something like this: function floatSafe(number:Number) : Number {return Math.round(float* 1024) / 1024; } ie dividing with only powers of 2 ? What do you think? . Ironically with the above method I got less accurate results: trace( floatSafe(3/5) ) // 0.599609375 where as with the other method(dividing with 1000), or just tracing the raw value I am getting 3/5 = 0.6 or Maybe thats what 3/5 actually is, IE 0.6 cannot really be represented with a floatpoint datatype, and would be more consistent across different platforms?

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• Basic AI FSM - Handling state transition

  - by Galvanize

  I'm starting to study on how to implement game AI, and it seems to me that a very simple FSM for my Pong demo would be a nice way to start. My vision on implementing this would be to have a basic state interface and a class for each state, then the NPC would have an instance of the current state. The class should have an update method and directions on wich state to go next, depending on the event received. The question is: How do I handle this event? Should I have a regular addEventListener and a costum event system? Or should I check on update for the things that could change the current state? I'm feeling a bit lost, I feel I have a good grasp on the FSM concept but a good implementation seems tricky, thanks in advance.

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• Fastest bit-blit in C# ?

  - by AttackingHobo

  I know there is Unity, and XNA that both use C#, but I am don't know what else I could use. The reason I say C# is that the syntax and style is similar to AS3, which I am familiar with, and I want to choose the correct framework to start learning with. What should I use to be able to do the most possible bit-blit(direct pixel copy) objects per frame. EDIT: I should not need to add this, but I am looking for the most possible amount of objects per frame because I am making a few Bullet-Hell SHMUPS. I need thousands and thousands of bullets, particles, and hundreds of enemies on the screen at once. I am looking for a solution to do as many bit-blit operations per frame, I am not looking for a general purpose engine. EDIT2: I want bit-blitting because I do not want to exclude people who have lower end video cards but a fast processor from playing my games.

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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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• 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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• How exactly does XNA's SpriteBatch work?

  - by David Gouveia

  To be more precise, if I needed to recreate this functionality from scratch in another API (e.g. in OpenGL) what would it need to be capable of doing? I do have a general idea of some of the steps, such as how it prepares an orthographic projection matrix and creates a quad for each draw call. I'm not too familiar, however, with the batching process itself. Are all quads stored in the same vertex buffer? Does it need an index buffer? How are different textures handled? If possible I'd be grateful if you could guide me through the process from when SpriteBatch.Begin() is called until SpriteBatch.End(), at least when using the default Deferred mode.

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• Why do we use Pythagoras in game physics?

  - by Starkers

  I've recently learned that we use Pythagoras a lot in our physics calculations and I'm afraid I don't really get the point. Here's an example from a book to make sure an object doesn't travel faster than a MAXIMUM_VELOCITY constant in the horizontal plane: MAXIMUM_VELOCITY = <any number>; SQUARED_MAXIMUM_VELOCITY = MAXIMUM_VELOCITY * MAXIMUM_VELOCITY; function animate(){ var squared_horizontal_velocity = (x_velocity * x_velocity) + (z_velocity * z_velocity); if( squared_horizontal_velocity <= SQUARED_MAXIMUM_VELOCITY ){ scalar = squared_horizontal_velocity / SQUARED_MAXIMUM_VELOCITY; x_velocity = x_velocity / scalar; z_velocity = x_velocity / scalar; } } Let's try this with some numbers: An object is attempting to move 5 units in x and 5 units in z. It should only be able to move 5 units horizontally in total! MAXIMUM_VELOCITY = 5; SQUARED_MAXIMUM_VELOCITY = 5 * 5; SQUARED_MAXIMUM_VELOCITY = 25; function animate(){ var x_velocity = 5; var z_velocity = 5; var squared_horizontal_velocity = (x_velocity * x_velocity) + (z_velocity * z_velocity); var squared_horizontal_velocity = 5 * 5 + 5 * 5; var squared_horizontal_velocity = 25 + 25; var squared_horizontal_velocity = 50; // if( squared_horizontal_velocity <= SQUARED_MAXIMUM_VELOCITY ){ if( 50 <= 25 ){ scalar = squared_horizontal_velocity / SQUARED_MAXIMUM_VELOCITY; scalar = 50 / 25; scalar = 2.0; x_velocity = x_velocity / scalar; x_velocity = 5 / 2.0; x_velocity = 2.5; z_velocity = z_velocity / scalar; z_velocity = 5 / 2.0; z_velocity = 2.5; // new_horizontal_velocity = x_velocity + z_velocity // new_horizontal_velocity = 2.5 + 2.5 // new_horizontal_velocity = 5 } } Now this works well, but we can do the same thing without Pythagoras: MAXIMUM_VELOCITY = 5; function animate(){ var x_velocity = 5; var z_velocity = 5; var horizontal_velocity = x_velocity + z_velocity; var horizontal_velocity = 5 + 5; var horizontal_velocity = 10; // if( horizontal_velocity >= MAXIMUM_VELOCITY ){ if( 10 >= 5 ){ scalar = horizontal_velocity / MAXIMUM_VELOCITY; scalar = 10 / 5; scalar = 2.0; x_velocity = x_velocity / scalar; x_velocity = 5 / 2.0; x_velocity = 2.5; z_velocity = z_velocity / scalar; z_velocity = 5 / 2.0; z_velocity = 2.5; // new_horizontal_velocity = x_velocity + z_velocity // new_horizontal_velocity = 2.5 + 2.5 // new_horizontal_velocity = 5 } } Benefits of doing it without Pythagoras: Less lines Within those lines, it's easier to read what's going on ...and it takes less time to compute, as there are less multiplications Seems to me like computers and humans get a better deal without Pythagoras! However, I'm sure I'm wrong as I've seen Pythagoras' theorem in a number of reputable places, so I'd like someone to explain me the benefit of using Pythagoras to a maths newbie. Does this have anything to do with unit vectors? To me a unit vector is when we normalize a vector and turn it into a fraction. We do this by dividing the vector by a larger constant. I'm not sure what constant it is. The total size of the graph? Anyway, because it's a fraction, I take it, a unit vector is basically a graph that can fit inside a 3D grid with the x-axis running from -1 to 1, z-axis running from -1 to 1, and the y-axis running from -1 to 1. That's literally everything I know about unit vectors... not much :P And I fail to see their usefulness. Also, we're not really creating a unit vector in the above examples. Should I be determining the scalar like this: // a mathematical work-around of my own invention. There may be a cleverer way to do this! I've also made up my own terms such as 'divisive_scalar' so don't bother googling var divisive_scalar = (squared_horizontal_velocity / SQUARED_MAXIMUM_VELOCITY); var divisive_scalar = ( 50 / 25 ); var divisive_scalar = 2; var multiplicative_scalar = (divisive_scalar / (2*divisive_scalar)); var multiplicative_scalar = (2 / (2*2)); var multiplicative_scalar = (2 / 4); var multiplicative_scalar = 0.5; x_velocity = x_velocity * multiplicative_scalar x_velocity = 5 * 0.5 x_velocity = 2.5 Again, I can't see why this is better, but it's more "unit-vector-y" because the multiplicative_scalar is a unit_vector? As you can see, I use words such as "unit-vector-y" so I'm really not a maths whiz! Also aware that unit vectors might have nothing to do with Pythagoras so ignore all of this if I'm barking up the wrong tree. I'm a very visual person (3D modeller and concept artist by trade!) and I find diagrams and graphs really, really helpful so as many as humanely possible please!

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• Bouncing ball slowing down over time

  - by user46610

  I use the unreal engine 4 to bounce a ball off of walls in a 2D space, but over time the ball gets slower and slower. Movement happens in the tick function of the ball FVector location = GetActorLocation(); location.X += this->Velocity.X * DeltaSeconds; location.Y += this->Velocity.Y * DeltaSeconds; SetActorLocation(location, true); When a wall gets hit I get a Hit Event with the normal of the collision. This is how I calculate the new velocity of the ball: FVector2D V = this->Velocity; FVector2D N = FVector2D(HitNormal.X, HitNormal.Y); FVector2D newVelocity = -2 * (V.X * N.X + V.Y * N.Y) * N + V; this->Velocity = newVelocity; Over time, the more the ball bounced around, the velocity gets smaller and smaller. How do I prevent speed loss when bouncing off walls like that? It's supposed to be a perfect bounce without friction or anything.

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• What are the reasons for MMOs to have level caps [on hold]

  - by SamStephens

  In many MMOs players character progression is artificially capped, e.g. by level 60 or 90 or 100 or whatever. Why do MMOs have these level caps in the first place? Why not just allow characters to continue to arbitrary levels with a mathematically designed leveling system that keeps the leveling experience interesting and endless? Answers to this question may help us to see the reason behind the feature and decide if and how this should be implemented in our MMOs.

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