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• What are some good resources for creating a game engine in XNA?

  - by Glasser

  I'm currently a student game programmer working on an indie project. We have a team of eleven people (five programmers, four artists, and two audio designers) aboard, all working hard to help design this game. We've been meeting for months now and so far we have a pretty buffed out Game Design Document as well as much audio/visual concept art. Our programmers are itching to progress on our own end. Each person in our programming team is well versed in C++, but is very familiar with C#. We have enough experience and skill that we're confident that we will be successful with our game, and we're looking to build our own game engine in XNA as it seems like it would be worth our time and effort in the end. The game itself will be a 2D beat 'em up style game to be released over xbox live and the PC. It's play style will be similar to that of Castle Crashers or Scott Pilgrim vs The World. We want to design the game engine to allow us to better implement our assets into the game as well as to simplify the creation of design elements/mechanics. Currently between our programmers, we have books such as "XNA 4.0" and "Game Coding Complete, Third Edition," but we'd still like more information on both XNA and (especially) building a game engine from scratch. What are any other good books, websites, or resources we could use to further map out and program our game engine?

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• 3ds Max CAT to XNA

  - by user12214

  Has anyone successfully used the CAT bone system in 3ds Max and exported the file into XNA? If so, what was your method of doing so? There are a number of methods of doing this apparently, but the ones I've tried have not worked. I used the Panda Exporter which creates a .X file. This seems to be the latest way of going about this, but when it's loaded in XNA, there is an error saying something about the bone weights. This happens when I export with and without CAT bones.

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• exact point oh a rotating sphere

  - by nkint

  I have a sphere that represents the heart textured with real pictures. It's rotating about the x axis, and when user click down it has to show me the exact place he clicked on. For example if he clicked on Singapore and the system should be able to: understand that user clicked on the sphere (OK, I'll do it with unProject) understand where user clicked on the sphere (ray-sphere collision?) and take into account the rotation transform sphere-coordinate to some coordinate system good for some web-api service ask to api (OK, this is the simpler thing for me ;-) some advice?

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• Which physics phenomenons can be simulated properly with Box2d or bullet physics? [on hold]

  - by user3585425

  Knowing that box2d or bullet physics can't simulate Newton's cradle (because of multiple bodies being in contact at the same time if I understand correctly), is there a sets of physics phenomenons that imply two or more objects that still can be simulated properly ? For example, I'm thinking about lightweight objects launched towards heavyweight objects. If the object is destroyed on contact, this would not make a difference if the energy is not transmitted correctly on impact.

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• Image loaded from TGA texture isn't displayed correctly

  - by Ramy Al Zuhouri

  I have a TGA texture containing this image: The texture is 256x256. So I'm trying to load it and map it to a cube: #import <OpenGL/OpenGL.h> #import <GLUT/GLUT.h> #import <stdlib.h> #import <stdio.h> #import <assert.h> GLuint width=640, height=480; GLuint texture; const char* const filename= "/Users/ramy/Documents/C/OpenGL/Test/Test/texture.tga"; void init() { // Initialization glEnable(GL_DEPTH_TEST); glViewport(-500, -500, 1000, 1000); glMatrixMode(GL_PROJECTION); glLoadIdentity(); gluPerspective(45, width/(float)height, 1, 1000); glMatrixMode(GL_MODELVIEW); glLoadIdentity(); gluLookAt(0, 0, -100, 0, 0, 0, 0, 1, 0); // Texture char bitmap[256][256][3]; FILE* fp=fopen(filename, "r"); assert(fp); assert(fread(bitmap, 3*sizeof(char), 256*256, fp) == 256*256); fclose(fp); glGenTextures(1, &texture); glBindTexture(GL_TEXTURE_2D, texture); glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_LINEAR); glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_LINEAR); glTexImage2D(GL_TEXTURE_2D, 0, GL_RGB, 256, 256, 0, GL_RGB, GL_UNSIGNED_BYTE, bitmap); } void display() { glClearColor(0, 0, 0, 0); glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT); glEnable(GL_TEXTURE_2D); glBindTexture(GL_TEXTURE_2D, texture); glColor3ub(255, 255, 255); glBegin(GL_QUADS); glVertex3f(0, 0, 0); glTexCoord2f(0.0, 0.0); glVertex3f(40, 0, 0); glTexCoord2f(0.0, 1.0); glVertex3f(40, 40, 0); glTexCoord2f(1.0, 1.0); glVertex3f(0, 40, 0); glTexCoord2f(1.0, 0.0); glEnd(); glDisable(GL_TEXTURE_2D); glutSwapBuffers(); } int main(int argc, char** argv) { glutInit(&argc, argv); glutInitDisplayMode(GLUT_RGB | GLUT_DEPTH | GLUT_DOUBLE); glutInitWindowPosition(100, 100); glutInitWindowSize(width, height); glutCreateWindow(argv[0]); glutDisplayFunc(display); init(); glutMainLoop(); return 0; } But this is what I get when the window loads: So just half of the image is correctly displayed, and also with different colors.Then if I resize the window I get this: Magically the image seems to fix itself, even if the colors are wrong.Why?

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• Avoiding lag when rendering Texture2D for first time

  - by Emir Lima

  I have found a similar question here, but it is about playing sounds. I am using 2048 x 2048 textures for sprite sheets and every time I call spriteBatch.Draw using a sheet for the first time in game execution, causes a considerable lag. The lag doesn't appears for the next times. Someone has faced this problem before? What can I do to overcome this? Update: I inserted a code in the end of content load routine that draws EVERY Texture2D that is loaded into ContentManager before follow to the game screen. This works well. None lag occurs when different textures are rendered over the time, EXCEPT if the IsFullScreen are changed. Apparently, changing this property makes the textures loaded in the GPU gone. Is that correct?

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• Passing an objects rotation down through its children

  - by MintyAnt

  In my topdown 2d game you have a player with a sword, like an old Zelda game. The sword is a seperate entity, and its collision box "rotates" around the player like an orbit, but always follows the player wherever he goes. The player and sword both have a vector2 heading. The sword is a weapon object that is attached to the character. In order to allow swinging in a direction, I have the following property inside sword (RotateCopy returns a copy of the mHeading after rotation) public Vector2 Heading { get { return mHeading.RotateCopy(mOwner.Rotation); } } This seems a bit messy to me, and slower than it could be. Is there a better way to "translate" the base/owner component rotations through to whatever component I am using, like this sword? Would using a rotation MATRIX be better? (Curretnly rotates by sin/cos) If so, how can I "add" up the matrices? Thank you.

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• Expiring timed actions a good idea?

  - by Bart van Heukelom

  We have an online game where players sometimes have to wait a while (say 30 minutes) before a process they intiated completes. This encourages them to come back later. An example of this is growing crops in Farmville or basically any action in the Sims Play4Free. Now, however, there is the idea to let these processes expire, so if the player doesn't 'reap' them in time (e.g. within 4 hours) they are aborted. I'm a bit sceptical about this. How will this make players come back more often? Is not the reward of reaping the process enough for that? Can we expect players to fit their daily schedule around our game, maybe even set the alarm clock at night? Won't this just cause players to give up on starting these processes in the first place? I realise this may be too subjective for this site, so I'll end with a concrete question: Do (m)any other online free-to-play games employ this technique?

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• How to determine if a 3D voxel-based room is sealed, efficiently

  - by NigelMan1010

  I've been having some issues with efficiently determining if large rooms are sealed in a voxel-based 3D rooms. I'm at a point where I have tried my hardest to solve the problem without asking for help, but not tried enough to give up, so I'm asking for help. To clarify, sealed being that there are no holes in the room. There are oxygen sealers, which check if the room is sealed, and seal depending on the oxygen input level. Right now, this is how I'm doing it: Starting at the block above the sealer tile (the vent is on the sealer's top face), recursively loop through in all 6 adjacent directions If the adjacent tile is a full, non-vacuum tile, continue through the loop If the adjacent tile is not full, or is a vacuum tile, check if it's adjacent blocks are, recursively. Each time a tile is checked, decrement a counter If the count hits zero, if the last block is adjacent to a vacuum tile, return that the area is unsealed If the count hits zero and the last block is not a vacuum tile, or the recursive loop ends (no vacuum tiles left) before the counter is zero, the area is sealed If the area is not sealed, run the loop again with some changes: Checking adjacent blocks for "breathable air" tile instead of a vacuum tile Instead of using a decrementing counter, continue until no adjacent "breathable air" tiles are found. Once loop is finished, set each checked block to a vacuum tile. Here's the code I'm using: http://pastebin.com/NimyKncC The problem: I'm running this check every 3 seconds, sometimes a sealer will have to loop through hundreds of blocks, and a large world with many oxygen sealers, these multiple recursive loops every few seconds can be very hard on the CPU. I was wondering if anyone with more experience with optimization can give me a hand, or at least point me in the right direction. Thanks a bunch.

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• Store and create game objects at positions along terrain

  - by Alex

  I have a circular character that rolls down terrain like that shown in the picture below. The terrain is created from an array holding 1000 points. The ground is drawn one screen width infront and one screen width behind. So as the character moves, edges are created infront and edges are removed behind. My problem is, I want to create box2d bodies at certain locations along the path and need a way to store these creator methods or objects. I need some way to store a position at which they are created and some pointer to a function to create them, once the character is in range. I guess this would be an array of some sort that is checked each time the ground is updated and then if in range, the function is executed and removed from the array. But I'm not sure if its even possible to store pointers to functions with parameters included... any help is much appreciated!

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• C++: Checking if an object faces a point (within a certain range)

  - by bojoradarial

  I have been working on a shooter game in C++, and am trying to add a feature whereby missiles shot must be within 90 degrees (PI/2 radians) of the direction the ship is facing. The missiles will be shot towards the mouse. My idea is that the ship's angle of rotation is compared with the angle between the ship and the mouse (std::atan2(mouseY - shipY, mouseX - shipX)), and if the difference is less than PI/4 (45 degrees) then the missile can be fired. However, I can't seem to get this to work. The ship's angle of rotation is increased and decreased with the A and D keys, so it is possible that it isn't between 0 and 2*PI, hence the use of fmod() below. Code: float userRotation = std::fmod(user->Angle(), 6.28318f); if (std::abs(userRotation - missileAngle) > 0.78f) return; Any help would be appreciated. Thanks!

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• "Super meatboy"-ish replay

  - by Ron

  I'm making a platformer built from mini-levels - and I want to create a sort of a replay of all the player tries that the player did for the level. My question is - what is the best way to record the player's actions in-game, so that I could replay them later when he finishes the level. I thought about recording only the player's input and replay them later on, each on a clone of the player. The problem I have with this is with dynamic obstacles (that could be moved around) - if one clone moves them, it throws the simulation off for the rest of the clones. So then I thought about recording every frame the X/Y of the player, and then just replay it - but that seems it could cause a major memory leak and very ineffective. So - does anyone have any ideas? :)

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• Solution for lightweight LAN peer discovering?

  - by DevilWithin

  I built a library for purely cross-platform programming. My games made with it run fine in Android , Pc, Linux, Mac etc. The networking capabilities are provided by ENET library, therefore all communication between my apps is not TCP or UDP compatible, but only in the custom protocol, even tough its based on the UDP ultimately. I don't think its possible to do what i want with ENET, thats why I ask here for help! Lets say I have the same game running in my Android phone, my laptop and my pc. They are all in the same wifi network, and therefore in a LAN, whether its Wifi hotspot(?) or the household router. I need each of those 3 peers to discover the other two in the network. This is meant only to find the IP of alive apps in the LAN network, to be able to host multiplayer games between them. I can only think of one effective way to do this, UDP broadcast, wait responses, but if that is the solution, i need something small, since its the only purpose of the implementation. Other way could be to try to connect to all IPs in the LAN address subrange, but I don't think the OS would be with me on this one :p Sorry for the long question!

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• Calculate travel time on road map with semaphores

  - by Ivansek

  I have a road map with intersections. At intersections there are semaphores. For each semaphore I generate a red light time and green light time which are represented with syntax [R:T1, G:T2], for example: 119 185 250 A ------- B: [R:6, G:4] ------ C: [R:5, G:5] ------ D I want to calculate a car travel time from A - D. Now I do this with this pseudo code: function get_travel_time(semaphores_configuration) { time = 0; for( i=1; i<path.length;i++) { prev_node = path[i-1]; next_node = path[i]); cost = cost_between(prev_node, next_node) time += (cost/movement_speed) // movement_speed = 50px per second light_times = get_light_times(path[i], semaphore_configurations) lights_cycle = get_lights_cycle(light_times) // Eg: [R,R,R,G,G,G,G], where [R:3, G:4] lights_sum = light_times.green_time+light_times.red_light; // Lights cycle time light = lights_cycle[cost%lights_sum]; if( light == "R" ) { time += light_times.red_light; } } return time; } So for distance 119 between A and B travel time is, 119/50 = 2.38s ( exactly mesaured time is between 2.5s and 2.6s), then we add time if we came at a red light when at B. If we came at a red light is calculated with lines: lights_cycle = get_lights_cycle(light_times) // Eg: [R,R,R,G,G,G,G], where [R:3, G:4] lights_sum = light_times.green_time+light_times.red_light light = lights_cycle[cost%lights_sum]; if( light == "R" ) { time += light_times.red_light; } This pseudo code doesn't calculate exactly the same times as they are mesaured, but the calculations are very close to them. Any idea how I would calculate this?

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• How to generate portal zones?

  - by Meow

  I'm developing a portal-based scene manager. Basically all it does is to check the portals against the camera frustum, and render their associated portal zones accordingly. Is there any way my editor can generate portal zones automatically with the user having to set the portals themselves only? For example, the Max Payne 1/2 engine ("Max-FX") only required to set the portal quads, unlike the C4 engine where you also have to explicitly set the portal zones.

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• XNA Drag Gestures - fractional delta values

  - by Den

  I have an issue with objects moving roughly twice as far as expected when dragging them. I am comparing my application to the standard TouchGestureSample sample from MSDN. For some reason in my application gesture samples have fractional positions and deltas. Both are using same Microsoft.Xna.Framework.Input.Touch.dll, v4.0.30319. I am running both apps using standard Windows Phone Emulator. I am setting my break point immediately after this line of code in a simple Update method: GestureSample gesture = TouchPanel.ReadGesture(); Typical values in my app: Delta = {X:-13.56522 Y:4.166667} Position = {X:184.6956 Y:417.7083} Typical values in sample app: Delta = {X:7 Y:16} Position = {X:497 Y:244} Have anyone seen this issue? Does anyone have any suggestions? Thank you.

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• GPU based procedual terrain borders?

  - by OnePie

  I'm working on a game that preferibly should feature a combination of designed and procedually generated terrain where the designer specifies in somewhat detailed terms what type of terrain a given area will have (grasslands, forest etc...) and then a precedual algorithm takes care of the rest. I'm not talking about minecraft style biomoes, but rather the game map for a strategy game. Each 'area' will not take up that much of the screen, and thus be more akin to a tile whose texture is procedually generated. While procedually generating terrain textures on the GPU are not that difficult, the hard part is making the borders between them look good. Currently, the 'tiles' are large enough to be visible (due to memory constraints mainly, we are talking planetary sized textures for a game taking place in space and on a continental ground view with seamless transitions between them) and creating good borders between them with an algorithm that is fast enough to be useful has proven difficult. Sampling the n-surrounding pixels and using the combiened result did not yield very good borders and was fairly slow on the GPU to boot (ca 12ms for me, that is without any lighning or shading and with very simple terrain texture shaders). So are there any practical known methods to solve this problem?

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• What common interface would be appropriate for these game object classes?

  - by Jefffrey

  Question A component based system's goal is to solve the problems that derives from inheritance: for example the fact that some parts of the code (that are called components) are reused by very different classes that, hypothetically, would lie in a very different branch of the inheritance tree. That's a very nice concept, but I've found out that CBS is often hard to accomplish without using ugly hacks. Implementations of this system are often far from clean. But I don't want to discuss this any further. My question is: how can I solve the same problems a CBS try to solve with a very clean interface? (possibly with examples, there are a lot of abstract talks about the "perfect" design already). Context Here's an example I was going for before realizing I was just reinventing inheritance again: class Human { public: Position position; Movement movement; Sprite sprite; // other human specific components }; class Zombie { Position position; Movement movement; Sprite sprite; // other zombie specific components }; After writing that I realized I needed an interface, otherwise I would have needed N containers for N different types of objects (or to use boost::variant to gather them all together). So I've thought of polymorphism (move what systems do in a CBS design into class specific functions): class Entity { public: virtual void on_event(Event) {} // not pure virtual on purpose virtual void on_update(World) {} virtual void on_draw(Window) {} }; class Human : public Entity { private: Position position; Movement movement; Sprite sprite; public: virtual void on_event(Event) { ... } virtual void on_update(World) { ... } virtual void on_draw(Window) { ... } }; class Zombie : public Entity { private: Position position; Movement movement; Sprite sprite; public: virtual void on_event(Event) { ... } virtual void on_update(World) { ... } virtual void on_draw(Window) { ... } }; Which was nice, except for the fact that now the outside world would not even be able to know where a Human is positioned (it does not have access to its position member). That would be useful to track the player position for collision detection or if on_update the Zombie would want to track down its nearest human to move towards him. So I added const Position& get_position() const; to both the Zombie and Human classes. And then I realized that both functionality were shared, so it should have gone to the common base class: Entity. Do you notice anything? Yes, with that methodology I would have a god Entity class full of common functionality (which is the thing I was trying to avoid in the first place). Meaning of "hacks" in the implementation I'm referring to I'm talking about the implementations that defines Entities as simple IDs to which components are dynamically attached. Their implementation can vary from C-stylish: int last_id; Position* positions[MAX_ENTITIES]; Movement* movements[MAX_ENTITIES]; Where positions[i], movements[i], component[i], ... make up the entity. Or to more C++-style: int last_id; std::map<int, Position> positions; std::map<int, Movement> movements; From which systems can detect if an entity/id can have attached components.

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• RPG Item processing

  - by f00b4r

  I started working on an item system for my (first) game, and I'm having a problem conceptualizing how it should work. Since Items can produce a bunch of potentially non-standard actions (revive a character vs increasing some stat) or have use restrictions (can only revive if a character is dead). For obvious reasons, I don't want to create a new Item class for every item type. What is the best way to handle this? Should I make a handful of item types (field modifiers, status modifiers, )? Is it normal to script item usage? Could (should?) this be combined with the above mentioned solution (have a couple of different sub item types, make special case items usage scripted)? Thanks.

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• Looking for a royalty free sci-fi sounding song thats 1:00+ long, and costs <= $5

  - by CyanPrime

  I'm looking for a royalty free sci-fi sounding song thats 1:00+ long, and costs less then, or is $5 usd. I want to have a nice BGM for my engine demo I'm going to release for a game I'm planing on having go commercial. I don't want to spend too much money on it, so my limit is $5 usd. I want it to be at least a 1:00 in length. Where should I look? Or even better, do you have a link to a song that meets the criteria?

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• Ease Rotate RigidBody2D toward arbitrary angle

  - by Plastic Sturgeon

  I'm trying to make a rigidbody2D circle return to an orientation after a collision. But there is a weird behavior I do not expect - it always orients to the same direction. This is what I call in FixedUpdate(): rotationdifference = -halfPI + rigidbody2D.rotation; rigidbody2D.AddTorque (rotationdifference * ease); I would expect this would rotate 90 degrees (1/2 Pi Radians) off of the neutral axis. But it does not. In fact it performs exactly the same as: rotationdifference = rigidbody2D.rotation; rigidbody2D.AddTorque (rotationdifference * ease); What is going on? How would I be able to set an angle I want it to ease towards, and then have it ease towards it when its not colliding with some other force?

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• Is there a size limit when using UICollectionView as tiled map for iOS game?

  - by Alexander Winn

  I'm working on a turn-based strategy game for iOS, (picture Civilization 2 as an example), and I'm considering using a UICollectionView as my game map. Each cell would be a tile, and I could use the "didSelectCell" method to handle player interaction with each tile. Here's my question: I know that UICollectionViewCells are dequeued and reused by the OS, so does that mean that the map could support an effectively infinitely-large map, so long as only a few cells are onscreen at a time? However many cells were onscreen would be held in memory, and obviously the data source would take up some memory, but would my offscreen map be limited to a certain size or could it be enormous so long as the number of cells visible at any one time wasn't too much for the device to handle? Basically, is there any memory weight to offscreen cells, or do only visible cells have any impact?

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• Making efficeint voxel engines using "chunks"

  - by Wardy

  Concept I'm currently looking in to how voxel engines work with a view to possibly making one myself. I see a lot of stuff like this ... https://sites.google.com/site/letsmakeavoxelengine/home/chunks ... which talks about how to go about reducing the draw calls. What I can't seem to understand is how it actually saves draw call counts on the basis of the logic being something like this ... Without chunks foreach voxel in myvoxels DrawIfVisible() With Chunks foreach chunk in mychunks DrawIfVisible() which then does ... foreach voxel in myvoxels DrawIfVisible() So surely you saved nothing ?!?! You still make a draw call for each visible voxel do you not? A visible voxel needs a draw call in either scenario. The only real saving I can see is that the logic that evaluates a chunk will be able to determine if a large number of voxels are visible or not effectively saving a bit of "is this chunk visible" cpu time. But it's the draw calls that interest me ... The fewer of those, the faster the application. EDIT: In case it makes any difference I will probably be using XNA (DX not OpenGL) for my engine so don't consider my choice of example in the link above my choice of technology. But this question is such that I doubt it would matter.

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• Generating tileable terrain using Perlin Noise [duplicate]

  - by terrorcell

  This question already has an answer here: How do you generate tileable Perlin noise? 9 answers I'm having trouble figuring out the solution to this particular algorithm. I'm using the Perlin Noise implementation from: https://code.google.com/p/mikeralib/source/browse/trunk/Mikera/src/main/java/mikera/math/PerlinNoise.java Here's what I have so far: for (Chunk chunk : chunks) { PerlinNoise noise = new PerlinNoise(); for (int y = 0; y < CHUNK_SIZE_HEIGHT; ++y) { for (int x = 0; x < CHUNK_SIZE_WIDTH; ++x) { int index = get1DIndex(y, CHUNK_SIZE_WIDTH, x); float val = 0; for (int i = 2; i <= 32; i *= i) { double n = noise.tileableNoise2(i * x / (float)CHUNK_SIZE_WIDTH, i * y / (float)CHUNK_SIZE_HEIGHT, CHUNK_SIZE_WIDTH, CHUNK_SIZE_HEIGHT); val += n / i; } // chunk tile at [index] gets set to the colour 'val' } } } Which produces something like this: Each chunk is made up of CHUNK_SIZE number of tiles, and each tile has a TILE_SIZE_WIDTH/HEIGHT. I think it has something to do with the inner-most for loop and the x/y co-ords given to the noise function, but I could be wrong. Solved: PerlinNoise noise = new PerlinNoise(); for (Chunk chunk : chunks) { for (int y = 0; y < CHUNK_SIZE_HEIGHT; ++y) { for (int x = 0; x < CHUNK_SIZE_WIDTH; ++x) { int index = get1DIndex(y, CHUNK_SIZE_WIDTH, x); float val = 0; float xx = x * TILE_SIZE_WIDTH + chunk.x; float yy = y * TILE_SIZE_HEIGHT + chunk.h; int w = CHUNK_SIZE_WIDTH * TILE_SIZE_WIDTH; int h = CHUNK_SIZE_HEIGHT * TILE_SIZE_HEIGHT; for (int i = 2; i <= 32; i *= i) { double n = noise.tileableNoise2(i * xx / (float)w, i * yy / (float)h, w, h); val += n / i; } // chunk tile at [index] gets set to the colour 'val' } } }

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• Finding the shorter turning direction towards a target

  - by A.B.

  I'm trying to implement a type of movement where the object gradually faces the target. The problem I've run into is figuring out which turning direction is faster. The following code works until the object's orientation crosses the -PI or PI threshold, at which point it will start turning into the opposite direction void moveToPoint(sf::Vector2f destination) { if (destination == position) return; auto distance = distanceBetweenPoints(position, destination); auto direction = angleBetweenPoints(position, destination); /// Decides whether incrementing or decrementing orientation is faster /// the next line is the problem if (atan2(sin(direction - rotation), cos(direction - rotation)) > 0 ) { /// Increment rotation rotation += rotation_speed; } else { /// Decrement rotation rotation -= rotation_speed; } if (distance < movement_speed) { position = destination; } else { position.x = position.x + movement_speed*cos(rotation); position.y = position.y + movement_speed*sin(rotation); } updateGraphics(); } 'rotation' and 'rotation_speed' are implemented as custom data type for radians which cannot have values lower than -PI and greater than PI. Any excess or deficit "wraps around". For example, -3.2 becomes ~3.08.

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