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  • Why is my shadowmap all white?

    - by Berend
    I was trying out a shadowmap. But all my shadow is white. I think there is some problem with my homogeneous component. Can anybody help me? The rest of my code is written in xna Here is the hlsl code I used float4x4 xWorld; float4x4 xView; float4x4 xProjection; struct VertexToPixel { float4 Position : POSITION; float4 ScreenPos : TEXCOORD1; float Depth : TEXCOORD2; }; struct PixelToFrame { float4 Color : COLOR0; }; //------- Technique: ShadowMap -------- VertexToPixel MyVertexShader(float4 inPos: POSITION0, float3 inNormal: NORMAL0) { VertexToPixel Output = (VertexToPixel)0; float4x4 preViewProjection = mul(xView, xProjection); float4x4 preWorldViewProjection = mul(xWorld, preViewProjection); Output.Position =mul(inPos, mul(xWorld, preViewProjection)); Output.Depth = Output.Position.z / Output.Position.w; Output.ScreenPos = Output.Position; return Output; } float4 MyPixelShader(VertexToPixel PSIn) : COLOR0 { PixelToFrame Output = (PixelToFrame)0; Output.Color = PSIn.ScreenPos.z/PSIn.ScreenPos.w; return Output.Color; } technique ShadowMap { pass Pass0 { VertexShader = compile vs_2_0 MyVertexShader(); PixelShader = compile ps_2_0 MyPixelShader(); } }

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  • Help understand GLSL directional light on iOS (left handed coord system)

    - by Robse
    I now have changed from GLKBaseEffect to a own shader implementation. I have a shader management, which compiles and applies a shader to the right time and does some shader setup like lights. Please have a look at my vertex shader code. Now, light direction should be provided in eye space, but I think there is something I don't get right. After I setup my view with camera I save a lightMatrix to transform the light from global space to eye space. My modelview and projection setup: - (void)setupViewWithWidth:(int)width height:(int)height camera:(N3DCamera *)aCamera { aCamera.aspect = (float)width / (float)height; float aspect = aCamera.aspect; float far = aCamera.far; float near = aCamera.near; float vFOV = aCamera.fieldOfView; float top = near * tanf(M_PI * vFOV / 360.0f); float bottom = -top; float right = aspect * top; float left = -right; // projection GLKMatrixStackLoadMatrix4(projectionStack, GLKMatrix4MakeFrustum(left, right, bottom, top, near, far)); // identity modelview GLKMatrixStackLoadMatrix4(modelviewStack, GLKMatrix4Identity); // switch to left handed coord system (forward = z+) GLKMatrixStackMultiplyMatrix4(modelviewStack, GLKMatrix4MakeScale(1, 1, -1)); // transform camera GLKMatrixStackMultiplyMatrix4(modelviewStack, GLKMatrix4MakeWithMatrix3(GLKMatrix3Transpose(aCamera.orientation))); GLKMatrixStackTranslate(modelviewStack, -aCamera.position.x, -aCamera.position.y, -aCamera.position.z); } - (GLKMatrix4)modelviewMatrix { return GLKMatrixStackGetMatrix4(modelviewStack); } - (GLKMatrix4)projectionMatrix { return GLKMatrixStackGetMatrix4(projectionStack); } - (GLKMatrix4)modelviewProjectionMatrix { return GLKMatrix4Multiply([self projectionMatrix], [self modelviewMatrix]); } - (GLKMatrix3)normalMatrix { return GLKMatrix3InvertAndTranspose(GLKMatrix4GetMatrix3([self modelviewProjectionMatrix]), NULL); } After that, I save the lightMatrix like this: [self.renderer setupViewWithWidth:view.drawableWidth height:view.drawableHeight camera:self.camera]; self.lightMatrix = [self.renderer modelviewProjectionMatrix]; And just before I render a 3d entity of the scene graph, I setup the light config for its shader with the lightMatrix like this: - (N3DLight)transformedLight:(N3DLight)light transformation:(GLKMatrix4)matrix { N3DLight transformedLight = N3DLightMakeDisabled(); if (N3DLightIsDirectional(light)) { GLKVector3 direction = GLKVector3MakeWithArray(GLKMatrix4MultiplyVector4(matrix, light.position).v); direction = GLKVector3Negate(direction); // HACK -> TODO: get lightMatrix right! transformedLight = N3DLightMakeDirectional(direction, light.diffuse, light.specular); } else { ... } return transformedLight; } You see the line, where I negate the direction!? I can't explain why I need to do that, but if I do, the lights are correct as far as I can tell. Please help me, to get rid of the hack. I'am scared that this has something to do, with my switch to left handed coord system. My vertex shader looks like this: attribute highp vec4 inPosition; attribute lowp vec4 inNormal; ... uniform highp mat4 MVP; uniform highp mat4 MV; uniform lowp mat3 N; uniform lowp vec4 constantColor; uniform lowp vec4 ambient; uniform lowp vec4 light0Position; uniform lowp vec4 light0Diffuse; uniform lowp vec4 light0Specular; varying lowp vec4 vColor; varying lowp vec3 vTexCoord0; vec4 calcDirectional(vec3 dir, vec4 diffuse, vec4 specular, vec3 normal) { float NdotL = max(dot(normal, dir), 0.0); return NdotL * diffuse; } ... vec4 calcLight(vec4 pos, vec4 diffuse, vec4 specular, vec3 normal) { if (pos.w == 0.0) { // Directional Light return calcDirectional(normalize(pos.xyz), diffuse, specular, normal); } else { ... } } void main(void) { // position highp vec4 position = MVP * inPosition; gl_Position = position; // normal lowp vec3 normal = inNormal.xyz / inNormal.w; normal = N * normal; normal = normalize(normal); // colors vColor = constantColor * ambient; // add lights vColor += calcLight(light0Position, light0Diffuse, light0Specular, normal); ... }

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  • My image is not showing in java, using ImageIcon

    - by user1048606
    I'd like to know why my images are now showing up when I use ImageIcon and when I have specified the directory the image is in. All I get is a black blank screen with nothing else on it. import java.awt.Image; import java.awt.event.KeyEvent; import javax.swing.ImageIcon; import java.awt.Image; import java.awt.event.KeyEvent; import java.util.ArrayList; import javax.swing.ImageIcon; // Class for handling key input public class Craft { private int dx; private int dy; private int x; private int y; private Image image; private Image image2; private ArrayList missiles; private final int CRAFT_SIZE = 20; private String craft = "C:\\Users\\Jimmy\\Desktop\\Jimmy's Folder\\programs\\craft.png"; public Craft() { ImageIcon ii = new ImageIcon(craft); image2 = ii.getImage(); missiles = new ArrayList(); x = 40; y = 60; } public void move() { x += dx; y += dy; } public int getX() { return x; } public int getY() { return y; } public Image getImage() { return image; } public ArrayList getMissiles() { return missiles; } public void keyPressed(KeyEvent e) { int key = e.getKeyCode(); // Shooting key if (key == KeyEvent.VK_SPACE) { fire(); } if (key == KeyEvent.VK_LEFT) { dx = -1; } if (key == KeyEvent.VK_RIGHT) { dx = 1; } if (key == KeyEvent.VK_UP) { dy = -1; } if (key == KeyEvent.VK_DOWN) { dy = 1; } } // Handles the missile object firing out of the ship public void fire() { missiles.add(new Missile(x + CRAFT_SIZE, y + CRAFT_SIZE/2)); } public void keyReleased(KeyEvent e) { int key = e.getKeyCode(); if (key == KeyEvent.VK_LEFT) { dx = 0; } if (key == KeyEvent.VK_RIGHT) { dx = 0; } if (key == KeyEvent.VK_UP) { dy = 0; } if (key == KeyEvent.VK_DOWN) { dy = 0; } } }

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  • Projected trajectory of a vehicle?

    - by mac
    In the game I am developing, I have to calculate if my vehicle (1) which in the example is travelling north with a speed V, can reach its target (2). The example depict the problem from atop: There are actually two possible scenarios: V is constant (resulting in trajectory 4, an arc of a circle) or the vehicle has the capacity to accelerate/decelerate (trajectory 3, an arc of a spiral). I would like to know if there is a straightforward way to verify if the vehicle is able to reach its target (as opposed to overshooting it). I'm particularly interested in trajectory #3, as I the only thing I could think of is integrating the position of the vehicle over time. EDIT: of course the vehicle has always the capacity to steer, but the steer radius vary with its speed (think to a maximum lateral g-force). EDIT2: also notice that (as most of the vehicles in real life) there is a minimum steering radius for the in-game ones too).

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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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  • How to add isometric (rts-alike) perspective and scolling in unity?

    - by keinabel
    I want to develop some RTS/simulation game. Therefore I need a camera perspective like one knows it from Anno 1602 - 1404, as well as the camera scrolling. I think this is called isometric perspective (and scrolling). But I honestly have no clue how to manage this. I tried some things I found on google, but they were not satisfying. Can you give me some good tutorials or advice for managing this? Thanks in advance

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  • Making retro games: Any good known game architectures?

    - by A.Quiroga
    I'm trying to do a remake of Snowbros . I'm doing it using libgdx but at each time i must try to thought how things got done . For example the physics of the jump and collisions . It seams to be time perfect , but i use the deltaTime to try to aproximate the value in game . I think in this case maybe its using some calcs with processor Hz , but i don't know. Then the simple question , is there any resources of how did they programm this games? Or any idea of the simple ideas repeated each game to game in the old style retro games.

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  • Geometry Shader : points + Triangles

    - by CmasterG
    I have different Shaders and for each Shader a instance of the ShaderClass class, which initializes the Shaders, Renders the Shaders, etc. I use most of the Shaderclasses without Geometry Shader, but in one Shader Class i also use a Geometry Shader. The problem is, that when I render one object with the Shaderclass that uses the Geometry shader, all other object are rendered with the same geometry that I create in the Geometry Shader. Can you help me? Is it possible that I have to use a Geometry Shader for each object, when I use one for one object? I use DirectX 11 with C++.

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  • Finding vectors with two points

    - by Christian Careaga
    We're are trying to get the direction of a projectile but we can't find out how For example: [1,1] will go SE [1,-1] will go NE [-1,-1] will go NW and [-1,1] will go SW we need an equation of some sort that will take the player pos and the mouse pos and find which direction the projectile needs to go. Here is where we are plugging in the vectors: def update(self): self.rect.x += self.vector[0] self.rect.y += self.vector[1] Then we are blitting the projectile at the rects coords.

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  • How to render a retro-like pixel graphics from 3d models?

    - by momijigari
    I was wondering if there's a possibility to render a retro-pixel-like graphics from 3d model in real time? I'm talking about the Starfarer-like graphics. I know it's hand drawn, and it's 2d. But if I need a 3d objects with the same aesthetics? I'm currently working with Flash. But I don't need any ready-solutions, I just want to understand the principle from any other platform if there is one. So if anybody met anything like this I would appreciate your help. (If it's not possible to do in real time, I could at least pre-render a sequence of sprites. It would be much better than creating hundreds of hand-drawn ones)

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  • Am I missing something about these considerations about Leaderboard's database's schema?

    - by misiMe
    I just finished to develop a mobile game, now I want to implement an online leaerboard using mysql. I'm wondering about the database's schema, I thought about some possibilities: (I didn't got in detail with syntax because my question is just about the logic of it) Name: string; Score: integer I thought to ask the name just the first time. If, in the future, you will modify that, it will call just an update to the name associated with your id. Leaderboard(ID, Name, Score) ID: integer autoincrement, PrimaryKey With this kind of idea maybe the db will grow fast because if you choose everytime a different name for the score, it will add a new entry. Leaderboard(PhoneId, Name, Score) Here PhoneId will be the unique identifier of the phone, PrimaryKey. A con of this choice is that if you want to play with your friends' phone, you can't put a different name for the score. Leaderboard(Name, Score) Here Name is PrimaryKey. With that, if you enter a name that already exists, you will be prompted to choose another one. Do you agree with this considerations? What will you do? Am I missing something?

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  • Why does my player stop when stepping onto a new tile?

    - by user220631
    Me and my friend are creating a game from scratch. He is in charge of art design and I am in charge of coding. I have done well so far with the code, but I have a collision detection problem when the character moves right: Once the player moves right, whenever a new block is encountered, the player stops. I don't know if this is a problem with collision or the player but I can't work around it. Here is the collision code: this.IsColliding = function(obj) { if(this.X > obj.X + obj.Width) return false; else if(this.X + this.Width < obj.X) return false; else if(this.Y > obj.Y + obj.Height) return false; else if(this.Y + this.Height < obj.Y) return false; else return true; } I also wanted to see if there as a way to make the player collide with the bottom of the block and the right side of the block instead of running through it.

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  • How do I render an animation where some frames appear twice?

    - by hustlerinc
    I am animating a sprite. The sprite has 7 different frames, but the animation is 10 frames long. This is because 3 of the original frames appear twice in the animation: 3 -> 4 -> 5 -> 6 -> 4 -> 3 -> 2 -> 1 -> 0 -> 2 Frames 2, 3 and 4 appear twice. This avoids having to store duplicate frames in the spritesheet. How can I render the animation in this sequence with repeated frames?

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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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  • Trouble with speed and vectors

    - by Eegabooga
    I'm working on adding bullets to my game. Right now I can shoot bullets in the direction that I would like from a ship by getting the ship's angle: int speed = 5; int dx = -(cos(degreesToRadians(ship.angle)) * speed); // rate of change in the x direction int dy = -(sin(degreesToRadians(ship.angle)) * speed); // rate of change in the y direction bulletPosition.addX(dx); // addX(dx) is simply bulletPosition.x += dx bulletPosition.addY(dy); The ship is pretty much the exact same thing, except I use the += operator: int dx += -(cos(degreesToRadians(angle)) * 0.15) int dy += -(sin(degreesToRadians(angle)) * 0.15); shipPosition.addX(dx); shipPosition.addY(dy); I would like to be able to add the ship's velocity to the bullet's velocity, but I'm a little confused as to how should get the speed from the ship's vector. I thought that adding the ship's dx to the bullet's dx like int dx = -(cos(degreesToRadians(ship.angle)) * speed * dx) would work because I'm adding the rate of change of the ship to the rate of change of the bullet, but that doesn't work. So here's the final question: How can I get the speed of my ship and apply it to my bullet's speed? Thanks in advance for all help :)

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  • How should I structure moving from overworld to menu system / combat?

    - by persepolis
    I'm making a text-based "Arena" game where the player is the owner of 5 creatures that battle other teams for loot, experience and glory. The game is very simple, using Python and a curses emulator. I have a static ASCII map of an "overworld" of sorts. My character, represented by a glyph, can move about this static map. There are locations all over the map that the character can visit, that break down into two types: 1) Towns, which are a series of menus that will allow the player to buy equipment for his team, hire new recruits or do other things. 2) Arenas, where the player's team will have a "battle" interface with actions he can perform, messages about the fight, etc. Maybe later, an ASCII representation of the fight but for now, just screens of information with action prompts. My main problem is what kind of design or structure I should use to implement this? Right now, the game goes through a master loop which waits for keyboard input and then moves the player about the screen. My current thinking is this: 1) Upon keyboard input, the Player coordinates are checked against a list of Location objects and if the Player coords match the Location coords then... 2) ??? I'm not sure if I should then call a seperate function to initiate a "menu" or "combat" mode. Or should I create some kind of new GameMode object that contains a method itself for drawing the screen, printing the necessary info? How do I pass my player's team data into this object? My main concern is passing around the program flow into all these objects. Should I be calling straight functions for different parts of my game, and objects to represent "things" within my game? I was reading about the MVC pattern and how this kind of problem might benefit - decouple the GUI from the game logic and user input but I have no idea how this applies to my game.

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  • Line Intersection from parametric equation

    - by Sidar
    I'm sure this question has been asked before. However, I'm trying to connect the dots by translating an equation on paper into an actual function. I thought It would be interesting to ask here instead on the Math sites (since it's going to be used for games anyway ). Let's say we have our vector equation : x = s + Lr; where x is the resulting vector, s our starting point/vector. L our parameter and r our direction vector. The ( not sure it's called like this, please correct me ) normal equation is : x.n = c; If we substitute our vector equation we get: (s+Lr).n = c. We now need to isolate L which results in L = (c - s.n) / (r.n); L needs to be 0 < L < 1. Meaning it needs to be between 0 and 1. My question: I want to know what L is so if I were to substitute L for both vector equation (or two lines) they should give me the same intersection coordinates. That is if they intersect. But I can't wrap my head around on how to use this for two lines and find the parameter that fits the intersection point. Could someone with a simple example show how I could translate this to a function/method?

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  • Server-side Architecture for Online Game

    - by Draiken
    basically I have a game client that has communicate with a server for almost every action it takes, the game is in Java (using LWJGL) and right now I will start making the server. The base of the game is normally one client communicating with the server alone, but I will require later on for several clients to work together for some functionalities. I've already read how authentication server should be sepparated and I intend on doing it. The problem is I am completely inexperienced in this kind of server-side programming, all I've ever programmed were JSF web applications. I imagine I'll do socket connections for pretty much every game communication since HTML is very slow, but I still don't really know where to start on my server. I would appreciate reading material or guidelines on where to start, what architecture should the game server have and maybe some suggestions on frameworks that could help me getting the client-server communication. I've looked into JNAG but I have no experience with this kind of thing, so I can't really tell if it is a solid and good messaging layer. Any help is appreciated... Thanks ! EDIT: Just a little more information about the game. It is intended to be a very complex game with several functionalities, making some functionalities a "program" inside the program. It is not an usual game, like FPS or RPG but I intend on having a lot of users using these many different "programs" inside the game. If I wasn't clear enough, I'd really appreciate people that have already developed games with java client/server architecture, how they communicated, any frameworks, apis, messaging systems, etc. It is not a question of lack of knowledge of language, more a question for advice, so I don't end up creating something that works, but in the later stages will have to be rewriten for any kind of limiting reason. PS: sorry if my english is not perfect...

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  • Updates for IOS AppStore Multiplayer Game

    - by TobiHeidi
    I am developing a multiplayer game for the web, android and ios. For the web and android i can instantly push out new versions of my game because they support executing remotly loaded code. But with IOS i need to wait for an Apple approval taking about 10 days. I want to push updates more then weekly. What if my server code changes so the client MUST update? Run an old version of the server code just for IOS? How do other multiplayer devs handle this ?

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  • converting 2d grid of squares to polygon nav mesh

    - by Roflha
    I haven't actually started programming for this one yet, but I wanted to see how I would go about doing this anyway. Say I have a 2D matrix of squares, all of the same size, some traversable and some not. How would I go about creating a navigation mesh of polygons from this grid. Is there any reading I can look at until I get a chance to get to my computer or should I just give it a go. My idea was to take the non-traversable squares out and extend lines from there edges to make polygons.. that's all I have got so far. Any advice?

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  • What forms of non-interactive RPG battle systems exist?

    - by Landstander
    I am interested in systems that allow players to develop a battle plan or setup strategy for the party or characters prior to entering battle. During the battle the player either cannot input commands or can choose not to. Rule Based In this system the player can setup a list of rules in the form of [Condition - Action] that are then ordered by priority. Gambits in Final Fantasy XII Tactics in Dragon Age Origin & II

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  • Profiling and containing memory per system

    - by chadb
    I have been interesting in profiling and keeping a managed memory pool for each subsystem, so I could get statistic on how much memory was being used in something such as sounds or graphics. However, what is the best design for doing this? I was thinking of using multiple allocators and just using one per subsystem, however, that would result in global variables for my allocators (or so it would seem to me). Another approach I have seen/been suggested is to just overload new and pass in an allocator for a parameter. I had a similar question over on stackoverflow here with a bounty, however, it seems as if perhaps I was too vague or just there is not enough people with knowledge in the subject.

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  • how to solve ArrayList outOfBoundsExeption?

    - by iQue
    Im getting: 09-02 17:15:39.140: E/AndroidRuntime(533): java.lang.IndexOutOfBoundsException: Invalid index 1, size is 1 09-02 17:15:39.140: E/AndroidRuntime(533): at java.util.ArrayList.throwIndexOutOfBoundsException(ArrayList.java:251) when Im killing enemies using this method: private void checkCollision() { Rect h1 = happy.getBounds(); for (int i = 0; i < enemies.size(); i++) { for (int j = 0; j < bullets.size(); j++) { Rect b1 = bullets.get(j).getBounds(); Rect e1 = enemies.get(i).getBounds(); if (b1.intersect(e1)) { enemies.get(i).damageHP(5); bullets.remove(j); Log.d("TAG", "HERE: LOLTHEYTOUCHED"); } if (h1.intersect(e1)){ happy.damageHP(5); } if(enemies.get(i).getHP() <= 0){ enemies.remove(i); } if(happy.getHP() <= 0){ //end-screen !!!!!!! } } } } using this ArrayList: private ArrayList<Enemy> enemies = new ArrayList<Enemy>(); and adding to array like this: public void createEnemies() { Bitmap bmp = BitmapFactory.decodeResource(getResources(), R.drawable.female); if (enemyCounter < 24) { enemies.add(new Enemy(bmp, this, controls)); } enemyCounter++; } I dont really understand what the problem is, Ive been looking around for a while but cant really find anything that helps me. If you know or if you can link me someplace where they have a solution for a similar problem Ill be a very happy camper! Thanks for ur time.

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  • Stop animation playing automatically

    - by Starkers
    I've created an animation to animate a swinging mace. To do this I select the mace object in the scene pane, open the animation pane, and key it at a certain position at 0:00. I'm prompted to save this animation in my assets folder, which I do, as maceswing I then rotate the mace, move the slider through time and key it in a different position. I move the slider through time again, move the object to the original position and key it. There are now three things in my assets folder: maceswing appears to be my animation, but I have no idea what Mace Mace 1 and Mace 2 are. (I've been mucking around trying to get this working so it's possible Mace 1 and Mace 2 are just duplicates of Mace. I still want to know what they are though) When I play my game, the mace is constantly swinging, even though I didn't apply maceswing to it. I can't stop it. People say there's some kind of tick box to stop it constantly animating but I can't find it. My mace object only has an Animator component: Unticking this component doesn't stop the animation playing so I have no idea where the animation is coming from. Or what the Animator component actually does. I don't want this animation constantly playing. I only want it to play once when someone clicks a certain button: var Mace : Transform; if(Input.GetButtonDown('Fire1')){ Mace.animation.Play('maceswing'); }; Upon clicking the 'Fire1' button, I get this error: MissingComponentException: There is no 'Animation' attached to the "Mace" game object, but a script is trying to access it. You probably need to add a Animation to the game object "Mace". Or your script needs to check if the component is attached before using it. There is no 'Animation' attached to the "Mace" game object, and yet I can see it swinging away constantly. Infact I can't stop it! So what's causing the animation if the game object doesn't have an 'Animation' attached to it?

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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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