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  • Euler Problem 13

    - by MarkPearl
    The Problem Work out the first ten digits of the sum of the following one-hundred 50-digit numbers. 37107287533902102798797998220837590246510135740250 46376937677490009712648124896970078050417018260538 74324986199524741059474233309513058123726617309629 91942213363574161572522430563301811072406154908250 23067588207539346171171980310421047513778063246676 89261670696623633820136378418383684178734361726757 28112879812849979408065481931592621691275889832738 44274228917432520321923589422876796487670272189318 47451445736001306439091167216856844588711603153276 70386486105843025439939619828917593665686757934951 62176457141856560629502157223196586755079324193331 64906352462741904929101432445813822663347944758178 92575867718337217661963751590579239728245598838407 58203565325359399008402633568948830189458628227828 80181199384826282014278194139940567587151170094390 35398664372827112653829987240784473053190104293586 86515506006295864861532075273371959191420517255829 71693888707715466499115593487603532921714970056938 54370070576826684624621495650076471787294438377604 53282654108756828443191190634694037855217779295145 36123272525000296071075082563815656710885258350721 45876576172410976447339110607218265236877223636045 17423706905851860660448207621209813287860733969412 81142660418086830619328460811191061556940512689692 51934325451728388641918047049293215058642563049483 62467221648435076201727918039944693004732956340691 15732444386908125794514089057706229429197107928209 55037687525678773091862540744969844508330393682126 18336384825330154686196124348767681297534375946515 80386287592878490201521685554828717201219257766954 78182833757993103614740356856449095527097864797581 16726320100436897842553539920931837441497806860984 48403098129077791799088218795327364475675590848030 87086987551392711854517078544161852424320693150332 59959406895756536782107074926966537676326235447210 69793950679652694742597709739166693763042633987085 41052684708299085211399427365734116182760315001271 65378607361501080857009149939512557028198746004375 35829035317434717326932123578154982629742552737307 94953759765105305946966067683156574377167401875275 88902802571733229619176668713819931811048770190271 25267680276078003013678680992525463401061632866526 36270218540497705585629946580636237993140746255962 24074486908231174977792365466257246923322810917141 91430288197103288597806669760892938638285025333403 34413065578016127815921815005561868836468420090470 23053081172816430487623791969842487255036638784583 11487696932154902810424020138335124462181441773470 63783299490636259666498587618221225225512486764533 67720186971698544312419572409913959008952310058822 95548255300263520781532296796249481641953868218774 76085327132285723110424803456124867697064507995236 37774242535411291684276865538926205024910326572967 23701913275725675285653248258265463092207058596522 29798860272258331913126375147341994889534765745501 18495701454879288984856827726077713721403798879715 38298203783031473527721580348144513491373226651381 34829543829199918180278916522431027392251122869539 40957953066405232632538044100059654939159879593635 29746152185502371307642255121183693803580388584903 41698116222072977186158236678424689157993532961922 62467957194401269043877107275048102390895523597457 23189706772547915061505504953922979530901129967519 86188088225875314529584099251203829009407770775672 11306739708304724483816533873502340845647058077308 82959174767140363198008187129011875491310547126581 97623331044818386269515456334926366572897563400500 42846280183517070527831839425882145521227251250327 55121603546981200581762165212827652751691296897789 32238195734329339946437501907836945765883352399886 75506164965184775180738168837861091527357929701337 62177842752192623401942399639168044983993173312731 32924185707147349566916674687634660915035914677504 99518671430235219628894890102423325116913619626622 73267460800591547471830798392868535206946944540724 76841822524674417161514036427982273348055556214818 97142617910342598647204516893989422179826088076852 87783646182799346313767754307809363333018982642090 10848802521674670883215120185883543223812876952786 71329612474782464538636993009049310363619763878039 62184073572399794223406235393808339651327408011116 66627891981488087797941876876144230030984490851411 60661826293682836764744779239180335110989069790714 85786944089552990653640447425576083659976645795096 66024396409905389607120198219976047599490197230297 64913982680032973156037120041377903785566085089252 16730939319872750275468906903707539413042652315011 94809377245048795150954100921645863754710598436791 78639167021187492431995700641917969777599028300699 15368713711936614952811305876380278410754449733078 40789923115535562561142322423255033685442488917353 44889911501440648020369068063960672322193204149535 41503128880339536053299340368006977710650566631954 81234880673210146739058568557934581403627822703280 82616570773948327592232845941706525094512325230608 22918802058777319719839450180888072429661980811197 77158542502016545090413245809786882778948721859617 72107838435069186155435662884062257473692284509516 20849603980134001723930671666823555245252804609722 53503534226472524250874054075591789781264330331690   The Solution private static List<string> table = new List<string> { "37107287533902102798797998220837590246510135740250", "46376937677490009712648124896970078050417018260538", "74324986199524741059474233309513058123726617309629", "91942213363574161572522430563301811072406154908250", "23067588207539346171171980310421047513778063246676", "89261670696623633820136378418383684178734361726757", "28112879812849979408065481931592621691275889832738", "44274228917432520321923589422876796487670272189318", "47451445736001306439091167216856844588711603153276", "70386486105843025439939619828917593665686757934951", "62176457141856560629502157223196586755079324193331", "64906352462741904929101432445813822663347944758178", "92575867718337217661963751590579239728245598838407", "58203565325359399008402633568948830189458628227828", "80181199384826282014278194139940567587151170094390", "35398664372827112653829987240784473053190104293586", "86515506006295864861532075273371959191420517255829", "71693888707715466499115593487603532921714970056938", "54370070576826684624621495650076471787294438377604", "53282654108756828443191190634694037855217779295145", "36123272525000296071075082563815656710885258350721", "45876576172410976447339110607218265236877223636045", "17423706905851860660448207621209813287860733969412", "81142660418086830619328460811191061556940512689692", "51934325451728388641918047049293215058642563049483", "62467221648435076201727918039944693004732956340691", "15732444386908125794514089057706229429197107928209", "55037687525678773091862540744969844508330393682126", "18336384825330154686196124348767681297534375946515", "80386287592878490201521685554828717201219257766954", "78182833757993103614740356856449095527097864797581", "16726320100436897842553539920931837441497806860984", "48403098129077791799088218795327364475675590848030", "87086987551392711854517078544161852424320693150332", "59959406895756536782107074926966537676326235447210", "69793950679652694742597709739166693763042633987085", "41052684708299085211399427365734116182760315001271", "65378607361501080857009149939512557028198746004375", "35829035317434717326932123578154982629742552737307", "94953759765105305946966067683156574377167401875275", "88902802571733229619176668713819931811048770190271", "25267680276078003013678680992525463401061632866526", "36270218540497705585629946580636237993140746255962", "24074486908231174977792365466257246923322810917141", "91430288197103288597806669760892938638285025333403", "34413065578016127815921815005561868836468420090470", "23053081172816430487623791969842487255036638784583", "11487696932154902810424020138335124462181441773470", "63783299490636259666498587618221225225512486764533", "67720186971698544312419572409913959008952310058822", "95548255300263520781532296796249481641953868218774", "76085327132285723110424803456124867697064507995236", "37774242535411291684276865538926205024910326572967", "23701913275725675285653248258265463092207058596522", "29798860272258331913126375147341994889534765745501", "18495701454879288984856827726077713721403798879715", "38298203783031473527721580348144513491373226651381", "34829543829199918180278916522431027392251122869539", "40957953066405232632538044100059654939159879593635", "29746152185502371307642255121183693803580388584903", "41698116222072977186158236678424689157993532961922", "62467957194401269043877107275048102390895523597457", "23189706772547915061505504953922979530901129967519", "86188088225875314529584099251203829009407770775672", "11306739708304724483816533873502340845647058077308", "82959174767140363198008187129011875491310547126581", "97623331044818386269515456334926366572897563400500", "42846280183517070527831839425882145521227251250327", "55121603546981200581762165212827652751691296897789", "32238195734329339946437501907836945765883352399886", "75506164965184775180738168837861091527357929701337", "62177842752192623401942399639168044983993173312731", "32924185707147349566916674687634660915035914677504", "99518671430235219628894890102423325116913619626622", "73267460800591547471830798392868535206946944540724", "76841822524674417161514036427982273348055556214818", "97142617910342598647204516893989422179826088076852", "87783646182799346313767754307809363333018982642090", "10848802521674670883215120185883543223812876952786", "71329612474782464538636993009049310363619763878039", "62184073572399794223406235393808339651327408011116", "66627891981488087797941876876144230030984490851411", "60661826293682836764744779239180335110989069790714", "85786944089552990653640447425576083659976645795096", "66024396409905389607120198219976047599490197230297", "64913982680032973156037120041377903785566085089252", "16730939319872750275468906903707539413042652315011", "94809377245048795150954100921645863754710598436791", "78639167021187492431995700641917969777599028300699", "15368713711936614952811305876380278410754449733078", "40789923115535562561142322423255033685442488917353", "44889911501440648020369068063960672322193204149535", "41503128880339536053299340368006977710650566631954", "81234880673210146739058568557934581403627822703280", "82616570773948327592232845941706525094512325230608", "22918802058777319719839450180888072429661980811197", "77158542502016545090413245809786882778948721859617", "72107838435069186155435662884062257473692284509516", "20849603980134001723930671666823555245252804609722", "53503534226472524250874054075591789781264330331690"}; static void Main(string[] args) { BigInteger result = 0; table.ForEach(x => result += BigInteger.Parse(x)); Console.WriteLine(result.ToString().Substring(0,10)); Console.ReadLine(); }

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  • Why do I not get the correct answer for Euler 56 in J?

    - by Gregory Higley
    I've solved 84 of the Project Euler problems, mostly in Haskell. I am now going back and trying to solve in J some of those I already solved in Haskell, as an exercise in learning J. Currently, I am trying to solve Problem 56. Let me stress that I already know what the right answer is, since I've already solved it in Haskell. It's a very easy, trivial problem. I will not give the answer here. Here is my solution in J: digits =: ("."0)":"0 eachDigit =: adverb : 'u@:digits"0' NB. I use this so often I made it an adverb. cartesian =: adverb : '((#~ #) u ($~ ([:*~#)))' >./ +/ eachDigit x: ^ cartesian : i. 99 This produces a number less than the desired result. In other words, it's wrong somehow. Any J-ers out there know why? I'm baffled, since it's pretty straightforward and totally brute force.

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  • DVD authoring software that supports multiple angles?

    - by RandomEngy
    I'm writing a DVD ripping app and I need to get some sources with multiple angles. Unfortunately, they seem to be rather hard to come by. I figured my best bet would be to author a simple DVD with a multi-angle title. Does anyone know of any software on Windows that lets you make multi-angle titles? Preferably free or trialware? I don't need it to be super-usable, just enough to make one DVD.

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  • comparing two angles

    - by Elazar Leibovich
    Given four points in the plane, A,B,X,Y, I wish to determine which of the following two angles is smaller ?ABX or ?ABY. I'd rather not use cos or sqrt, in order to preserve accuracy. In the case where A=(-1,0),B=(0,0), I can compare the two angles ?ABX and ?ABY, by calculating the dot product of the vectors X,Y, and watch it's sign. What I can do in this case is: Determine whether or not ABX turns right or left If ABX turns left check whether or not Y and A are on the same side of the line on segment BX. If they are - ?ABX is a smaller than ABY. If ABX turns right, then Y and A on the same side of BX means that ?ABX is larger than ?ABY. But this seems too complicated to me. Any simpler approach?

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  • Ball bouncing at a certain angle and efficiency computations

    - by X Y
    I would like to make a pong game with a small twist (for now). Every time the ball bounces off one of the paddles i want it to be under a certain angle (between a min and a max). I simply can't wrap my head around how to actually do it (i have some thoughts and such but i simply cannot implement them properly - i feel i'm overcomplicating things). Here's an image with a small explanation . One other problem would be that the conditions for bouncing have to be different for every edge. For example, in the picture, on the two small horizontal edges i do not want a perfectly vertical bounce when in the middle of the edge but rather a constant angle (pi/4 maybe) in either direction depending on the collision point (before the middle of the edge, or after). All of my collisions are done with the Separating Axes Theorem (and seem to work fine). I'm looking for something efficient because i want to add a lot of things later on (maybe polygons with many edges and such). So i need to keep to a minimum the amount of checking done every frame. The collision algorithm begins testing whenever the bounding boxes of the paddle and the ball intersect. Is there something better to test for possible collisions every frame? (more efficient in the long run,with many more objects etc, not necessarily easy to code). I'm going to post the code for my game: Paddle Class public class Paddle : Microsoft.Xna.Framework.DrawableGameComponent { #region Private Members private SpriteBatch spriteBatch; private ContentManager contentManager; private bool keybEnabled; private bool isLeftPaddle; private Texture2D paddleSprite; private Vector2 paddlePosition; private float paddleSpeedY; private Vector2 paddleScale = new Vector2(1f, 1f); private const float DEFAULT_Y_SPEED = 150; private Vector2[] Normals2Edges; private Vector2[] Vertices = new Vector2[4]; private List<Vector2> lst = new List<Vector2>(); private Vector2 Edge; #endregion #region Properties public float Speed { get {return paddleSpeedY; } set { paddleSpeedY = value; } } public Vector2[] Normal2EdgesVector { get { NormalsToEdges(this.isLeftPaddle); return Normals2Edges; } } public Vector2[] VertexVector { get { return Vertices; } } public Vector2 Scale { get { return paddleScale; } set { paddleScale = value; NormalsToEdges(this.isLeftPaddle); } } public float X { get { return paddlePosition.X; } set { paddlePosition.X = value; } } public float Y { get { return paddlePosition.Y; } set { paddlePosition.Y = value; } } public float Width { get { return (Scale.X == 1f ? (float)paddleSprite.Width : paddleSprite.Width * Scale.X); } } public float Height { get { return ( Scale.Y==1f ? (float)paddleSprite.Height : paddleSprite.Height*Scale.Y ); } } public Texture2D GetSprite { get { return paddleSprite; } } public Rectangle Boundary { get { return new Rectangle((int)paddlePosition.X, (int)paddlePosition.Y, (int)this.Width, (int)this.Height); } } public bool KeyboardEnabled { get { return keybEnabled; } } #endregion private void NormalsToEdges(bool isLeftPaddle) { Normals2Edges = null; Edge = Vector2.Zero; lst.Clear(); for (int i = 0; i < Vertices.Length; i++) { Edge = Vertices[i + 1 == Vertices.Length ? 0 : i + 1] - Vertices[i]; if (Edge != Vector2.Zero) { Edge.Normalize(); //outer normal to edge !! (origin in top-left) lst.Add(new Vector2(Edge.Y, -Edge.X)); } } Normals2Edges = lst.ToArray(); } public float[] ProjectPaddle(Vector2 axis) { if (Vertices.Length == 0 || axis == Vector2.Zero) return (new float[2] { 0, 0 }); float min, max; min = Vector2.Dot(axis, Vertices[0]); max = min; for (int i = 1; i < Vertices.Length; i++) { float p = Vector2.Dot(axis, Vertices[i]); if (p < min) min = p; else if (p > max) max = p; } return (new float[2] { min, max }); } public Paddle(Game game, bool isLeftPaddle, bool enableKeyboard = true) : base(game) { contentManager = new ContentManager(game.Services); keybEnabled = enableKeyboard; this.isLeftPaddle = isLeftPaddle; } public void setPosition(Vector2 newPos) { X = newPos.X; Y = newPos.Y; } public override void Initialize() { base.Initialize(); this.Speed = DEFAULT_Y_SPEED; X = 0; Y = 0; NormalsToEdges(this.isLeftPaddle); } protected override void LoadContent() { spriteBatch = new SpriteBatch(GraphicsDevice); paddleSprite = contentManager.Load<Texture2D>(@"Content\pongBar"); } public override void Update(GameTime gameTime) { //vertices array Vertices[0] = this.paddlePosition; Vertices[1] = this.paddlePosition + new Vector2(this.Width, 0); Vertices[2] = this.paddlePosition + new Vector2(this.Width, this.Height); Vertices[3] = this.paddlePosition + new Vector2(0, this.Height); // Move paddle, but don't allow movement off the screen if (KeyboardEnabled) { float moveDistance = Speed * (float)gameTime.ElapsedGameTime.TotalSeconds; KeyboardState newKeyState = Keyboard.GetState(); if (newKeyState.IsKeyDown(Keys.Down) && Y + paddleSprite.Height + moveDistance <= Game.GraphicsDevice.Viewport.Height) { Y += moveDistance; } else if (newKeyState.IsKeyDown(Keys.Up) && Y - moveDistance >= 0) { Y -= moveDistance; } } else { if (this.Y + this.Height > this.GraphicsDevice.Viewport.Height) { this.Y = this.Game.GraphicsDevice.Viewport.Height - this.Height - 1; } } base.Update(gameTime); } public override void Draw(GameTime gameTime) { spriteBatch.Begin(SpriteSortMode.Texture,null); spriteBatch.Draw(paddleSprite, paddlePosition, null, Color.White, 0f, Vector2.Zero, Scale, SpriteEffects.None, 0); spriteBatch.End(); base.Draw(gameTime); } } Ball Class public class Ball : Microsoft.Xna.Framework.DrawableGameComponent { #region Private Members private SpriteBatch spriteBatch; private ContentManager contentManager; private const float DEFAULT_SPEED = 50; private float speedIncrement = 0; private Vector2 ballScale = new Vector2(1f, 1f); private const float INCREASE_SPEED = 50; private Texture2D ballSprite; //initial texture private Vector2 ballPosition; //position private Vector2 centerOfBall; //center coords private Vector2 ballSpeed = new Vector2(DEFAULT_SPEED, DEFAULT_SPEED); //speed #endregion #region Properties public float DEFAULTSPEED { get { return DEFAULT_SPEED; } } public Vector2 ballCenter { get { return centerOfBall; } } public Vector2 Scale { get { return ballScale; } set { ballScale = value; } } public float SpeedX { get { return ballSpeed.X; } set { ballSpeed.X = value; } } public float SpeedY { get { return ballSpeed.Y; } set { ballSpeed.Y = value; } } public float X { get { return ballPosition.X; } set { ballPosition.X = value; } } public float Y { get { return ballPosition.Y; } set { ballPosition.Y = value; } } public Texture2D GetSprite { get { return ballSprite; } } public float Width { get { return (Scale.X == 1f ? (float)ballSprite.Width : ballSprite.Width * Scale.X); } } public float Height { get { return (Scale.Y == 1f ? (float)ballSprite.Height : ballSprite.Height * Scale.Y); } } public float SpeedIncreaseIncrement { get { return speedIncrement; } set { speedIncrement = value; } } public Rectangle Boundary { get { return new Rectangle((int)ballPosition.X, (int)ballPosition.Y, (int)this.Width, (int)this.Height); } } #endregion public Ball(Game game) : base(game) { contentManager = new ContentManager(game.Services); } public void Reset() { ballSpeed.X = DEFAULT_SPEED; ballSpeed.Y = DEFAULT_SPEED; ballPosition.X = Game.GraphicsDevice.Viewport.Width / 2 - ballSprite.Width / 2; ballPosition.Y = Game.GraphicsDevice.Viewport.Height / 2 - ballSprite.Height / 2; } public void SpeedUp() { if (ballSpeed.Y < 0) ballSpeed.Y -= (INCREASE_SPEED + speedIncrement); else ballSpeed.Y += (INCREASE_SPEED + speedIncrement); if (ballSpeed.X < 0) ballSpeed.X -= (INCREASE_SPEED + speedIncrement); else ballSpeed.X += (INCREASE_SPEED + speedIncrement); } public float[] ProjectBall(Vector2 axis) { if (axis == Vector2.Zero) return (new float[2] { 0, 0 }); float min, max; min = Vector2.Dot(axis, this.ballCenter) - this.Width/2; //center - radius max = min + this.Width; //center + radius return (new float[2] { min, max }); } public void ChangeHorzDirection() { ballSpeed.X *= -1; } public void ChangeVertDirection() { ballSpeed.Y *= -1; } public override void Initialize() { base.Initialize(); ballPosition.X = Game.GraphicsDevice.Viewport.Width / 2 - ballSprite.Width / 2; ballPosition.Y = Game.GraphicsDevice.Viewport.Height / 2 - ballSprite.Height / 2; } protected override void LoadContent() { spriteBatch = new SpriteBatch(GraphicsDevice); ballSprite = contentManager.Load<Texture2D>(@"Content\ball"); } public override void Update(GameTime gameTime) { if (this.Y < 1 || this.Y > GraphicsDevice.Viewport.Height - this.Height - 1) this.ChangeVertDirection(); centerOfBall = new Vector2(ballPosition.X + this.Width / 2, ballPosition.Y + this.Height / 2); base.Update(gameTime); } public override void Draw(GameTime gameTime) { spriteBatch.Begin(); spriteBatch.Draw(ballSprite, ballPosition, null, Color.White, 0f, Vector2.Zero, Scale, SpriteEffects.None, 0); spriteBatch.End(); base.Draw(gameTime); } } Main game class public class gameStart : Microsoft.Xna.Framework.Game { GraphicsDeviceManager graphics; SpriteBatch spriteBatch; public gameStart() { graphics = new GraphicsDeviceManager(this); Content.RootDirectory = "Content"; this.Window.Title = "Pong game"; } protected override void Initialize() { ball = new Ball(this); paddleLeft = new Paddle(this,true,false); paddleRight = new Paddle(this,false,true); Components.Add(ball); Components.Add(paddleLeft); Components.Add(paddleRight); this.Window.AllowUserResizing = false; this.IsMouseVisible = true; this.IsFixedTimeStep = false; this.isColliding = false; base.Initialize(); } #region MyPrivateStuff private Ball ball; private Paddle paddleLeft, paddleRight; private int[] bit = { -1, 1 }; private Random rnd = new Random(); private int updates = 0; enum nrPaddle { None, Left, Right }; private nrPaddle PongBar = nrPaddle.None; private ArrayList Axes = new ArrayList(); private Vector2 MTV; //minimum translation vector private bool isColliding; private float overlap; //smallest distance after projections private Vector2 overlapAxis; //axis of overlap #endregion protected override void LoadContent() { spriteBatch = new SpriteBatch(GraphicsDevice); paddleLeft.setPosition(new Vector2(0, this.GraphicsDevice.Viewport.Height / 2 - paddleLeft.Height / 2)); paddleRight.setPosition(new Vector2(this.GraphicsDevice.Viewport.Width - paddleRight.Width, this.GraphicsDevice.Viewport.Height / 2 - paddleRight.Height / 2)); paddleLeft.Scale = new Vector2(1f, 2f); //scale left paddle } private bool ShapesIntersect(Paddle paddle, Ball ball) { overlap = 1000000f; //large value overlapAxis = Vector2.Zero; MTV = Vector2.Zero; foreach (Vector2 ax in Axes) { float[] pad = paddle.ProjectPaddle(ax); //pad0 = min, pad1 = max float[] circle = ball.ProjectBall(ax); //circle0 = min, circle1 = max if (pad[1] <= circle[0] || circle[1] <= pad[0]) { return false; } if (pad[1] - circle[0] < circle[1] - pad[0]) { if (Math.Abs(overlap) > Math.Abs(-pad[1] + circle[0])) { overlap = -pad[1] + circle[0]; overlapAxis = ax; } } else { if (Math.Abs(overlap) > Math.Abs(circle[1] - pad[0])) { overlap = circle[1] - pad[0]; overlapAxis = ax; } } } if (overlapAxis != Vector2.Zero) { MTV = overlapAxis * overlap; } return true; } protected override void Update(GameTime gameTime) { updates += 1; float ftime = 5 * (float)gameTime.ElapsedGameTime.TotalSeconds; if (updates == 1) { isColliding = false; int Xrnd = bit[Convert.ToInt32(rnd.Next(0, 2))]; int Yrnd = bit[Convert.ToInt32(rnd.Next(0, 2))]; ball.SpeedX = Xrnd * ball.SpeedX; ball.SpeedY = Yrnd * ball.SpeedY; ball.X += ftime * ball.SpeedX; ball.Y += ftime * ball.SpeedY; } else { updates = 100; ball.X += ftime * ball.SpeedX; ball.Y += ftime * ball.SpeedY; } //autorun :) paddleLeft.Y = ball.Y; //collision detection PongBar = nrPaddle.None; if (ball.Boundary.Intersects(paddleLeft.Boundary)) { PongBar = nrPaddle.Left; if (!isColliding) { Axes.Clear(); Axes.AddRange(paddleLeft.Normal2EdgesVector); //axis from nearest vertex to ball's center Axes.Add(FORMULAS.NormAxisFromCircle2ClosestVertex(paddleLeft.VertexVector, ball.ballCenter)); } } else if (ball.Boundary.Intersects(paddleRight.Boundary)) { PongBar = nrPaddle.Right; if (!isColliding) { Axes.Clear(); Axes.AddRange(paddleRight.Normal2EdgesVector); //axis from nearest vertex to ball's center Axes.Add(FORMULAS.NormAxisFromCircle2ClosestVertex(paddleRight.VertexVector, ball.ballCenter)); } } if (PongBar != nrPaddle.None && !isColliding) switch (PongBar) { case nrPaddle.Left: if (ShapesIntersect(paddleLeft, ball)) { isColliding = true; if (MTV != Vector2.Zero) ball.X += MTV.X; ball.Y += MTV.Y; ball.ChangeHorzDirection(); } break; case nrPaddle.Right: if (ShapesIntersect(paddleRight, ball)) { isColliding = true; if (MTV != Vector2.Zero) ball.X += MTV.X; ball.Y += MTV.Y; ball.ChangeHorzDirection(); } break; default: break; } if (!ShapesIntersect(paddleRight, ball) && !ShapesIntersect(paddleLeft, ball)) isColliding = false; ball.X += ftime * ball.SpeedX; ball.Y += ftime * ball.SpeedY; //check ball movement if (ball.X > paddleRight.X + paddleRight.Width + 2) { //IncreaseScore(Left); ball.Reset(); updates = 0; return; } else if (ball.X < paddleLeft.X - 2) { //IncreaseScore(Right); ball.Reset(); updates = 0; return; } base.Update(gameTime); } protected override void Draw(GameTime gameTime) { GraphicsDevice.Clear(Color.Aquamarine); spriteBatch.Begin(SpriteSortMode.BackToFront, BlendState.AlphaBlend); spriteBatch.End(); base.Draw(gameTime); } } And one method i've used: public static Vector2 NormAxisFromCircle2ClosestVertex(Vector2[] vertices, Vector2 circle) { Vector2 temp = Vector2.Zero; if (vertices.Length > 0) { float dist = (circle.X - vertices[0].X) * (circle.X - vertices[0].X) + (circle.Y - vertices[0].Y) * (circle.Y - vertices[0].Y); for (int i = 1; i < vertices.Length;i++) { if (dist > (circle.X - vertices[i].X) * (circle.X - vertices[i].X) + (circle.Y - vertices[i].Y) * (circle.Y - vertices[i].Y)) { temp = vertices[i]; //memorize the closest vertex dist = (circle.X - vertices[i].X) * (circle.X - vertices[i].X) + (circle.Y - vertices[i].Y) * (circle.Y - vertices[i].Y); } } temp = circle - temp; temp.Normalize(); } return temp; } Thanks in advance for any tips on the 4 issues. EDIT1: Something isn't working properly. The collision axis doesn't come out right and the interpolation also seems to have no effect. I've changed the code a bit: private bool ShapesIntersect(Paddle paddle, Ball ball) { overlap = 1000000f; //large value overlapAxis = Vector2.Zero; MTV = Vector2.Zero; foreach (Vector2 ax in Axes) { float[] pad = paddle.ProjectPaddle(ax); //pad0 = min, pad1 = max float[] circle = ball.ProjectBall(ax); //circle0 = min, circle1 = max if (pad[1] < circle[0] || circle[1] < pad[0]) { return false; } if (Math.Abs(pad[1] - circle[0]) < Math.Abs(circle[1] - pad[0])) { if (Math.Abs(overlap) > Math.Abs(-pad[1] + circle[0])) { overlap = -pad[1] + circle[0]; overlapAxis = ax * (-1); } //to get the proper axis } else { if (Math.Abs(overlap) > Math.Abs(circle[1] - pad[0])) { overlap = circle[1] - pad[0]; overlapAxis = ax; } } } if (overlapAxis != Vector2.Zero) { MTV = overlapAxis * Math.Abs(overlap); } return true; } And part of the Update method: if (ShapesIntersect(paddleRight, ball)) { isColliding = true; if (MTV != Vector2.Zero) { ball.X += MTV.X; ball.Y += MTV.Y; } //test if (overlapAxis.X == 0) //collision with horizontal edge { } else if (overlapAxis.Y == 0) //collision with vertical edge { float factor = Math.Abs(ball.ballCenter.Y - paddleRight.Y) / paddleRight.Height; if (factor > 1) factor = 1f; if (overlapAxis.X < 0) //left edge? ball.Speed = ball.DEFAULTSPEED * Vector2.Normalize(Vector2.Reflect(ball.Speed, (Vector2.Lerp(new Vector2(-1, -3), new Vector2(-1, 3), factor)))); else //right edge? ball.Speed = ball.DEFAULTSPEED * Vector2.Normalize(Vector2.Reflect(ball.Speed, (Vector2.Lerp(new Vector2(1, -3), new Vector2(1, 3), factor)))); } else //vertex collision??? { ball.Speed = -ball.Speed; } } What seems to happen is that "overlapAxis" doesn't always return the right one. So instead of (-1,0) i get the (1,0) (this happened even before i multiplied with -1 there). Sometimes there isn't even a collision registered even though the ball passes through the paddle... The interpolation also seems to have no effect as the angles barely change (or the overlapAxis is almost never (-1,0) or (1,0) but something like (0.9783473, 0.02743843)... ). What am i missing here? :(

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  • How to derive euler angles from matrix or quaternion?

    - by KlashnikovKid
    Currently working on steering behavior for my AI and just hit a little mathematical bump. I'm in the process of writing an align function, which basically tries to match the agent's orientation with a target orientation. I've got a good source material for implementing this behavior but it uses euler angles to calculate the rotational delta, acceleration, and so on. This is nice, however I store orientation as a quaternion and the math library I'm using doesn't provide any functionality for deriving the euler angles. But if it helps I also have rotational matrices at my disposal too. What would be the best way to decompose the quaternion or rotational matrix to get the euler information? I found one source for decomposing the matrix, but I'm not quite getting the correct results. I'm thinking it may be a difference of column/row ordering of my matrices but then again, math isn't my strong point. http://nghiaho.com/?page_id=846

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  • Calculate lookat vector from position and Euler angles

    - by Jaap
    I've implemented an FPS style camera, with the camera consisting of a position vector, and Euler angles pitch and yaw (x and y rotations). After setting up the projection matrix, I then translate to camera coordinates by rotating, then translating to the inverse of the camera position: // Load projection matrix glMatrixMode(GL_PROJECTION); glLoadIdentity(); // Set perspective gluPerspective(m_fFOV, m_fWidth/m_fHeight, m_fNear, m_fFar); // Load modelview matrix glMatrixMode(GL_MODELVIEW); glLoadIdentity(); // Position camera glRotatef(m_fRotateX, 1.0, 0.0, 0.0); glRotatef(m_fRotateY, 0.0, 1.0, 0.0); glTranslatef(-m_vPosition.x, -m_vPosition.y, -m_vPosition.z); Now I've got a few viewports set up, each with its own camera, and from every camera I render the position of the other cameras (as a simple box). I'd like to also draw the view vector for these cameras, except I haven't a clue how to calculate the lookat vector from the position and Euler angles. I've tried to multiply the original camera vector (0, 0, -1) by a matrix representing the camera rotations then adding the camera position to the transformed vector, but that doesn't work at all (most probably because I'm way off base): vector v1(0, 0, -1); matrix m1 = matrix::IDENTITY; m1.rotate(m_fRotateX, 0, 0); m1.rotate(0, m_fRotateY, 0); vector v2 = v1 * m1; v2 = v2 + m_vPosition; // add camera position vector glBegin(GL_LINES); glVertex3fv(m_vPosition); glVertex3fv(v2); glEnd(); What I'd like is to draw a line segment from the camera towards the lookat direction. I've looked all over the place for examples of this, but can't seem to find anything. Thanks a lot!

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  • Calculating angle a segment forms with a ray

    - by kr1zz
    I am given a point C and a ray r starting there. I know the coordinates (xc, yc) of the point C and the angle theta the ray r forms with the horizontal, theta in (-pi, pi]. I am also given another point P of which I know the coordinates (xp, yp): how do I calculate the angle alpha that the segment CP forms with the ray r, alpha in (-pi, pi]? Some examples follow: I can use the the atan2 function.

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

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

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  • Surface normal to screen angle

    - by Tannz0rz
    I've been struggling to get this working. I simply wish to take a surface normal and convert it to a screen angle. As an example, assuming we're working with the highlighted surface on the sphere below, where the arrow is the normal, the 2D angle would obviously be PI/4 radians. Here's one of the many things I've tried to no avail: float4 A = v.vertex; float4 B = v.vertex + float4(v.normal, 0.0); A = mul(VP, A); B = mul(VP, B); A.xy = (0.5 * (A.xy / A.w)) + 0.5; B.xy = (0.5 * (B.xy / B.w)) + 0.5; o.theta = atan2(B.y - A.y, B.x - A.x); I'm finally at my wit's end. Thanks for any and all help.

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  • Bridge made out of blocks at an angle

    - by Pozzuh
    I'm having a bit of trouble with the math behind my project. I want the player to be able to select 2 points (vectors). With these 2 points a floor should be created. When these points are parallel to the x-axis it's easy, just calculate the amount of blocks needed by a simple division, loop through that amount (in x and y) and keep increasing the coordinate by the size of that block. The trouble starts when the 2 vectors aren't parallel to an axis, for example at an angle of 45 degrees. How do I handle the math behind this? If I wasn't completely clear, I made this awesome drawing in paint to demonstrate what I want to achieve. The 2 red dots would be the player selected locations. (The blocks indeed aren't square.) http://i.imgur.com/pzhFMEs.png.

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  • How do you make a bullet ricochet off a vertical wall?

    - by Bagofsheep
    First things first. I am using C# with XNA. My game is top-down and the player can shoot bullets. I've managed to get the bullets to ricochet correctly off horizontal walls. Yet, despite using similar methods (e.g. http://stackoverflow.com/questions/3203952/mirroring-an-angle) and reading other answered questions about this subject I have not been able to get the bullets to ricochet off a vertical wall correctly. Any method I've tried has failed and sometimes made ricocheting off a horizontal wall buggy. Here is the collision code that calls the ricochet method: //Loop through returned tile rectangles from quad tree to test for wall collision. If a collision occurs perform collision logic. for (int r = 0; r < returnObjects.Count; r++) if (Bullets[i].BoundingRectangle.Intersects(returnObjects[r])) Bullets[i].doCollision(returnObjects[r]); Now here is the code for the doCollision method. public void doCollision(Rectangle surface) { if (Ricochet) doRicochet(surface); else Trash = true; } Finally, here is the code for the doRicochet method. public void doRicochet(Rectangle surface) { if (Position.X > surface.Left && Position.X < surface.Right) { //Mirror the bullet's angle. Rotation = -1 * Rotation; //Moves the bullet in the direction of its rotation by given amount. moveFaceDirection(Sprite.Width * BulletScale.X); } else if (Position.Y > surface.Top && Position.Y < surface.Bottom) { } } Since I am only dealing with vertical and horizontal walls at the moment, the if statements simply determine if the object is colliding from the right or left, or from the top or bottom. If the object's X position is within the boundaries of the tile's X boundaries (left and right sides), it must be colliding from the top, and vice verse. As you can see, the else if statement is empty and is where the correct code needs to go.

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  • Calculating the correct particle angle in an outwards explosion

    - by Sun
    I'm creating a simple particle explosion but am stuck in finding the correct angle to rotate my particle. The effect I'm going for is similar to this: Where each particle is going outwards from the point of origin and at the correct angle. This is what I currently have: As you can see, each particle is facing the same angle, but I'm having a little difficulty figuring out the correct angle. I have the vector for the point of emission and the new vector for each particle, how can I use this to calculate the angle? Some code for reference: private Particle CreateParticle() { ... Vector2 velocity = new Vector2(2.0f * (float)(random.NextDouble() * 2 - 1), 2.0f * (float)(random.NextDouble() * 2 - 1)); direction = velocity - ParticleLocation; float angle = (float)Math.Atan2(direction.Y, direction.X); ... return new Particle(texture, position, velocity, angle, angularVelocity, color, size, ttl, EmitterLocation); } I am then using the angle created as so in my particles Draw method: spriteBatch.Draw(Texture, Position, null, Color, Angle, origin, Size, SpriteEffects.None, 0f);

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  • Render angles of a 3D model into 2D images?

    - by Ricket
    Is there a tool out there that you can give a 3D model file, and it will output 2D renders of it from various angles? For example if you were making a 2D RPG but you want to make your character look nice, you might make the character in 3D and then just render the character from 8 or more angles into images which then are used by the 2D engine to give a pseudo-3D look. Does such a tool exist or will it need to be custom-written or done manually?

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  • read angles in radian and convert them in degrees/minutes/seconds

    - by Amadou
    n=0; disp('This program performs an angle conversion'); disp('input data set to a straight line. Enter the name'); disp('of the file containing the input Lambda in radian: '); filename = input(' ','s'); [fid,msg] = fopen(filename,'rt'); if fid < 0 disp(msg); else A=textscan(fid, '%g',1); while ~feof(fid) Lambda = A(1); n = n + 1; A = textscan(fid, '%f',1); end fclose(fid); end Alpha=Lambda*180/pi; fprintf('Angle converted from radian to degree/minutes/seconds:\n'); fprintf('Alpha =%12d\n',Alpha); fprintf('No of angles =%12d\n',n);

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  • JavaScript 3D space ship rotation

    - by user36202
    I am working with a fairly low-level JavaScript 3D API (not Three.js) which uses euler angles for rotation. In most cases, euler angles work quite well for doing things like aligning buildings, operating a hovercraft, or looking around in the first-person. However, in space there is no up or down. I want to control the ship's roll, pitch, and yaw. To do that, some people would use a local coordinate system or a permenant matrix or quaternion or whatever to represent the ship's angle. However, since I am not most people and am using a library that deals exclusively in euler angles, I will be using relative angles to represent how to rotate the ship in space and getting the resulting non-relative euler angles. For you math nerds, that means I need to convert 3 euler angles (with Y being the vertical axis, X representing the pitch, and Z representing a roll which is unaffected by the other angles, left-handed system) into a 3x3 orientation matrix, do something fancy with the matrix, and convert it back into the 3 euler angles. Euler to matrix to euler. Somebody has posted something similar to this on SO (http://stackoverflow.com/questions/1217775/rotating-a-spaceship-model-for-a-space-simulator-game) but he ended up just working with a matrix. This will not do for me. Also, I am using JavaScript, not C++. What I want essentially are the functions do_roll, do_pitch, and do_yaw which only take in and put out euler angles. Many thanks.

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  • Quaternions, Axis Angles and Rotation Matrices. Which of these should I use for FP Camera?

    - by Afonso Lage
    After 2 weeks of reading many math formulas and such I know what is a Quaternion, an Axis Angles and Matrices. I have made my own math libary (Java) to use on my game (LWJGL). But I'm really confused about all this. I want to have a 3D first person camera. The move (translation) is working fine but the rotation isnt working like I need. I need a camera to rotate arround world Axis and not about its own axis. But even using Quaternions, this doesnt work and no matter how much I read about Euler Angles, everybody says to me dont touch on it! This is a little piece of code that i'm using to make the rotation: Quaternion qPitch = Quaternion.createFromAxis(cameraRotate.x, 1.0f, 0.0f, 0.0f); Quaternion qYaw = Quaternion.createFromAxis(cameraRotate.y, 0.0f, 1.0f, 0.0f); this.multiplicate(qPitch.toMatrix4f().toArray()); this.multiplicate(qYaw.toMatrix4f().toArray()); Where this is a Matrix4f view matrix and cameraRotate is a Vector3f that just handle the angles to rotate obtained from mouse move. So I think I'm doing everything right: Translate the view Matrix Rotate the Move Matrix So, after reading all this, I just want to know: To obtain a correct first person camera rotate, I must need to use Quaternios to make the rotations, but how to rotate around world axis? Thanks for reading it. Best regards, Afonso Lage

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  • formula for best approximation for center of 2D rotation with small angles

    - by RocketSurgeon
    This is not a homework. I am asking to see if problem is classical (trivial) or non-trivial. It looks simple on a surface, and I hope it is truly a simple problem. Have N points (N = 2) with coordinates Xn, Yn on a surface of 2D solid body. Solid body has some small rotation (below Pi/180) combined with small shifts (below 1% of distance between any 2 points of N). Possibly some small deformation too (<<0.001%) Same N points have new coordinates named XXn, YYn Calculate with best approximation the location of center of rotation as point C with coordinates XXX, YYY. Thank you

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  • How to rotate 3D axis(XYZ) using Yaw,Pitch,Roll angles in Opengl

    - by user3639338
    I am working Pose estimation with capturing from camera with Opencv. Now I had three angle(Yaw,Pitch,Roll) from each frame(Head) using my code.How to rotate 3D axis(XYZ) those three angle using opengl ? I draw 3D axis using opengl. I have Problem with rotate this axis for returning each frame(Head) using VideoCapture camera input from my code.I cant rotate continuously using returning three angle my code.

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  • Calculating 2D angles for 3D objects in perspective

    - by Will
    Imagine a photo, with the face of a building marked out. Its given that the face of the building is a rectangle, with 90 degree corners. However, because its a photo, perspective will be involved and the parallel edges of the face will converge on the horizon. With such a rectangle, is it possible to calculate the angle in 2D of the edges of a face that is 90 degrees to it? In the image below, the blue is the face marked on the photo, and I'm wondering how to calculate the 2D vector of the red lines of the other face:

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  • Describe relative angles between points (like driving directions)

    - by aan234g
    I have a list of points with x, y coordinates. I know how to get the distance between points with sqrt(pow($x2 - $x1, 2) + pow($y2 - $y1, 2)) and the angle between points with atan2(y1 - y2, x1 - x2). How can I calculate the relative angle between the points (left, right, straight)? So, if I'm at point 1, what is the relative direction to point 2, then 2 to 3, 3 to 4, etc... Thanks for any help!

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