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  • How to rotate a set of points on z = 0 plane in 3-D, preserving pairwise distances?

    - by cagirici
    I have a set of points double n[] on the plane z = 0. And I have another set of points double[] m on the plane ax + by + cz + d = 0. Length of n is equal to length of m. Also, euclidean distance between n[i] and n[j] is equal to euclidean distance between m[i] and m[j]. I want to rotate n[] in 3-D, such that for all i, n[i] = m[i] would be true. In other words, I want to turn a plane into another plane, preserving the pairwise distances. Here's my code in java. But it does not help so much: double[] rotate(double[] point, double[] currentEquation, double[] targetEquation) { double[] currentNormal = new double[]{currentEquation[0], currentEquation[1], currentEquation[2]}; double[] targetNormal = new double[]{targetEquation[0], targetEquation[1], targetEquation[2]}; targetNormal = normalize(targetNormal); double angle = angleBetween(currentNormal, targetNormal); double[] axis = cross(targetNormal, currentNormal); double[][] R = getRotationMatrix(axis, angle); return rotated; } double[][] getRotationMatrix(double[] axis, double angle) { axis = normalize(axis); double cA = (float)Math.cos(angle); double sA = (float)Math.sin(angle); Matrix I = Matrix.identity(3, 3); Matrix a = new Matrix(axis, 3); Matrix aT = a.transpose(); Matrix a2 = a.times(aT); double[][] B = { {0, axis[2], -1*axis[1]}, {-1*axis[2], 0, axis[0]}, {axis[1], -1*axis[0], 0} }; Matrix A = new Matrix(B); Matrix R = I.minus(a2); R = R.times(cA); R = R.plus(a2); R = R.plus(A.times(sA)); return R.getArray(); } This is what I get. The point set on the right side is actually part of a point set on the left side. But they are on another plane. Here's a 2-D representation of what I try to do: There are two lines. The line on the bottom is the line I have. The line on the top is the target line. The distances are preserved (a, b and c). Edit: I have tried both methods written in answers. They both fail (I guess). Method of Martijn Courteaux public static double[][] getRotationMatrix(double[] v0, double[] v1, double[] v2, double[] u0, double[] u1, double[] u2) { RealMatrix M1 = new Array2DRowRealMatrix(new double[][]{ {1,0,0,-1*v0[0]}, {0,1,0,-1*v0[1]}, {0,0,1,0}, {0,0,0,1} }); RealMatrix M2 = new Array2DRowRealMatrix(new double[][]{ {1,0,0,-1*u0[0]}, {0,1,0,-1*u0[1]}, {0,0,1,-1*u0[2]}, {0,0,0,1} }); Vector3D imX = new Vector3D((v0[1] - v1[1])*(u2[0] - u0[0]) - (v0[1] - v2[1])*(u1[0] - u0[0]), (v0[1] - v1[1])*(u2[1] - u0[1]) - (v0[1] - v2[1])*(u1[1] - u0[1]), (v0[1] - v1[1])*(u2[2] - u0[2]) - (v0[1] - v2[1])*(u1[2] - u0[2]) ).scalarMultiply(1/((v0[0]*v1[1])-(v0[0]*v2[1])-(v1[0]*v0[1])+(v1[0]*v2[1])+(v2[0]*v0[1])-(v2[0]*v1[1]))); Vector3D imZ = new Vector3D(findEquation(u0, u1, u2)); Vector3D imY = Vector3D.crossProduct(imZ, imX); double[] imXn = imX.normalize().toArray(); double[] imYn = imY.normalize().toArray(); double[] imZn = imZ.normalize().toArray(); RealMatrix M = new Array2DRowRealMatrix(new double[][]{ {imXn[0], imXn[1], imXn[2], 0}, {imYn[0], imYn[1], imYn[2], 0}, {imZn[0], imZn[1], imZn[2], 0}, {0, 0, 0, 1} }); RealMatrix rotationMatrix = MatrixUtils.inverse(M2).multiply(M).multiply(M1); return rotationMatrix.getData(); } Method of Sam Hocevar static double[][] makeMatrix(double[] p1, double[] p2, double[] p3) { double[] v1 = normalize(difference(p2,p1)); double[] v2 = normalize(cross(difference(p3,p1), difference(p2,p1))); double[] v3 = cross(v1, v2); double[][] M = { { v1[0], v2[0], v3[0], p1[0] }, { v1[1], v2[1], v3[1], p1[1] }, { v1[2], v2[2], v3[2], p1[2] }, { 0.0, 0.0, 0.0, 1.0 } }; return M; } static double[][] createTransform(double[] A, double[] B, double[] C, double[] P, double[] Q, double[] R) { RealMatrix c = new Array2DRowRealMatrix(makeMatrix(A,B,C)); RealMatrix t = new Array2DRowRealMatrix(makeMatrix(P,Q,R)); return MatrixUtils.inverse(c).multiply(t).getData(); } The blue points are the calculated points. The black lines indicate the offset from the real position.

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  • genetic algorithm for leveling/build test

    - by Renan Malke Stigliani
    I'm starting o build a online PVP (duel like, one-to-one) game, where there is leveling, skill points, special attacks and all the common stuff. Since I never did anything like that, I'm still thinking about the maths behind the level/skill/special balances. So I thought good way of testing the best/combo builds would implement a Genetic Algorith. It'd be like that: Generate a big portion of random characters Make them fight, level them up accordingly to the victories(more XP)/losses(less XP) Mate the winners, crossing their builds, to try to make even best characters Add some more random chars, emulating new players Repeat the process for some time, or util find some chars who can beat everyone butts So I could play with the math and try to find the balance where the top x% chars would be a mix of various build types. So, is it a good idea, or there are some other easier method to do the balance? PS: I like this also, because it sounds funny

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  • What is wrong with my Dot Product? [Javascript]

    - by Clay Ellis Murray
    I am trying to make a pong game but I wanted to use dot products to do the collisions with the paddles, however whenever I make a dot product objects it never changes much from .9 this is my code to make vectors vector = { make:function(object){ return [object.x + object.width/2,object.y + object.height/2] }, normalize:function(v){ var length = Math.sqrt(v[0] * v[0] + v[1] * v[1]) v[0] = v[0]/length v[1] = v[1]/length return v }, dot:function(v1,v2){ return v1[0] * v2[0] + v1[1] * v2[1] } } and this is where I am calculating the dot in my code vector1 = vector.normalize(vector.make(ball)) vector2 = vector.normalize(vector.make(object)) dot = vector.dot(vector1,vector2) Here is a JsFiddle of my code currently the paddles don't move. Any help would be greatly appreciated

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  • My integer overfloweth

    - by darcy
    While certain classes like java.lang.Integer and java.lang.Math have been in the platform since the beginning, that doesn't mean there aren't more enhancements to be made in such places! For example, earlier in JDK 8, library support was added for unsigned integer arithmetic. More recently, my colleague Roger Riggs pushed a changeset to support integer overflow, that is, to provide methods which throw an ArithmeticException on overflow instead of returning a wrapped result. Besides being helpful for various programming tasks in Java, methods like the those for integer overflow can be used to implement runtimes supporting other languages, as has been requested at a past JVM language summit. This year's language summit is coming up in July and I hope to get some additional suggestions there for helpful library additions as part of the general discussions of the JVM and Java libraries as a platform.

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  • Matrix rotation of a rectangle to "face" a given point in 2d

    - by justin.m.chase
    Suppose you have a rectangle centered at point (0, 0) and now I want to rotate it such that it is facing the point (100, 100), how would I do this purely with matrix math? To give some more specifics I am using javascript and canvas and I may have something like this: var position = {x : 0, y: 0 }; var destination = { x : 100, y: 100 }; var transform = Matrix.identity(); this.update = function(state) { // update transform to rotate to face destination }; this.draw = function(ctx) { ctx.save(); ctx.transform(transform); // a helper that just calls setTransform() ctx.beginPath(); ctx.rect(-5, -5, 10, 10); ctx.fillStyle = 'Blue'; ctx.fill(); ctx.lineWidth = 2; ctx.stroke(); ctx.restore(); } Feel free to assume any matrix function you need is available.

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  • Why and when should I make a class 'static'? What is the purpose of 'static' keyword on classes?

    - by Saeed Neamati
    The static keyword on a member in many languages mean that you shouldn't create an instance of that class to be able to have access to that member. However, I don't see any justification to make an entire class static. Why and when should I make a class static? What benefits do I get from making a class static? I mean, after declaring a static class, one should still declare all members which he/she wants to have access to without instantiation, as static too. This means that for example, Math class could be declared normal (not static), without affecting how developers code. In other words, making a class static or normal is kind of transparent to developers.

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  • Multi database link and mix and match email alert

    - by menardmam
    I have a site which is a large database of people that have different knowledge in different domains, such as teaching (maths, french, science etc...) On the site there is a page where you can search people base on different request, such as distance from home, grade, sex. Now, I would like to add a page where people that are looking for mentor will fill a request, and when a tutor in his area of search will match request, a email will be send to this researcher. Because I know for sure, that when in January you look for a math teacher for your 10 year old son, and you find none, you won't go again in February, March... and on and on just to see. Maybe there is one now, you want to be informed when the tutor will get into database automatically (more or less like www.jobboom.com) So the question is, what CMS do I need to be able to do that ? Wordpress, drupal or something custom made?

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  • C#/.NET Little Wonders: The Generic Func Delegates

    - by James Michael Hare
    Once again, in this series of posts I look at the parts of the .NET Framework that may seem trivial, but can help improve your code by making it easier to write and maintain. The index of all my past little wonders posts can be found here. Back in one of my three original “Little Wonders” Trilogy of posts, I had listed generic delegates as one of the Little Wonders of .NET.  Later, someone posted a comment saying said that they would love more detail on the generic delegates and their uses, since my original entry just scratched the surface of them. Last week, I began our look at some of the handy generic delegates built into .NET with a description of delegates in general, and the Action family of delegates.  For this week, I’ll launch into a look at the Func family of generic delegates and how they can be used to support generic, reusable algorithms and classes. Quick Delegate Recap Delegates are similar to function pointers in C++ in that they allow you to store a reference to a method.  They can store references to either static or instance methods, and can actually be used to chain several methods together in one delegate. Delegates are very type-safe and can be satisfied with any standard method, anonymous method, or a lambda expression.  They can also be null as well (refers to no method), so care should be taken to make sure that the delegate is not null before you invoke it. Delegates are defined using the keyword delegate, where the delegate’s type name is placed where you would typically place the method name: 1: // This delegate matches any method that takes string, returns nothing 2: public delegate void Log(string message); This delegate defines a delegate type named Log that can be used to store references to any method(s) that satisfies its signature (whether instance, static, lambda expression, etc.). Delegate instances then can be assigned zero (null) or more methods using the operator = which replaces the existing delegate chain, or by using the operator += which adds a method to the end of a delegate chain: 1: // creates a delegate instance named currentLogger defaulted to Console.WriteLine (static method) 2: Log currentLogger = Console.Out.WriteLine; 3:  4: // invokes the delegate, which writes to the console out 5: currentLogger("Hi Standard Out!"); 6:  7: // append a delegate to Console.Error.WriteLine to go to std error 8: currentLogger += Console.Error.WriteLine; 9:  10: // invokes the delegate chain and writes message to std out and std err 11: currentLogger("Hi Standard Out and Error!"); While delegates give us a lot of power, it can be cumbersome to re-create fairly standard delegate definitions repeatedly, for this purpose the generic delegates were introduced in various stages in .NET.  These support various method types with particular signatures. Note: a caveat with generic delegates is that while they can support multiple parameters, they do not match methods that contains ref or out parameters. If you want to a delegate to represent methods that takes ref or out parameters, you will need to create a custom delegate. We’ve got the Func… delegates Just like it’s cousin, the Action delegate family, the Func delegate family gives us a lot of power to use generic delegates to make classes and algorithms more generic.  Using them keeps us from having to define a new delegate type when need to make a class or algorithm generic. Remember that the point of the Action delegate family was to be able to perform an “action” on an item, with no return results.  Thus Action delegates can be used to represent most methods that take 0 to 16 arguments but return void.  You can assign a method The Func delegate family was introduced in .NET 3.5 with the advent of LINQ, and gives us the power to define a function that can be called on 0 to 16 arguments and returns a result.  Thus, the main difference between Action and Func, from a delegate perspective, is that Actions return nothing, but Funcs return a result. The Func family of delegates have signatures as follows: Func<TResult> – matches a method that takes no arguments, and returns value of type TResult. Func<T, TResult> – matches a method that takes an argument of type T, and returns value of type TResult. Func<T1, T2, TResult> – matches a method that takes arguments of type T1 and T2, and returns value of type TResult. Func<T1, T2, …, TResult> – and so on up to 16 arguments, and returns value of type TResult. These are handy because they quickly allow you to be able to specify that a method or class you design will perform a function to produce a result as long as the method you specify meets the signature. For example, let’s say you were designing a generic aggregator, and you wanted to allow the user to define how the values will be aggregated into the result (i.e. Sum, Min, Max, etc…).  To do this, we would ask the user of our class to pass in a method that would take the current total, the next value, and produce a new total.  A class like this could look like: 1: public sealed class Aggregator<TValue, TResult> 2: { 3: // holds method that takes previous result, combines with next value, creates new result 4: private Func<TResult, TValue, TResult> _aggregationMethod; 5:  6: // gets or sets the current result of aggregation 7: public TResult Result { get; private set; } 8:  9: // construct the aggregator given the method to use to aggregate values 10: public Aggregator(Func<TResult, TValue, TResult> aggregationMethod = null) 11: { 12: if (aggregationMethod == null) throw new ArgumentNullException("aggregationMethod"); 13:  14: _aggregationMethod = aggregationMethod; 15: } 16:  17: // method to add next value 18: public void Aggregate(TValue nextValue) 19: { 20: // performs the aggregation method function on the current result and next and sets to current result 21: Result = _aggregationMethod(Result, nextValue); 22: } 23: } Of course, LINQ already has an Aggregate extension method, but that works on a sequence of IEnumerable<T>, whereas this is designed to work more with aggregating single results over time (such as keeping track of a max response time for a service). We could then use this generic aggregator to find the sum of a series of values over time, or the max of a series of values over time (among other things): 1: // creates an aggregator that adds the next to the total to sum the values 2: var sumAggregator = new Aggregator<int, int>((total, next) => total + next); 3:  4: // creates an aggregator (using static method) that returns the max of previous result and next 5: var maxAggregator = new Aggregator<int, int>(Math.Max); So, if we were timing the response time of a web method every time it was called, we could pass that response time to both of these aggregators to get an idea of the total time spent in that web method, and the max time spent in any one call to the web method: 1: // total will be 13 and max 13 2: int responseTime = 13; 3: sumAggregator.Aggregate(responseTime); 4: maxAggregator.Aggregate(responseTime); 5:  6: // total will be 20 and max still 13 7: responseTime = 7; 8: sumAggregator.Aggregate(responseTime); 9: maxAggregator.Aggregate(responseTime); 10:  11: // total will be 40 and max now 20 12: responseTime = 20; 13: sumAggregator.Aggregate(responseTime); 14: maxAggregator.Aggregate(responseTime); The Func delegate family is useful for making generic algorithms and classes, and in particular allows the caller of the method or user of the class to specify a function to be performed in order to generate a result. What is the result of a Func delegate chain? If you remember, we said earlier that you can assign multiple methods to a delegate by using the += operator to chain them.  So how does this affect delegates such as Func that return a value, when applied to something like the code below? 1: Func<int, int, int> combo = null; 2:  3: // What if we wanted to aggregate the sum and max together? 4: combo += (total, next) => total + next; 5: combo += Math.Max; 6:  7: // what is the result? 8: var comboAggregator = new Aggregator<int, int>(combo); Well, in .NET if you chain multiple methods in a delegate, they will all get invoked, but the result of the delegate is the result of the last method invoked in the chain.  Thus, this aggregator would always result in the Math.Max() result.  The other chained method (the sum) gets executed first, but it’s result is thrown away: 1: // result is 13 2: int responseTime = 13; 3: comboAggregator.Aggregate(responseTime); 4:  5: // result is still 13 6: responseTime = 7; 7: comboAggregator.Aggregate(responseTime); 8:  9: // result is now 20 10: responseTime = 20; 11: comboAggregator.Aggregate(responseTime); So remember, you can chain multiple Func (or other delegates that return values) together, but if you do so you will only get the last executed result. Func delegates and co-variance/contra-variance in .NET 4.0 Just like the Action delegate, as of .NET 4.0, the Func delegate family is contra-variant on its arguments.  In addition, it is co-variant on its return type.  To support this, in .NET 4.0 the signatures of the Func delegates changed to: Func<out TResult> – matches a method that takes no arguments, and returns value of type TResult (or a more derived type). Func<in T, out TResult> – matches a method that takes an argument of type T (or a less derived type), and returns value of type TResult(or a more derived type). Func<in T1, in T2, out TResult> – matches a method that takes arguments of type T1 and T2 (or less derived types), and returns value of type TResult (or a more derived type). Func<in T1, in T2, …, out TResult> – and so on up to 16 arguments, and returns value of type TResult (or a more derived type). Notice the addition of the in and out keywords before each of the generic type placeholders.  As we saw last week, the in keyword is used to specify that a generic type can be contra-variant -- it can match the given type or a type that is less derived.  However, the out keyword, is used to specify that a generic type can be co-variant -- it can match the given type or a type that is more derived. On contra-variance, if you are saying you need an function that will accept a string, you can just as easily give it an function that accepts an object.  In other words, if you say “give me an function that will process dogs”, I could pass you a method that will process any animal, because all dogs are animals.  On the co-variance side, if you are saying you need a function that returns an object, you can just as easily pass it a function that returns a string because any string returned from the given method can be accepted by a delegate expecting an object result, since string is more derived.  Once again, in other words, if you say “give me a method that creates an animal”, I can pass you a method that will create a dog, because all dogs are animals. It really all makes sense, you can pass a more specific thing to a less specific parameter, and you can return a more specific thing as a less specific result.  In other words, pay attention to the direction the item travels (parameters go in, results come out).  Keeping that in mind, you can always pass more specific things in and return more specific things out. For example, in the code below, we have a method that takes a Func<object> to generate an object, but we can pass it a Func<string> because the return type of object can obviously accept a return value of string as well: 1: // since Func<object> is co-variant, this will access Func<string>, etc... 2: public static string Sequence(int count, Func<object> generator) 3: { 4: var builder = new StringBuilder(); 5:  6: for (int i=0; i<count; i++) 7: { 8: object value = generator(); 9: builder.Append(value); 10: } 11:  12: return builder.ToString(); 13: } Even though the method above takes a Func<object>, we can pass a Func<string> because the TResult type placeholder is co-variant and accepts types that are more derived as well: 1: // delegate that's typed to return string. 2: Func<string> stringGenerator = () => DateTime.Now.ToString(); 3:  4: // This will work in .NET 4.0, but not in previous versions 5: Sequence(100, stringGenerator); Previous versions of .NET implemented some forms of co-variance and contra-variance before, but .NET 4.0 goes one step further and allows you to pass or assign an Func<A, BResult> to a Func<Y, ZResult> as long as A is less derived (or same) as Y, and BResult is more derived (or same) as ZResult. Sidebar: The Func and the Predicate A method that takes one argument and returns a bool is generally thought of as a predicate.  Predicates are used to examine an item and determine whether that item satisfies a particular condition.  Predicates are typically unary, but you may also have binary and other predicates as well. Predicates are often used to filter results, such as in the LINQ Where() extension method: 1: var numbers = new[] { 1, 2, 4, 13, 8, 10, 27 }; 2:  3: // call Where() using a predicate which determines if the number is even 4: var evens = numbers.Where(num => num % 2 == 0); As of .NET 3.5, predicates are typically represented as Func<T, bool> where T is the type of the item to examine.  Previous to .NET 3.5, there was a Predicate<T> type that tended to be used (which we’ll discuss next week) and is still supported, but most developers recommend using Func<T, bool> now, as it prevents confusion with overloads that accept unary predicates and binary predicates, etc.: 1: // this seems more confusing as an overload set, because of Predicate vs Func 2: public static SomeMethod(Predicate<int> unaryPredicate) { } 3: public static SomeMethod(Func<int, int, bool> binaryPredicate) { } 4:  5: // this seems more consistent as an overload set, since just uses Func 6: public static SomeMethod(Func<int, bool> unaryPredicate) { } 7: public static SomeMethod(Func<int, int, bool> binaryPredicate) { } Also, even though Predicate<T> and Func<T, bool> match the same signatures, they are separate types!  Thus you cannot assign a Predicate<T> instance to a Func<T, bool> instance and vice versa: 1: // the same method, lambda expression, etc can be assigned to both 2: Predicate<int> isEven = i => (i % 2) == 0; 3: Func<int, bool> alsoIsEven = i => (i % 2) == 0; 4:  5: // but the delegate instances cannot be directly assigned, strongly typed! 6: // ERROR: cannot convert type... 7: isEven = alsoIsEven; 8:  9: // however, you can assign by wrapping in a new instance: 10: isEven = new Predicate<int>(alsoIsEven); 11: alsoIsEven = new Func<int, bool>(isEven); So, the general advice that seems to come from most developers is that Predicate<T> is still supported, but we should use Func<T, bool> for consistency in .NET 3.5 and above. Sidebar: Func as a Generator for Unit Testing One area of difficulty in unit testing can be unit testing code that is based on time of day.  We’d still want to unit test our code to make sure the logic is accurate, but we don’t want the results of our unit tests to be dependent on the time they are run. One way (of many) around this is to create an internal generator that will produce the “current” time of day.  This would default to returning result from DateTime.Now (or some other method), but we could inject specific times for our unit testing.  Generators are typically methods that return (generate) a value for use in a class/method. For example, say we are creating a CacheItem<T> class that represents an item in the cache, and we want to make sure the item shows as expired if the age is more than 30 seconds.  Such a class could look like: 1: // responsible for maintaining an item of type T in the cache 2: public sealed class CacheItem<T> 3: { 4: // helper method that returns the current time 5: private static Func<DateTime> _timeGenerator = () => DateTime.Now; 6:  7: // allows internal access to the time generator 8: internal static Func<DateTime> TimeGenerator 9: { 10: get { return _timeGenerator; } 11: set { _timeGenerator = value; } 12: } 13:  14: // time the item was cached 15: public DateTime CachedTime { get; private set; } 16:  17: // the item cached 18: public T Value { get; private set; } 19:  20: // item is expired if older than 30 seconds 21: public bool IsExpired 22: { 23: get { return _timeGenerator() - CachedTime > TimeSpan.FromSeconds(30.0); } 24: } 25:  26: // creates the new cached item, setting cached time to "current" time 27: public CacheItem(T value) 28: { 29: Value = value; 30: CachedTime = _timeGenerator(); 31: } 32: } Then, we can use this construct to unit test our CacheItem<T> without any time dependencies: 1: var baseTime = DateTime.Now; 2:  3: // start with current time stored above (so doesn't drift) 4: CacheItem<int>.TimeGenerator = () => baseTime; 5:  6: var target = new CacheItem<int>(13); 7:  8: // now add 15 seconds, should still be non-expired 9: CacheItem<int>.TimeGenerator = () => baseTime.AddSeconds(15); 10:  11: Assert.IsFalse(target.IsExpired); 12:  13: // now add 31 seconds, should now be expired 14: CacheItem<int>.TimeGenerator = () => baseTime.AddSeconds(31); 15:  16: Assert.IsTrue(target.IsExpired); Now we can unit test for 1 second before, 1 second after, 1 millisecond before, 1 day after, etc.  Func delegates can be a handy tool for this type of value generation to support more testable code.  Summary Generic delegates give us a lot of power to make truly generic algorithms and classes.  The Func family of delegates is a great way to be able to specify functions to calculate a result based on 0-16 arguments.  Stay tuned in the weeks that follow for other generic delegates in the .NET Framework!   Tweet Technorati Tags: .NET, C#, CSharp, Little Wonders, Generics, Func, Delegates

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  • 2D tower defense - A bullet to an enemy

    - by Tashu
    I'm trying to find a good solution for a bullet to hit the enemy. The game is 2D tower defense, the tower is supposed to shoot a bullet and hit the enemy guaranteed. I tried this solution - http://blog.wolfire.com/2009/07/linear-algebra-for-game-developers-part-1/ The link mentioned to subtract the bullet's origin and the enemy as well (vector subtraction). I tried that but a bullet just follows around the enemy. float diffX = enemy.position.x - position.x; float diffY = enemy.position.y - position.y; velocity.x = diffX; velocity.y = diffY; position.add(velocity.x * deltaTime, velocity.y * deltaTime); I'm familiar with vectors but not sure what steps (vector math operations) to be done to get this solution working.

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  • libgdx rotation (animation, arrays) issues and help needed

    - by johnny-b
    well i am a noob at java and libgdx. i got the homing bullet working with the help of someone. now i am smashing my head as to how i can make it rotate so it faces the ball (which is the main character) when it goes around it or when it is coming towards it. the bullet is facing <--- and the code below is what i have done so far. also i used sprites for the bullet and also animation method. Also how do i make it an array/arraylist which is best so i can have multiple bullets at random or placed places. i tried many things nothing workd :( thank you for the help. // below is the bullet or enemy if you want to call it. public class Bullet extends Sprite { public static final float BULLET_HOMING = 6000; public static final float BULLET_SPEED = 300; private Vector2 velocity; private float lifetime; public Bullet(float x, float y) { velocity = new Vector2(0, 0); setPosition(x, y); } public void update(float delta) { float targetX = GameWorld.getBall().getX(); float targetY = GameWorld.getBall().getY(); float dx = targetX - getX(); float dy = targetY - getY(); float distToTarget = (float) Math.sqrt(dx * dx + dy * dy); dx /= distToTarget; dy /= distToTarget; dx *= BULLET_HOMING; dy *= BULLET_HOMING; velocity.x += dx * delta; velocity.y += dy * delta; float vMag = (float) Math.sqrt(velocity.x * velocity.x + velocity.y * velocity.y); velocity.x /= vMag; velocity.y /= vMag; velocity.x *= BULLET_SPEED; velocity.y *= BULLET_SPEED; Vector2 v = velocity.cpy().scl(delta); setPosition(getX() + v.x, getY() + v.y); setOriginCenter(); setRotation(velocity.angle()); lifetime += delta; setRegion(AssetLoader.bulletAnimation.getKeyFrame(lifetime)); } } // this is where i load the images. public class AssetLoader { public static Animation bulletAnimation; public static Sprite bullet1, bullet2; public static void load() { texture = new Texture(Gdx.files.internal("SpriteN1.png")); texture.setFilter(TextureFilter.Nearest, TextureFilter.Nearest); bullet1 = new Sprite(texture, 380, 350, 45, 20); bullet1.flip(false, true); bullet2 = new Sprite(texture, 425, 350, 45, 20); bullet2.flip(false, true); Sprite[] bullets = { bullet1, bullet2 }; bulletAnimation = new Animation(0.06f, aims); bulletAnimation.setPlayMode(Animation.PlayMode.LOOP); } public static void dispose() { // We must dispose of the texture when we are finished. texture.dispose(); } // this is for the rendering of the images etc public class GameRenderer { private Bullet bullet; private Ball ball; public GameRenderer(GameWorld world) { myWorld = world; cam = new OrthographicCamera(); cam.setToOrtho(true, 480, 320); batcher = new SpriteBatch(); // Attach batcher to camera batcher.setProjectionMatrix(cam.combined); shapeRenderer = new ShapeRenderer(); shapeRenderer.setProjectionMatrix(cam.combined); // Call helper methods to initialize instance variables initGameObjects(); initAssets(); } private void initGameObjects() { ball = GameWorld.getBall(); bullet = myWorld.getBullet(); scroller = myWorld.getScroller(); } private void initAssets() { ballAnimation = AssetLoader.ballAnimation; bulletAnimation = AssetLoader.bulletAnimation; } public void render(float runTime) { Gdx.gl.glClearColor(0, 0, 0, 1); Gdx.gl.glClear(GL30.GL_COLOR_BUFFER_BIT); batcher.begin(); // Disable transparency // This is good for performance when drawing images that do not require // transparency. batcher.disableBlending(); // The ball needs transparency, so we enable that again. batcher.enableBlending(); batcher.draw(AssetLoader.ballAnimation.getKeyFrame(runTime), ball.getX(), ball.getY(), ball.getWidth(), ball.getHeight()); batcher.draw(AssetLoader.bulletAnimation.getKeyFrame(runTime), bullet.getX(), bullet.getY()); // End SpriteBatch batcher.end(); } } // this is to load the image etc on the screen i guess public class GameWorld { public static Ball ball; private Bullet bullet; private ScrollHandler scroller; public GameWorld() { ball = new Ball(480, 273, 32, 32); bullet = new Bullet(10, 10); scroller = new ScrollHandler(0); } public void update(float delta) { ball.update(delta); bullet.update(delta); scroller.update(delta); } public static Ball getBall() { return ball; } public ScrollHandler getScroller() { return scroller; } public Bullet getBullet() { return bullet; } } so there is the whole thing. the images are loaded via the AssetLoader then to the GameRenderer and GameWorld via the Bullet class. i am guessing that is how it is. sorry newbie so still learning. thank you in advace for the help or any advice.

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  • Which programming language should I learn? [on hold]

    - by Ashkan
    I'm Ashkan and I'm from Iran, I started programming when I was 13 and I learned a lot of stuff since then, But now I'm totally lost. Since I live in Iran there are no counselor or any professionals out there to help me, so I decided to ask here. I started with Visual Basic and after 1 year I started to learn HTML , CSS , Javascript and JQuery. And for the past 6 months I've been learning PHP,and I have a basic understanding of OOP. I want to move to America to continue my studies and I was wondering which programming language helps me the most to get there? Should I learn C++ or JAVA or should I study Computer Science and Math? also since We are not in a good place financially, I want a programming language that helps me in college and lets me make some money? Thanks in advance and sorry for my poor English skills.

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  • How to change the sprite colors

    - by Mr_Qqn
    In my rhythm game, I have a note object which can be of different colors depending on the note chart. I could use a sprite sheet with all the different color variations I use, but I would prefer to parametrize this. (For information, a note sprite is compound with one main color, for example a red note has only red, light red and dark red.) So, how to change the colors of a sprite basing on a new color ? I'm working with opengl, but any algorithm or math explanation will do. :) Thanks

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  • Number crunching algo for learning multithreading?

    - by Austin Henley
    I have never really implemented anything dealing with threads; my only experience with them is reading about them in my undergrad. So I want to change that by writing a program that does some number crunching, but splits it up into several threads. My first ideas for this hopefully simple multithreaded program were: Beal's Conjecture brute force based on my SO question. Bailey-Borwein-Plouffe formula for calculating Pi. Prime number brute force search As you can see I have an interest in math and thought it would be fun to incorporate it into this, rather than coding something such as a server which wouldn't be nearly as fun! But the 3 ideas don't seem very appealing and I have already done some work on them in the past so I was curious if anyone had any ideas in the same spirit as these 3 that I could implement?

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  • Markdown, LaTeX combined in WYSIWYG editor. Is there any?

    - by om-nom-nom
    I really like the way markdown is implemented in SE bunch of sites, where I can easily write code blocks, performing formatting or even use latex on some of sites like writing $\pi$. I also like how this online editor looks and feels. But it's all online. Is there any offline WYSIWYG analogs of notepag or WMD in Ubuntu that optionally supports pdf as an output format? Both markdown and latex desired. I desire to simultaneously use Markdown and LaTeX. I'm planing to use an editor for writing some technical stuff with math, but it's annoying to be constantly in "LaTeX-mode". So it would be awesome to immerse in LaTeX when I need formulas and use markdown when I need to speak on natural language. UPD. Almost all answers was quite useful, but none of them answers directly on my question. I'll accept @N.N. answer as a most complete.

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  • AI control for a ship with physics model

    - by Petteri Hietavirta
    I am looking for ideas how to implement following in 2D space. Unfortunately I don't know much about AI/path finding/autonomous control yet. Let's say this ship can move freely but it has mass and momentum. Also, external forces might affect it (explosions etc). The player can set a target for the ship at any time and it should reach that spot and stop. Without physics this would be simple, just point to the direction and go. But how to deal with existing momentum and then stopping on the spot? I don't want to modify ship's placement directly. edit: Just to make clear, the physics related math of the ship itself is not the problem.

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  • Issues with ILMerge, Lambda Expressions and VS2010 merging?

    - by John Blumenauer
    A little Background For quite some time now, it’s been possible to merge multiple .NET assemblies into a single assembly using ILMerge in Visual Studio 2008.  This is especially helpful when writing wrapper assemblies for 3rd-party libraries where it’s desirable to minimize the number of assemblies for distribution.  During the merge process, ILMerge will take a set of assemblies and merge them into a single assembly.  The resulting assembly can be either an executable or a DLL and is identified as the primary assembly. Issue During a recent project, I discovered using ILMerge to merge assemblies containing lambda expressions in Visual Studio 2010 is resulting in invalid primary assemblies.  The code below is not where the initial issue was identified, I will merely use it to illustrate the problem at hand. In order to describe the issue, I created a console application and a class library for calculating a few math functions utilizing lambda expressions.  The code is available for download at the bottom of this blog entry. MathLib.cs using System; namespace MathLib { public static class MathHelpers { public static Func<double, double, double> Hypotenuse = (x, y) => Math.Sqrt(x * x + y * y); static readonly Func<int, int, bool> divisibleBy = (int a, int b) => a % b == 0; public static bool IsPrimeNumber(int x) { { for (int i = 2; i <= x / 2; i++) if (divisibleBy(x, i)) return false; return true; }; } } } Program.cs using System; using MathLib; namespace ILMergeLambdasConsole { class Program { static void Main(string[] args) { int n = 19; if (MathHelpers.IsPrimeNumber(n)) { Console.WriteLine(n + " is prime"); } else { Console.WriteLine(n + " is not prime"); } Console.ReadLine(); } } } Not surprisingly, the preceding code compiles, builds and executes without error prior to running the ILMerge tool.   ILMerge Setup In order to utilize ILMerge, the following changes were made to the project. The MathLib.dll assembly was built in release configuration and copied to the MathLib folder.  The following folder hierarchy was used for this example:   The project file for ILMergeLambdasConsole project file was edited to add the ILMerge post-build configuration.  The following lines were added near the bottom of the project file:  <Target Name="AfterBuild" Condition="'$(Configuration)' == 'Release'"> <Exec Command="&quot;..\..\lib\ILMerge\Ilmerge.exe&quot; /ndebug /out:@(MainAssembly) &quot;@(IntermediateAssembly)&quot; @(ReferenceCopyLocalPaths->'&quot;%(FullPath)&quot;', ' ')" /> <Delete Files="@(ReferenceCopyLocalPaths->'$(OutDir)%(DestinationSubDirectory)%(Filename)%(Extension)')" /> </Target> The ILMergeLambdasConsole project was modified to reference the MathLib.dll located in the MathLib folder above. ILMerge and ILMerge.exe.config was copied into the ILMerge folder shown above.  The contents of ILMerge.exe.config are: <?xml version="1.0" encoding="utf-8" ?> <configuration> <startup useLegacyV2RuntimeActivationPolicy="true"> <requiredRuntime safemode="true" imageVersion="v4.0.30319" version="v4.0.30319"/> </startup> </configuration> Post-ILMerge After compiling and building, the MathLib.dll assembly will be merged into the ILMergeLambdasConsole executable.  Unfortunately, executing ILMergeLambdasConsole.exe now results in a crash.  The ILMerge documentation recommends using PEVerify.exe to validate assemblies after merging.  Executing PEVerify.exe against the ILMergeLambdasConsole.exe assembly results in the following error:    Further investigation by using Reflector reveals the divisibleBy method in the MathHelpers class looks a bit questionable after the merge.     Prior to using ILMerge, the same divisibleBy method appeared as the following in Reflector: It’s pretty obvious something has gone awry during the merge process.  However, this is only occurring when building within the Visual Studio 2010 environment.  The same code and configuration built within Visual Studio 2008 executes fine.  I’m still investigating the issue.  If anyone has already experienced this situation and solved it, I would love to hear from you.  However, as of right now, it looks like something has gone terribly wrong when executing ILMerge against assemblies containing Lambdas in Visual Studio 2010. Solution Files ILMergeLambdaExpression

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  • Can SpriteBatch be used to fill a polygon with a texture?

    - by can poyrazoglu
    I basically need to fill a texture into a polygon using the SpriteBatch. I've done some research but couldn't find anything useful except polygon triangulation method, which works well only with convex polygons (without diving into super math which is definitely not something I'm pretty good at). Are there any solutions for filling in a polygon in a basic way? I of course need something dynamic (I'll have a map editor that you can define polygons, and the game will render them (and collision detection will also use them but that's off topic), basically I can't accept solutions like "pre-calculated" bitmaps or anything like that. I need to draw a polygon with the segments provided, to the screen, using the SpriteBatch.

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  • How important is Discrete Mathematics for a Computer Scientist?

    - by mort
    As the title says, How important is Discrete Mathematics for a Computer Scientist? Background: I'm pursuing a Master's degree with a focus on fundamentals such as Algorithms, Complexity and Computability Theory and Programming Languages to get a good foundation for working in the field of Parallel Computing. Some more background: My university grants a lot of freedom in the choices of courses for my Master's degree. It's officially called "Software Engineering", but due to a the broad range of electives, a different focus is possible. Interestingly, none of the electives is a lecture in Math! I'm thinking about doing a course about Discrete Mathematics that would take half a semester to complete successfully, even if I can't use it for my degree. So with this question I'm trying to find out if the effort is justifiable.

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  • Isometric Screen View to World View

    - by Sleepy Rhino
    I am having trouble working out the math to transform the screen coordinates to the Grid coordinates. The code below is how far I have got but it is totally wrong any help or resources to fix this issue would be great, had a complete mind block with this for some reason. private Point ScreenToIso(int mouseX, int mouseY) { int offsetX = WorldBuilder.STARTX; int offsetY = WorldBuilder.STARTY; Vector2 startV = new Vector2(offsetX, offsetY); int mapX = offsetX - mouseX; int mapY = offsetY - mouseY + (WorldBuilder.tileHeight / 2); mapY = -1 * (mapY / WorldBuilder.tileHeight); mapX = (mapX / WorldBuilder.tileHeight) + mapY; return new Point(mapX, mapY); }

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  • how to select categories for user generated content site?

    - by Frederik Creemers
    On the site I'm building, users can create tutorials. I want the users to be able to create tutorials on as many subjects as possible, but still have some preset categories. What's the best way to select these categories? The reason I don't just let users add keywords, and use these for categorization, is because users gain experience points in a certain subject when their tutorial is liked by someone, and in a similar way the Stack Exchange network does, create communities around these subjects. I will give visiters the possibility to suggest new categories. here are the categories that I'm thinking of at the moment: health gardening cooking technology science & math music visual art

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  • Coding style advice? [closed]

    - by user1064918
    I'm a newly grad. I've got a lot of complaints from my supervisor at work during code-review sessions with regard to my coding style (Surprise!). I don't know if it's just him being cranky or my style is really that annoying to read. I come from the low-level language world (assembly, mostly), so I've been taught to use bitwise ops and all the cool tricks to do math whenever possible. I also have the habits of doing some other things that've been regarded as "too excessively dense to read". So I'm hoping to get some feedback from any experienced programmers! :) Also how should I justify between code performance and readability? Thanks!!

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  • Continuous Movement of gun bullet

    - by Siddharth
    I was using box2d for the movement of the body. When I apply gravity (0,0) the bullet continuously move but when I change gravity to the earth the behavior was changed. I also try to apply continuous force to the bullet body but the behavior was not so good. So please provide any suggestion to continuously move bullet body in earth gravity. currentVelocity = bulletBody.getLinearVelocity(); if (currentVelocity.len() < speed|| currentVelocity.len() > speed + 0.25f) { velocityChange = Math.abs(speed - currentVelocity.len()); currentVelocity.set(currentVelocity.x* velocityChange, currentVelocity.y*velocityChange); bulletBody.applyLinearImpulse(currentVelocity,bulletBody.getWorldCenter()); } I apply above code for the continuous velocity of the body. And also I did not able to find any setGravityScale method in the library.

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  • xbox thumbstick used to rotate sprite, basic formula makes it "stick" or feel "sticky" at 90 degree intervals! how do get smooth rotation?

    - by Hugh
    Context: C#, XNA game I am using a very basic formula to calculate what angle my sprite (spaceship for example) should be facing based on the xbox controller thumbstick ie. you use the thumbstick to rotate the ship! in my main update method: shuttleAngle = (float) Math.Atan2(newGamePadState.ThumbSticks.Right.X, newGamePadState.ThumbSticks.Right.Y); in my main draw method: spriteBatch.Draw(shuttle, shuttleCoords, sourceRectangle, Color.White, shuttleAngle, origin, 1.0f, SpriteEffects.None, 1); as you can see its quite simple, i take the current radians from the thumbstick and store it in a float "shuttleAngle" and then use this as the rotation angle (in radians) arguement for drawing the shuttle. For some reason when i rotate the sprint it feels sticky at 0, 90, 180 and 270 degrees angles, it wants to settle at those angles. its not giving me a smooth and natural rotation like i would feel in a game that uses a similar mechanic. PS: my xbox controller is fine!

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  • Trying to detect collision between two polygons using Separating Axis Theorem

    - by Holly
    The only collision experience i've had was with simple rectangles, i wanted to find something that would allow me to define polygonal areas for collision and have been trying to make sense of SAT using these two links Though i'm a bit iffy with the math for the most part i feel like i understand the theory! Except my implementation somewhere down the line must be off as: (excuse the hideous font) As mentioned above i have defined a CollisionPolygon class where most of my theory is implemented and then have a helper class called Vect which was meant to be for Vectors but has also been used to contain a vertex given that both just have two float values. I've tried stepping through the function and inspecting the values to solve things but given so many axes and vectors and new math to work out as i go i'm struggling to find the erroneous calculation(s) and would really appreciate any help. Apologies if this is not suitable as a question! CollisionPolygon.java: package biz.hireholly.gameplay; import android.graphics.Canvas; import android.graphics.Color; import android.graphics.Paint; import biz.hireholly.gameplay.Types.Vect; public class CollisionPolygon { Paint paint; private Vect[] vertices; private Vect[] separationAxes; CollisionPolygon(Vect[] vertices){ this.vertices = vertices; //compute edges and separations axes separationAxes = new Vect[vertices.length]; for (int i = 0; i < vertices.length; i++) { // get the current vertex Vect p1 = vertices[i]; // get the next vertex Vect p2 = vertices[i + 1 == vertices.length ? 0 : i + 1]; // subtract the two to get the edge vector Vect edge = p1.subtract(p2); // get either perpendicular vector Vect normal = edge.perp(); // the perp method is just (x, y) => (-y, x) or (y, -x) separationAxes[i] = normal; } paint = new Paint(); paint.setColor(Color.RED); } public void draw(Canvas c, int xPos, int yPos){ for (int i = 0; i < vertices.length; i++) { Vect v1 = vertices[i]; Vect v2 = vertices[i + 1 == vertices.length ? 0 : i + 1]; c.drawLine( xPos + v1.x, yPos + v1.y, xPos + v2.x, yPos + v2.y, paint); } } /* consider changing to a static function */ public boolean intersects(CollisionPolygon p){ // loop over this polygons separation exes for (Vect axis : separationAxes) { // project both shapes onto the axis Vect p1 = this.minMaxProjection(axis); Vect p2 = p.minMaxProjection(axis); // do the projections overlap? if (!p1.overlap(p2)) { // then we can guarantee that the shapes do not overlap return false; } } // loop over the other polygons separation axes Vect[] sepAxesOther = p.getSeparationAxes(); for (Vect axis : sepAxesOther) { // project both shapes onto the axis Vect p1 = this.minMaxProjection(axis); Vect p2 = p.minMaxProjection(axis); // do the projections overlap? if (!p1.overlap(p2)) { // then we can guarantee that the shapes do not overlap return false; } } // if we get here then we know that every axis had overlap on it // so we can guarantee an intersection return true; } /* Note projections wont actually be acurate if the axes aren't normalised * but that's not necessary since we just need a boolean return from our * intersects not a Minimum Translation Vector. */ private Vect minMaxProjection(Vect axis) { float min = axis.dot(vertices[0]); float max = min; for (int i = 1; i < vertices.length; i++) { float p = axis.dot(vertices[i]); if (p < min) { min = p; } else if (p > max) { max = p; } } Vect minMaxProj = new Vect(min, max); return minMaxProj; } public Vect[] getSeparationAxes() { return separationAxes; } public Vect[] getVertices() { return vertices; } } Vect.java: package biz.hireholly.gameplay.Types; /* NOTE: Can also be used to hold vertices! Projections, coordinates ect */ public class Vect{ public float x; public float y; public Vect(float x, float y){ this.x = x; this.y = y; } public Vect perp() { return new Vect(-y, x); } public Vect subtract(Vect other) { return new Vect(x - other.x, y - other.y); } public boolean overlap(Vect other) { if( other.x <= y || other.y >= x){ return true; } return false; } /* used specifically for my SAT implementation which i'm figuring out as i go, * references for later.. * http://www.gamedev.net/page/resources/_/technical/game-programming/2d-rotated-rectangle-collision-r2604 * http://www.codezealot.org/archives/55 */ public float scalarDotProjection(Vect other) { //multiplier = dot product / length^2 float multiplier = dot(other) / (x*x + y*y); //to get the x/y of the projection vector multiply by x/y of axis float projX = multiplier * x; float projY = multiplier * y; //we want to return the dot product of the projection, it's meaningless but useful in our SAT case return dot(new Vect(projX,projY)); } public float dot(Vect other){ return (other.x*x + other.y*y); } }

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  • Rotations and Origins

    - by Theodore Enderby
    I was hoping someone could explain to me, or help me understand, the math behind rotations and origins. I'm working on a little top down space sim and I can rotate my ship just how I want it. Now, when I get my blasters going it'd be nice if they shared the same rotation. Here's a picture. and here's some code! blast.X = ship.X+5; blast.Y = ship.Y; blast.RotationAngle = ship.RotationAngle; blast.Origin = new Vector2(ship.Origin.X,ship.Origin.Y); I add five so the sprite adds up when facing right. I tried adding five to the blast origin but no go. Any help is much appreciated

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