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  • Street-Fighting Mathematics

    Sanjoy Mahajan's new book lays out practical tools for educated guessing and down-and-dirty problem-solving Problem solving - Math - Recreations - Competitions - Methods and Theories

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  • Will taking two years off for school destroy my 4 year old development career?

    - by rsteckly
    Hi, I know some people have asked about getting back into programming after a break and this is a potential duplicate. I just am in a position where I can go back to school in Stat/Applied Math. But I'm very worried about the impact it will have on my career and ability to find a job afterwards. I have 3 years experience in .NET on top of a couple of years in PHP. Right now, I'm a senior software engineer. Do you think taking two years off to do math is going to dramatically hurt my marketability?

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  • Can I use a genetic algorithm for balancing character builds?

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

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  • FAQ: GridView Calculation with JavaScript - Displaying Quantity Total

    - by Vincent Maverick Durano
    Previously we've talked about how calculate the sub-totals and grand total in GridView here, how to format the numbers into a currency format and how to validate the quantity to just accept whole numbers using JavaScript here. One of the users in the forum (http://forums.asp.net) is asking if how to modify the script to display the quantity total in the footer. In this post I'm going to show you how to it. Basically we just need to modify the javascript CalculateTotals function and add the codes there for calculating the quantity total and display it in the footer. Here are the code blocks below:   <html xmlns="http://www.w3.org/1999/xhtml" > <head runat="server"> <title></title> <script type="text/javascript"> function CalculateTotals() { var gv = document.getElementById("<%= GridView1.ClientID %>"); var tb = gv.getElementsByTagName("input"); var lb = gv.getElementsByTagName("span"); var sub = 0; var total = 0; var indexQ = 1; var indexP = 0; var price = 0; var qty = 0; var totalQty = 0; for (var i = 0; i < tb.length; i++) { if (tb[i].type == "text") { ValidateNumber(tb[i]); price = lb[indexP].innerHTML.replace("$", "").replace(",", ""); sub = parseFloat(price) * parseFloat(tb[i].value); if (isNaN(sub)) { lb[i + indexQ].innerHTML = "0.00"; sub = 0; } else { lb[i + indexQ].innerHTML = FormatToMoney(sub, "$", ",", "."); ; } indexQ++; indexP = indexP + 2; if (isNaN(tb[i].value) || tb[i].value == "") { qty = 0; } else { qty = tb[i].value; } totalQty += parseInt(qty); total += parseFloat(sub); } } lb[lb.length - 2].innerHTML = totalQty; lb[lb.length - 1].innerHTML = FormatToMoney(total, "$", ",", "."); } function ValidateNumber(o) { if (o.value.length > 0) { o.value = o.value.replace(/[^\d]+/g, ''); //Allow only whole numbers } } function isThousands(position) { if (Math.floor(position / 3) * 3 == position) return true; return false; }; function FormatToMoney(theNumber, theCurrency, theThousands, theDecimal) { var theDecimalDigits = Math.round((theNumber * 100) - (Math.floor(theNumber) * 100)); theDecimalDigits = "" + (theDecimalDigits + "0").substring(0, 2); theNumber = "" + Math.floor(theNumber); var theOutput = theCurrency; for (x = 0; x < theNumber.length; x++) { theOutput += theNumber.substring(x, x + 1); if (isThousands(theNumber.length - x - 1) && (theNumber.length - x - 1 != 0)) { theOutput += theThousands; }; }; theOutput += theDecimal + theDecimalDigits; return theOutput; } </script> </head> <body> <form id="form1" runat="server"> <asp:gridview ID="GridView1" runat="server" ShowFooter="true" AutoGenerateColumns="false"> <Columns> <asp:BoundField DataField="RowNumber" HeaderText="Row Number" /> <asp:BoundField DataField="Description" HeaderText="Item Description" /> <asp:TemplateField HeaderText="Item Price"> <ItemTemplate> <asp:Label ID="LBLPrice" runat="server" Text='<%# Eval("Price","{0:C}") %>'></asp:Label> </ItemTemplate> <FooterTemplate> <b>Total Qty:</b> </FooterTemplate> </asp:TemplateField> <asp:TemplateField HeaderText="Quantity"> <ItemTemplate> <asp:TextBox ID="TXTQty" runat="server" onkeyup="CalculateTotals();"></asp:TextBox> </ItemTemplate> <FooterTemplate> <asp:Label ID="LBLQtyTotal" runat="server" Font-Bold="true" ForeColor="Blue" Text="0" ></asp:Label>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <b>Total Amount:</b> </FooterTemplate> </asp:TemplateField> <asp:TemplateField HeaderText="Sub-Total"> <ItemTemplate> <asp:Label ID="LBLSubTotal" runat="server" ForeColor="Green" Text="0.00"></asp:Label> </ItemTemplate> <FooterTemplate> <asp:Label ID="LBLTotal" runat="server" ForeColor="Green" Font-Bold="true" Text="0.00"></asp:Label> </FooterTemplate> </asp:TemplateField> </Columns> </asp:gridview> </form> </body> </html>   Here's the output below when you run it on the page: I hope someone find this post useful! Technorati Tags: ASP.NET,C#,JavaScript,GridView

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  • Android Can't get two virtual joysticks to move independently and at the same time

    - by Cole
    @Override public boolean onTouch(View v, MotionEvent event) { // TODO Auto-generated method stub float r = 70; float centerLx = (float) (screenWidth*.3425); float centerLy = (float) (screenHeight*.4958); float centerRx = (float) (screenWidth*.6538); float centerRy = (float) (screenHeight*.4917); float dx = 0; float dy = 0; float theta; float c; int action = event.getAction(); int actionCode = action & MotionEvent.ACTION_MASK; int pid = (action & MotionEvent.ACTION_POINTER_INDEX_MASK) >> MotionEvent.ACTION_POINTER_INDEX_SHIFT; int fingerid = event.getPointerId(pid); int x = (int) event.getX(pid); int y = (int) event.getY(pid); c = FloatMath.sqrt(dx*dx + dy*dy); theta = (float) Math.atan(Math.abs(dy/dx)); switch (actionCode) { case MotionEvent.ACTION_DOWN: case MotionEvent.ACTION_POINTER_DOWN: //if touching down on left stick, set leftstick ID to this fingerid. if(x < screenWidth/2 && c<r*.8) { lsId = fingerid; dx = x-centerLx; dy = y-centerLy; touchingLs = true; } else if(x > screenWidth/2 && c<r*.8) { rsId = fingerid; dx = x-centerRx; dy = y-centerRy; touchingRs = true; } break; case MotionEvent.ACTION_MOVE: if (touchingLs && fingerid == lsId) { dx = x - centerLx; dy = y - centerLy; }else if (touchingRs && fingerid == rsId) { dx = x - centerRx; dy = y - centerRy; } c = FloatMath.sqrt(dx*dx + dy*dy); theta = (float) Math.atan(Math.abs(dy/dx)); //if touching outside left radius and moving left stick if(c >= r && touchingLs && fingerid == lsId) { if(dx>0 && dy<0) { //top right quadrant lsX = r * FloatMath.cos(theta); lsY = -(r * FloatMath.sin(theta)); Log.i("message", "top right"); } if(dx<0 && dy<0) { //top left quadrant lsX = -(r * FloatMath.cos(theta)); lsY = -(r * FloatMath.sin(theta)); Log.i("message", "top left"); } if(dx<0 && dy>0) { //bottom left quadrant lsX = -(r * FloatMath.cos(theta)); lsY = r * FloatMath.sin(theta); Log.i("message", "bottom left"); } else if(dx > 0 && dy > 0){ //bottom right quadrant lsX = r * FloatMath.cos(theta); lsY = r * FloatMath.sin(theta); Log.i("message", "bottom right"); } } if(c >= r && touchingRs && fingerid == rsId) { if(dx>0 && dy<0) { //top right quadrant rsX = r * FloatMath.cos(theta); rsY = -(r * FloatMath.sin(theta)); Log.i("message", "top right"); } if(dx<0 && dy<0) { //top left quadrant rsX = -(r * FloatMath.cos(theta)); rsY = -(r * FloatMath.sin(theta)); Log.i("message", "top left"); } if(dx<0 && dy>0) { //bottom left quadrant rsX = -(r * FloatMath.cos(theta)); rsY = r * FloatMath.sin(theta); Log.i("message", "bottom left"); } else if(dx > 0 && dy > 0) { rsX = r * FloatMath.cos(theta); rsY = r * FloatMath.sin(theta); Log.i("message", "bottom right"); } } else { if(c < r && touchingLs && fingerid == lsId) { lsX = dx; lsY = dy; } if(c < r && touchingRs && fingerid == rsId){ rsX = dx; rsY = dy; } } break; case MotionEvent.ACTION_UP: case MotionEvent.ACTION_POINTER_UP: if (fingerid == lsId) { lsId = -1; lsX = 0; lsY = 0; touchingLs = false; } else if (fingerid == rsId) { rsId = -1; rsX = 0; rsY = 0; touchingRs = false; } break; } return true; } There's a left joystick and a right joystick. Right now only one will move at a time. If someone could set me on the right track I would be incredibly grateful cause I've been having nightmares about this problem.

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  • Parabolic throw with set Height and range (libgdx)

    - by Tauboga
    Currently i'm working on a minigame for android where you have a rotating ball in the center of the display which jumps when touched in the direction of his current angle. I'm simply using a gravity vector and a velocity vector in this way: positionBall = positionBall.add(velocity); velocity = velocity.add(gravity); and velocity.x = (float) Math.cos(angle) * 12; /* 12 to amplify the velocity */ velocity.y = (float) Math.sin(angle) * 15; /* 15 to amplify the velocity */ That works fine. Here comes the problem: I want to make the jump look the same on all possible resolutions. The velocity needs to be scaled in a way that when the ball is thrown straight upwards it will touch the upper display border. When thrown directly left or right the range shall be exactly long enough to touch the left/right display border. Which formula(s) do I need to use and how to implement them correctly? Thanks in advance!

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  • (Libgdx) Move Vector2 along angle?

    - by gemurdock
    I have seen several answers on here about moving along angle, but I can't seem to get this to work properly for me and I am new to LibGDX... just trying to learn. These are my Vector2's that I am using for this function. public Vector2 position = new Vector2(); public Vector2 velocity = new Vector2(); public Vector2 movement = new Vector2(); public Vector2 direction = new Vector2(); Here is the function that I use to move the position vector along an angle. setLocation() just sets the new location of the image. public void move(float delta, float degrees) { position.set(image.getX() + image.getWidth() / 2, image.getY() + image.getHeight() / 2); direction.set((float) Math.cos(degrees), (float) Math.sin(degrees)).nor(); velocity.set(direction).scl(speed); movement.set(velocity).scl(delta); position.add(movement); setLocation(position.x, position.y); // Sets location of image } I get a lot of different angles with this, just not the correct angles. How should I change this function to move a Vector2 along an angle using the Vector2 class from com.badlogic.gdx.math.Vector2 within the LibGDX library? I found this answer, but not sure how to implement it. Update: I figured out part of the issue. Should convert degrees to radians. However, the angle of 0 degrees is towards the right. Is there any way to fix this? As I shouldn't have to add 90 to degrees in order to have correct heading. New code is below public void move(float delta, float degrees) { degrees += 90; // Set degrees to correct heading, shouldn't have to do this position.set(image.getX() + image.getWidth() / 2, image.getY() + image.getHeight() / 2); direction.set(MathUtils.cos(degrees * MathUtils.degreesToRadians), MathUtils.sin(degrees * MathUtils.degreesToRadians)).nor(); velocity.set(direction).scl(speed); movement.set(velocity).scl(delta); position.add(movement); setLocation(position.x, position.y); }

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  • Compute directional light frustum from view furstum points and light direction

    - by Fabian
    I'm working on a friends engine project and my task is to construct a new frustum from the light direction that overlaps the view frustum and possible shadow casters. The project already has a function that creates a frustum for this but its way to big and includes way to many casters (shadows) which can't be seen in the view frustum. Now the only parameter of this function are the normalized light direction vector and a view class which lets me extract the 8 view frustum points in world space. I don't have any additional infos about the scene. I have read some of the related Questions here but non seem to fit very well to my problem as they often just point to cascaded shadow maps. Sadly i can't use DX or openGl functions directly because this engine has a dedicated math library. From what i've read so far the steps are: Transform view frustum points into light space and find min/max x and y values (or sometimes minima and maxima of all three axis) and create a AABB using the min/max vectors. But what comes after this step? How do i transform this new AABB back to world space? What i've done so far: CVector3 Points[8], MinLight = CVector3(FLT_MAX), MaxLight = CVector3(FLT_MAX); for(int i = 0; i<8;++i){ Points[i] = Points[i] * WorldToShadowMapMatrix; MinLight = Math::Min(Points[i],MinLight); MaxLight = Math::Max(Points[i],MaxLight); } AABox box(MinLight,MaxLight); I don't think this is the right way to do it. The near plain probably has to extend into the direction of the light source to include potentional shadow casters. I've read the Microsoft article about cascaded shadow maps http://msdn.microsoft.com/en-us/library/windows/desktop/ee416307%28v=vs.85%29.aspx which also includes some sample code. But they seem to use the scenes AABB to determine the near and far plane which I can't since i cant access this information from the funtion I'm working in. Could you guys please link some example code which shows the calculation of such frustum? Thanks in advance! Additional questio: is there a way to construct a WorldToFrustum matrix that represents the above transformation?

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  • Should I be an algorithm developer, or java web frameworks type developer?

    - by Derek
    So - as I see it, there are really two kinds of developers. Those that do frameworks, web services, pretty-making front ends, etc etc. Then there are developers that write the algorithms that solve the problem. That is, unless the problem is "display this raw data in some meaningful way." In that case, the framework/web developer guy might be doing both jobs. So my basic problem is this. I have been an algorithms kind of software developer for a few years now. I double majored in Math and Computer science, and I have a master's in systems engineering. I have never done any web-dev work, with the exception of a couple minor jobs, and some hobby level stuff. I have been job interviewing lately, and this is what happens: Job is listed as "programmer- 5 years of experience with the following: C/C++, Java,Perl, Ruby, ant, blah blah blah" Recruiter calls me, says they want me to come in for interview In the interview, find out they have some webservices development, blah blah blah When asked in the interview, talk about my experience doing algorithms, optimization, blah blah..but very willing to learn new languages, frameworks, etc Get a call back saying "we didn't think you were a fit for the job you interviewed wtih, but our algorithm team got wind of you and wants to bring you on" This has happened to me a couple times now - see a vague-ish job description looking for a "programmer" Go in, find out they are doing some sort of web-based tool, maybe with some hardcore algorithms running in the background. interview with people for the web-based tool, but get an offer from the algorithms people. So the question is - which job is the better job? I basically just want to get a wide berth of experience at this level of my career, but are algorithm developers so much in demand? Even more so than all these supposed hot in demand web developer guys? Will I be ok in the long run if I go into the niche of math based algorithm development, and just little to no, or hobby level web-dev experience? I basically just don't want to pigeon hole myself this early. My salary is already starting to get pretty high - and I can see a company later on saying "we really need a web developer, but we'll hire this 50k/year college guy, instead of this 100k/year experience algorithm guy" Cliffs notes: I have been doing algorithm development. I consider myself to be a "good programmer." I would have no problem picking up web technologies and those sorts of frameworks. During job interviews, I keep getting "we think you've got a good skillset - talk to our algorithm team" instead of wanting me to learn new skills on the job to do their web services or whhatever other new technology they are doing. Edit: Whenever I am talking about algorithm development here - I am talking about the code that produces the answer. Typically I think of more math-based algorithms: solving a financial problem, solving a finite element method, image processing, etc

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  • How to make this game loop deterministic

    - by Lanaru
    I am using the following game loop for my pacman clone: long prevTime = System.currentTimeMillis(); while (running) { long curTime = System.currentTimeMillis(); float frameTime = (curTime - prevTime) / 1000f; prevTime = curTime; while (frameTime > 0.0f) { final float deltaTime = Math.min(frameTime, TIME_STEP); update(deltaTime); frameTime -= deltaTime; } repaint(); } The thing is, I don't always get the same ghost movement every time I run the game (their logic is deterministic), so it must be the game loop. I imagine it's due to the final float deltaTime = Math.min(frameTime, TIME_STEP); line. What's the best way of modifying this to perform the exact same way every time I run it? Also, any further improvements I can make?

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  • Trying to implement fling events on an object

    - by Adam Short
    I have a game object, well a bitmap, which I'd like to "fling". I'm struggling to get it to fling ontouchlistener due to it being a bitmap and not sure how to proceed and I'm struggling to find the resources to help. Here's my code so far: https://github.com/addrum/Shapes GameActivity class: package com.main.shapes; import android.app.Activity; import android.content.Context; import android.graphics.Bitmap; import android.graphics.BitmapFactory; import android.graphics.Canvas; import android.os.Bundle; import android.view.GestureDetector; import android.view.MotionEvent; import android.view.SurfaceHolder; import android.view.SurfaceView; import android.view.View.OnTouchListener; import android.view.Window; public class GameActivity extends Activity { private GestureDetector gestureDetector; View view; Bitmap ball; float x, y; @Override protected void onCreate(Bundle savedInstanceState) { super.onCreate(savedInstanceState); //Remove title bar this.requestWindowFeature(Window.FEATURE_NO_TITLE); view = new View(this); ball = BitmapFactory.decodeResource(getResources(), R.drawable.ball); gestureDetector = new GestureDetector(this, new GestureListener()); x = 0; y = 0; setContentView(view); ball.setOnTouchListener(new OnTouchListener() { @Override public boolean onTouch(android.view.View v, MotionEvent event) { // TODO Auto-generated method stub return false; } }); } @Override protected void onPause() { super.onPause(); view.pause(); } @Override protected void onResume() { super.onResume(); view.resume(); } public class View extends SurfaceView implements Runnable { Thread thread = null; SurfaceHolder holder; boolean canRun = false; public View(Context context) { super(context); holder = getHolder(); } public void run() { while (canRun) { if (!holder.getSurface().isValid()) { continue; } Canvas c = holder.lockCanvas(); c.drawARGB(255, 255, 255, 255); c.drawBitmap(ball, x - (ball.getWidth() / 2), y - (ball.getHeight() / 2), null); holder.unlockCanvasAndPost(c); } } public void pause() { canRun = false; while (true) { try { thread.join(); } catch (InterruptedException e) { e.printStackTrace(); } break; } thread = null; } public void resume() { canRun = true; thread = new Thread(this); thread.start(); } } } GestureListener class: package com.main.shapes; import android.view.GestureDetector.SimpleOnGestureListener; import android.view.MotionEvent; public class GestureListener extends SimpleOnGestureListener { private static final int SWIPE_MIN_DISTANCE = 120; private static final int SWIPE_THRESHOLD_VELOCITY = 200; @Override public boolean onFling(MotionEvent e1, MotionEvent e2, float velocityX, float velocityY) { if (e1.getX() - e2.getX() > SWIPE_MIN_DISTANCE && Math.abs(velocityX) > SWIPE_THRESHOLD_VELOCITY) { //From Right to Left return true; } else if (e2.getX() - e1.getX() > SWIPE_MIN_DISTANCE && Math.abs(velocityX) > SWIPE_THRESHOLD_VELOCITY) { //From Left to Right return true; } if (e1.getY() - e2.getY() > SWIPE_MIN_DISTANCE && Math.abs(velocityY) > SWIPE_THRESHOLD_VELOCITY) { //From Bottom to Top return true; } else if (e2.getY() - e1.getY() > SWIPE_MIN_DISTANCE && Math.abs(velocityY) > SWIPE_THRESHOLD_VELOCITY) { //From Top to Bottom return true; } return false; } @Override public boolean onDown(MotionEvent e) { //always return true since all gestures always begin with onDown and<br> //if this returns false, the framework won't try to pick up onFling for example. return true; } }

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  • Applications: The mathematics of movement, Part 1

    - by TechTwaddle
    Before you continue reading this post, a suggestion; if you haven’t read “Programming Windows Phone 7 Series” by Charles Petzold, go read it. Now. If you find 150+ pages a little too long, at least go through Chapter 5, Principles of Movement, especially the section “A Brief Review of Vectors”. This post is largely inspired from this chapter. At this point I assume you know what vectors are, how they are represented using the pair (x, y), what a unit vector is, and given a vector how you would normalize the vector to get a unit vector. Our task in this post is simple, a marble is drawn at a point on the screen, the user clicks at a random point on the device, say (destX, destY), and our program makes the marble move towards that point and stop when it is reached. The tricky part of this task is the word “towards”, it adds a direction to our problem. Making a marble bounce around the screen is simple, all you have to do is keep incrementing the X and Y co-ordinates by a certain amount and handle the boundary conditions. Here, however, we need to find out exactly how to increment the X and Y values, so that the marble appears to move towards the point where the user clicked. And this is where vectors can be so helpful. The code I’ll show you here is not ideal, we’ll be working with C# on Windows Mobile 6.x, so there is no built-in vector class that I can use, though I could have written one and done all the math inside the class. I think it is trivial to the actual problem that we are trying to solve and can be done pretty easily once you know what’s going on behind the scenes. In other words, this is an excuse for me being lazy. The first approach, uses the function Atan2() to solve the “towards” part of the problem. Atan2() takes a point (x, y) as input, Atan2(y, x), note that y goes first, and then it returns an angle in radians. What angle you ask. Imagine a line from the origin (0, 0), to the point (x, y). The angle which Atan2 returns is the angle the positive X-axis makes with that line, measured clockwise. The figure below makes it clear, wiki has good details about Atan2(), give it a read. The pair (x, y) also denotes a vector. A vector whose magnitude is the length of that line, which is Sqrt(x*x + y*y), and a direction ?, as measured from positive X axis clockwise. If you’ve read that chapter from Charles Petzold’s book, this much should be clear. Now Sine and Cosine of the angle ? are special. Cosine(?) divides x by the vectors length (adjacent by hypotenuse), thus giving us a unit vector along the X direction. And Sine(?) divides y by the vectors length (opposite by hypotenuse), thus giving us a unit vector along the Y direction. Therefore the vector represented by the pair (cos(?), sin(?)), is the unit vector (or normalization) of the vector (x, y). This unit vector has a length of 1 (remember sin2(?) + cos2(?) = 1 ?), and a direction which is the same as vector (x, y). Now if I multiply this unit vector by some amount, then I will always get a point which is a certain distance away from the origin, but, more importantly, the point will always be on that line. For example, if I multiply the unit vector with the length of the line, I get the point (x, y). Thus, all we have to do to move the marble towards our destination point, is to multiply the unit vector by a certain amount each time and draw the marble, and the marble will magically move towards the click point. Now time for some code. The application, uses a timer based frame draw method to draw the marble on the screen. The timer is disabled initially and whenever the user clicks on the screen, the timer is enabled. The callback function for the timer follows the standard Update and Draw cycle. private double totLenToTravelSqrd = 0; private double startPosX = 0, startPosY = 0; private double destX = 0, destY = 0; private void Form1_MouseUp(object sender, MouseEventArgs e) {     destX = e.X;     destY = e.Y;     double x = marble1.x - destX;     double y = marble1.y - destY;     //calculate the total length to be travelled     totLenToTravelSqrd = x * x + y * y;     //store the start position of the marble     startPosX = marble1.x;     startPosY = marble1.y;     timer1.Enabled = true; } private void timer1_Tick(object sender, EventArgs e) {     UpdatePosition();     DrawMarble(); } Form1_MouseUp() method is called when ever the user touches and releases the screen. In this function we save the click point in destX and destY, this is the destination point for the marble and we also enable the timer. We store a few more values which we will use in the UpdatePosition() method to detect when the marble has reached the destination and stop the timer. So we store the start position of the marble and the square of the total length to be travelled. I’ll leave out the term ‘sqrd’ when speaking of lengths from now on. The time out interval of the timer is set to 40ms, thus giving us a frame rate of about ~25fps. In the timer callback, we update the marble position and draw the marble. We know what DrawMarble() does, so here, we’ll only look at how UpdatePosition() is implemented; private void UpdatePosition() {     //the vector (x, y)     double x = destX - marble1.x;     double y = destY - marble1.y;     double incrX=0, incrY=0;     double distanceSqrd=0;     double speed = 6;     //distance between destination and current position, before updating marble position     distanceSqrd = x * x + y * y;     double angle = Math.Atan2(y, x);     //Cos and Sin give us the unit vector, 6 is the value we use to magnify the unit vector along the same direction     incrX = speed * Math.Cos(angle);     incrY = speed * Math.Sin(angle);     marble1.x += incrX;     marble1.y += incrY;     //check for bounds     if ((int)marble1.x < MinX + marbleWidth / 2)     {         marble1.x = MinX + marbleWidth / 2;     }     else if ((int)marble1.x > (MaxX - marbleWidth / 2))     {         marble1.x = MaxX - marbleWidth / 2;     }     if ((int)marble1.y < MinY + marbleHeight / 2)     {         marble1.y = MinY + marbleHeight / 2;     }     else if ((int)marble1.y > (MaxY - marbleHeight / 2))     {         marble1.y = MaxY - marbleHeight / 2;     }     //distance between destination and current point, after updating marble position     x = destX - marble1.x;     y = destY - marble1.y;     double newDistanceSqrd = x * x + y * y;     //length from start point to current marble position     x = startPosX - (marble1.x);     y = startPosY - (marble1.y);     double lenTraveledSqrd = x * x + y * y;     //check for end conditions     if ((int)lenTraveledSqrd >= (int)totLenToTravelSqrd)     {         System.Console.WriteLine("Stopping because destination reached");         timer1.Enabled = false;     }     else if (Math.Abs((int)distanceSqrd - (int)newDistanceSqrd) < 4)     {         System.Console.WriteLine("Stopping because no change in Old and New position");         timer1.Enabled = false;     } } Ok, so in this function, first we subtract the current marble position from the destination point to give us a vector. The first three lines of the function construct this vector (x, y). The vector (x, y) has the same length as the line from (marble1.x, marble1.y) to (destX, destY) and is in the direction pointing from (marble1.x, marble1.y) to (destX, destY). Note that marble1.x and marble1.y denote the center point of the marble. Then we use Atan2() to get the angle which this vector makes with the positive X axis and use Cosine() and Sine() of that angle to get the unit vector along that same direction. We multiply this unit vector with 6, to get the values which the position of the marble should be incremented by. This variable, speed, can be experimented with and determines how fast the marble moves towards the destination. After this, we check for bounds to make sure that the marble stays within the screen limits and finally we check for the end condition and stop the timer. The end condition has two parts to it. The first case is the normal case, where the user clicks well inside the screen. Here, we stop when the total length travelled by the marble is greater than or equal to the total length to be travelled. Simple enough. The second case is when the user clicks on the very corners of the screen. Like I said before, the values marble1.x and marble1.y denote the center point of the marble. When the user clicks on the corner, the marble moves towards the point, and after some time tries to go outside of the screen, this is when the bounds checking comes into play and corrects the marble position so that the marble stays inside the screen. In this case the marble will never travel a distance of totLenToTravelSqrd, because of the correction is its position. So here we detect the end condition when there is not much change in marbles position. I use the value 4 in the second condition above. After experimenting with a few values, 4 seemed to work okay. There is a small thing missing in the code above. In the normal case, case 1, when the update method runs for the last time, marble position over shoots the destination point. This happens because the position is incremented in steps (which are not small enough), so in this case too, we should have corrected the marble position, so that the center point of the marble sits exactly on top of the destination point. I’ll add this later and update the post. This has been a pretty long post already, so I’ll leave you with a video of how this program looks while running. Notice in the video that the marble moves like a bot, without any grace what so ever. And that is because the speed of the marble is fixed at 6. In the next post we will see how to make the marble move a little more elegantly. And also, if Atan2(), Sine() and Cosine() are a little too much to digest, we’ll see how to achieve the same effect without using them, in the next to next post maybe. Ciao!

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  • Rotate an image in a scaled context

    - by nathan
    Here is my working piece of code to rotate an image toward a point (in my case, the mouse cursor). float dx = newx - ploc.x; float dy = newy - ploc.y; float angle = (float) Math.toDegrees(Math.atan2(dy, dx)); Where ploc is the location of the image i'm rotating. And here is the rendering code: g.rotate(loc.x + width / 2, loc.y + height / 2, angle); g.drawImage(frame, loc.x, loc.y); Where loc is the location of the image and "width" and "height" are respectively the width and height of the image. What changes are needed to make it works on a scaled context? e.g make it works with something like g.scale(sx, sy).

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  • Truly Random Numbers

    German researchers use a "flip-flop" to improve random number generator Random number generation - Algorithms - Pseudorandom Numbers - Math - Recreation

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  • What are the fundamentals of game development?

    - by Matt
    Hi, I completely do not understand how a video game can be coded. I'm a beginner programmer and only have experience writing console applications that do math and what not. I do not understand how these logical processes can make images move on the screen (video games). Obviously if i jumped into a game development book or something like that I would understand but I am currently still getting a grasp of the fundamentals of programming in general. Could anyone give a simple explanation , coding wise, on the jump between making a computer do simple math to making a computer produce amazing graphical programs such as video games? Maybe there are some intro videos someone can point me to? I

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  • When the obvious answer is obviously wrong

    - by John Paul Cook
    This post is about how simple math in T-SQL can produce undesirable results, but first we begin with a math quiz. Answer the following as quickly as possible: You just read pages 100-300 of a book. How many pages did you read? QUICKLY NOW! For those of you who answered 200 pages, I have a new question: Which page did you not read? There were 201 pages to read. If you read 200 pages, you skipped a page! What your answer be if I asked you how many pages did you read if you read pages 1-3? Three pages!...(read more)

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  • Keeping rotation between two objects

    - by user99
    In my XNA game I have two objects that collide. When the first object collides with the other it is able to latch on to it and move it about the world. I am having a problem with the math here (Math isn't my strong point). I currently have the second object latch on to the first and move around with it, but I cannot get it to keep it's original direction. So, if the object is facing up it should keep this direction relative to how it is being rotated with the original item. Any tips on how I could best to achieve this?

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  • Deterministic Multiplayer RTS game questions?

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

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  • HedgeWar code confusion

    - by BluFire
    I looked at an open source project(HedgeWars) that was built using many programming languages such as C++ and Java. While I was looking through the code, I couldn't help noticing that all the math and physics were gone from the Java code. HedgeWars I imported the project file called "SDL-android-project" which was a sub folder to "android build" and project files. My question is where is all the math and physics inside the code? Do I have to look at the C++ code in order to see it? I think Hedgewars was originally programmed in C++ but the files are confusing be because of its size and the fact that it has several programming languages inside.

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  • Passive Income for a programmer : Teaching

    - by Victor
    While looking into passive income streams for someone with a Science/math/Engineering/Programming background, I ran into various ideas. I was looking to generate a passive income that would not take too much of an initiall learning curve. And it occurs to me that teaching/writing books/ on High School math/Physics/English is something I can do without a lot of prepwork. I am in Toronto . what are the average income opportunities for something like this? Where should I start looking?

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  • What kind of spam is this?

    - by SSilk
    I realize this is a pretty vague question, but I occasionally get spam messages through my contact form on a Drupal 6 site. The contact form does not have any anti-spam protection (i.e. math question). The messages I get are all very similar and just jumbled junk, like below, so I think they're all from the same source. Example: ylsaf0V bpsdfuxnhjjd, [url=http://wwgfsggzgyjyjm.com/]wwgrfgzrgsjyjm[/url], [link=http://xmgvyghcuufvb.com/]xmjyhvyjyfjirovb[/link], http://frgxmdghrgruhfc.com/ Anyway, I'm just wondering what the point of such a message is. All the links are dead, it's illegible, and it's not trying to sell me a product or get me to do anything, so I'm a bit perplexed. Is there any way to tell where they're coming from? And how concerned should I be? To be clear, I'm not asking how to avoid them, I realize just adding a simple math challenge or captcha would likely do the job.

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  • Trouble with AABB collision response and physics

    - by WCM
    I have been racking my brain trying to figure out a problem I am having with physics and basic AABB collision response. I am fairly close as the physics are mostly right. Gravity feels good and movement is solid. The issue I am running into is that when I land on the test block in my project, I can jump off of it most of the time. If I repeatedly jump in place, I will eventually get stuck one or two pixels below the surface of the test block. If I try to jump, I can become free of the other block, but it will happen again a few jumps later. I feel like I am missing something really obvious with this. I have two functions that support the detection and function to return a vector for the overlap of the two rectangle bounding boxes. I have a single update method that is processing the physics and collision for the entity. I feel like I am missing something very simple, like an ordering of the physics vs. collision response handling. Any thoughts or help can be appreciated. I apologize for the format of the code, tis prototype code mostly. The collision detection function: public static bool Collides(Rectangle source, Rectangle target) { if (source.Right < target.Left || source.Bottom < target.Top || source.Left > target.Right || source.Top > target.Bottom) { return false; } return true; } The overlap function: public static Vector2 GetMinimumTranslation(Rectangle source, Rectangle target) { Vector2 mtd = new Vector2(); Vector2 amin = source.Min(); Vector2 amax = source.Max(); Vector2 bmin = target.Min(); Vector2 bmax = target.Max(); float left = (bmin.X - amax.X); float right = (bmax.X - amin.X); float top = (bmin.Y - amax.Y); float bottom = (bmax.Y - amin.Y); if (left > 0 || right < 0) return Vector2.Zero; if (top > 0 || bottom < 0) return Vector2.Zero; if (Math.Abs(left) < right) mtd.X = left; else mtd.X = right; if (Math.Abs(top) < bottom) mtd.Y = top; else mtd.Y = bottom; // 0 the axis with the largest mtd value. if (Math.Abs(mtd.X) < Math.Abs(mtd.Y)) mtd.Y = 0; else mtd.X = 0; return mtd; } The update routine (gravity = 0.001f, jumpHeight = 0.35f, moveAmount = 0.15f): public void Update(GameTime gameTime) { Acceleration.Y = gravity; Position += new Vector2((float)(movement * moveAmount * gameTime.ElapsedGameTime.TotalMilliseconds), (float)(Velocity.Y * gameTime.ElapsedGameTime.TotalMilliseconds)); Velocity.Y += Acceleration.Y; Vector2 previousPosition = new Vector2((int)Position.X, (int)Position.Y); KeyboardState keyboard = Keyboard.GetState(); movement = 0; if (keyboard.IsKeyDown(Keys.Left)) { movement -= 1; } if (keyboard.IsKeyDown(Keys.Right)) { movement += 1; } if (Position.Y + 16 > GameClass.Instance.GraphicsDevice.Viewport.Height) { Velocity.Y = 0; Position = new Vector2(Position.X, GameClass.Instance.GraphicsDevice.Viewport.Height - 16); IsOnSurface = true; } if (Collision.Collides(BoundingBox, GameClass.Instance.block.BoundingBox)) { Vector2 mtd = Collision.GetMinimumTranslation(BoundingBox, GameClass.Instance.block.BoundingBox); Position += mtd; Velocity.Y = 0; IsOnSurface = true; } if (keyboard.IsKeyDown(Keys.Space) && !previousKeyboard.IsKeyDown(Keys.Space)) { if (IsOnSurface) { Velocity.Y = -jumpHeight; IsOnSurface = false; } } previousKeyboard = keyboard; } This is also a full download to the project. https://www.box.com/s/3rkdtbso3xgfgc2asawy P.S. I know that I could do this with the XNA Platformer Starter Kit algo, but it has some deep flaws that I am going to try to live without. I'd rather go the route of collision response via an overlay function. Thanks for any and all insight!

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