28. November 2012

In a prior recipe, we looked at how to handle collisions using an axis aligned bounding box, but there was one major problem.  If our bounding box is axis aligned, how do we handle rotation?  As you can probably tell by gigantic spoiler of a rotating jet to our right, the answer is we resize the bounding box to match the new extents of the rotated sprite.  Let's look at how:

## Just the Math

if(createjs.Bitmap.prototype.getBoundingRect == null){

createjs.Bitmap.prototype.getBoundingRect = function(){

var bb =  new createjs.Rectangle(

this.x - this.image.width/2,

this.y - this.image.height/2,

this.image.width,

this.image.height);

var corners = new Array();

corners[0] = new createjs.Point(bb.x,bb.y); //Top left

corners[1] = new createjs.Point(bb.x + bb.width,bb.y); //Top right

corners[2] = new createjs.Point(bb.x,bb.y + bb.height); // Bottom Left

corners[3] = new createjs.Point(bb.x + bb.width,bb.y + bb.height); //Bottom Right

var midPoint = new createjs.Point(this.x,this.y);

for(var i = 0; i < corners.length; i++){

corners[i] = rotatePoint(corners[i],midPoint,this.rotation);

}

var minX,minY,maxX,maxY;

minX = maxX = corners[0].x;

minY = maxY = corners[0].y;

for(var i =1; i < corners.length; i++){

if(corners[i].x < minX) minX = corners[i].x;

if(corners[i].x > maxX) maxX = corners[i].x;

if(corners[i].y < minY) minY = corners[i].y;

if(corners[i].y > maxY) maxY = corners[i].y;

}

bb.width = maxX - minX;

bb.height = maxY - minY;

bb.x = this.x - bb.width/2;

bb.y = this.y - bb.height/2;

return bb;

}

}

Controls:
Click on the box to focus and press B to toggle the blue box from being displayed.

## Description

That code excerpt makes it look more complicated than it actually is, not the version at the bottom of this post in the Complete Code section is more heavily commented.

Essentially as our underlying sprite rotates, the bounding box around it changes in size.  Now when we are creating our bounding box, we have to take the rotation into consideration.  Please note, there are a number of opportunities to optimize this code for performance, I favoured readability over performance, although I did note a few of the opportunities for improvement in the code comments.

First thing we have to do is get the original, untranslated bounding box of the sprite.  This is simply the image dimensions of our source sprite.  Unfortunately EaselJS doesn't provide a mechanism for defining a rectangle about it's mid point, like we have with our sprite, so we need to calculate the x and y values of our bounding box, which is at the top left corner of the rectangle.  This value is calculated by subtracting half the sprites width and height from it's location ( at it's mid point ).  If your library of choice allows you to specify a rectangle using it's mid point, width and height, you can remove some of this ugliness.

Now that we have our untranslated bounding box, we want to apply the sprite's rotation to each corner of the sprite.  We accomplish by applying a rotation around the centre of the sprite to each corner of the bounding box, see the See Also section for more details about rotation.  Note, this is one of those areas you could easily optimize for performance down the road.

Now that all 4 corners have been rotated, we need to figure out what the smallest rectangle that will encompass our translated points is.  To determine this, we loop through each point in our array, looking for the largest and smallest values in the X and Y axis.  Once we have determined what the new boundaries our, we construct our newly resized bounding box using these values.  Once again, we can't specify a rectangle using it's centre point in EaselJS, so once again we need to calculated the top left corner using the same logic as before.

If you turn off the blue debug lines I've drawn around the translated shape ( click the window and press B to toggle ), you will notice there is a ton of empty space as the sprite rotates, making it easy for collisions to appear to happen even though the space is actually empty.  You are very correct, and this is one of the biggest downsides to using AABBs.  There are however options for dealing with this, some of which we will discuss later on.

When looking at the complete code below, realize that a great deal of it is for rendering debug information on screen and wouldn't normally be required in your collision detection code.

## Complete Code

<!DOCTYPE html>

<html>

<script src="http://code.createjs.com/easeljs-0.5.0.min.js"></script>

<script>

var jetSprite;

var stage;

// Actual bounds is the Shape used to store the drawn blue bounding lines

var actualBounds;

// hideActualBounds is a toggle for making the debug lines visible or not

var hideActualBounds = false;

document.onkeydown = function(e){

switch(e.keyCode)

{

case 66: // up arrow

hideActualBounds = !hideActualBounds;

break;

}

}

function rotatePoint(point, center, angle){

angle = (angle ) * (Math.PI/180); // Convert to radians

var rotatedX = Math.cos(angle) * (point.x - center.x) - Math.sin(angle) * (point.y-center.y) + center.x;

var rotatedY = Math.sin(angle) * (point.x - center.x) + Math.cos(angle) * (point.y - center.y) + center.y;

return new createjs.Point(rotatedX,rotatedY);

}

if(createjs.Rectangle.prototype.intersects == null){

createjs.Rectangle.prototype.intersects = function(rect){

return (this.x <= rect.x + rect.width &&

rect.x <= this.x + this.width &&

this.y <= rect.y + rect.height &&

rect.y <= this.y + this.height);

}

}

if(createjs.Bitmap.prototype.getBoundingRect == null){

createjs.Bitmap.prototype.getBoundingRect = function(){

var bb =  new createjs.Rectangle(

this.x - this.image.width/2,

this.y - this.image.height/2,

this.image.width,

this.image.height);

// Get the 4 corners of the bounding box, order doesn't matter since they can potentially change

// Note, you could optimize this two only require the top left and bottom right corners

var corners = new Array();

corners[0] = new createjs.Point(bb.x,bb.y); //Top left

corners[1] = new createjs.Point(bb.x + bb.width,bb.y); //Top right

corners[2] = new createjs.Point(bb.x,bb.y + bb.height); // Bottom Left

corners[3] = new createjs.Point(bb.x + bb.width,bb.y + bb.height); //Bottom Right

var midPoint = new createjs.Point(this.x,this.y);

// Now apply the rotation of the sprite to the corners of the bounding box

// This loop could be merged with the min/max loop for optimization purposes

// But for readability I keep it separate for now.

for(var i = 0; i < corners.length; i++){

corners[i] = rotatePoint(corners[i],midPoint,this.rotation);

}

// Draw the rotated shape for debug reasons

// This draws a rectangle as 4 lines around the actual rotated image bounding area

if(actualBounds){

stage.removeChild(actualBounds);

}

if(!hideActualBounds){

var g = new createjs.Graphics();

g.setStrokeStyle(1);

g.beginStroke(createjs.Graphics.getRGB(0,0,255));

g.moveTo(corners[0].x,corners[0].y);

g.lineTo(corners[1].x,corners[1].y);

g.lineTo(corners[3].x,corners[3].y);

g.lineTo(corners[2].x,corners[2].y);

g.lineTo(corners[0].x,corners[0].y);

actualBounds = new createjs.Shape(g);

}

// These variables hold the smallest and largest X and Y values found in the Point array

var minX,minY,maxX,maxY;

// Small optimization here, start assuming first point is correct to eliminate a loop iteration

minX = maxX = corners[0].x;

minY = maxY = corners[0].y;

// Loop through Points determining the boundaries of our newly rotated rectangle

for(var i =1; i < corners.length; i++){

if(corners[i].x < minX) minX = corners[i].x;

if(corners[i].x > maxX) maxX = corners[i].x;

if(corners[i].y < minY) minY = corners[i].y;

if(corners[i].y > maxY) maxY = corners[i].y;

}

// We now have the four extreme points of our new bounding box, update bb with new box dimensions

bb.width = maxX - minX;

bb.height = maxY - minY;

bb.x = this.x - bb.width/2;

bb.y = this.y - bb.height/2;

return bb;

}

}

// This function is responsible for actually drawing the bounding box on screen

function updateBoundingBox(){

// Draw the bounding rect and create a new Shape with it

var g = new createjs.Graphics();

g.setStrokeStyle(1);

g.beginStroke(createjs.Graphics.getRGB(255,255,255));

var bb = jetSprite.getBoundingRect();

g.drawRect(bb.x,bb.y,bb.width,bb.height);

if(jetSprite.boundingBox){

stage.removeChild(jetSprite.boundingBox);

}

jetSprite.boundingBox = new createjs.Shape(g);

}

function demo(){

stage = new createjs.Stage("theCanvas");

jetSprite = new createjs.Bitmap("jetsprite.png");

jetSprite.boundingBox = null;

actualBounds = null;

// Add a Image load handler, as image.width and image.height are meaningless until

// load is done and DOMContentLoaded doesn't seem to take into account dynamic images

jetSprite.y = 200;

jetSprite.x = 200;

jetSprite.regX = jetSprite.image.width/2;

jetSprite.regY = jetSprite.image.height/2;

updateBoundingBox();

}

//And go...

stage.update();

// onFrame will be called each "tick". Default is 50ms, or 20FPS

}

function onFrame(elapsedTime) {

// Convert from milliseconds to fraction of a second

var delta = elapsedTime /1000;

jetSprite.rotation = jetSprite.rotation + 1;

if(jetSprite.rotation > 360) jetSprite.rotation = 0;

updateBoundingBox();

stage.update();

}

</script>

<body>

<canvas width=400 height=400 id="theCanvas" style="background-color:black"/>

</body>

</html>

See Collision Detection using an axis-aligned bounding box for part one of this recipe.

See Rotating one point around another point for more information on the code used to rotate the bounding box.

26. November 2012

Collisions are one of those things almost every game deal with eventually.  This is going to be a multi-part recipe on collision detection.  This part specifically explains what an axis aligned bounding box actually is, as well as how to detect if two such bounding boxes have collided.

Let's start straight away with some code, then we will discuss the details a bit more later on.  This example simply animates one bounded sprite until it collides with another.  Once an intersection is detected, the positions are reset and the whole things starts all over again.

## Just the Math

Creating the bounding box:

if(createjs.Bitmap.prototype.getBoundingRect == null){

createjs.Bitmap.prototype.getBoundingRect = function(){

return new createjs.Rectangle(

this.x - this.image.width/2,

this.y - this.image.height/2,

this.image.width,

this.image.height);

}

}

Checking if two bounding boxes intersect:

if(createjs.Rectangle.prototype.intersects == null){

createjs.Rectangle.prototype.intersects = function(rect){

return (this.x <= rect.x + rect.width &&

rect.x <= this.x + this.width &&

this.y <= rect.y + rect.height &&

rect.y <= this.y + this.height);

}

}

## Description

The creation of a bounding box is pretty simple.  In this case, our sprite's pivot point is at it's centre, so our top left corner is half the height and width away from our position.  If you are unfamiliar with JavaScript, some of this code might look a bit confusing.  Basically what we are doing is adding a method to the "class" Bitmap named getBoundingRect, but first we want to make sure it hasn't already been added.  We perform the same process when we add the intersects method to the Rectangle "class".  Obviously if you aren't using JavaScript or your language/library of choice includes such functionality already, you can skip that part of the process.

The intersects method works using this simple logic.

Given two rectangles, say R1 and R2, they intersect if:

• The left side of R1 is NOT to the right of the right side of R2
• The left side of R2 is NOT to the right of the right side of R1
• The top of R1 is NOT below the bottom of R2
• The top of R2 is NOT below the bottom of R1

If all of those conditions are true, the two rectangles intersect.  The concept is extremely simple, but making sense of the words isn't always the case.  So here is an image illustrating how it works:

Now earlier on I used the words axis-aligned bounding boxes.  What do I mean by axis-aligned?  Well don't worry, it's a lot less scary than it sounds.  It simply means that the two sides of the bounding box are aligned with both the X and Y axis.  Again, Ill use a graphic to illustrate.

Both the top and bottom bounding boxes are axis aligned, in that the sides of the bounding box are parallel to the X and Y axis.  Using axis aligned bounding boxes make the collision test a great deal faster, but comes at a price.  As you see from the middle image, you cannot simply rotate the bounding box if you rotate the sprite, instead as you can see from the bottom example, you resize the bounding box to encompass the new dimensions of the rotated ( or scaled ) sprite.

How do you do this?  That we will discuss in the next section!

## Complete Code

A word of warning, much of the code below is a) extending the EaselJS to have bounding box support b) to actually (hackishly I admit) render the bounding box on screen.  Do not let the size deter you, the process is actually quite simple and obviously you don't need to draw the bounding box most of the time.

<!DOCTYPE html>

<html>

<script src="http://code.createjs.com/easeljs-0.5.0.min.js"></script>

<script>

var jetSprite,jetSprite2;

var stage;

if(createjs.Rectangle.prototype.intersects == null){

createjs.Rectangle.prototype.intersects = function(rect){

return (this.x <= rect.x + rect.width &&

rect.x <= this.x + this.width &&

this.y <= rect.y + rect.height &&

rect.y <= this.y + this.height);

}

}

if(createjs.Bitmap.prototype.getBoundingRect == null){

createjs.Bitmap.prototype.getBoundingRect = function(){

return new createjs.Rectangle(

this.x - this.image.width/2,

this.y - this.image.height/2,

this.image.width,

this.image.height);

}

}

function demo(){

stage = new createjs.Stage("theCanvas");

jetSprite = new createjs.Bitmap("jetsprite.small.png");

jetSprite.regX = 30; // Half image width

jetSprite.regY = 40; // Half image height

jetSprite.y = 200;

jetSprite.x = 100;

// Add a Image load handler, as image.width and image.height are meaningless until

// load is done and DOMContentLoaded doesn't seem to take into account dynamic images

// Draw the bounding rect and create a new Shape with it

var g = new createjs.Graphics();

g.setStrokeStyle(1);

g.beginStroke(createjs.Graphics.getRGB(255,255,255));

var bb = jetSprite.getBoundingRect();

g.drawRect(bb.x,bb.y,bb.width,bb.height);

jetSprite.boundingBox = new createjs.Shape(g);

}

jetSprite2 = new createjs.Bitmap("jetsprite.small.png");

jetSprite2.regX = 30; // Half image width

jetSprite2.regY = 40; // Half image height

jetSprite2.y = 200;

jetSprite2.x = 300;

var g = new createjs.Graphics();

g.setStrokeStyle(1);

g.beginStroke(createjs.Graphics.getRGB(255,255,255));

var bb = jetSprite2.getBoundingRect();

g.drawRect(bb.x,bb.y,bb.width,bb.height);

jetSprite2.boundingBox = new createjs.Shape(g);

}

//And go...

stage.update();

// onFrame will be called each "tick". Default is 50ms, or 20FPS

}

function onFrame(elapsedTime) {

// Convert from milliseconds to fraction of a second

var delta = elapsedTime /1000;

// Move sprite and bounding box shape to the right

jetSprite.boundingBox.x++;

jetSprite.x++;

if(jetSprite.getBoundingRect().intersects(jetSprite2.getBoundingRect())){

// If a collision occurs, reset position and start all over again

jetSprite.x = 100;

jetSprite.boundingBox.x = 0;

}

stage.update();

}

</script>

<body>

<canvaswidth=400 height=400 id="theCanvas" style="background-color:black"/>

</body>

</html>

Part two looks at how you handle rotating a bounding box.

24. November 2012

Looking for the perfect gift for the geek who has everything?  Well, Learn Lua for iOS Game Development is coming out just before Christmas , plus it’s on sale for 25 bucks.  ( What’s with pre-release books already being on sale??? ).

Alright, hundreds of computer texts are released every year, dozens of them about game programming… so why the interest in this particular book?  You may remember a while back I put together  Battle of the Lua Game Engines: Corona vs. Gideros vs. Love vs. Moai and I actually enjoyed working with all three technologies.  Well this book covers using all three SDKs as well as Codea which I hadn’t heard of until this point.

Obviously the book isn’t going to cover any of those technologies in detail, each one could probably merit it’s own book.  It should however teach you the required bits of Lua and expose you to a little more detail than my comparison.  Lua is a wonderful little language, one you should certainly look into if you haven’t already.  This book may just be the right introduction, it releases on December 17th.

Part 1 – Lua

1. Introduction to Lua
2. System Libraries
3. File IO
4. Math
5. Strings
7. Tips and Tricks

Part 2 - Frameworks

8. CoronaSDK
9. Gideros Studio
10. MoaiSDK
11. Löve
12. Codea

Part 3 - Libraries
13. Libraries
14. 3rd Party Apps

Most APress books end up on Safari Books Online, so expect a review shortly after this book is released.  It does strike me a bit odd that they would limit the title to iOS games, when Corona, Gideros and Moai all support Android as well ( without change in most cases ) and I don’t believe Love supports iOS at all…?  So if you are interested in Android development, don’t let the title put you off.

24. November 2012

It is quite common to want to rotate one point relative to another the location of another point.  This math recipe looks at exactly this process.

## Just the math

angle = (angle ) * (Math.PI/180); // Convert to radians

var rotatedX = Math.cos(angle) * (point.x - center.x) - Math.sin(angle) * (point.y-center.y) + center.x;

var rotatedY = Math.sin(angle) * (point.x - center.x) + Math.cos(angle) * (point.y - center.y) + center.y;

return new createjs.Point(rotatedX,rotatedY);

## Description

The angle conversion is entirely dependant on your math libraries.  In the case of JavaScript's Math library ( and the standard C++ libraries ), cos and sign expect the angles to be expressed in radians.  As you can see, the conversion formula is quit simple.

As to the math, the rotated location of the X value is found by taking the cos of the angle to rotate by, multiplied by the distance between the X value of the point you want to rotate and the point to rotate around minus the sin of the angle multiplied by the distance between the points, then finally add the x location of the point.  The calculation for rotating in the Y direction is basically identical, except the sin and cos calculations are swapped and you subtract instead of adding.

One thing to keep in mind here is the rotation is relative to the current position not the total rotation.  For example, if you are currently at 90 degrees and want to rotate to 135 degrees, you would use an angle of 45, not 135.

## Complete code

<!DOCTYPE html>

<html>

<script src="http://code.createjs.com/easeljs-0.5.0.min.js"></script>

<script>

var ball1,ball2;

var stage;

function rotatePoint(point, center, angle){

angle = (angle ) * (Math.PI/180); // Convert to radians

var rotatedX = Math.cos(angle) * (point.x - center.x) - Math.sin(angle) * (point.y-center.y) + center.x;

var rotatedY = Math.sin(angle) * (point.x - center.x) + Math.cos(angle) * (point.y - center.y) + center.y;

return new createjs.Point(rotatedX,rotatedY);

}

function demo(){

stage = new createjs.Stage("theCanvas");

var g = new createjs.Graphics();

g.setStrokeStyle(1);

g.beginFill(createjs.Graphics.getRGB(0,0,255));

g.drawCircle(0,0,30);

ball1 = new createjs.Shape(g);

ball2 = new createjs.Shape(g);

ball1.x = stage.canvas.width/2;

ball1.y = stage.canvas.height/2;

ball2.x = stage.canvas.width/2;

ball2.y = 30;

//And go...

stage.update();

// onFrame will be called each "tick". Default is 50ms, or 20FPS

}

function onFrame(elapsedTime) {

// Convert from milliseconds to fraction of a second

var delta = elapsedTime /1000;

// Rotate by 90 degrees per second, or 1 full rotation per 4 seconds.

var rotateBy = 90 * delta;

// Current position of ball2

var ballPosition = new createjs.Point(ball2.x,ball2.y);

// Updated position rotated by... um... rotateBy value

var rotatedPosition = rotatePoint(ballPosition,

new createjs.Point(ball1.x,ball1.y),

rotateBy);

// Update ball's position to the newly rotated coordinates

ball2.x = rotatedPosition.x;

ball2.y = rotatedPosition.y;

stage.update();

}

</script>

<body>

<canvaswidth=400height=400id="theCanvas"style="background-color:black"/>

</body>

</html>

22. November 2012

This recipe takes a look at the concept of velocity.  At first glance you might think velocity… oh, that’s speed.  But that isn't quite all of it.

Velocity is simply put, something with speed and a direction. You can use velocity for hundreds of game related tasks, firing a bullet, flying a spaceship, etc.  As part of the recipe, we will also look at normalizing update speed using elapsed time, so the code runs the same on various machines.

Let's start with a very simple form, velocity along a single axis.

## Just the math

var delta = elapsedTime /1000;

jetSprite.y = jetSprite.y - (speed * delta);

if(jetSprite.y < -(jetSprite.image.height/2))

jetSprite.y = stage.canvas.height;

## Description

One of the problems with dealing with speed is that different computers and devices run at different speeds.  You can't simply update a sprite's location in a loop, because that loop will run at a different speed on every machine.  Therefore we need a value to normalize the movement by.  In the case of EaselJS, our event loop is passed a value elapsedTime, containing the number of milliseconds that have elapsed since it was last called.  What we want to do is convert this value from milliseconds to fractions of a second, which we do by dividing it by 1000.

Next we update our sprites movement in the y direction by subtracting ( since Y decreases as it goes towards the top of the canvas ) speed * delta from the current Y value.  Our speed is a per second value, so a speed of 50 means we want to move 50 pixels over the course of a second.  By multiplying the speed against the time the previous frame took to complete as a fraction of a second, we essentially increment by little pieces that over the course of a second should add up to our total speed.

Let's take a look with real world numbers.  Let's say that last frame took 100ms to complete, or 1/10th of a second.  100/1000 = 0.1.  Now we multiply our speed of 50 by 0.1 and see that we should update by 5 pixels this frame.  Assuming the game continues to run about 100ms per frame, that means after 10 frames, a second will have elapsed and we will have moved the desired amount.  The nice part is, the movement is now tied to actual time elapsed instead of processing speed.

The rest is simply a matter of checking to see if our game sprite went off the top of the screen and if it has, we send it back to the starting position.

### Velocity along a single axis

Controls:

Click top half the canvas to increase speed
Click lower half to decrease the speed
Arrow up/ Arrow down to increase/decrease speed

## The Complete Code

<!DOCTYPE html>

<html>

<script src="http://code.createjs.com/easeljs-0.5.0.min.js"></script>

<script>

var jetSprite;

var stage;

// Speed is total pixels moved in a second

var speed = 50;

document.onkeydown = function(e){

switch(e.keyCode)

{

case 38: // up arrow

speed += 10;

break;

case 40: // down arrow

speed -= 10;

break;

}

}

function demo(){

stage = new createjs.Stage("theCanvas");

// When the user clicks mouse, if the on the top half, increase speed

// If clicked on the bottom half, reduce speed.  Yes, it will go in reverse eventually

stage.onMouseDown = function(e){

if(e.stageY < 200)

speed += 50;

else

speed -= 50;

}

// Create and configure our jet sprite. regX/Y set the pivot point, we center it

jetSprite = new createjs.Bitmap("jetsprite.png");

jetSprite.regX =91; //Hardcode image widths because HTML sucks and fires onLoad

jetSprite.x = stage.canvas.width/2;

jetSprite.y = stage.canvas.height;

//And go...

stage.update();

// onFrame will be called each "tick". Default is 50ms, or 20FPS

}

function onFrame(elapsedTime) {

// Convert from milliseconds to fraction of a second

var delta = elapsedTime /1000;

jetSprite.y = jetSprite.y - (speed * delta);

if(jetSprite.y < -(jetSprite.image.height/2))

jetSprite.y = stage.canvas.height;

stage.update();

}

</script>

<body>

<canvas width=400 height=400 id="theCanvas"style="background-color:black"/>

</body>

</html>

So velocity along an axis is remarkably easy, but not entirely useful if you want to travel in different directions.  You can of course move along both axis independently, but this quickly becomes annoying, especially when you want to deal with multiple sprites positions relative to each other.  A much better way to express the direction component of velocity than using an axis is to use an angle.

## Just the Math

var delta = elapsedTime /1000;

var velocityX = Math.cos((angleAdjustment + angle) * Math.PI / 180) * (speed * delta);

var velocityY = Math.sin((angleAdjustment + angle) * Math.PI / 180) * (speed * delta);

jetSprite.rotation = angle;

jetSprite.x = jetSprite.x + velocityX;

jetSprite.y = jetSprite.y + velocityY;

if(jetSprite.y < -(jetSprite.image.height/2))

jetSprite.y = stage.canvas.height;

if(jetSprite.x > stage.canvas.width+(jetSprite.image.width/2) ||

jetSprite.x < 0-(jetSprite.image.width/2)){

jetSprite.y = stage.canvas.height;

jetSprite.x = stage.canvas.width/2;

}

## Description

Logic in this example is very similar to the linear velocity example.  Of course, first we need to determine what how many pixels to move by in the X and Y address.  To figure this out, we solve X and Y separately.

The X component is found by taking the Cos of the angle in radians.  We convert a value to radians by multiplying it by pi/180.  The angle adjustment is to account for the fact our sprite was drawn as though 0 is straight up, while the math treats 0 as being to the right.  At this point we have the direction of the x coordinate to travel in our given angle, we now need to figure out the amount to travel in that direction.  This is determined by multiplying the speed by the delta.  Remember the delta is the amount of time as a fraction of a second that our frame takes to run, so if our game is running at 100ms a frame, it's value is .10.  So for the jet to travel at a total of 50 pixels per second, its going to travel 5 pixels this frame.

To solve the Y component, its virtually an identical process, but this time we figure out the y direction by taking the Sin of the angle instead.  We then update our X and Y values by the newly calculated velocity values.

Now in addition to being able to leave the top of the screen, it is also possible for our sprite to leave the right or left side of the screen, so we check to make sure the sprite hasn't exited in those directions either.  If it has, we send it back to where it started.

### Angled Velocity

In addition to the above controls you can now:
Press left and right arrows to turn

** Be sure to click to focus the canvas for input may not be received.

## The Complete Code

<!DOCTYPE html>

<html>

<script src="http://code.createjs.com/easeljs-0.5.0.min.js"></script>

<script>

var jetSprite;

var stage;

// Speed is total pixels moved in a second

var speed = 50;

// angle to travel, with 0 being straight up the Y-axis

var angle = 45;

// Angle adjustment to make 0 up to match how our sprite was drawn.

document.onkeydown = function(e){

switch(e.keyCode)

{

case 37: // left arrow

angle-=5;

break;

case 38: // up arrow

speed += 10;

break;

case 39: // right arrow

angle+=5;

break;

case 40: // down arrow

speed -= 10;

break;

}

}

function demo(){

stage = new createjs.Stage("theCanvas");

// When the user clicks mouse, if the on the top half, increase speed

// If clicked on the bottom half, reduce speed.  Yes, it will go in reverse eventually

stage.onMouseDown = function(e){

if(e.stageY < 200)

speed += 50;

else

speed -= 50;

}

// Create and configure our jet sprite. regX/Y set the pivot point, we center it

jetSprite = new createjs.Bitmap("jetsprite.png");

jetSprite.regX =91; //Hardcode image widths because HTML sucks and fires onLoad

jetSprite.x = stage.canvas.width/2;

jetSprite.y = stage.canvas.height;

//And go...

stage.update();

// onFrame will be called each "tick". Default is 50ms, or 20FPS

}

function onFrame(elapsedTime) {

// Convert from milliseconds to fraction of a second

var delta = elapsedTime /1000;

var velocityX = Math.cos((angleAdjustment + angle) * Math.PI / 180) * (speed * delta);

var velocityY = Math.sin((angleAdjustment + angle) * Math.PI / 180) * (speed * delta);

jetSprite.rotation = angle;

jetSprite.x = jetSprite.x + velocityX;

jetSprite.y = jetSprite.y + velocityY;

if(jetSprite.y < -(jetSprite.image.height/2))

jetSprite.y = stage.canvas.height;

if(jetSprite.x > stage.canvas.width+(jetSprite.image.width/2) ||

jetSprite.x < 0-(jetSprite.image.width/2)){

jetSprite.y = stage.canvas.height;

jetSprite.x = stage.canvas.width/2;

}

stage.update();

}

</script>

<body>

<canvas width=400 height=400 id="theCanvas"style="background-color:black"/>

</body>

</html>

To actually understand WHY you use the cos to solve X and sin to solve Y, check out the following.

SOHCAHTOA.  It's a simple mnemonic device, one I learned almost 20 years ago and I still remember to this day, it is how you solve each angle using the different sides of a triangle:

Sin = Opposite over the Hypotenuse   Cos = Adjacent over the Hypotenuse  Tan = Opposite over Adjacent == SOHCAHTOA

http://www.mathwords.com/s/sohcahtoa.htm

Fundamentally this is all trigonometry in action, you can learn a hell of a lot at the Kahn Academy

#### Month List

Unreal Engine 4.10 Released

# Home > GameDev News >

11. November 2015

Unreal Engine 4.10 was just released today.

Welcome to Unreal Engine 4.10! This release is packed with a number of great new features, but our main focus has been to increase engine stability and fix outstanding issues. Hundreds of reported bugs have been bashed, many new quality of life improvements were added, and virtually every supported platform has received updates. Unreal Engine is designed for incredible VR experiences, and every release it gets better. Epic's "Bullet Train" VR demo is powered by new features in this version, with new rendering optimizations designed specifically for head mounted displays. Mobile gets a nice upgrade in this release too, with new scalability features and support for refraction. Last but not least, great news for programmers: You can now use Visual Studio 2015 for development on Windows. And on Mac, we've revamped our Xcode projects to allow you to work more efficiently. We've also refreshed our target platforms with support for latest SDKs.

New Major Features Include:

• Refraction Effects for Mobile
• Optimized VR Rendering
• Visual Studio 2015 Support
• Mobile Material Quality Settings
• Landscape Mirror Tool
• Low Latency VR Motion Controllers
• Automatic Blueprint Node Arrangement
• Web Browser UI on Android
• Amazon Fire Game Controller and Fire TV Remote Support
• NVidia Shield Controller and Portable Support
• XCode Project Overhaul
• Mobile Provisioning Selector
• Misc bug fixes

Click here for full details of this release or fire up the Epic Launcher to update.