I have added a pair of books, and replaced a duplicate entry with a different book on the Unity 3D Book Round-up. Another two Unity 4 books have been announced with release dates in March of 2013.

The first newish entry is Essential 3D Game Programming which replaced the duplicate entry of Unity 3.x Scripting on the list ( thanks for the heads up in comments! ). This book has been on my radar for some time but had minimal information, now there is a bit more available. That said, something about this book is really setting off my warning alarms… starting with the fact the artist on the cover graphic doesn’t match the author of the book. Caveat emptor and all of that!

The other two are from established publishers, so no concern in that regard, both are upcoming books on Unity 4.

This math recipe is a bit different. It is in direct response to a question I received about how to give your sprite the ability to shoot. That is exactly what we will be doing in this recipe. There is no actual new math, it actually is just applying our prior recipes on Velocity and our recipe on Rotating to face a point. As those prior recipes both explained how they work, this particular entry is going to be light on description.

Just the Math

// calculate the speed relative to the mouse click distance

bullet.speed *= (bullet.y - bullet.targetY)/100;

// now calculate the angle between the bullet and mouse click

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

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

bullet.x += velocityX;

bullet.y += velocityY;

}

Shooting

Controls:

Click anywhere on screen to shoot. The location determines the angle of the shot, while distance from the jet determines the speed

Description

The actual description behind the mathematics are available at the two linked tutorials at the beginning and end of this recipe. This is just a quick explanation of exactly what this application does. We are creating an Array of bullet objects, a class we define ourselves inline. The bullet simply contains its location (x,y), the location it is targeting (the user click position, targetX and targetY), the angle, speed ( pixels per second ) and finally a graphic that we will create in a moment. We set the users speed using a multiple relative to the click distance away from the jet sprite. For example, if the user clicks at 40 on the Y axis, the bullet be moving at 50 * (340-40)/100 == 50 * 3 == 150 pixels / second. For the record, don't click at 340 in the Y axis or your bullet won't go anywhere! :)

Now that we have the speed, we calculate the initial angle between the jet and the location the user clicked. Next we register an on tick() method that will be called each frame to update the bullet. We simply check to see if the bullet is completely off screen in any direction, and if it is, we remove it from our array. Otherwise we apply our velocity along our given angle, and update the X and Y values accordingly. The remains of the tick function simply draw the newly updated bullet.

Whoops. I generally keep on top of new Blender releases, but this one slipped past my radar. So, this new is a bit dated.

Anyways, Blender 2.65 was released a couple days ago. This post takes a look at what's in this release of interest for game developers. At first glance, not too much. At second glance, quite a bit actually. At third glance, you are glancing too much and it's time to simply look!

First off, stability. Over 200 items were knocked off the bug list. More stability is always nice.

Stuff not really all that gamedev related

Fire simulation and smoke flow force field added

Open Shading language support added to Cycles renderer

anisotrophic shading node added

anti-aliased viewport drawing

Game dev related additions

decimator modifier rewritten and now preserves UV

new smooth modifier that can preserve edges and volumes

triangulate modifier which can be used for creating baked normal maps

bevel now includes round and no longer sucks

a symmetrize tool was added

a tool for transferring vertex weights between objects

Bevel

There is not a ton to the bevel controls:

Basically you have offset and segment.

Offset is the amount to bevel by

Segments is the number of iterations or edges to use when composing the bevel

More impressive are the results, before bevelling multiple edges was… ugly. Now:

Symmetrize

So how exactly does Symmetrize work in Blender? Remarkably well actually… Check this out.

Before:

After:

Too damned cool. So, basically it's like a mirror modifier… that you can apply after the fact. I like. Options are pretty simple over all.

Basically you just pick the axis and direction you want the symmetry applied along. Again, very cool.

Torque2D is a 2D version of the Torque game engine that also includes WYSIWYG level editing tools and it’s own scripting language, TorqueScript.

As you can see from the picture to the right, iTorque2D, the iOS version of Torque2D, is being folded in to this release. Torque2DMIT will be released early next year. However there is one gotcha with that release date:

In order to work in an open source environment as soon as possible, we made a decision to publish our initial version of Torque 2D MIT without the editors; in other words, the initial version will be an API only engine with tool development to follow thereafter.

So basically that WYSIWIG level editor I just mentioned? Well, it wont be ready day one.

As to the license, the MIT license is one of the least restrictive open source licenses available. Basically you can do what you want with it.

In our prior tutorial we looked at using an axis aligned bounding box to perform collision testing. One big downside was the handling of sprite rotation. Today, we will look at using a circle instead of a rectangle for our collision detection. The circle has the obvious advantage of being the same size no matter how much you rotate it. It is also extremely fast to calculate and test for collisions. Although as you can see from the application to the right, it isn't extremely accurate.

function circlesIntersect(c1X,c1Y,c1Radius, c2X, c2Y, c2Radius){

var distanceX = c2X - c1X;

var distanceY = c2Y - c1Y;

var magnitude =Math.sqrt(distanceX * distanceX + distanceY * distanceY);

return magnitude < c1Radius + c2Radius;

}

Description

As mentioned earlier, a bounding circle removes the complexity of dealing with rotation. This is a bit of a double edge sword though. An axis aligned bounding box can be tighter and more accurate than a bounding circle, but as it rotates it quickly becomes less so. The following application illustrates the same shape bounded by both a bounding box and a bounding circle. As you can see, at some points the bounding box is a great deal more accurate, but as it rotates, it becomes a great deal less accurate:

The calculations for the bounding circle are however a great deal easier to perform. Let's take a look at them now.

First we start off by calculating the radius of our sprite's image. This is a matter of calculating the length of furthest point from the centre, giving us the smallest possible radius that encompasses our sprite. The process is rather straight forward and is calculated using pythagorean theorem again. We are essentially calculating the magnitude (or distance) from the centre of our sprite to the corner, we do this by forming a right angle triangle.

For a bit of a refresher on pythagorean theorem (which is used A LOT), consider this diagram I stole:

a is the X coordinate of our corner, b is the Y coordinate of our corner, therefore the distance or magnitude ( the second is the correct term mathematically ) between those two points is c, which you can calculate by taking the square root of the square of a plus the square of b. Or using our actual variable names, distance = square root( x * x + y * y). The resulting value of this equation is the distance between x and y. So, how did we come up with the values for x and y? That part was simple, since our pivot is at the centre of our sprite, x is simply half the width of the image, while y is half the height.

If that just confused the hell out of you, the following diagram might help a bit. It illustrates how pythagorean theorem is being applied to our actual jet sprite to calculate the distance to the corner.

So, now we have the distance to the corner, which we can now use it as our circle's radius. Now we need to figure out how to determine if an intersection occurs.

var distanceX = c2X - c1X;

var distanceY = c2Y - c1Y;

var magnitude =Math.sqrt(distanceX * distanceX + distanceY * distanceY);

return magnitude < c1Radius + c2Radius;

This again is a simple and quick equation. Actually, its the exact same formula again, this time though, we calculate x and y by measuring the magnitude ( distance ) between each of our circles centre points. Once we have calculate the magnitude between the two circles, we simply check to see if that distance value is less than the total radius of both circles. If the magnitude is less than the radius of both circles combined, they intersect, otherwise they don't.

One thing you should be aware of ( but not too concerned with initially ) is the square root operation is an expensive one and generally something you want to avoid. A square root is many times slower to perform than a multiplication or division. In this situation, it is a very easy to eliminate, you simply square both sides, like so:

function circlesIntersect(c1X,c1Y,c1Radius, c2X, c2Y, c2Radius){

var distanceX = c2X - c1X;

var distanceY = c2Y - c1Y;

var magnitudeSquared = distanceX * distanceX + distanceY * distanceY;

If you are still struggling with the math though, these kinds of optimizations can happen later if they are needed at all. It's often easier to optimize after the fact anyways, so don't worry too much about being fast quite yet. It's far too easy to get caught up optimizing prematurely.

If you are still struggling with the use of triangles, you really need to wrap your head around this concept. This Youtube video ( with horrible audio ), gives a good example of pythagorean theorem in action: