Rocket Science: Acceleration

Building the Game

The Black Hole game is based on most of the code we’ve developed in each of the previous hours of the book, and there really is no single previous hour that gets more credit than others since each hour has built upon the hours that came before. Let’s dig into the game by going over the major sections and get something up and running fairly quickly. Then we’ll continue our work on the game into the following hour, where it will get some polish and fine-tuning of the fun factor.

This game is based on the theories of Stephen Hawking. If you’re interested in black hole physics, be sure to read his popular books for more information! The Universe in a Nutshell is one of my favorites.

Gravity Well Regions

There are three regions around the black hole that affect game objects. The outer gravity well affects objects passing by, drawing them toward the black hole with relatively light force. This force is increased by an equal amount in the next two inner regions, with each region generating an equivalent gravity “tug” on objects. But the cumulative effect of all three gravity wells in the inner region of the black hole will cause objects to become hopelessly trapped.

The third and innermost region might be thought of as the event horizon, that region of a black hole where things disappear into the void, never to be seen again. It is this region that mathematics cannot penetrate, so while it appears that gravity increases toward infinity in the middle of a black hole, the truth of the matter is, there may be nothing at the very center of a black hole! The gravity might be so powerful that matter just rotates around the center of mass and no matter actually exists at that center point, which would be quite small at the center of a black hole. Then again, there might be a superdense material like a neutron star. It is at this point that physics just cannot explain it, because we don’t actually have a black hole nearby to study. Even if we did, it’s not like a spacecraft could be sent to investigate!

Figure 23.1 shows an illustration of the gravity well of the black hole in the game. The outer gravity well is quite large and draws most game objects inward at a steady “weight” or “pull,” with some help from the inner core of the black hole, also exerting force. The inner gravity well is the region where energy can be mined by the “Hawking” satellites. At any rate, that’s one of the enjoyable aspects of this game, pondering the infinite possibilities!

The code to simulate the gravitational pull of the black hole is coming up. Now let’s just take a look again at some of our earlier helper methods used in this game. All the collision code in the Black Hole game is based around this RadialCollision() method and its overloaded friend:

[code]
public bool RadialCollision(Sprite A, Sprite B)
{
float radius1 = A.image.Width / 2;
float radius2 = B.image.Width / 2;
return RadialCollision(A.position, B.position,
radius1, radius2);
}
public bool RadialCollision(Vector2 A, Vector2 B, float radius1,
float radius2)
{
float dist = Distance(A, B);
return (dist < radius1 + radius2);
}
public float Distance(Vector2 A, Vector2 B)
{
double diffX = A.X – B.X;
double diffY = A.Y – B.Y;
double dist = Math.Sqrt(Math.Pow(diffX, 2) +
Math.Pow(diffY, 2));
return (float)dist;
}
[/code]

The gravity well of the black hole covers most of the Windows Phone screen.
FIGURE 23.1 The gravity well of the black hole covers most of the Windows Phone screen.

Enhancing MassiveObject

Some minor changes need to be made to MassiveObject to support some new features needed in the game that were not in the example in the preceding hour. Following is what the class now looks like, with the new variables and updated constructor:

[code]
class MassiveObject : Sprite
{
public string name;
public bool captured;
public double mass;
public Vector2 acceleration;
public float radius, angle;
public int lifetime, startTime;
public MassiveObject(ContentManager content,
SpriteBatch spriteBatch)
: base(content, spriteBatch)
{
name = “object”;
mass = 1.0f;
acceleration = Vector2.Zero;
radius = 50.0f;
angle = 0.0f;
captured = false;
lifetime = 0;
startTime = 0;
}
// . . . note: some code omitted here
}
[/code]

Game1.cs

There are no changes to be made to Game1.cs, because the main source code file is now PlayingModule.cs. In the final hour coming up, we will again use the game state modules for a more polished gameplay experience.

Gameplay Source Code

The most significant code of the game is found in PlayingModule.cs. If you skipped ahead, you may have missed Hour 21, “Finite State Gameplay,” which explained how to use states to improve a game in many ways. The PlayingModule class is the primary gameplay class where the bulk of the game code will be found. The first lines of code in the class declare all the variables, including the key objects variable, defined as a List of MassiveObjects. We also see the black hole, the super core gravity well, and the player’s ship here, among other things. Figure 23.2 shows the game as it is just getting started, and Listing 23.1 shows the source code for the class.

The Black Hole game soon after startup.
FIGURE 23.2 The Black Hole game soon after startup.

LISTING 23.1 Source Code for the PlayingModule Class

[code]
public class PlayingModule : IGameModule
{
Game1 game;
SpriteFont font;
Random rand;
Sprite background;
MassiveObject blackHole;
MassiveObject superCore;
MassiveObject ship;
float energy = 100.0f;
int startTime, lifetime;
List<MassiveObject> objects;
public PlayingModule(Game1 game)
{
this.game = game;
rand = new Random();
startTime = 0;
lifetime = 4000;
}
public void LoadContent(ContentManager content)
{
font = content.Load<SpriteFont>(“WascoSans”);
background = new Sprite(game.Content, game.spriteBatch);
background.Load(“space”);
background.origin = Vector2.Zero;
blackHole = new MassiveObject(game.Content, game.spriteBatch);
blackHole.Load(“blackhole”);
blackHole.position = new Vector2(500, 240);
blackHole.scale = 2.0f;
blackHole.mass = 40;
blackHole.color = new Color(255, 100, 100, 200);
blackHole.velocityAngular = 0.1f;
superCore = new MassiveObject(game.Content, game.spriteBatch);
superCore.image = blackHole.image;
superCore.position = new Vector2(blackHole.position.X,
blackHole.position.Y);
superCore.scale = blackHole.scale * 0.4f;
superCore.mass = 60;
superCore.color = new Color(200, 100, 100, 180);
superCore.velocityAngular = 4.0f;
superCore.origin = new Vector2(64, 64);
//create objects list
objects = new List<MassiveObject>();
//create player ship
ship = new MassiveObject(game.Content, game.spriteBatch);
ship.Load(“ship”);
ship.position = new Vector2(200, 240);
ship.mass = 100f;
ship.scale = 0.2f;
ship.rotation = MathHelper.ToRadians(90);
}
[/code]

The Update() method is a bit monolithic at this stage, but the code is easier to follow this way than if it had been divided into several smaller methods. I usually divide a method like this when it grows too large to be easily maintained, but since the gameplay code in PlayingModule is only 300 lines long, there isn’t too much to consume here at once. There’s a lot going on here in Update(), but we won’t break up the code listing and break the flow of the code, which can be distracting.

First of all, the blackHole and superCore objects are updated. Then we go into a foreach loop that processes all the MassiveObject objects in the objects list (there’s a tongue twister!). Each object is updated, rotated, and animated. Within the foreach is where the bulk of the code is found for the game.

When one of the satellites grows to a certain size (from collecting energy), that triggers a subset of code here in the foreach block where the player’s ship actually attracts the satellite toward it, using the same code used to simulate the gravitational pull of the black hole on the same objects. The slight gravity “tug” causes the satellites to veer toward the ship and increase the chances of their being caught by it, without making it too easy for the player. After all, the ship doesn’t move yet, it only rotates in place!

Next up is the code that tugs objects inward toward the black hole, if they are in range. Figure 23.3 shows another screenshot of the game, this time with a lot of satellites in orbit. Note the addition of animated asteroids in the scene. The asteroids serve no purpose, but just fill in some detail to make the scene look more interesting. A new asteroid is added every few seconds at a random direction and velocity, and over time they do tend to add up to quite a large mass of rotation around the black hole, which only increases the fun factor. Now, there is also potential use for these asteroid sprites beyond just “for looks.”

A large number of objects are orbiting the black hole, and they tend to fall in quite frequently.
FIGURE 23.3 A large number of objects are orbiting the black hole, and they tend to fall in quite frequently.

Listing 23.2 contains the source code for the Update() method.

It’s quite a challenge to come up with mass values for the black hole, the super core, and each of the objects that not only result in a realistic simulation of gravity’s effect on objects of mass but also make the game fun. Fun is more important than realism, but we want to have a little of both if possible. But when a trade-off is required, always go with that which helps the game to sell: the fun factor.

LISTING 23.2 Source Code for the Update() Method

[code]
public void Update(TouchLocation touch, GameTime gameTime)
{
int time = gameTime.ElapsedGameTime.Milliseconds;
blackHole.Update(gameTime);
blackHole.Rotate();
superCore.Update(gameTime);
superCore.Rotate();
foreach (MassiveObject obj in objects)
{
if (!obj.alive) continue;
obj.Update(gameTime);
obj.Rotate();
obj.Animate(time); //frame animation
obj.Animate(); //mod animation
//allow ship to collect energy satellites for bonus energy
if (obj.scale > 3.0f && obj.name == “satellite”)
{
obj.Attract(ship);
obj.color = Color.White;
if (game.RadialCollision(obj.position, ship.position,
obj.size.X, 40))
{
obj.alive = false;
energy += obj.scale;
}
}
if (!obj.captured)
{
//attract when object is near the black hole
if (game.RadialCollision(obj.position,
blackHole.position, 10, 500))
{
obj.Attract(blackHole);
obj.Attract(superCore);
//is object touching the outer edges of the black hole?
if (game.RadialCollision(obj.position,
blackHole.position, 10, 120))
{
obj.color = Color.Red;
if (obj.name == “satellite”)
{
obj.scale += 0.1f;
energy += 0.5f;
}
obj.Attract(blackHole); //outer black hole
obj.Attract(superCore); //inner black hole
//oh no, object is caught by the black hole!
if (game.RadialCollision(obj.position,
superCore.position, 16, 60))
{
obj.captured = true;
obj.lifetime = 3000;
obj.startTime = (int)
gameTime.TotalGameTime.TotalMilliseconds;
OrbitalMovement anim1 = new OrbitalMovement(
blackHole.position, 10 + rand.Next(40),
obj.rotation, -0.8f);
obj.animations.Add(anim1);
}
}
else
{
obj.color = Color.White;
}
}
}
//when captured, time runs out
if (obj.lifetime > 0)
{
if (obj.startTime + obj.lifetime <
gameTime.TotalGameTime.TotalMilliseconds)
obj.alive = false;
}
//see if object has gone too far out of bounds
if (obj.position.X < -200 || obj.position.X > 1000 ||
obj.position.Y < -200 || obj.position.Y > 700)
obj.alive = false;
}
//update ship
ship.Update(gameTime);
ship.Rotate();
ship.Animate(time);
if (energy <= 0)
{
ship.Attract(blackHole);
//object is caught by the black hole
if (game.RadialCollision(ship.position, superCore.position,
64, 40))
{
ship.captured = true;
ship.lifetime = 3000;
ship.startTime = (int)
gameTime.TotalGameTime.TotalMilliseconds;
OrbitalMovement anim1 = new OrbitalMovement(
blackHole.position, 10 + rand.Next(40),
ship.rotation, -0.8f);
ship.animations.Add(anim1);
}
//done being squished?
if (ship.lifetime > 0)
{
if (ship.startTime + ship.lifetime <
gameTime.TotalGameTime.TotalMilliseconds)
ship.alive = false;
}
}
else
{
energy -= 0.05f;
ship.velocityLinear.X = 0.0f;
}
//check user input
if (touch.State == TouchLocationState.Released)
{
if (touch.Position.X > ship.position.X)
{
CreateSatellite();
}
else
{
if (touch.Position.Y < 200)
ship.velocityAngular = -0.01f;
else if (touch.Position.Y > 280)
ship.velocityAngular = 0.01f;
else
ship.velocityAngular = 0;
}
}
//time to add another random asteroid?
if (startTime + lifetime < gameTime.TotalGameTime.
TotalMilliseconds)
{
startTime = (int)gameTime.TotalGameTime.TotalMilliseconds;
CreateAsteroid();
}
//clean out the dead objects
foreach (MassiveObject obj in objects)
{
if (obj.alive == false)
{
objects.Remove(obj);
break;
}
}
}
[/code]

The Draw() method is next, with its source code in Listing 23.3. This is a rather small method because the gameplay objects are managed.

LISTING 23.3 Source Code for the Draw() Method

[code]
public void Draw(GameTime gameTime)
{
background.Draw();
superCore.Draw();
blackHole.Draw();
ship.Draw();
foreach (MassiveObject obj in objects)
{
if (obj.alive)
{
obj.Draw();
}
}
string text = “Ship rot “ + MathHelper.ToDegrees(
ship.rotation).ToString();
game.spriteBatch.DrawString(font, text, new Vector2(0, 0),
Color.White);
text = “Objects “ + objects.Count.ToString();
game.spriteBatch.DrawString(font, text, new Vector2(0, 20),
Color.White);
text = “Energy “ + energy.ToString(“N0”);
game.spriteBatch.DrawString(font, text, new Vector2(650, 0),
Color.White);
}
[/code]

Finally, we have two helper methods, CreateAsteroid() and CreateSatellite(), that generate a random asteroid and random satellite, respectively. These two methods, shown in Listing 23.4, are quite important to the gameplay because they determine whether the objects will actually move reasonably on the screen. I say reasonably rather than realistically because, again, we don’t want absolute realism; we want some realism with gobs of fun gameplay. The asteroids aren’t important to the gameplay, because they are just for looks, but we do want them to start off in such a way that they end up rotating around the black hole. Likewise, the satellite must be launched in such a way that it moves reasonably well. At this stage, our satellites move at a constant speed, but in the next (and final) hour, we will add GUI controls that allow the player to adjust the power.

LISTING 23.4 Source Code for the CreateAsteroid() and CreateSatellite() Methods

[code]
public void CreateAsteroid()
{
MassiveObject obj = new MassiveObject(game.Content, game.spriteBatch);
obj.Load(“asteroid”);
obj.columns = 8;
obj.totalFrames = 64;
obj.scale = 0.1f + (float)rand.NextDouble();
obj.size = new Vector2(60, 60);
obj.radius = 80;
//randomly place at top or bottom of screen
obj.position = new Vector2(rand.Next(100, 800), -100);
obj.velocityLinear = new Vector2(4.0f, (float)(rand.NextDouble() *
6.0));
if (rand.Next(2) == 1)
{
obj.position.Y = -obj.position.Y;
obj.velocityLinear.Y = -obj.velocityLinear.Y;
}
obj.scale = 0.4f;
obj.mass = 1;
obj.velocityAngular = 0.001f;
obj.lifetime = 0;
obj.name = “asteroid”;
objects.Add(obj);
}
public void CreateSatellite()
{
MassiveObject obj;
obj = new MassiveObject(game.Content, game.spriteBatch);
obj.Load(“plasma32”);
obj.position = ship.position;
obj.mass = 1;
obj.scale = 0.5f;
obj.lifetime = 0;
obj.name = “satellite”;
//calculate velocity based on ship’s angle
float accel = 4.0f;
float angle = ship.rotation – MathHelper.ToRadians(90);
float x = (float)Math.Cos(angle) * accel;
float y = (float)Math.Sin(angle) * accel;
obj.velocityLinear = new Vector2(x,y);
//load energy to launch
energy -= 1;
objects.Add(obj);
}
}
[/code]
This all sounds like fun, but is there even a way to lose the game? Certainly! If the player runs out of energy, the ship will fall into the black hole! At this stage, the ship just loses its “traction” or station-keeping thrusters and is drawn into the black hole, only to be whipped around by the acceleration code. Some sort of fantastic animation will have to be added so that the ship gets sucked into the black hole like the other objects—a task for the next hour! Figure 23.4 shows what happens now if the player runs out of energy. Another improvement to be made in the next hour is an energy bar rather than just a text display. We have a lot of work yet to do on this game, but it’s already showing promise.

Running out of energy spells doom for the poor ship and its crew!
FIGURE 23.4 Running out of energy spells doom for the poor ship and its crew!

When Objects Collide

Boundary Collision Detection

The first type of collision test we’ll examine uses the boundaries of two rectangles for the test condition. Also called “bounding box” collision detection, this technique is simple and fast, which makes it ideal in situations in which a lot of objects are interacting on the screen at once. Not as precise as the radial technique (coming up next), boundary collision detection does return adequate results for a high-speed arcade game. Interestingly, this is also useful in a graphical user interface (GUI), comparing the boundary of the mouse cursor with GUI objects for highlighting and selection purposes. On the WP7, however, we can’t actually track mouse movement because a “mouse” does not even exist on Windows Phone, only touch points.

XNA provides a useful struct called Rectangle. Among the many methods in this struct is Intersects(), which accepts a single parameter—another Rectangle. The return value of Intersects() is just a bool (true/false). The trick to using Rectangle.Intersects() effectively is creating a bounding rectangle around a sprite at its current location on the screen, taking into account the sprite’s width and height. When we get into animation a couple of hours from now, we’ll have to adapt this code to take into account the width and height of individual frames. In the meantime, we can use the width and height of the whole texture since we’re just working with simple static sprite images at this point. Figure 10.1 illustrates the boundary around a sprite image.

The image dimensions are used as the boundary.
FIGURE 10.1 The image dimensions are used as the boundary.

As you can see in this illustration, boundary collision does not require that the image have an equal width and height, since the bounding rectangle can handle a nonuniform aspect ratio. However, it is usually better to store game artwork in square images for best results.

Accounting for Pivot

Remember that Sprite.position references the pivot point of the object, also known as the origin. Normally, the origin is at the center of the sprite. If the origin is changed from the center of the sprite, the boundary will return an incorrect result! Therefore, if you change the origin, it’s up to you to take that into account when calculating boundaries. The Sprite class does not account for such changes. The calculation for the boundary might be done like so at this point:

[code]
int halfw = image.Width / 2;
int halfh = image.Height / 2;
return new Rectangle(
(int)position.X – halfw,
(int)position.Y – halfh,
image.Width,
image.Height);
[/code]

Accounting for Scaling

That should work nicely, all things being equal. But another important factor that must be considered is scaling. Has the scale been changed from 1.0, or full image size? If so, that will affect the boundary of the sprite, and we have to account for that or else false results will come back while the game is running, causing a sprite to collide when it clearly did not touch another sprite (due to scaling errors). When the boundary is calculated, not only the origin must be accounted for, but the scaling as well, which adds a bit of complexity to the Boundary() method. Not to worry, though—it’s calculated by the method for us. Here is a new version that takes into account the scaling factor:

[code]
int halfw = (int)( (float)(image.Width / 2) * scaleV.X );
int halfh = (int)( (float)(image.Height / 2) * scaleV.Y );
return new Rectangle(
(int)position.X – halfw,
(int)position.Y – halfh,
halfw * 2,
halfh * 2);
[/code]

What is happening in this code is that the width and height are each divided by two, and the scaling is multiplied by these halfw and halfh values to arrive at scaled dimensions, which are then multiplied by two to get the full width and height when returning the Rectangle.

Sprite Class Changes

To simplify the code, we can add a new method to the Sprite class that will return the boundary of a sprite at its current location on the screen. While we’re at it, it’s time to give Sprite a new home in its own source code file. The new file will be called Sprite.cs. The namespace is a consideration, because the class needs a home. I propose just calling it GameLibrary, and in any program that uses Sprite, a simple using statement will import it.

The new version of this class includes the Boundary() method discussed earlier. An additional new method is also needed for debugging purposes. Every class has the capability to override the ToString() method and return any string value. We can override ToString() and have it return information about the sprite. This string can be logged to a text file if desired, but it is easier to just print it on the screen. The code in ToString() is quite messy due to all the formatting codes used, but the result looks nice when printed. It can be very helpful to add a ToString() to a custom class for this purpose, for quick debugging. For example, it is helpful to see the position and boundary of a sprite to verify whether collision is working correctly. See the demo coming up shortly to see an example of this in action. Our Sprite class, the source code for which is shown in Listing 10.1, sure has grown since its humble beginning!

LISTING 10.1 Revised source code for the Sprite class.

[code]
public class Sprite
{
private ContentManager p_content;
private SpriteBatch p_spriteBatch;
public Texture2D image;
public Vector2 position;
public Vector2 velocityLinear;
public Color color;
public float rotation;
public float velocityAngular;
public Vector2 scaleV;
public Vector2 origin;
public bool alive;
public bool visible;
public Sprite(ContentManager content, SpriteBatch spriteBatch)
{
p_content = content;
p_spriteBatch = spriteBatch;
image = null;
position = Vector2.Zero;
velocityLinear = Vector2.Zero;
color = Color.White;
rotation = 0.0f;
velocityAngular = 0.0f;
scaleV = new Vector2(1.0f);
origin = Vector2.Zero;
alive = true;
visible = true;
}
public float scale
{
get { return scaleV.X; }
set
{
scaleV.X = value;
scaleV.Y = value;
}
}
public bool Load(string assetName)
{
try
{
image = p_content.Load<Texture2D>(assetName);
origin = new Vector2(image.Width / 2, image.Height / 2);
}
catch (Exception) { return false; }
return true;
}
public void Draw()
{
p_spriteBatch.Draw(image, position, null, color, rotation,
origin, scaleV, SpriteEffects.None, 0.0f);
}
public void Move()
{
position += velocityLinear;
}
public void Rotate()
{
rotation += velocityAngular;
if (rotation > Math.PI * 2)
rotation -= (float)Math.PI * 2;
else if (rotation < 0.0f)
rotation = (float)Math.PI * 2 – rotation;
}
public Rectangle Boundary()
{
int halfw = (int)( (float)(image.Width / 2) * scaleV.X );
int halfh = (int)( (float)(image.Height / 2) * scaleV.Y );
return new Rectangle(
(int)position.X – halfw,
(int)position.Y – halfh,
halfw * 2,
halfh * 2);
}
public override string ToString()
{
string s = “Texture {W:” + image.Width.ToString() +
“ H:” + image.Height.ToString() + “}n” +
“Position {X:” + position.X.ToString(“N2”) + “ Y:” +
position.Y.ToString(“N2”) + “}n” +
“Lin Vel “ + velocityLinear.ToString() + “n” +
“Ang Vel {“ + velocityAngular.ToString(“N2”) + “}n” +
“Scaling “ + scaleV.ToString() + “n” +
“Rotation “ + rotation.ToString() + “n” +
“Pivot “ + origin.ToString() + “n”;
Rectangle B = Boundary();
s += “Boundary {X:” + B.X.ToString() + “ Y:” +
B.Y.ToString() + “ W:” + B.Width.ToString() +
“ H:” + B.Height.ToString() + “}n”;
return s;
}
}
[/code]

Boundary Collision Demo

Let’s put the new Sprite method to use in an example. This example has four asteroids moving across the screen, and our spaceship pilot must cross the asteroid belt without getting hit by an asteroid. This example is automated—there’s no user input. So just watch it run this time. The source code is found within Listing 10.2, while Figure 10.2 shows a screenshot of the program running. When the ship collides with an asteroid, it simply stops until the asteroid goes on by. But to give the ship more survivability, additional intelligence code has to be added.

The ship tries to dodge asteroids as it crosses the asteroid field.
FIGURE 10.2 The ship tries to dodge asteroids as it crosses the asteroid field.

When the demo is completed later in the hour, it will also have dodging capability. If an asteroid is directly above or below the ship when a “grazing” collision occurs, the ship can simply stop to avoid being destroyed. But if an asteroid is coming from the left or right, destruction is imminent! When this happens, the pilot has to use emergency thrusters to quickly move forward to get out of the way of the asteroid. This is also automated, so again, just watch it run, as input is ignored. We’ll start by just having the ship stop when a collision occurs, and add the capability to speed up in the section coming up on collision response.

Note that the using statements are included here just to show that GameLibrary must be included (the namespace containing the Sprite class), but they will again be omitted in future listings.

LISTING 10.2 Source code for the boundary collision demo program.

[code]
using System;
using System.Collections.Generic;
using System.Linq;
using Microsoft.Xna.Framework;
using Microsoft.Xna.Framework.Audio;
using Microsoft.Xna.Framework.Content;
using Microsoft.Xna.Framework.GamerServices;
using Microsoft.Xna.Framework.Graphics;
using Microsoft.Xna.Framework.Input;
using Microsoft.Xna.Framework.Input.Touch;
using Microsoft.Xna.Framework.Media;
using GameLibrary;
namespace Bounding_Box_Collision
{
public class Game1 : Microsoft.Xna.Framework.Game
{
GraphicsDeviceManager graphics;
SpriteBatch spriteBatch;
Random rand;
Viewport screen;
SpriteFont font;
Sprite[] asteroids;
Sprite ship;
const float SHIP_VEL = -1.5f;
int collisions = 0;
int escapes = 0;
public Game1()
{
graphics = new GraphicsDeviceManager(this);
Content.RootDirectory = “Content”;
TargetElapsedTime = TimeSpan.FromTicks(333333);
}
protected override void Initialize()
{
base.Initialize();
}
protected override void LoadContent()
{
spriteBatch = new SpriteBatch(GraphicsDevice);
screen = GraphicsDevice.Viewport;
rand = new Random();
font = Content.Load<SpriteFont>(“WascoSans”);
//create asteroids
asteroids = new Sprite[4];
for (int n=0; n<4; n++)
{
asteroids[n] = new Sprite(Content, spriteBatch);
asteroids[n].Load(“asteroid”);
asteroids[n].position.Y = (n+1) * 90;
asteroids[n].position.X = (float)rand.Next(0, 760);
int factor = rand.Next(2, 12);
asteroids[n].velocityLinear.X = (float)
((double)factor * rand.NextDouble());
}
//create ship
ship = new Sprite(Content, spriteBatch);
ship.Load(“ship”);
ship.position = new Vector2(390, screen.Height);
ship.scale = 0.2f;
ship.velocityLinear.Y = SHIP_VEL;
}
protected override void Update(GameTime gameTime)
{
if (GamePad.GetState(PlayerIndex.One).Buttons.Back ==
ButtonState.Pressed)
this.Exit();
//move asteroids
foreach (Sprite ast in asteroids)
{
ast.Move();
if (ast.position.X < 0 – ast.image.Width)
ast.position.X = screen.Width;
else if (ast.position.X > screen.Width)
ast.position.X = 0 – ast.image.Width;
}
//move ship
ship.Move();
if (ship.position.Y < 0)
{
ship.position.Y = screen.Height;
escapes++;
}
//look for collision
int hit = 0;
foreach (Sprite ast in asteroids)
{
if (BoundaryCollision(ship.Boundary(), ast.Boundary()))
{
//oh no, asteroid collision is imminent!
EvasiveManeuver(ast);
collisions++;
hit++;
break;
}
//if no collision, resume course
if (hit == 0)
ship.velocityLinear.Y = SHIP_VEL;
}
base.Update(gameTime);
}
protected override void Draw(GameTime gameTime)
{
GraphicsDevice.Clear(Color.CornflowerBlue);
spriteBatch.Begin();
foreach (Sprite ast in asteroids)
ast.Draw();
ship.Draw();
string text = “Collisions:” + collisions.ToString();
spriteBatch.DrawString(font, text, new Vector2(600, 0),
Color.White);
text = “Escapes:” + escapes.ToString();
spriteBatch.DrawString(font, text, new Vector2(600, 25),
Color.White);
spriteBatch.DrawString(font, ship.ToString(), new Vector2(0, 0),
Color.White);
spriteBatch.End();
base.Draw(gameTime);
}
void EvasiveManeuver(Sprite ast)
{
//for now, just stop the ship
ship.velocityLinear.Y = 0.0f;
}
bool BoundaryCollision(Rectangle A, Rectangle B)
{
return A.Intersects(B);
}
}
}
[/code]

Radial Collision Detection

The term “radial” refers to rays or radii (plural for radius), implying that this form of collision detection uses the radii of objects. Another common term is “distance” or “spherical” collision testing. In some cases, a bounding sphere is used to perform 3D collision testing of meshes in a rendered scene, the 3D version of a bounding circle. (Likewise, a bounding cube represents the 3D version of rectangular boundary collision testing.) Although radial collision can be done with an image that has an unbalanced aspect ratio (of width to height), best results will be had when the image has uniform dimensions. The first figure here, Figure 10.3, shows how a bounding circle will not correspond to the image’s width and height correctly, and this radius would have to be set manually.

A bounding circle around a nonsquare image.
FIGURE 10.3 A bounding circle around a nonsquare image.

But if the image’s width and height are uniform, as illustrated in Figure 10.4, then the width or height of the image can be used for the radius, simplifying everything. The beauty of radial collision testing is that only a single float is needed—the radius, along with a method to calculate the distance between two objects. This illustration also shows the importance of reducing the amount of empty space in an image. The transparent background pixels in this illustration (the area within the box) should be as close to the edges of the visible pixels of the shuttle as possible to improve collision results. The radius and distance factors will never be perfect, so reducing the overall radii of both sprites is often necessary. I have found in testing that 80% produces good results. Due to the shape of some images, reducing the radius by 50% might even be helpful, especially in a high-speed arcade-style game in which the velocity would exceed the collision error anyway.

Here is a method that will be helpful when radial collision detection is being used:

[code]
bool RadialCollision(Vector2 A, Vector2 B, float radius1, float radius2)
{
double diffX = A.X – B.X;
double diffY = A.Y – B.Y;
double dist = Math.Sqrt(Math.Pow(diffX, 2) + Math.Pow(diffY, 2));
return (dist < radius1 + radius2);
}
[/code]

An overload with Sprite properties will make using the method even more useful in a game:

[code]
bool RadialCollision(Sprite A, Sprite B)
{
float radius1 = A.image.Width / 2;
float radius2 = B.image.Width / 2;
return RadialCollision(A.position, B.position, radius1, radius2);
}
[/code]

The bounding circle shows the radius at all points from the center.
FIGURE 10.4 The bounding circle shows the radius at all points from the center.

To test radial collision, just make a change to the Boundary Collision program so that RadialCollision() is called instead of BoundaryCollision() in the program’s Update() method.

Assessing the Damage

We now have two algorithms to test for sprite collisions: boundary and radial. Detecting collisions is the first half of the overall collision-handling code in a game. The second half involves responding to the collision event in a meaningful way.

There are as many ways to respond to the collision are there are games in the computer networks of the world—that is, there is no fixed “right” or “wrong” way to do this; it’s a matter of gameplay. I will share one rather generic way to respond to collision events by figuring out where the offending sprite is located in relation to the main sprite.

First, we already know that a collision occurred, so this is post-collision response, not predictive response. The question is not whether a collision occurred, but where the offending sprite is located. Remember that the center of a sprite represents its position. So if we create four virtual boxes around our main sprite, and then use those to test for collision with the offender, we can get a general idea of where it is located: above, below, left, or right, as Figure 10.5 shows.

Four collision response boxes are used to quickly determine colliding object position.
FIGURE 10.5 Four collision response boxes are used to quickly determine colliding object position.

There will be cases in which the offender is within two of these virtual boxes at the same time, but we aren’t concerned with perfect results, just a general result that is “good enough” for a game. If you are doing a slow-paced game in which pixel-perfect collision is important, it would be vital to write more precise collision response code, perhaps a combination of boundary and radial collision values hand-coded for each sprite’s unique artwork. It might even be helpful to separate appendages into separate sprites and move them in relation to the main body, then perform collision testing on each item of the overall “game object.” Figure 10.6 shows a screenshot of the new boundary collision example, which now has some collision-avoidance intelligence built in. The source code for the program is contained in Listing 10.3.

The ship now has a rudimentary intelligence to avoid collisions.
FIGURE 10.6 The ship now has a rudimentary intelligence to avoid collisions.

LISTING 10.3 Source code for the new boundary collision program with collision-avoidance A.I.

[code]
public class Game1 : Microsoft.Xna.Framework.Game
{
GraphicsDeviceManager graphics;
SpriteBatch spriteBatch;
Random rand;
Viewport screen;
SpriteFont font;
Sprite[] asteroids;
Sprite ship;
int collisions = 0;
int escapes = 0;
int kills = 0;
int hit = 0;
const float SHIP_VEL = 1.5f;
const float SHIP_ACCEL = 0.2f;
const float ESCAPE_VEL = 2.5f;
public Game1()
{
graphics = new GraphicsDeviceManager(this);
Content.RootDirectory = “Content”;
TargetElapsedTime = TimeSpan.FromTicks(333333);
}
protected override void Initialize()
{
base.Initialize();
}
protected override void LoadContent()
{
spriteBatch = new SpriteBatch(GraphicsDevice);
screen = GraphicsDevice.Viewport;
rand = new Random();
font = Content.Load<SpriteFont>(“WascoSans”);
//create asteroids
asteroids = new Sprite[4];
for (int n=0; n<4; n++)
{
asteroids[n] = new Sprite(Content, spriteBatch);
asteroids[n].Load(“asteroid”);
asteroids[n].position.Y = (n+1) * 90;
asteroids[n].position.X = (float)rand.Next(0, 760);
int factor = rand.Next(2, 12);
asteroids[n].velocityLinear.X = (float)
((double)factor * rand.NextDouble());
}
//create ship
ship = new Sprite(Content, spriteBatch);
ship.Load(“ship”);
ship.position = new Vector2(390, screen.Height);
ship.scale = 0.2f;
ship.velocityLinear.Y = -SHIP_VEL;
}
protected override void Update(GameTime gameTime)
{
if (GamePad.GetState(PlayerIndex.One).Buttons.Back ==
ButtonState.Pressed)
this.Exit();
//move asteroids
foreach (Sprite ast in asteroids)
{
ast.Move();
if (ast.position.X < 0 – ast.image.Width)
ast.position.X = screen.Width;
else if (ast.position.X > screen.Width)
ast.position.X = 0 – ast.image.Width;
}
//move ship
ship.Move();
if (ship.position.Y < 0)
{
ship.position.Y = screen.Height;
escapes++;
}
//look for collision
foreach (Sprite ast in asteroids)
{
if (RadialCollision(ship, ast))
{
//oh no, asteroid collision is imminent!
EvasiveManeuver(ast);
collisions++;
hit++;
}
}
//accelerate
if (ship.velocityLinear.Y >= -SHIP_VEL)
{
ship.velocityLinear.Y -= SHIP_ACCEL;
if (ship.velocityLinear.Y < -SHIP_VEL)
ship.velocityLinear.Y = -SHIP_VEL;
}
else if (ship.velocityLinear.Y < SHIP_VEL)
{
ship.velocityLinear.Y += SHIP_ACCEL;
if (ship.velocityLinear.Y > SHIP_VEL)
ship.velocityLinear.Y = SHIP_VEL;
}
base.Update(gameTime);
}
protected override void Draw(GameTime gameTime)
{
GraphicsDevice.Clear(Color.Black);
spriteBatch.Begin();
foreach (Sprite ast in asteroids)
{
ast.Draw();
ast.color = Color.White;
}
ship.Draw();
string text = “Intersections:” + collisions.ToString();
spriteBatch.DrawString(font, text, new Vector2(600, 0), Color.White);
text = “Kills:” + kills.ToString();
spriteBatch.DrawString(font, text, new Vector2(600, 25), Color.White);
text = “Escapes:” + escapes.ToString();
spriteBatch.DrawString(font, text, new Vector2(600, 50), Color.White);
float survival = 100.0f – (100.0f / ((float)collisions
/ (float)kills));
text = “Survival:” + survival.ToString(“N2”) + “%”;
spriteBatch.DrawString(font, text, new Vector2(600, 75), Color.White);
spriteBatch.DrawString(font, ship.ToString(), new Vector2(0, 0),
Color.White);
spriteBatch.End();
base.Draw(gameTime);
}
void EvasiveManeuver(Sprite ast)
{
ast.color = Color.Red;
//shortcuts for ship
int SW = (int)(float)(ship.image.Width * ship.scale);
int SH = (int)(float)(ship.image.Height * ship.scale);
int SX = (int)ship.position.X – SW/2;
int SY = (int)ship.position.Y – SH/2;
//create boundary boxes around the ship
Rectangle[] boxes = new Rectangle[4];
boxes[0] = ship.Boundary(); //upper
boxes[0].Y -= SH;
boxes[1] = ship.Boundary(); //lower
boxes[1].Y += SH;
boxes[2] = ship.Boundary(); //left
boxes[2].X -= SW;
boxes[3] = ship.Boundary(); //right
boxes[3].X += SW;
if (boxes[0].Intersects(ast.Boundary()))
ship.velocityLinear.Y = SHIP_VEL * ESCAPE_VEL;
else if (boxes[1].Intersects(ast.Boundary()))
ship.velocityLinear.Y = -SHIP_VEL * ESCAPE_VEL;
else if (boxes[2].Intersects(ast.Boundary()))
ship.velocityLinear.Y = -SHIP_VEL * ESCAPE_VEL;
else if (boxes[3].Intersects(ast.Boundary()))
ship.velocityLinear.Y = -SHIP_VEL * ESCAPE_VEL;
//check for a “kill,” intersection with small inner box
Rectangle kill = ship.Boundary();
int shrinkh = kill.Width / 4;
int shrinkv = kill.Height / 4;
kill.Inflate(-shrinkh, -shrinkv);
if (kill.Intersects(ast.Boundary()))
kills++;
}
bool BoundaryCollision(Rectangle A, Rectangle B)
{
return A.Intersects(B);
}
bool RadialCollision(Sprite A, Sprite B)
{
float radius1 = A.image.Width / 2;
float radius2 = B.image.Width / 2;
return RadialCollision(A.position, B.position, radius1, radius2);
}
bool RadialCollision(Vector2 A, Vector2 B, float radius1, float radius2)
{
double diffX = A.X – B.X;
double diffY = A.Y – B.Y;
double dist = Math.Sqrt(Math.Pow(diffX, 2) + Math.Pow(diffY, 2));
return (dist < radius1 + radius2);
}
}
[/code]

This is perhaps our longest sample program so far, even taking into account that that Sprite class is now found in a different source code file. Game A.I. is a challenging subject. By studying the way the algorithm responds to asteroid collisions, you could use this technique for any number of game scenarios to improve gameplay and/or increase the difficulty by making your A.I. sprites more intelligent.

We learned about collision detection via boundary and radial collision methods, and used these algorithms to study collision response in gameplay code. When a collision algorithm is available, it really opens up our ability to make a game for the first time. As we saw in the final example of this hour, the level of response to collisions can be basic or advanced, rudimentary or quite intelligent, as the spaceship in this example demonstrated.