Antimatroid, The

thoughts on computer science, electronics, mathematics

Posts Tagged ‘Shoot’em up

Space Cowboy: A Shoot’em up game in C#: Part 3

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I’ve been working on a small video game the past few months and recent finished its development. You can read up on the original vision of the game and then check out how the prototype went. In this final installment of the series, I am going to present two sides of the application: the first is the layout of the application and how some of the high-level organizational aspects were implemented. The second side of the application is the gameplay and how some of the more interesting aspects were implemented. Here is a full demo of the game:

User Interface


The majority of the application is based around the idea of stories and storyboards. Stories are analogous to tasks and storyboards to work flows. The transition between stories on a storyboard is initiated by the end user or by an automatic timer. The application has three main storyboards:

  • Main Storyboard – describes the stories that constitute the application oriented stories
  • Game Storyboard – defines the stories that make up the gameplay
  • High Scores Storyboard – how the end user interacts with the high score stories

Main Storyboard

When the user launches the game, they will be presented the Title Story. The Title Story displays the application logo and will transition to the Menu Story after a few seconds. The Menu Story displays a list of actions that the user can initiate. The user may start a new game, view the high scores, review the settings or exit the application. When the user starts a new game, they will be presented the Game Storyboard. When the user views the high scores, they will be presented the High Scores Storyboard. When the user reviews the settings, they will be presented the Settings Story. The Settings will list out all the keyboard commands. When the user exits the application, the End Title Story is displayed. The End Title Story will display the application tagline for a few seconds and then the application will terminate.

Game Storyboard

When the user elects to start a new game, the Countdown Story is displayed. The Countdown Story will display 3… 2… 1… prior to transitioning to the Gameplay Story. The Gameplay Story allows the user to play the actual game. When a user completes a level in the game, the user will be shown the Level Completed Story. The user will be able to review their performance and decide if they are done playing or want to play the next level. If they elect to quit playing, they will be taken to the High Scores Storyboard, otherwise they will be presented the Countdown Story prior to beginning the next level. If the user is destroyed and has no more lives, the user is presented the Game Over Story and after a few seconds elapses, the user will be presented the High Scores Storyboard. If a user completes all of the levels in the game, they will be presented the Game Completed Story. Similar to the Game Over Story, the Game Completed Story will transition to the High Scores Storyboard after a few seconds.

High Scores Storyboard

If a user had received a new high score during their game, they will be presented with the New High Score Story. They will enter in their name and then be transitioned to the High Scores Story. If user did not receive a new high score during their game, they will be presented the High Scores Story. The High Scores Story will display the top highest scores recorded in the game. Once the user is done reviewing the scores, they may return to the Main Storyboard. If the user had transitioned from the Main Storyboard to the High Scores Storyboard, then they will only be presented the High Scores Story.


Each of the of storyboards is responsible for the displaying stories on the screen and transitioning between stories and storyboards (in the following I use each interchangeably). This functionality is achieved by keeping references to each story and instantiating each story on demand. When a new story is to be displayed, the storyboard will unload the current story and load up the new story. Unloading a story consists of removing the instance from the Controls collection, unregistering all event handlers and disposing of the story. Loading a story creates a new instance of the story, registers all relevant event handlers and then displays the story by adding it to the Controls collection.

To illustrate a concrete example of this practice, here is the implementation of the Main Storyboard.

using System;
using System.Windows.Forms;
using UserInterface.GameScreen.Presentation;
using UserInterface.HighScoreScreen.Presentation;
using UserInterface.HomeScreen.Presentation;
using UserInterface.Resources;
using UserInterface.SettingsScreen.Presentation;
using UserInterface.ShutdownScreen.Presentation;
using UserInterface.StartupScreen.Presentation;

namespace UserInterface {
	public class MainWindow : Form {
		private DisplayStartupStory displayStartupStory;
		private MainMenuUserControl mainMenuUserControl;
		private HighScoreStoryBoard highScoreStoryBoard;
		private DisplaySettingsStory displaySettingsStory;
		private GameStoryBoard gameStoryBoard;
		private DisplayShutdownStory displayShutdownStory;

		public MainWindow() {
			base.Width = 320;
			base.Height = 480;
			base.FormBorderStyle = FormBorderStyle.FixedSingle;
			base.MaximizeBox = false;
			base.SizeGripStyle = SizeGripStyle.Hide;
			base.BackColor = InMemoryResources.BackgroundColor;
			base.Text = "Space Cowboy";
			base.Icon = InMemoryResources.LogoIcon;

		protected override void OnLoad(EventArgs e) {
			this.Location = this.DesktopLocation = new System.Drawing.Point(400, 100);

		private void handleStartupDisplayed() {

		private void handleNewGame() {

		private void handleGameOver(int score) {

		private void handleShowHighScores() {

		private void handleHighscoreShowMenu() {

		private void handleShowSettings() {

		private void handleSettingsShowMenu() {

		private void handleExit() {

		private void handleShutdownDisplayed() {

		private void loadStartup() {
			displayStartupStory = new DisplayStartupStory();
			displayStartupStory.Dock = DockStyle.Fill;
			displayStartupStory.Displayed += new Action(handleStartupDisplayed);

		private void unloadStartup() {
			displayStartupStory.Displayed -= handleStartupDisplayed;
			displayStartupStory = null;

		private void loadMenu() {
			mainMenuUserControl = new MainMenuUserControl();
			mainMenuUserControl.Dock = DockStyle.Fill;
			mainMenuUserControl.NewGame += new Action(handleNewGame);
			mainMenuUserControl.ShowHighScores += new Action(handleShowHighScores);
			mainMenuUserControl.ShowSettings += new Action(handleShowSettings);
			mainMenuUserControl.Exit += new Action(handleExit);
		private void unloadMenu() {
			mainMenuUserControl.NewGame -= handleNewGame;
			mainMenuUserControl.ShowHighScores -= handleShowHighScores;
			mainMenuUserControl.ShowSettings -= handleShowSettings;
			mainMenuUserControl.Exit -= handleExit;
			mainMenuUserControl = null;

		private void loadGame() {
			gameStoryBoard = new GameStoryBoard();
			gameStoryBoard.Dock = DockStyle.Fill;
			gameStoryBoard.GameOver += new Action<int>(handleGameOver);

		private void unloadGame() {
			gameStoryBoard.GameOver -= handleGameOver;
			gameStoryBoard = null;

		private void loadHighScores(int? score) {
			highScoreStoryBoard = (score == null) ? new HighScoreStoryBoard() : new HighScoreStoryBoard(score.Value);
			highScoreStoryBoard.ShowMenu += new Action(handleHighscoreShowMenu);
			highScoreStoryBoard.Dock = DockStyle.Fill;

		private void unloadHighScores() {
			highScoreStoryBoard.ShowMenu -= handleHighscoreShowMenu;
			highScoreStoryBoard = null;

		private void loadSettings() {

			displaySettingsStory = new DisplaySettingsStory();
			displaySettingsStory.ShowMenu += new Action(handleSettingsShowMenu);
			displaySettingsStory.Dock = DockStyle.Fill;

		private void unloadSettings() {
			displaySettingsStory.ShowMenu -= handleSettingsShowMenu;
			displaySettingsStory = null;

		private void loadShutdown() {
			displayShutdownStory = new DisplayShutdownStory();
			displayShutdownStory.Dock = DockStyle.Fill;
			displayShutdownStory.Displayed += new Action(handleShutdownDisplayed);

		private void unloadShutdown() {
			displayShutdownStory.Displayed -= handleShutdownDisplayed;
			displayShutdownStory = null;

A typical story contains a few controls and a sparse amount of logic. The following is the Game Story and a custom control called the LevelCanvas which is responsible for drawing the actors of the universe on the screen. The LevelCanvas derives from a custom control that uses a manual double buffering scheme that I’ve written about in some of my previous posts.

using System.Windows.Forms;
using UserInterface.GameScreen.Gameplay;

namespace UserInterface.GameScreen.Presentation {
	public class GameStory : UserControl {
		private TableLayoutPanel panel;
		private GameStatisticsView headsUpDisplay;
		private LevelCanvas levelUserControl;

		public GameStory(Game game) {
			headsUpDisplay = new GameStatisticsView(game.GameStatistics);
			headsUpDisplay.Dock = DockStyle.Fill;

			levelUserControl = new LevelCanvas(game);
			levelUserControl.Dock = DockStyle.Fill;

			panel = new TableLayoutPanel();
			panel.ColumnStyles.Add(new ColumnStyle() { SizeType = SizeType.Percent, Width = 100.0f });
			panel.RowStyles.Add(new RowStyle() { SizeType = SizeType.Absolute, Height = 48.0f });
			panel.RowStyles.Add(new RowStyle() { SizeType = SizeType.Percent, Height = 100.0f });
			panel.Dock = DockStyle.Fill;
			panel.Controls.Add(headsUpDisplay, 0, 0);
			panel.Controls.Add(levelUserControl, 0, 1);


	public class LevelCanvas : DoubleBufferedUserControl {
		private Game game;
		private Level currentLevel;

		public LevelCanvas(Game game) { = game;

			this.BorderStyle = BorderStyle.FixedSingle;

			game.StartLevel += new Action<Level>(handleStartLevel);
			game.LevelCompleted += new Action<SessionStatistics>(handleLevelCompleted);
			game.LevelOver += new Action(handleLevelOver);

		override protected void Dispose(bool disposing) {

			if (disposing) {
				game.StartLevel -= handleStartLevel;
				game.LevelCompleted -= handleLevelCompleted;
				game.LevelOver -= handleLevelOver;

		override protected void Draw(Graphics graphics) {
			if (currentLevel == null)

			graphics.InterpolationMode = InterpolationMode.Bicubic;
			graphics.PixelOffsetMode = PixelOffsetMode.HighSpeed;
			graphics.SmoothingMode = SmoothingMode.AntiAlias;

			foreach (Actor actor in currentLevel.Actors) {
				try {
					actor.View.Draw(graphics, ClientRectangle);
				} catch (Exception E) {

		private void handleLevelChanged() {
			if (InvokeRequired) {
				Invoke(new Action(handleLevelChanged));


		private void handleLevelCompleted(SessionStatistics statistics) {
			if (InvokeRequired) {
				Invoke(new Action<SessionStatistics>(handleLevelCompleted), statistics);

			currentLevel.LevelChanged -= handleLevelChanged;
			currentLevel = null;


		private void handleLevelOver() {
			if (InvokeRequired) {
				Invoke(new Action(handleLevelOver));

			currentLevel.LevelChanged -= handleLevelChanged;
			currentLevel = null;


		private void handleStartLevel(Level level) {
			if (InvokeRequired) {
				Invoke(new Action<Level>(handleStartLevel));

			currentLevel = level;
			currentLevel.LevelChanged += new Action(handleLevelChanged);
			currentLevel.User.Behavior = new KeyboardActorBehavior(currentLevel, this);





Much of the gameplay design was focused on providing a positive end user experience. The end user experience revolves around making the gameplay predictable, so that the end user could learn how to play quickly, then shifts to introduce new dynamics keeping the experience fresh. The core concepts that constitute the end user experience can be summarized as:

  • Mechanics – how things in the game universe behave
  • Incentives – making the end user want to play the game again and again
  • Extras – making the game more interesting and requiring new strategies

  • The end user is given the ability to maneuver about the universe and to fire weapons. The user is able to issue commands to move the ship north, east, south or west. Each command results in a small amount of thrust being produced
  • A user can rotate the ship’s weapons to the target an object in the universe and engage the weapons to emit projectiles. Projectiles follow the same rules as every other object in the universe
  • The user is given a fixed number of health points. Each time a ship collides with another object in the universe, both objects have their health depleted by a fixed amount. If the total points goes to zero, the user has two additional lives to use. Once all the lives have been used up, the game is over
  • All enemies in the universe will attempt to destroy the user at all costs

  • Each time a user destroys an object in the universe, they may receive a variable amount of points that contributes to their overall score

  • The head-up display will flash and then fade back to normal whenever a value changes
  • An object’s overall health can be determined by the object’s opacity on the screen. A completely healthy object will be full opaque and the closer an object is to be destroyed, the more transparent it will appear
  • When an object is destroyed, it may reveal power-ups that were hidden inside or breakup into smaller pieces of debris. Power-ups come in the following flavors:
    • Health – Set’s the object’s health to 100%
    • Engine – Increases the propulsion of the object’s engine
    • Weapon – Replaces the standard weapon with three standard weapons


Game state

The Level class is responsible for driving the game in terms of notifying the UI to redraw the universe and for evolving the universe according to the design rules. The main method of interest is the handleTick method, which is responsible for running through the objects in the universe and then firing off different events based on the state of the universe. The class also takes care of the process of breaking an object into debris and applying non-physical behavior to collisions.

using System;
using System.Collections.Generic;
using Library.Mathematics;
using UserInterface.GameScreen.Gameplay.Behavior;
using UserInterface.GameScreen.Physics;

namespace UserInterface.GameScreen.Gameplay {
	public class Level {
		static private Random RNG;

		static Level() {
			RNG = new Random((int)(DateTime.Now.Ticks & 0xffffff));

		public event Action LevelChanged;
		public event Action<SessionStatistics> LevelCompleted;
		public event Action UserDestroyed;
		public event Action<int> UserScored;

		private LevelStatistics levelStatistics;
		private TimePiece timePiece;
		private PhysicsEngine physicsEngine;
		public List<Actor> Actors { get; protected set; }
		public UserActor User { get; protected set; }

		public Level(double width, double height) {
			physicsEngine = new PhysicsEngine(width, height);
			physicsEngine.Collided += new Action<Actor, Actor>(handleCollided);

			levelStatistics = new LevelStatistics();

			timePiece = new TimePiece();
			timePiece.Tick += new Action(handleTick);

			User = new UserActor();
			Actors = new List<Actor>() { User };

		public void Start() {

		public void Stop() {

		private List<Actor> breakUp(Actor actor) {
			List<Actor> actors = new List<Actor>();
			if (actor.Body.Radius <= 6)
				return actors;

			if (actor.GetType().Equals(typeof(PowerUpNeutralActor)))
				return actors;

			for (int n = 0; n < 3; n++) {
				Actor fragment = null;

				if (0.4 * actor.Body.Radius == 6.0) {
					int x = RNG.Next(0, 10);
					if (x == 0) {
						fragment = new HealthPowerUpNeutralActor();
					} else if (x == 1) {
						fragment = new EnginePowerUpNeutralActor();
					} else if (x == 2) {
						fragment = new WeaponPowerUpNeutralActor();
					} else {
						fragment = new DebrisNeutralActor();
				} else {
					fragment = new DebrisNeutralActor();

				fragment.Body = new Body() {
					CurrentMass = 0.1 * actor.Body.StartingMass,
					Radius = 0.4 * actor.Body.Radius

				fragment.AngularMovement = new AngularMovement() {
					Acceleration = actor.AngularMovement.Acceleration,
					Heading = actor.AngularMovement.Heading,
					Velocity = actor.AngularMovement.Velocity

				fragment.LinearMovement = new LinearMovement() {
					Acceleration = new Vector(2, (i) => actor.LinearMovement.Acceleration[i]),
					Location = new Vector(2, (i) => actor.LinearMovement.Location[i]),
					Velocity = new Vector(2, (i) => actor.LinearMovement.Velocity[i])

				fragment.Points = 0;

				fragment.Behavior = new MeanderActorBehavior(fragment);

				Vector direction = new Vector(2);
				direction[0] = Math.Cos((n * 120.0) * (Math.PI / 180.0));
				direction[1] = Math.Sin((n * 120.0) * (Math.PI / 180.0));

				fragment.LinearMovement.Location += (actor.Body.Radius * 0.5) * direction;
				fragment.LinearMovement.Velocity = (0.3 * actor.LinearMovement.Velocity.Length()) * direction;


			return actors;

		private void handleCollided(Actor A, Actor B) {
			bool aIsPowerUp = A is PowerUpNeutralActor;
			bool bIsPowerUp = B is PowerUpNeutralActor;
			if (!(aIsPowerUp ^ bIsPowerUp))

			PowerUpNeutralActor powerUpActor = null;
			Actor receipentActor = null;
			if (aIsPowerUp) {
				powerUpActor = A as PowerUpNeutralActor;
				receipentActor = B;
			} else {
				powerUpActor = B as PowerUpNeutralActor;
				receipentActor = A;

			if (receipentActor is BulletUserActor || receipentActor is BulletEnemyActor)


		private void handleTick() {
			physicsEngine.Step(0.1, Actors);

			List<Actor> actorsToAdd = new List<Actor>();
			for (int n = 0; n < Actors.Count; n++) {

				if (Actors[n].Body.CurrentMass <= 0.0) {
					if (Actors[n].Equals(User)) {
					} else {
						if (Actors[n] is BulletUserActor || Actors[n] is BulletEnemyActor) {

						} else {


			if (isLevelComplete())

			int actorCount = Actors.Count;
			for (int n = 0; n < actorCount; n++)


		private bool isLevelComplete() {
			for (int n = 0; n < Actors.Count; n++) {
				if (Actors[n] is BulletEnemyActor || Actors[n] is BulletUserActor)

				if (Actors[n] is EnemyActor || Actors[n] is NeutralActor)
					return false;
			return true;

		private void levelChanged() {
			if (LevelChanged != null)

		private void levelCompleted() {
			if (LevelCompleted != null) {
				levelStatistics.TimeTaken = TimeSpan.FromMilliseconds(timePiece.ElapsedTimeMilliseconds);
				LevelCompleted(new SessionStatistics() {
					LevelStatistics = levelStatistics

		private void userDestroyed() {

			if (UserDestroyed != null)

		private void userScored(int points) {
			levelStatistics.Scored += points;

			if (UserScored != null)

One of the key features of the game is providing a realistic enough perception of a simulated universe and that the user is able to interact with objects. This is done by providing a handful of basic physical attributes that are implemented by the PhysicsEngine class. The core responsibilities of the class is to apply physical rules over the course of a slice of time. Objects in the universe can be destroyed and created during this process.

Collisions between actors is handled through the typical conservation of linear momentum approach. Two objects, A and B, with momentums, p_{A} and p_{B}, must have the same amount of momentum before and after the collision. Assuming a totally elastic collision, we end up with p_{A}^{(b)} + p_{B}^{(b)} = p_{A}^{(a)} + p_{B}^{(a)}. Momentum is defined as p = \frac{1}{2} m v^{2}, where m is the mass of an object and v is its velocity. Since no mass is being lost in the collision, the velocities must change as a result. Solving for the v^{(a)} velocities yields the trajectories that the objects will follow after the collision.

Collisions between actors and walls is once again handled through the typical conservation of momentum. Since the wall is of infinite mass and has zero velocity, the colliding object’s velocity is reflected about the wall’s normal vector.

Any object that escapes or has invalid numerical data is removed from the universe.

using System;
using System.Collections.Generic;
using Library.Mathematics;

namespace UserInterface.GameScreen.Physics {
	public class PhysicsEngine {
		public event Action<Actor, Actor> Collided;

		private double Width, Height;

		public PhysicsEngine(double width, double height) {
			Width = width;
			Height = height;

		public void Step(double dt, List<Actor> actors) {
			// Actor-Actor interactions
			for (int n = 0; n < actors.Count; n++)
				for (int m = n + 1; m < actors.Count; m++)
					if (intersects(actors[n], actors[m])) {
						collide(actors[n], actors[m]);

			// Actor-Wall interactions
			for (int n = 0; n < actors.Count; n++) {
				Vector l = actors[n].LinearMovement.Location;
				Vector v = actors[n].LinearMovement.Velocity;
				double r = actors[n].Body.Radius;

				if (l[0] - r < 0)
					l[0] = r;

				if (l[0] + r > Width)
					l[0] = Width - r;

				if (l[1] - r < 0)
					l[1] = r;

				if (l[1] + r > Height)
					l[1] = Height - r;

				Vector N = getWallNormal(l, r);
				if (N != null)
					actors[n].LinearMovement.Velocity = v - (2 * * N;

			// get rid of anything that escaped the universe.
			for (int n = 0; n < actors.Count; n++) {
				Vector l = actors[n].LinearMovement.Location;
				double r = actors[n].Body.Radius;

				if (double.IsInfinity(l[0]) || double.IsInfinity(l[1])) {

				if (double.IsNaN(l[0]) || double.IsNaN(l[1])) {

				if (l[0] - r < -5 || l[0] + r > Width + 5 || l[1] - r < -5 || l[1] + r > Height + 5)

		private bool intersects(Actor A, Actor B) {
			Vector pointDistance = (A.LinearMovement.Location - B.LinearMovement.Location);
			double touchingPointDistance = (A.Body.Radius + B.Body.Radius);
			return pointDistance.Length() <= touchingPointDistance;

		private void collide(Actor A, Actor B) {
			Vector a = (1.0 / (A.Body.CurrentMass + B.Body.CurrentMass)) * ((A.Body.CurrentMass - B.Body.CurrentMass) * A.LinearMovement.Velocity + (2 * B.Body.CurrentMass) * B.LinearMovement.Velocity);
			Vector b = (1.0 / (A.Body.CurrentMass + B.Body.CurrentMass)) * ((B.Body.CurrentMass - A.Body.CurrentMass) * B.LinearMovement.Velocity + (2 * A.Body.CurrentMass) * A.LinearMovement.Velocity);

			A.LinearMovement.Velocity = a;
			B.LinearMovement.Velocity = b;

			A.Body.CurrentMass -= 2.5;
			B.Body.CurrentMass -= 2.5;

			if (Collided != null)
				Collided(A, B);

		private Vector getWallNormal(Vector l, double r) {
			Vector N = null;
			if (l[0] - r <= 0.0) {
				// left side of the body is against the left side of the frame
				if (l[1] - r <= 0.0) {
					// top of the body is against the top of the frame
					// => two point of contact
					N = new Vector(2, (i) => i == 0 ? 1 : -1);
				} else if (l[1] + r >= Height) {
					// bottom of the body is against the bottom of the frame
					// => two points of contact
					N = new Vector(2, (i) => i == 0 ? 1 : 1);
				} else {
					// body is between the top and bottom
					// => single point of contact
					N = new Vector(2, (i) => i == 0 ? 1 : 0);
			} else if (l[0] + r >= Width) {
				// right side of the body is against the right side of the frame
				if (l[1] - r <= 0.0) {
					// top of the body is against the top of the frame
					// => two points of contact
					N = new Vector(2, (i) => i == 0 ? -1 : -1);
				} else if (l[1] + r >= Height) {
					// bottom of the body is against the bottom of the frame
					// => two points of contact
					N = new Vector(2, (i) => i == 0 ? -1 : 1);
				} else {
					// body is between the top and bottom
					// => single point of contact
					N = new Vector(2, (i) => i == 0 ? -1 : 0);
			} else {
				// body is between the left and right
				if (l[1] - r <= 0.0) {
					// top of the body is against the top of the frame
					// => single point of contact
					N = new Vector(2, (i) => i == 1 ? -1 : 0);
				} else if (l[1] + r >= Height) {
					// bottom of the body is against the bottom of the frame
					// => single point of contact
					N = new Vector(2, (i) => i == 1 ? +1 : 0);
				} else {
					// body is between the top and bottom
					// => zero points of contact
			return N;

Enemy Targeting

To make the game more interesting, the enemy ships are able to target the user’s ship. Since the enemy must adhere to the same mechanics that the user does, it incrementally rotates clockwise and counterclockwise to keep the user in target. When the user is within an acceptable window of error, the enemy will fire its weapons in hopes of hitting the user.

The first approach here was to simply keep track of which direction the enemy is rotating and to rotate next in the direction that minimized the distance in radians between the enemy’s heading and the direction that the user is traveling. Unfortunately, this will result in overshooting the desired destination.

The second approach is to take into account how long it will take the rotation to slow down given its current angular velocity. If there is enough time then the rotation will increase, otherwise it will slowdown. Given the second approach, the enemies exhibit a reasonable accurate behavior of tracking the user’s ship.

using System;
using Library.Mathematics;
using UserInterface.GameScreen.Gameplay.Components;
using UserInterface.GameScreen.Physics;

namespace UserInterface.GameScreen.Gameplay.Behavior {
	public class TargetingActorBehavior : IBehavior {
		private Actor toControl;
		private Actor toTarget;
		private Level level;

		public TargetingActorBehavior(Actor toControl, Actor toTarget, Level level) {
			this.toControl = toControl;
			this.toTarget = toTarget;
			this.level = level;

		public void Step(double dt) {
			Vector d = toTarget.LinearMovement.Location - toControl.LinearMovement.Location;
			Vector h = toControl.AngularMovement.HeadingVector;
			double radsToTarget = d.RadsBetween(h);
			double a = Math.PI / 5.0;

			AngularMovement cw = new AngularMovement();
			cw.Heading = toControl.AngularMovement.Heading - a;
			double radsToTargetCW = d.RadsBetween(cw.HeadingVector);

			AngularMovement ccw = new AngularMovement();
			ccw.Heading = toControl.AngularMovement.Heading + a;
			double radsToTargetCCW = d.RadsBetween(ccw.HeadingVector);

			double v = toControl.AngularMovement.Velocity;

			if (v < 0) {
				// rotating cw
				if (radsToTargetCW < radsToTargetCCW) { 
					// continuing to rotate cw will bring us closer to zero
					// first, check to see if we are going to overshoot if we
					// continue to rotate cw.
					double radsToStop = 1.5 * v * (v + -a * dt) / (-a * dt);
					if (radsToTarget <= radsToStop) {
					} else if (radsToTarget > radsToStop) {
				} else if (radsToTargetCW >= radsToTargetCCW) { 
					// continuing to rotate cw will bring us further away from zero
					// => rotate the opposite direction
			} else if (v == 0) {
				// not rotating
				// pick which ever direction is closer to zero
				if (radsToTargetCW < radsToTargetCCW) {
				} else if(radsToTargetCW >= radsToTargetCCW) {
			} else if (v > 0) { 
				// rotating ccw
				if (radsToTargetCCW < radsToTargetCW) {
					// continuing to rotate ccw will bring us closer to zero
					// first, check to see if we are going to overshoot if we
					// continue to rotate ccw.
					double radsToStop = 1.5 * v * (v + a * dt) / (a * dt);
					if (radsToTarget <= radsToStop) {
					} else if (radsToTarget > radsToStop) {
				} else if (radsToTargetCCW >= radsToTargetCW) {
					// continuing to rotate ccw will bring us further away from zero
					// => rotate the opposite direction

			// If the angle is less than five degrees (pi/36), then fire.
			if (radsToTarget < Math.PI / 36.0)

Written by lewellen

2011-05-01 at 8:00 am

Posted in Projects

Tagged with ,

Space Cowboy: A Shoot’em up game in Haskell: Part 2

with one comment


A couple months back I wrote about a shoot’em up game that I was planning on making in Haskell. My goal was to make something a little more elaborate than my previous games and also take my understanding of Haskell further. Ultimately, I did not use Haskell and instead decided to use C# for the final product (main reason was productivity). Nonetheless, I felt it was worthwhile to post the work that was done on the prototype and talk a bit about the development process.

To get started, here is a quick demo of the features that were implemented in the prototype, namely, the user’s ability to navigate the ship and fire its weapons using the keyboard.

As others have put it, programming in Haskell is like writing a proof, so in similar vein I’m going to present the core modules of the prototype and then build upon those to present the more complicated ones (which follows more or less the development process). The code that is posted here was authored in Leksah, which replaces a lot of common syntax with “source candy”, so hopefully you will be able to deduce the formal syntax.

Mathematics Module

Since I didn’t have a lot experience in designing a game like this in Haskell, I decided I’d start with the basic mathematical model of the game. I thought about the concepts that were needed to represent bodies in a universe and settled on points, vectors and shapes to represent the ideas I had brewing in my head.


The Point data type represents a single coordinate pair on the Euclidean Plane.

type Coordinate = Float

data Point = Point Coordinate Coordinate

pointZero :: Point
pointZero = Point 0.0 0.0

type Distance = Float

pointDistance :: Point →  Point →  Distance
pointDistance (Point x y) (Point u v) = sqrt ((x - u)↑2 + (y - v)↑2)


The Vector data type serves two purposes: the first is to describe the translation of points along the plane and the second is to describe the direction in which bodies are moving. The usual set of operations on Euclidean Vectors were implemented.

data Vector = Vector Coordinate Coordinate

instance Eq Vector where
    (Vector x y) ≡ (Vector u v) = (x ≡ u) ∧ (y ≡ v)
    (Vector x y) ≠ (Vector u v) = (x ≠ u) ∨ (y ≠ v)

vectorZero :: Vector
vectorZero = Vector 0.0 0.0

vectorUp :: Vector
vectorUp = Vector 0 1

vectorLeft :: Vector
vectorLeft = Vector (-1) 0

vectorDown :: Vector
vectorDown = Vector 0 (-1)

vectorRight :: Vector
vectorRight = Vector 1 0

vectorIdentity :: Vector →  Vector
vectorIdentity (Vector x y) = Vector x y

vectorAdd :: Vector →  Vector →  Vector
vectorAdd (Vector x y) (Vector x' y') = Vector (x + x') (y + y')

vectorDotProduct :: Vector →  Vector →  Float
vectorDotProduct (Vector x y) (Vector x' y') = (x * x') + (y * y')

vectorScale :: Float →  Vector →  Vector
vectorScale a (Vector x' y') = Vector (a * x') (a * y')

vectorMinus :: Vector →  Vector →  Vector
vectorMinus (Vector x y) (Vector x' y') = Vector (x - x') (y - y')

vectorMagnitude :: Vector →  Float
vectorMagnitude (u) = sqrt $ vectorDotProduct u u

vectorNormalize :: Vector →  Vector
vectorNormalize (u)
    | vectorMagnitude u ≡ 0 = Vector 0 0
    | otherwise = vectorScale (1.0 / (vectorMagnitude u)) u

pointAdd :: Point →  Vector →  Point
pointAdd (Point x y) (Vector u v) = Point (x + u) (y + v)


Bodies are represented as simple shapes. In the initial round of design, rectangles and ellipses were considered, but for the purpose of developing a prototype, I settled on circles. The benefit is that determining the minimum distance between two circles is simpler and consequently so is detecting collisions.

data Shape =
    Circle {
        center :: Point,
        radius :: Distance

unitCircle :: Shape
unitCircle = Circle {
    center = pointZero,
    radius = 1.0

shapeDistance :: Shape →  Shape →  Distance
shapeDistance (Circle c r) (Circle c' r') = (pointDistance c c') - (r + r')

shapeCollide :: Shape →  Shape →  Bool
shapeCollide a b = distance ≤ 0
        distance = shapeDistance a b

Physics Module

Now that I had a mathematical model of the objects that would be considered, it made sense to tackle the physics model of the game. Bodies in the game are treated as simple Rigid Bodies with non-rotational Kinematics.


To capture the kinematics of the bodies, the Movement data type captures the location, velocity and acceleration of a body. The heart of the physics engine is captured in movementEvolved- it is responsible for updating the location, velocity and acceleration over a slice of time.

type Velocity = Vector

type Acceleration = Vector

data Movement = Movement {
    location :: Point,
    velocity :: Velocity,
    acceleration :: Acceleration

movementZero :: Movement
movementZero = Movement {
    location = pointZero,
    velocity = vectorZero,
    acceleration = vectorZero

type Time = Float

movementEvolve :: Movement →  Time →  Movement
movementEvolve (Movement l v a) t = Movement l' v' a'
    where a' = vectorIdentity a
          v' = vectorAdd (vectorScale t a) v
          l' = pointAdd l (vectorAdd (vectorScale (t * t / 2.0) a) (vectorScale t v))


Each physical body in the universe has a mass, shape and movement. The second key component of the physics engine is the process of detecting collisions. bodiesCollide is responsible for taking a collection of bodies and for each one, collecting the bodies that collide with it and then supplying that body and its contacts to a function that determines the outcome of the collision.

type Mass = Float

data Body a = Body {
        shape :: Shape,
        mass :: Mass,
        movement :: Movement,
        description :: a

bodyAddMass :: Body a →  Mass →  Body a
bodyAddMass (Body s m mo d) amount = Body {
        shape = s,
        mass = m + amount,
        movement = mo,
        description = d

bodiesCollide :: [Body a] →  (Body a →  [Body a] →  [Body a]) →  [Body a]
bodiesCollide xs f = apply [] xs f

apply :: [Body a] →  [Body a] →  (Body a →  [Body a] →  [Body a]) →  [Body a]
apply _ [] _ = []
apply leftList (item:rightList) mapping = processed ⊕ remaining
        processed =
            if null collisions
            then [item]
            else mapping item collisions
        collisions = filter (λx →  bodyCollide (item, x)) (leftList ⊕ rightList)
        remaining = apply (leftList ⊕ [item]) rightList mapping

bodyCollide :: (Body a, Body a) →  Bool
bodyCollide (a, b) = shapeCollide (shape a) (shape b)

bodyEvolve :: Body a →  Time →  Body a
bodyEvolve (Body (Circle c r) mass m d) t = Body {
    shape = Circle (location m') r,
    mass = mass,
    movement = m',
    description = d
        m' = movementEvolve m t


The game universe spans the plane, contains a collection of bodies and a sense of time. The universe brings together the two main components of the physics engine and exposes a way to remove items from the universe.

data Universe a = Universe {
    bodies :: [Body a],
    time :: Time

universeAddBodies :: Universe a →  [Body a] →  Universe a
universeAddBodies u bs = Universe {
        bodies = (bodies u) ⊕ bs,
        time = time u

universeCollide :: Universe a →  (Body a →  [Body a] →  [Body a]) →  Universe a
universeCollide (Universe bs t) f = Universe {
    bodies = bodiesCollide bs f,
    time = t

universeEvolve :: Universe a →  Time →  Universe a
universeEvolve u t = Universe {
    bodies = map (λb →  bodyEvolve b t) (bodies u),
    time = t + (time u)

universeFilter :: (Universe a) →  (Body a →  Bool) →  (Universe a)
universeFilter u p = Universe {
        bodies = filter p (bodies u),
        time = time u

Game Module

Now that the physics of the universe have been described, we can start describing specific aspects of the game.


Each ship has some number of weapons capable of doing some amount of damage and can fire projectiles with a given acceleration.

data Weapon =

type Damage = Int

weaponDamage :: Weapon →  Damage
weaponDamage Torpedo = 2
weaponDamage _ = defined

type Thrust = Float

weaponThrust :: Weapon →  Thrust
weaponThrust Torpedo = 0.5
weaponThrust _ = undefined


Each ship has some number of engines capable of providing some amount of acceleration.

data Engine =

engineThrust :: Engine →  Thrust
engineThrust Rocket = 0.05
engineThrust _ = undefined


A ship is any body in the universe, described here as either a Projectile or a Fighter. It is what will be captured in the parametric type of the Universe data type.

data Ship =
    Projectile Thrust Damage
    | Fighter Engine Weapon

shipEngines :: Ship →  [Engine]
shipEngines (Fighter e _) = [e]
shipEngines _ = []

shipThrust :: Ship →  Thrust
shipThrust s = sum $ map engineThrust (shipEngines s)

shipWeapons :: Ship →  [Weapon]
shipWeapons (Fighter _ w) = [w]
shipWeapons _ = []

shipFireWeapons :: Ship →  [Ship]
shipFireWeapons s = map newProjectile $ shipWeapons s


A projectile is any body fired from a weapon.

newProjectile :: Weapon →  Ship
newProjectile w = Projectile (weaponThrust w) (weaponDamage w)

projectileToBody :: Ship →  Movement →  Body Ship
projectileToBody p@(Projectile t d) m@(Movement l v a) = Body {
        shape = Circle {
            center = pointAdd l (vectorScale 1.1 vectorUp),
            radius = 0.2
        movement = Movement {
            location = pointAdd l (vectorScale 1.25 vectorUp),
            velocity = vectorScale t vectorUp,
            acceleration = vectorIdentity a
        description = p,
        mass = 1


The Fighter represents the end user and has a number of functions for controlling it. Notably, firing of the weapons and navigating the plane.

shipIsFighter :: Ship →  Bool
shipIsFighter (Fighter _ _) = True
shipIsFighter _ = False

fighterDestroyed :: (Universe Ship) →  Bool
fighterDestroyed (Universe bs t) = null $ filter (λb →  shipIsFighter (description b)) bs

fighterMove :: Body Ship →  Vector →  [Body Ship]
fighterMove (Body s mass (Movement l v a) d) direction = [Body {
        movement = Movement {
            location = l,
            velocity = vectorAdd δ v,
            acceleration = a
        mass = mass,
        shape = s,
        description = d
        δ = vectorScale (shipThrust d) direction

fighterFire :: Body Ship →  [Body Ship]
fighterFire b@(Body s mass m d) = [b] ⊕ bs
        bs = map (λx →  projectileToBody x m) $ projectiles
        projectiles = shipFireWeapons d
        direction = vectorUp

universeActOnFighter :: (Universe Ship) →  (Body Ship →  [Body Ship]) →  (Universe Ship)
universeActOnFighter u f = Universe {
        bodies = bodiesActOnFighter (bodies u) f,
        time = time u

bodiesActOnFighter :: [Body Ship] →  (Body Ship →  [Body Ship]) →  [Body Ship]
bodiesActOnFighter [] _ = []
bodiesActOnFighter (b:bs) f = b' ⊕ bs'
        b' = bodyActOnFighter b f
        bs' = bodiesActOnFighter bs f

bodyActOnFighter :: Body Ship →  (Body Ship →  [Body Ship]) →  [Body Ship]
bodyActOnFighter b f
    | shipIsFighter $ description b = f b
    | otherwise = [b]

Graphics Module

The Graphics module deals with mapping the above data types into their corresponding HOpenGL counterparts. (I looked at a number of Haskell’s graphics libraries and ultimately chose to go with HOpenGL since I was the most familiar with OpenGL.)

coordinateToGLfloat :: Coordinate →  GLfloat
coordinateToGLfloat c = realToFrac c

type OpenGLPoint = (GLfloat, GLfloat, GLfloat)

pointToOpenGLPoint :: Geometry.Point →  OpenGLPoint
pointToOpenGLPoint (Geometry.Point x y) = (x', y', 0.0::GLfloat)
        x' = coordinateToGLfloat x
        y' = coordinateToGLfloat y

type OpenGLView = [OpenGLPoint]

shapeToView :: Shape →  OpenGLView
shapeToView (Circle c r) = map pointToOpenGLPoint points
        points = map (λθ →  Geometry.Point (r * (cos θ)) (r * (sin θ))) degrees
        degrees = map (λn →  n * increment ) [0..steps - 1]
        increment = 2.0 * pi / steps
        steps = 16

shipToView :: Ship →  OpenGLView
shipToView (Projectile _ _) = [ ... ]
shipToView (Fighter _ _) = [ ... ]
shipToView _ = undefined

openGLPointTranslate :: OpenGLPoint →  OpenGLPoint →  OpenGLPoint
openGLPointTranslate (x, y, z) (dx, dy, dz) = (x + dx, y + dy, z + dz)

openGLViewTranslate :: OpenGLView →  OpenGLPoint →  OpenGLView
openGLViewTranslate xs d = map (openGLPointTranslate d) xs

openGLPointToIO :: OpenGLPoint →  IO ()
openGLPointToIO (x, y, z) = vertex $ Vertex3 x y z

openGLViewToIO :: OpenGLView →  IO ()
openGLViewToIO ps = mapM_ openGLPointToIO ps

displayBody :: Body Ship →  IO()
displayBody (Body s mass m d) =
    color (Color3 (1.0::GLfloat) 1.0 1.0) >>
    renderPrimitive LineLoop ioShip
        ioBody = openGLViewToIO $ openGLViewTranslate (shapeToView s) dl
        ioShip = openGLViewToIO $ openGLViewTranslate (shipToView d) dl
        dl = pointToOpenGLPoint l
        l = location m

displayUniverse :: Universe Ship →  IO ()
displayUniverse universe = mapM_ displayBody $ bodies universe

Main Module

The Main Module is the glue that brings together all of the other modules. Much of the functions described here are for gluing together the OpenGL callbacks to the functions described above.

theUniverse :: Universe Ship
theUniverse = ...

main :: IO()
main = do
    (programName, _) ←  getArgsAndInitialize
    initialDisplayMode $= [ DoubleBuffered ]
    createWindow "Space Cowboy"
    universe ←  newIORef theUniverse
    displayCallback $= (display universe)
    idleCallback $= Just (idle universe)
    keyboardMouseCallback $= Just (keyboardMouse universe)

display :: IORef (Universe Ship) →  IO ()
display ioRefUniverse = do
    clear [ ColorBuffer ]
    scale 0.2 0.2 (0.2::GLfloat)
    universe ←  get ioRefUniverse
    displayUniverse universe

idle :: IORef (Universe Ship) →  IO ()
idle ioRefUniverse = do
    universe ←  get ioRefUniverse
    ioRefUniverse $= stepUniverse universe game
    threadDelay 10
    postRedisplay Nothing

stepUniverse :: (Universe Ship) →  (Universe Ship)
stepUniverse u = collided
        collided = universeCollide filtered collide
        filtered = universeFilter evolved inBounds
        evolved = universeEvolve u 0.1

collide :: Body Ship →  [Body Ship] →  [Body Ship]
collide b@(Body s mass m (Projectile d t)) xs = []
collide b _ = [b]

inBounds :: Body Ship →  Bool
inBounds b@(Body _ _ (Movement (Geometry.Point x y) _ _) d)
    | shipIsFighter d = True
    | otherwise = and [abs x < 10, abs y < 10]

keyboardMouse ioRefUniverse key state modifiers position =
    keyboard ioRefUniverse key state

keyboard :: IORef (Universe Ship) →  Key →  KeyState →  IO ()
keyboard ioRefUniverse (Char 'q') Down = do exitSuccess
keyboard ioRefUniverse (Char ' ') Down = fire ioRefUniverse
keyboard ioRefUniverse (SpecialKey KeyLeft) Down = navigate ioRefUniverse vectorLeft
keyboard ioRefUniverse (SpecialKey KeyRight) Down = navigate ioRefUniverse vectorRight
keyboard ioRefUniverse (SpecialKey KeyUp) Down = navigate ioRefUniverse vectorUp
keyboard ioRefUniverse (SpecialKey KeyDown) Down = navigate ioRefUniverse vectorDown
keyboard _ _ _ = return ()

fire :: IORef (Universe Ship) →  IO()
fire ioRefUniverse = do
    universe ←  get ioRefUniverse
    ioRefUniverse $= universeActOnFighter universe fighterFire

navigate :: IORef (Universe Ship) →  Vector →  IO ()
navigate ioRefUniverse direction = do
    universe ←  get ioRefUniverse
    ioRefUniverse $= universeActOnFighter universe (λf →  fighterMove f direction)


For a month of on-again, off-again work, the prototype turned out reasonably well and I got a lot out of it. I think that as I continue to use Haskell, my brain will slowly switch from thinking in terms of structures of data to flows of data and I will ultimately be able to be more productive in Haskell. Until then, I’m going to stick with my current technology stack and continue to experiment with Haskell. Keep an eye for part three of this series which will go over the completed product.

Written by lewellen

2011-04-01 at 8:00 am

Posted in Projects

Tagged with , , ,

Space Cowboy: A Shoot’em up game in Haskell: Part 1

with 2 comments

It’s the start of a new year and January always marks the return of Antimatroid, The. The past few months I’ve been busy working on a number of project around the house and spending some time working on a few projects for around here. This article serves as an introduction to a shoot’em up game that I’ve been working on since July. Future installments will cover the implementation and design aspects of the project.


The past few months I’ve been working on a Shoot’em up game in Haskell and decided that I’d gotten to a point where a writeup was in order. I’ve always enjoyed the genre and I wanted to create something with a degree of complexity greater than my previous arcade games. Along the same lines, I decided to go with Haskell so that I could get a better hang of the language and build something tangible and practical beyond the utilities and solvers I’ve written. The title of the game is a nod to various Space Westerns that inspired me to get started. The following writeup goes over the software development process I applied to the project from specification to implementation.


Space Cowboy is a single player game consisting of a sequence of levels. The user starts on the first level and plays until he or she has completed the level and progresses onto the next level and so on. Once there are no more levels left, the user has won the game. If a user fails to complete a level, then the game is over. Each level is of a fixed length and contains a fixed number of opponents. To complete a level, the user either gets to the end of the level or destroys all of the opponents. If an opponent destroys the user, then the user does not complete the level and the game is over.

The user and the opponents are represented by ships. Ships start with a fixed number of hit points and lose hit points any time the ship is attacked or it collides with another ship. Once a ship has lost enough hit points to match its initial hit points, then it is considered destroyed. Ships can attack one another using weapons that come in a variety of rates of fire and magnitude of damage. Each ship can can maneuver around the level using engines that come in a variety of thrusts and rates of propulsion. The user’s ship can be maneuvered left, right, up and down and instructed to fire its weapons. Opponents ships are maneuvered by the game. Ships can improve their abilities by colliding with power-ups which upgrade weapons, engines and hit points. Power-ups are produced randomly whenever a ship is destroyed.

A score system keeps track of the user’s progress. When the user starts the game, his or her score is set to zero and increases as he or she plays each level. Whenever a user gets a power-up or destroys a ship, then their score increments proportionally to the magnitude of the power-up or ship destroyed. A user’s score is never decremented. The user is incentivised to play again to obtain a higher score than his or her previous trial.


User Interface

The user interface will be a portfolio view consisting of four screens:

  • Logo Screen: displays the developer’s logo and copyright information
  • Menu Screen: allows the user to start a new game, view high scores and exit the application
  • Game Screen: contains information about what level the user is on, their score, the number of lives they have left and the view of the game universe
  • High Scores Screen: contains a list of the top five high scores achieved in the game

When the application starts, the user will see the Logo Screen which will transition to the Main Menu Screen after a few seconds. When the user presses the New Game Button, the application will go to the Game Screen. When the user presses the High Scores Button, the application will go to the High Scores Screen. When a user completes their game, they will transition to the High Scores Screen. If the user has a new high score, they will be asked to enter the name they want to associate with the score. The user may go back to the Main Menu Screen by clicking on the Menu Button.


The game universe is a simplified model of the physical universe. The game universe has two spatial dimensions and one temporal dimension. Both spatial dimensions are bounded and residents of the game universe may not exist outside of those boundaries. When the game starts, the user will be at one extreme of these boundaries and must reach the other extreme to complete the level.

Every resident in the game universe has a dimension, heading and location. No two residents of the game universe may occupy the same space at the same time. When two residents collide, their resulting motions will follow Newton’s laws of motion. If the damage done on either body during the collision is material, then the body will be reduced to debris and power-ups.

When a ship fires its engines, the thrust of the engine will advance the ship in the direction indicated by the user with respect to the ship’s heading. When the ship fires its weapons, the ship will experience kickback in accordance with Newton’s third law of motion. As the user’s ship moves through the game universe, the view of the game universe will be centered on the user’s ship.

Written by lewellen

2011-01-01 at 8:00 am

Posted in Projects

Tagged with ,