This is the first installment of a series of tutorials in which we aim to make a 3D Driving Simulation Game. With every successive tutorial we will try to make the game cooler by adding new features in graphics, physics and gameplay. The aim of this first tutorial is to simulate a car over an infinitely large plane. I know this is not exactly what we have in the real world. But we will get more realistic in later tutorials. For now imagine the world as a perfect plane with no obstacles.
This article is not for the absolute beginner. A basic understanding of XNA Game Studio 2.0 is necessary. But If you are a beginner, I would suggest the following.
Reasonable Knowledge of Newtonian Mechanics and Geometry is necessary to understand the formulas.
The application has been divided into three classes Game1, Stuff, Car . The class Stuff represents any material body than can be rendered on the screen. The class Car is a specialization of the Class Stuff which represents a Car. The class Game1 is the main application and uses objects of Stuff and Car.
Let us first understand the class Stuff. If you go through the code you will see that I have tried to encapsulate everything required to store information of any material body and render it on screen. I am only providing an overview of the member variable and function since the code is fairly straight forward.
viewMatrix and projectionMatrix are static because they are same for all renderable objects. position and rotation represent the position of the object and its orientation respectively in 3D Space. cameraRotation represents the orientation of the camera. Storing this is necessary to achieve the effect of camera delay. model represents the 3D Model of the body. UpdateCamera updates the viewMatrix according to the position and orientation of car. Draw renders the 3D Model on the screen. Now for the most difficult part - understanding the class Car. There are two concepts at work. The first one is the effect of hitting the accelerator, releasing it, and braking on the cars motion. The second one is how the car turns when the steering is turned left or right.
The first concept. At any instant the car is in some gear represented by the variable gear. The speed of the vehicle determines the gear. We have the top speed at each gear stored in the variable topSpeeds. The top speed at gear x is also the minimum speed for gear x+1. The acceleration is different at each gear.
public void Accelerate()
{
free = false;
if ((gear<7)&&(speed > topSpeeds[gear]))
{
gear++;
}
if (gear == 0)
{
acceleration = accelerations[1];
}
else if (gear < 7)
acceleration = accelerations[gear];
else
{
gear = 6;
acceleration = 0;
speed = topSpeeds[6];
}
}
Now when the brake is applied the effect is that a negative acceleration whose magnitude is the acceleration at that gear added to a constant as shown. Here you also have to consider the reverse gear and the maximum speed in reverse.
public void Brake()
{
free = false;
if((gear>0)&&speed<=topSpeeds[gear-1])
{
gear--;
}
if ((gear == 0) && (speed < -maxReverseSpeed))
{
acceleration = 0;
speed = -maxReverseSpeed;
}
else
{
acceleration = -accelerations[gear]-6.7f;
}
}
Also when the accelerator is released, even then a negative acceleration with magnitude same as acceleration at that gear has to be applied. And eventually the car comes at rest
public void Free()
{
free = true;
if ((gear>0)&&(speed < topSpeeds[gear - 1]))
{
gear--;
}
acceleration = - accelerations[gear];
}
To determine the new position of car after every instant the following code is placed in the Update method.
float speed = speed + acceleration * time;
float dist = speed * time;
Vector3 addVector = Vector3.Transform(new Vector3(0, 0, -1), rotation);
position += addVector * dist;
To make sure the car eventually comes to stop when neither accelerator nor brake is pressed this code is used:
float newSpeed = speed + acceleration * time;
if ((free == true) && (newSpeed * speed <= 0.0f))
{
gear = 1;
acceleration = accelerations[gear];
speed = 0.0f;
}
else
speed = newSpeed;
Now let us understand how a car turns. When the driver steers left or right, the plane surface makes and angle theta with the body of the car as shown in figure. Theta should uniformly increase from to 0 to a Maximum Value. Also when the steering is left free theta should eventually become zero. The code for this is as follows:
if (turn == 0)
{
float newAngle = steerAngle;
if (steerAngle < 0.0f)
{
newAngle = steerAngle + time * steerSpeed;
}
else if (steerAngle > 0.0f)
{
newAngle = steerAngle - time * steerSpeed;
}
if (newAngle * steerAngle < 0.0f)
{
steerAngle = 0.0f;
}
else
steerAngle = newAngle;
}
else
{
if (turn == -1)
{
float newAngle = steerAngle - time * steerSpeed;
if (newAngle < -maxSteerAngle)
{
steerAngle = -maxSteerAngle;
}
else
{
steerAngle = newAngle;
}
}
else
{
float newAngle = steerAngle + time * steerSpeed;
if (newAngle > maxSteerAngle)
{
steerAngle = maxSteerAngle;
}
else
{
steerAngle = newAngle;
}
}
}
Now that we have understood how the tire turns, let us figure out how the car turns. Look at the figure carefully.
You will at once understand what the constants HD,VD and L represent.O is the origin of the 3D Model. We assume that the car will rotate about the point marked "Center Of Turning" with radius r. The value of r can be calculated using trignometry
float x = (VD / Math.Abs((float)Math.Tan(steerAngle)) + HD / 2);
float r = (float)Math.Sqrt(x * x + L * L);
Now we have the radius. The angle by which the car rotates can be found out and corresponding Quaternion is created.
float theta = speed * time / r;
if (steerAngle < 0.0f)
theta = -theta;
rotation = rotation * Quaternion.CreateFromAxisAngle(new Vector3(0, -1, 0), theta);
New position of car can be determined as follows.
speed = speed + acceleration * time;
float dist = speed * time;
Vector3 addVector = Vector3.Transform(new Vector3(0, 0, -1), rotation);
position += addVector * dist;
The rest of the code is pretty much straight forward.
I would like to thank my friend Tarang Bakshi for his help with the game physics and ideas.
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