Trigonometry in Game Development - Gr8-Tools/game-developer-roadmap-doc GitHub Wiki

Total time: 11.5 hours

Trigonometry plays a crucial role in game development, especially when working with Unity game engine. It enables developers to create realistic movement, positioning, and animation within a game world. In this article, we will explore key concepts of trigonometry that are frequently used in game development with Unity.

1. Angles

Angles are fundamental in trigonometry and game development. In Unity, angles are usually measured in degrees or radians. Understanding how to convert between these units is essential when working with trigonometric functions.

2. Rotation

Rotation is a core concept in game development. Unity provides numerous built-in functions to manipulate rotations using angles. Understanding trigonometry helps in smoothly rotating game objects, aligning them with certain directions, or creating visually appealing animations.

3. Vectors

Vectors are extensively used in game development to represent positions, directions, velocities, and forces. Trigonometric functions provide valuable tools to calculate vector components, angles between vectors, and perform vector operations.

4. Positioning

Accurate positioning of game objects is crucial for creating a realistic game world. Trigonometry aids in determining the position of objects based on their initial position, speed, and angle of movement. It is also beneficial for implementing movement patterns such as circular or oscillatory motion.

5. Collision Detection

Collision detection is an essential aspect of game development. Trigonometry helps in calculating collision points, angles of incidence and reflection, and determining appropriate responses to collisions. It enables accurate collision detection between game objects with irregular shapes.

6. Camera Control

Proper camera control enhances the overall gaming experience. Trigonometry facilitates the implementation of smooth camera movements, tracking objects, and creating visual effects like parallax scrolling or zooming based on the player's position or movement.

7. Projectile Trajectories

In many game genres, projectiles play a significant role. Trigonometry assists in calculating projectile trajectories based on their initial position, velocity, and angle of launch. It enables developers to accurately predict the path of projectiles and implement mechanics like arching or bouncing.

8. Pathfinding

Pathfinding algorithms are essential for creating intelligent non-player characters (NPCs) or enemies. Trigonometry helps in determining the correct angles and distances to navigate game characters along a path, avoid obstacles, or follow the player's movements.

9. Volume

In game development, a "volume" is often used to define a specific area within a game world that triggers certain events or applies specific effects. These volumes are commonly known as "trigger volumes" or "collision volumes." They are invisible boundaries defined by geometric shapes like boxes, spheres, or cylinders. These volumes help determine when a player or an object enters or leaves a designated region in a game.

Here is an example to help clarify the usage of volumes in game development:

Let's say you're developing a first-person shooter game and want to create an area where if a player enters, an enemy is triggered to start attacking. You can define a box-shaped volume in that specific area of your game world. When the player's character enters that volume, it triggers the enemy AI to become active, and it starts attacking the player.

Another example could be a racing game where you want to have a specific region on the track that boosts the player's speed. You can define a cylindrical volume and, when the player's vehicle enters that volume, it boosts their speed temporarily.

In both cases, the volumes serve as invisible boundaries that allow developers to detect specific events or apply desired effects based on a player or object's position within the game world.

Trigonometry is a versatile mathematical tool that empowers game developers in numerous ways. Having a strong understanding of trigonometric concepts and their applications in Unity enables the creation of visually appealing, realistic, and engaging games.

Additional materials

Articles

  1. Cheat-sheet

Video

  1. Trigonometry - full trigonometry guide.

7 hours

Tasks

Math Lib

The following tasks should be realised in special project "Math Lib". Write functions that resolve the tasks issues in one class and demonstrate the functionality in any way on "Scene"- or "Editor"-windows.

All inputs and outputs of tasks should be visualised. You can use Gizmos or LineRenderer (or any other tool) for this purpose.

  1. Calculate the angle between two vectors: Write a program that takes as input two vectors in 3D space (specified by their x, y, and z components) and calculates the angle between them. The program should output the angle in degrees.

30 minutes

  1. Rotate a game object around a point: Create a program that rotates a game object (specified by its position in 2D space) around a given point (specified by its coordinates). The program should take as input the initial position of the object, the point of rotation, and the angle of rotation. The output should be the new position of the object after the rotation.

30 minutes

  1. Reflect an object off a surface: Create a program that reflects a game object off a surface. The program should take as input the initial position of the object, the normal vector of the surface, and the coefficient of restitution. Imagine that velocity of object is directed to the center of coordinate system, that intercects the surface space. The output should be the new position of the object after the reflection accordingly the coefficient of restitution.

1.5 hour

  1. Calculate the trajectory of a projectile: Design a program that calculates the trajectory of a projectile launched in a 2D space. The program should take as input the initial position and velocity of the projectile, the angle of launch, and the gravitational force. The output should be the positions of the projectile at regular intervals of time.

2 hour