Essential Maths For Beginner Gamedevs - Which Math is Useful?

Summary

This video explores essential mathematical concepts used in game development, including basic operations, binary logic, vectors, trigonometry, and graph theory. It highlights how these concepts are applied for tasks such as pathfinding, AI behavior, object positioning, and 3D rotations. The tutorial also covers the importance of finite state machines in animating game objects and modeling behaviors. By emphasizing real-world applications, it offers a practical understanding of how mathematics powers the mechanics behind game development, making complex math concepts accessible and useful for creators.

Takeaways

• 😀 Basic mathematics, such as numbers and arithmetic, forms the foundation for game development and is crucial for understanding computer processing.
• 😀 Discrete mathematics plays an important role in game development, particularly in binary logic, trigonometry, and vector operations.
• 😀 Understanding binary logic (AND, OR, etc.) is essential for condition checks, enabling basic decisions in game behavior and AI.
• 😀 Coordinate systems, such as Cartesian coordinates, are fundamental in positioning objects in 2D and 3D game environments.
• 😀 Trigonometry, including sine, cosine, and Pythagoras’ theorem, is vital for calculating movement, rotations, and visual effects in games.
• 😀 Vectors are central in tracking directions, positions, and velocities, which are critical for game physics and movement mechanics.
• 😀 Quaternions, while complex, are important for handling rotations in 3D space, with Unity simplifying their use for developers.
• 😀 Graph theory, particularly in pathfinding algorithms, helps AI navigate levels and ensures that procedurally generated levels are traversable.
• 😀 Finite State Machines (FSMs) are used to model behaviors, such as transitions between different states (e.g., alert, resting) in games.
• 😀 Many mathematical concepts can be used more as planning tools for structuring game mechanics, rather than being directly implemented into the code.

Q & A

Why isn't everyone a super smart, galaxy brain level genius, despite the vast resources available on the internet?

The two main reasons are that we don't always know what we don't know, and school, which introduces a wide variety of topics but often lacks practical real-world connections.

Why is calculus considered less useful for making games compared to other subjects?

While calculus is incredibly useful in fields like physics, engineering, and chemistry, when it comes to game development, its direct applications are minimal, making it less essential for the everyday process of creating games.

How essential are basic arithmetic skills in game development?

Basic arithmetic skills like addition, subtraction, multiplication, and division are essential, as almost every aspect of a game, including health, position, and timers, is based on numbers, even if the computer performs the calculations.

What is discrete math and why is it important for game development?

Discrete math involves the study of mathematical structures that are fundamentally discrete rather than continuous. It is crucial for game development because computers operate on discrete values, making discrete math essential for tasks like logic, binary operations, and data structure handling in programming.

What role does binary logic play in game development?

Binary logic is used in game development through constructs like 'if' statements and operators such as AND, OR. It allows for decisions based on true/false conditions, helping control game mechanics like jumping, movement, and interaction with objects.

Why are coordinate systems important in game development?

Coordinate systems are vital because they define the position of objects within a game, whether in 2D or 3D. Understanding coordinates like the x, y, and z axes allows developers to accurately place and move objects on the screen or within the game world.

How does trigonometry apply to game development?

Trigonometry, particularly the sine and cosine functions, is used to calculate angles and positions. For example, they help determine the movement of objects in specific directions and animate periodic effects, like bobbing or stretching.

What is the significance of Pythagoras' Theorem in game development?

Pythagoras' Theorem is used to calculate distances between two points, essential for collision detection and figuring out the distance between objects. It is a key element in tasks like waypoint calculations and object proximity checks.

What are vectors, and why are they important in game development?

Vectors represent both magnitude and direction and are used to handle positions, movements, and velocities of objects in games. They are central to physics engines, camera systems, and even lighting, making them one of the most important concepts in game development.

How do quaternions differ from other methods of rotation in 3D space?

Quaternions are a mathematical approach to rotation that avoids the gimbal lock issue present in Euler angles, making them highly useful for smooth, continuous rotations. While they are essential in 3D game development, many game engines like Unity handle quaternions automatically, so developers rarely need to work with them directly.

What role does graph theory play in game development?

Graph theory is used for modeling relationships between objects in games. It is especially useful in pathfinding algorithms (e.g., AI movement), finite state machines (FSMs), and ensuring that levels are traversable by characters or entities without obstructions.