Foundations of Game Engine Development: Volume - Mathematics

Game engines are complex software systems that power the vast majority of modern video games. They are responsible for handling everything from rendering graphics to simulating physics to managing artificial intelligence. As such, they require a strong foundation in mathematics in order to function properly.

Foundations of Game Engine Development, Volume 1: Mathematics

by Eric Lengyel

4.6 out of 5

Language	:	English
File size	:	16647 KB
Screen Reader	:	Supported
Print length	:	465 pages

FREE

This article provides an to the mathematical foundations of game engine development. It covers topics such as linear algebra, geometry, and calculus, and explains how these concepts are used in game engines to create realistic and immersive experiences.

Linear Algebra

Linear algebra is a branch of mathematics that deals with vectors and matrices. Vectors are mathematical objects that represent points in space or directions, while matrices are mathematical objects that represent transformations. Linear algebra is used in game engines for a variety of purposes, including:

• Transforming objects: Linear algebra is used to transform objects in space. This is necessary for a variety of tasks, such as rotating characters, moving objects around the world, and scaling objects up or down.
• Calculating lighting: Linear algebra is used to calculate lighting in game engines. This is necessary to create realistic shadows and reflections, and to make objects appear more three-dimensional.
• Simulating physics: Linear algebra is used to simulate physics in game engines. This is necessary to make objects move and interact realistically with each other.

Geometry

Geometry is a branch of mathematics that deals with the shapes and sizes of objects. Geometry is used in game engines for a variety of purposes, including:

• Creating models: Geometry is used to create models of objects in game engines. These models are used to represent characters, objects, and environments.
• Collision detection: Geometry is used to perform collision detection in game engines. This is necessary to prevent objects from passing through each other, and to make sure that objects interact with each other correctly.
• Pathfinding: Geometry is used to perform pathfinding in game engines. This is necessary to find the shortest path from one point to another, which is used for AI characters to navigate the world.

Calculus

Calculus is a branch of mathematics that deals with change. Calculus is used in game engines for a variety of purposes, including:

• Simulating motion: Calculus is used to simulate the motion of objects in game engines. This is necessary to make objects move smoothly and realistically.
• Calculating physics: Calculus is used to calculate physics in game engines. This is necessary to make objects interact with each other correctly.
• Creating animations: Calculus is used to create animations in game engines. This is necessary to make characters and objects move smoothly and realistically.

Mathematics is essential for game engine development. It is used to create realistic and immersive experiences, from graphics to physics to AI. This article has provided a brief overview of the mathematical foundations of game engine development. For more in-depth information, there are a number of excellent resources available online and in libraries.

Foundations of Game Engine Development, Volume 1: Mathematics

by Eric Lengyel

4.6 out of 5

Language	:	English
File size	:	16647 KB
Screen Reader	:	Supported
Print length	:	465 pages

FREE