Unity 3D Game Development Math

• This study guide covers math and 3D concepts for advanced game development using Unity, including vectors, 3D rendering, and related math methods.

Introduction

• Unity 3D may appear complex initially, but vector and render pipeline familiarity is key to becoming as comfortable as working in 2D.

Key Vocabulary

• Vectors are primary tools that inform the compiler of an object's position relative to the zero point.
• Materials dictate an object's texture, light bouncing, and depth.
• Vertices are reference points in the game world that provide fixed X, Y, and Z values.

Vector Basics

• The course will cover both 3D and 2D vectors.

Two Types of Vectors

• Vector2D focuses solely on two coordinates: X and Y.
• Vector3D uses three coordinates, X and Y for horizontal and vertical position, and Z for object depth.

Magnitude

• Vector Magnitude refers to the length of a Vector direction away from 0, calculated using the Pythagorean theorem.

Pythagoras Theorem

• Magnitude = √X2+Y2
• Magnitude is used to determine the distance from a specific location.
• Weapons at range of 5 units away, by calculating it we would come out as 7.071.

Normalization in Math

• Unity uses vector direction to indicate direction instead of angles.
• Normalization is used to obtain the exact direction by setting the magnitude to 1 and focusing on the X, Y, and Z axes.

Vector Methods

• Vector methods speed up calculations for positioning, distance, and direction in Unity.

Distance

• Vectors pinpoint the position of gameObjects.
• Distance between two vectors is calculated as the magnitude between two vertices.
• .Distance(vectorA, vectorB)
• Vector distance can be used to identify the closest target for an enemy or an NPC.

LERP & Move Towards

• .Lerp(posA, posB, progress) requires three parameters.
• The first vector indicates the starting position.
• The second vector indicates the ending position.
• The third parameter is a float between 0 and 1, specifying where the return vector is located between those two vectors.
• This can be used for player movement or moving platforms.
• MoveTowards moves at a constant speed, with the third value determining the rate of increase per frame.
• .MoveTowards(posA, posB, distance) should be used for a more static increase instead of smooth movements.

Reflect

• Reflect is typically used for objects that bounce against walls.
• It takes two variables: the travel direction of the moving object, and the normal of the reflecting surface indicating the direction to reflect the ball toward.
• Returns the vector pointing to the object's new direction.

Dot

• The dot function returns a value between -1 and 1.
• 0 indicates the vectors are perpendicular.
• The value depends on the directions of the two vectors.
• .Dot(VectorA, VectorB) can be used to check if a plane is pointing up or down to increase or decrease drag.

Cross Method

• .Cross(dirA, dirB) returns the vector perpendicular to two provided vectors.
• The cross method is used when you want to rotate something to a certain angle, cross helps on knowing which way to turn an object to achieve the direction it is trying to get by rotating the object.

3D Rendering

• Fundamentals of 3D Development

Unity 3D Graphics

• Unity 3D offers easy to understand and use 3D game development processes.
• Importing models is easier than ever, with most formats being compatible.

Shaders

• Shaders create textures using base color, metallic properties, roughness, normal, and ambient occlusions.

Optimization

• Unity uses Level of Detail (LOD) to utilize textures shown at a distance.
• Lower poly models reduce stress on the computer.