Unity Math classes: Mathf, Random, Quaternion

Mathf class

• Manual: Mathf class
• Script Reference: Mathf class
• Min, Max, Clamp, Abs: See Helpful Math functions
• See Interpolation (lerp, slerp...)

Trigonometric functions

• Sin, Cos, Tan, Asin, Acos, Atan, Atan2
• Rad2Deg, Deg2Rad
• PI

Other functions

• Pow, Sqrt, Exp, Log
• Abs

Limits & repeats

• Max, Min
• Clamp, Clamp01
  • (value, min, max)
• Repeat, PingPong
• Ceil, Floor
• Mathf.DeltaAngle(a,b): Shortest difference between two given angles

Random class

• Important classes: Random
  • This page has all the random examples you need
• Script Reference: Random class

Random.Range

• Script Reference: Random.Range
• Note: For integers, the maximum value is exclusive (it's not included!)
  • For floats it's inclusive (it IS included!)
• For example:
  • Random.Range(0,10) returns random integer values (not !)
  • Random.Range(0f,10f) returns random float values

Quaternion class

• Manual: Rotation and Orientation in Unity
• Euler angles are a rather simple way of representing rotation with three X,Y,Z values
• Quaternions: A four-dimensional extension of complex numbers with three imaginary axes

What you really need to know about Quaternions

• They're used for representing rotation angles instead of Euler angles that can result in a gimbal lock

• Most Unity devs don't really need to understand the underlying maths

• Even though rotation is stored as a quaternion...

  • four components: x, y, z, w

• ...it is shown in Inspector with Euler angles

Quaternion note

• Never adjust Quaternion components independently, use ready-made functions from the Quaternion class
• transform.rotation = Quaternion.LookRotation(target.position - transform.position)
• transform.rotation = Quaternion.LookRotation(target.position - transform.position, new Vector3.Up)

Reading

• GMTK: The two types of random in game design