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Mathfs

Freya's expanded math functionality for Unity!

  • This is primarily a way for me to share the math functionality I write and use in my own personal projects
  • I will recklessly edit and adapt things without too much thought into backwards compatibility
  • Minimum Unity version is currently 2021.2 due to using newer C# version features. It may be possible to auto-downgrade through your IDE if necessary
  • Commits with version tags should be relatively stable. Other commits may not be

Installation instructions

There are several ways to install this library into your project:

  • Plain install
    • Clone or download this repository and put it somewhere in the Assets folder of your Unity project
  • Unity Package Manager (UPM):
    • Add either of the the following lines to Packages/manifest.json:
    • "com.acegikmo.mathfs": "https://github.com/FreyaHolmer/Mathfs.git#0.1.0", if you want to target a specific version (recommended)
    • "com.acegikmo.mathfs": "https://github.com/FreyaHolmer/Mathfs.git", if you want to pull the latest commit (potentially unstable)
    • More information about UPM and git here
  • OpenUPM
    • After installing openupm-cli, run the following command:
    • openupm add com.acegikmo.mathfs

After installation you will be able to access the library in scripts by including the namespace using Freya

Features

  • 2D Intersection tests between all combinations of:
    • Ray
    • LineSegment
    • Line
    • Circle
  • Curves & Splines
    • Bézier (Quadratic, Cubic & Generalized)
    • Hermite
    • Catmull-Rom
    • B-Spline (Uniform Cubic & Generalized Non-Uniform)
    • NURBS (Non-Unifrom Rational B-Spline)
    • Trajectory (Cubic & Generalized)
  • Trajectory math
    • GetDisplacement (point in trajectory), given gravity, angle, speed & time
    • GetLaunchSpeed, given gravity, angle & lateral distance
    • GetLaunchAngles, given gravity, speed & lateral distance
    • GetMaxRange, given gravity & speed
    • GetHeightPotential, given gravity, current height and speed
    • GetSpeedFromHeightPotential, given gravity, current height and height potential
  • Triangle math
    • Area / SignedArea, given three points or base and height
    • Contains check, given three triangle vertices and a point to test by
    • Right-angle trig functions to calculate Opposite/Adjacent/Hypotenuse/Angle
    • Incenter / Centroid
    • Incircle / Circumcircle
    • SmallestAngle
  • Polygon math
    • Area / SignedArea
    • IsClockwise
    • WindingNumber
    • Contains
  • Circle math
    • FromTwoPoints (get smallest circle passing through both points)
    • FromThreePoints (get unique circle passing through three points)
    • RadiusToArea / AreaToRadius
    • AreaToCircumference / CircumferenceToArea
    • RadiusToCircumference / CircumferenceToRadius
  • 2D Angle helpers (AngToDir, DirToAng...)
  • 2D Vector extension methods (Rotate90CCW/CW, Rotate, RotateAround...)
  • Quadratic & Linear Root finders
  • Remap functions
  • Constants (Tau, Pi, Golden Ratio, e, sqrt2)
  • Vector extension methods (WithMagnitude, ClampMagnitude(min,max)...)
  • Expanded basic math operations to vectors (Clamp, Round, Abs...)
  • Color extensions (WithAlpha, MultiplyRGB...)
  • Smoothing functions (Smooth01, SmoothCos01...)
  • Triangle Math helpers (SignedArea, Circumcenter, Incircle...)
  • Circle Math helpers (Area, Circumference...)
  • All functions use radians
  • And more!

Changes

Mathfs.cs does not fully match Unity's Mathf.cs, I've made a few changes:

  • All angles are in radians, no methods use degrees
  • Lerp and InverseLerp:
    • Unclamped by default
    • LerpClamped/InverseLerpClamped are now the special case functions/exceptions
    • Uses the more numerically stable evaluation
  • Smoothstep is removed in favor of the more explicit:
    • LerpSmooth (which is how it was implemented) and
    • InverseLerpSmooth (which is how it is implemented everywhere but Unity's Mathf.cs)
  • Min/Max functions with arbitrary inputs/array input will throw on empty instead of returning 0