niuage/Mathfs

Expanded Math Functionality for Unity

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#0.1.0", if you want to target a specific version (recommended)
  • "com.acegikmo.mathfs": "https://github.com/FreyaHolmer/Mathfs", 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