Freya's expanded math functionality for Unity, brought to Godot!

• This is primarily a way to use and share Freya's awesome math stuff to Godot users
• I will also recklessly edit and adapt things without too much thought into backwards compatibility
• Minimum Godot version is currently 4.3. It may be possible to downgrade, but below 4 is completely untested

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

• Plain install
  • Clone or download this repository and put it somewhere in the addons folder of your project

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

• 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!

Mathfs.cs differs a bit from common/standard Math functions (specifically, Unity's):

• 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