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To do #8

@moble

Description

@moble

Implement and test:

  • Add and test frules
  • Add r/frules for log, sqrt, etc. Maybe squad and slerp?
  • axis-angle converters
  • Find more precise conversion to spherical coordinates. Note that acos is not a stable approach.
  • distance
    • intrinsic rotor
    • intrinsic rotation
    • chordal rotor
    • chordal rotation
  • Subtypes
    • Use AbstractQuaternion everywhere possible
    • Add Rotor type (or maybe UnitQuaternion)
    • Add Vec type
    • Specialize functions to work with them — especially exp, log, and sqrt
    • Extend wrapper to take an op argument along with two types, and return the appropriate wrapper type
    • Look at every function and consider every combination of types
    • Test new types and combinations
  • interpolation
    • squad
    • slerp
    • unflip rotors
  • time series
    • from_angular_velocity
    • to_angular_velocity
    • minimal rotation
  • Add conjugate function to efficiently rotate vectors by rotors
  • Reduce direct dependencies using extensions, with backwards compatibility via Requires
  • Simplify quaternion.jl
    • Remove parameters wherever possible
    • Add quaternion, rotor, and quatvec functions
      • Use rotor(...; normalize=false)
      • Accept arbitrary arrays, and return arrays of the corresponding type
      • Accept type parameter as optional argument or keyword argument, with default as detection

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