Naming principles:

All classes have constructors that accept a small number of different types, typically:

• no arguments, create a null value (eg. null rotation, null pose etc.)
• same type argument, clone the argument
• native value, eg. numpy array or list
• parametric representation, eg. x, y, θ
• lists of native values or parametric representations, initialise the internal list

To handle different parameteric representations we use class methods as alternative constructors, for example:

• SO3.RPY(roll, pitch, yaw)
• SO3.Eul(phi, theta, psi)
• SO3.AngVec(angle, vector)
• SO3.Exp(twist)

These are methods on the class and are capitalised or have an initial capital letter.

These are methods on an instance and convert to a different parameterisation, for example:

• x.rpy() convert SO3 or SE3 to roll-pitch-yaw angles
• x.eul() convert to Euler angles

While they have similar names to the variant constructors:

• they perform an inverse function, the constructors are parameters → object, while the converters are object → parameters
• there can be no ambiguity since converters operators on instances whereas constructors operate on classes

Converters are always methods, since they may accept parameters.

A is for "array" and is the underlying NumPy representation of the type, a matrix for SO2, SE2, SO3 and SE3, or a vector for Twist2, Twist, Plane and Plucker.

For most types the arithmetic operators *, /, +, - and ** are overloaded. Some general principles:

• Some inplace operations are supported, ie. *= and /= using the dunder methods __iXXX___
• If operations is commutative the operator support this, eg. a * b or b * a are equivalent
• If the result of an operation is not in the group the result will be a numpy array
• The operation performed depends on the types of the left and right operands
• Each class supports its own operators
• For operations that involve different types, the support is implemented by the left-hand class

• reverse
• append
• extend
• insert
• len
• clear
• pop

Other standard list operations are not supported since they make little sense in this context: count, index, sort, remove