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RollPitchYawAngles

RollPitchYawAngles

RollPitchYawAngles[r]

gives the roll-pitch-yaw angles {α,β,γ} corresponding to the rotation matrix r.

RollPitchYawAngles[r,{a,b,c}]

gives the roll-pitch-yaw angles {α,β,γ} corresponding to rotation order {a,b,c}.

Details

RollPitchYawAngles is used to decompose into fixed axis-oriented rotations.
RollPitchYawAngles[r,{a,b,c}] gives angles {α,β,γ} such that RollPitchYawMatrix[{α,β,γ},{a,b,c}]r.
RollPitchYawAngles[r] is equivalent to RollPitchYawAngles[r,{3,2,1}], the z-y-x rotation.
The default z-y-x angles RollPitchYawAngles[r,{3,2,1}] decompose rotation into three steps:

The rotation axes a, b, and c can be any integer 1, 2, or 3, but there are only twelve combinations that are general enough to be able to specify any 3D rotation.
Rotations with the first and last axis repeated:

	{3,2,3}	z-y-z rotation
	{3,1,3}	z-x-z rotation
	{2,3,2}	y-z-y rotation
	{2,1,2}	y-x-y rotation
	{1,3,1}	x-z-x rotation
	{1,2,1}	x-y-x rotation

Rotations with all three axes different:

	{1,2,3}	x-y-z rotation
	{1,3,2}	x-z-y rotation
	{2,1,3}	y-x-z rotation
	{2,3,1}	y-z-x rotation
	{3,1,2}	z-x-y rotation
	{3,2,1}	z-y-x rotation (default)

Rotations with subsequent axes repeated may not be invertible since these are not capable of representing all possible rotations in 3D.

Examples

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Basic Examples (2)

Get roll-pitch-yaw angles from the rotation matrix:

Get roll-pitch-yaw angles from the rotation matrix with the given rotation order:

Scope (2)

Get roll-pitch-yaw angles from a rotation matrix:

Get roll-pitch-yaw angles from a rotation matrix with the given rotation order:

Properties & Relations (1)

RollPitchYawAngles returns angles for which RollPitchYawMatrix gives the same rotation matrix:

The angles need not be the same:

However, both sets of angles produce the same rotation matrix:

Possible Issues (1)

RollPitchYawMatrix allows equal consecutive axes, and this generates a rotation matrix:

However, RollPitchYawAngles requires consecutive axes to be distinct:

This is because with consecutive axes equal, some rotation matrices cannot be represented:

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