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Quaternions are generally used for calculative simplicity - it's a lot easier (and faster) to do things like composing transformations when using quaternions. To quote the Wikipedia page you linked,

Combining two successive rotations, each represented by an Euler axis and angle, is not straightforward, and in fact does not satisfy the law of vector addition, which shows that finite rotations are not really vectors at all. It is best to employ the direction cosine matrix (DCM), or tensor, or quaternion notation, calculate the product, and then convert back to Euler axis and angle.

They also do not suffer from a problem common to axis/angle form, gimbal lock.

Quaternions are generally used for calculative simplicity - it's a lot easier (and faster) to do things like composing transformations when using quaternions. To quote the Wikipedia page you linked,

Combining two successive rotations, each represented by an Euler axis and angle, is not straightforward, and in fact does not satisfy the law of vector addition, which shows that finite rotations are not really vectors at all. It is best to employ the direction cosine matrix (DCM), or tensor, or quaternion notation, calculate the product, and then convert back to Euler axis and angle.

Quaternions are generally used for calculative simplicity - it's a lot easier (and faster) to do things like composing transformations when using quaternions. To quote the Wikipedia page you linked,

Combining two successive rotations, each represented by an Euler axis and angle, is not straightforward, and in fact does not satisfy the law of vector addition, which shows that finite rotations are not really vectors at all. It is best to employ the direction cosine matrix (DCM), or tensor, or quaternion notation, calculate the product, and then convert back to Euler axis and angle.

They also do not suffer from a problem common to axis/angle form, gimbal lock.

Source Link
Amber
Amber
  • 531.3k
  • 89
  • 643
  • 558

Quaternions are generally used for calculative simplicity - it's a lot easier (and faster) to do things like composing transformations when using quaternions. To quote the Wikipedia page you linked,

Combining two successive rotations, each represented by an Euler axis and angle, is not straightforward, and in fact does not satisfy the law of vector addition, which shows that finite rotations are not really vectors at all. It is best to employ the direction cosine matrix (DCM), or tensor, or quaternion notation, calculate the product, and then convert back to Euler axis and angle.