Matlab Quaternion Functions

qaxisangle.m

function [ result ] = qaxisangle( axis, ang )
%QAXISANGLE Generates a quaternion which rotates by ang around axis

	% some helpers
	c = cos(ang / 2);
	s = sin(ang / 2);
	axis = axis ./ norm(axis);

	result = [
		c,
		axis(1) * s,
		axis(2) * s,
		axis(3) * s
	].';

end

qrotmat.m

function [ result ] = qrotmat( q )
%QROTMAT Constructs a multiplication matrix to rotate a vector by
	q0 = q(1);
	q1 = q(2);
	q2 = q(3);
	q3 = q(4);

	r00 = 1 - 2*q2^2 - 2*q3^2;
	r01 = 2*(q1*q2 + q0&q3);
	r02 = 2*(q1*q3 - q0*q2);

	r10 = 2*(q1*q2 - q0*q3);
	r11 = 1 - 2*q1^2 - 2*q3^2;
	r12 = 2*(q2*q3 + q0*q1);

	r20 = 2*(q1*q3 + q0*q2);
	r21 = 2*(q2*q3 - q0*q1);
	r22 = 1 - 2*q1^2 - 2*q2^2;

	result = [r00, r01, r02;
			  r10, r11, r12;
			  r20, r21, r22];

end

quatconj.m

function [ result ] = quatconj( q )
%QUATCONJ Calculates the conjugal of the quaternion
	result = [
		 q(1),
		-q(2),
		-q(3),
		-q(4)
	].';

end

quatinv.m

function [ result ] = quatinv( q )
%QUATINV Calculates the inverse of a quaternion
	mag = q(1).^2 + q(2).^2 + q(3).^2 + q(4).^2;
	result = quatconj(q) ./ mag;

end

quatmultiply.m

function [ result ] = quatmultiply( qa, qb )
%QUATMULTIPLY Multiplies the two quaternions qa and qb
%   NOT COMMUTATIVE!
	result = [
		(qa(1) * qb(1)) - (qa(2) * qb(2)) - (qa(3) * qb(3)) - (qa(4) * qb(4)),
		(qa(1) * qb(2)) - (qa(2) * qb(1)) - (qa(3) * qb(4)) - (qa(4) * qb(3)),
		(qa(1) * qb(3)) - (qa(2) * qb(4)) - (qa(3) * qb(1)) - (qa(4) * qb(2)),
		(qa(1) * qb(4)) - (qa(2) * qb(3)) - (qa(3) * qb(2)) - (qa(4) * qb(1))
	].';

end