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q2ea.m
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function ea = q2ea(q, seq)
% Copyright 2016 An Uncommon Lab
%#codegen
if nargin < 2, seq = [3 2 1]; end;
% Check dimensions.
if size(q, 1) ~= 4 && size(q, 2) == 4, q = q.'; end;
assert(size(q, 1) == 4, ...
'%s: The quaternions must be 4-by-n.', mfilename);
assert(size(seq, 1) == 1 && size(seq, 2) == 3, ...
'%s: The Euler angle rotation sequence must be 1-by-3.', ...
mfilename);
assert(seq(1) ~= seq(2) && seq(2) ~= seq(3), ...
['%s: The Euler angle sequence cannot repeat rotations ' ...
'about the same axis.'], mfilename);
% Determine signs.
i = seq(1);
j = seq(2);
if (i == 1 && j == 2) ...
|| (i == 2 && j == 3) ...
|| (i == 3 && j == 1)
alpha = 1;
else
alpha = -1;
end
% Preallocate.
n = size(q, 2);
ea = zeros(3, n, class(q));
% If symmetric...
if seq(1) == seq(3)
% Determine the other axis.
if (i == 1 && j == 2) || (i == 2 && j == 1)
k = 3;
elseif (i == 1 && j == 3) || (i == 3 && j == 1)
k = 2;
else
k = 1;
end
ea(2,:) = acos( q(i,:).*q(i,:) - q(j,:).*q(j,:) ...
- q(k,:).*q(k,:) + q(4,:).*q(4,:));
% MATLAB
if isempty(coder.target)
i1 = ea(2,:) == 0;
i2 = ea(2,:) == pi;
i3 = ~i1 & ~i2;
ea(1,i1) = 2 * atan2(q(i,i1), q(4,i1));
if alpha > 0
ea(1,i2) = 2 * atan2(q(k,i2), q(j,i2));
a2 = atan2(q(k,i3), q(j,i3));
else
ea(1,i2) = 2 * atan2(-q(k,i2), q(j,i2));
a2 = atan2(-q(k,i3), q(j,i3));
end
a1 = atan2(q(i,i3), q(4,i3));
ea(1,i3) = a1 + a2;
ea(3,i3) = a1 - a2;
% codegen
else
if alpha > 0
for z = 1:n
if ea(2,z) == 0
ea(1,z) = 2*atan2(q(i,z), q(4,z)); % Shuster misses a 2 here.
elseif ea(2,z) == pi
ea(1,z) = 2*atan2(q(k,z), q(j,z));
else
a1 = atan2(q(i,z), q(4,z));
a2 = atan2(q(k,z), q(j,z));
ea(1,z) = a1 + a2;
ea(3,z) = a1 - a2;
end
end
else
for z = 1:n
if ea(2,z) == 0
ea(1,z) = 2*atan2(q(i,z), q(4,z)); % Shuster misses a 2 here.
elseif ea(2,z) == pi
ea(1,z) = 2*atan2(-q(k,z), q(j,z));
else
a1 = atan2(q(i,z), q(4,z));
a2 = atan2(-q(k,z), q(j,z));
ea(1,z) = a1 + a2;
ea(3,z) = a1 - a2;
end
end
end
end
% Otherwise, must be asymmetric.
else
k = seq(3);
if alpha > 0
ea(2,:) = asin(2 * (q(4,:) .* q(j,:) + q(k,:) .* q(i,:)));
else
ea(2,:) = asin(2 * (q(4,:) .* q(j,:) - q(k,:) .* q(i,:)));
end
% MATLAB
if isempty(coder.target)
i1 = ea(2,:) == pi/2;
i2 = ea(2,:) == -pi/2;
i3 = ~i1 & ~i2;
if alpha > 0
ea(1,i1) = atan2(q(i,i1) + q(k,i1), ...
q(4,i1) + q(j,i1));
ea(1,i2) = atan2(q(i,i2) - q(k,i2), ...
q(4,i2) - q(j,i2));
a1 = atan2(q(i,i3) + q(k,i3), q(4,i3) + q(j,i3));
a2 = atan2(q(i,i3) - q(k,i3), q(4,i3) - q(j,i3));
else
ea(1,i1) = atan2(q(i,i1) - q(k,i1), ...
q(4,i1) - q(j,i1));
ea(1,i2) = atan2(q(i,i2) + q(k,i2), ...
q(4,i2) + q(j,i2));
a1 = atan2(q(i,i3) + q(k,i3), q(4,i3) - q(j,i3));
a2 = atan2(q(i,i3) - q(k,i3), q(4,i3) + q(j,i3));
end
ea(1,i3) = a1 + a2;
ea(3,i3) = a1 - a2;
% codegen
else
if alpha > 0
for z = 1:n
if ea(2,z) == pi/2
ea(1,:) = atan2(q(i,z) + q(k,z), ...
q(4,z) + q(j,z));
elseif ea(2,z) == -pi/2
ea(1,:) = atan2(q(i,z) - q(k,z), ...
q(4,z) - q(j,z));
else
a1 = atan2(q(i,z) + q(k,z), q(4,z) + q(j,z));
a2 = atan2(q(i,z) - q(k,z), q(4,z) - q(j,z));
ea(1,z) = a1 + a2;
ea(3,z) = a1 - a2;
end
end
else
for z = 1:n
if ea(2,z) == pi/2
ea(1,:) = atan2(q(i,z) - q(k,z), ...
q(4,z) - q(j,z));
elseif ea(2,z) == -pi/2
ea(1,:) = atan2(q(i,z) + q(k,z), ...
q(4,z) + q(j,z));
else
a1 = atan2(q(i,z) + q(k,z), q(4,z) - q(j,z));
a2 = atan2(q(i,z) - q(k,z), q(4,z) + q(j,z));
ea(1,z) = a1 + a2;
ea(3,z) = a1 - a2;
end
end
end
end
end
end % q2ea