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[37] | 1 | function Y = sin(X) |
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| 2 | % SIN Sine. |
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| 3 | % (Quaternion overloading of standard Matlab function.) |
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| 4 | |
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| 5 | % Copyright © 2006 Stephen J. Sangwine and Nicolas Le Bihan. |
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| 6 | % See the file : Copyright.m for further details. |
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| 7 | |
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| 8 | error(nargchk(1, 1, nargin)), error(nargoutchk(0, 1, nargout)) |
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| 9 | |
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| 10 | if isreal(X) |
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| 11 | |
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| 12 | % X is a real quaternion, and we compute the sine of an isomorphic |
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| 13 | % complex number using the standard Matlab sin function, then |
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| 14 | % construct a quaternion with the same axis as the original quaternion. |
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| 15 | |
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| 16 | Y = isoquaternion(sin(isocomplex(X)), X); |
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| 17 | else |
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| 18 | |
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| 19 | % X is a complex quaternion, and therefore we cannot use the method |
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| 20 | % above for real quaternions, because it is not possible to construct |
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| 21 | % an isomorphic complex number. We use instead a fundamental formula |
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| 22 | % for the sine in terms of the exponential. |
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| 23 | |
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| 24 | Y = (exp(i .* X) - exp(-i .* X)) ./ (2 .* i); |
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| 25 | end; |
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| 26 | |
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