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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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