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Simple Question about Finding Tangent Vectors for Surfaces...


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#1 datahead8888   Members   -  Reputation: 163

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Posted 28 April 2014 - 12:10 AM

Suppose you have a parametric equation for a surface, for example:

 

 

x = 3*cos(s)+cos(t)*cos(s)

y = 3*sin(s)+cos(t)*sin(s)

z = sin(t)

 

The partial derivative of this wrt s is:

dsx = -3*sin(s)-cos(t)*sin(s)

dsy = 3*cos(s)+cos(t)*cos(s)

dsz = 0

 

The partial derivative of this wrt t is:

dtx = -sin(t)*cos(s)

dty = -sin(t)*sin(s)

dtz = cos(t)

 

Which of these is the tangent in the s direction, and which of these is the tangent in the t direction? 

I would have thought the tangent in the s direction is the derivative wrt s above and that the tangent in the t direction is the derivative wrt t, but I seem to remember hearing the opposite.



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#2 Álvaro   Crossbones+   -  Reputation: 16539

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Posted 28 April 2014 - 05:32 AM

You would have thought correctly. You should compute some simple example to convince yourself that you are correct.

#3 cadjunkie   Members   -  Reputation: 1640

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Posted 28 April 2014 - 09:23 AM

Agree with Alvaro. You're right on about the tangents.






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