5 Abstract coordinate systems 29


u is (the locus of) a coordinate component curve: C



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u is (the locus of) a coordinate component curve: C1 S2S3, C2 = S1S3, and C3 = S2S1.

The CS type surface and CS type 2D cases:

If F is the generating function of a CS of CS type surface or CS type 2D, D is the CS domain, and u = (u0, v0) is in the interior of D, then the 1st- and 2nd-coordinate component curve at u is parametrically specified, respectively, by the following smooth functions:






, and






.



The domain for C1 is the connected component of which contains u0.
The domain for

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