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"Implied shape" of a coordinate system
Posted:
Apr 28, 2009 7:21 AM


Is there an agreed term for the shape that is naturally defined by a coordinate system?
By this I mean, the shape that is enclosed by incrementing each of the coordinates from some nonzero starting point.
For example a rectangular Cartesian coordinate system 'naturally' defines a cuboid, a cylindrical polar coordinate system naturally defines a cylinder, and a spherical polar coordinate system 'naturally' defines a segment of a cone with rounded base and top.
In this thread:
http://groups.google.com/group/geometry.research/browse_thread/thread/51639f52834f855b/c9281f3dbd694eaf?lnk=gst&q=implied+shape#c9281f3dbd694eaf
the term "implied shape" is used with the meaning that I have in mind, but I find no other web references to this term.
Note that the shape is not necessarily that of the coordinate system. For example the spherical polar coordinates could be said to define a sphere, but its 'natural shape' by my definition is a truncated cone whose base and top are spherically curved surfaces. Also, there is some notion of the shape being 'aligned' in some way with the coordinate axes (thought not necessarily with the origins).
Thanks,
Chris ============ Chris Bore BORES Signal Processing www.bores.com



