[pstricks] parametricplotThreeD and psplotThreeD and cartesian parametrization

A. Erhardt erhardt at fh-offenburg.de
Wed Jun 4 15:30:42 CEST 2008


I am trying to show the results or different parametrizations of 3D surfaces (example: demi-sphere) to my students 
in the subject of mathematics/vector analysis. 

I was trying to produce something like the enclosed picture "topf.tif". While I have no problem with the picture b) 
(except for the hidden line problem which I sent in a different email)
I had quite a problem with a) I finally made it but in a real glumsy way. 

While  pstricks provides a reale simple way to produce a plot with the parametrization in polar coordinates like
  \parametricplotThreeD[xPlotpoints=500, yPlotpoints=20, hiddenLine=true](0,360)(-90,90){%
	/r 1.0 def
	r t cos mul u sin mul 
	r t sin mul u sin mul 
	r u cos  mul
(and the statement with t and u reversed)

there is no simple way for the parametrizytion in cartesian coordinates.

	/r 1.0 def
        r dup mul t dup mul   sub dup 0.0 lt{ neg sqrt}{sqrt} ifelse  

produces not a satisfying result at all, so I had to do every coordinate line separately, even doing the "hidden line" algorithm by "vision and hand".

psplotThreeD on the other hand draws the horizontal lines z=0, y=0 to the limits of the picture frame, which is also not very satisfying.

My question: Is there an easier way to do this?

Enclosed please find the files

a) kugparaone.tex (the file with the problem clumsy way)
b) header.bil to include in file a) (you might have to change the path)
c)  kugparaone.ps which shows my result.
d) topf.tif

Best regards 
Angelika Erhardt

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