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Comment/Response 
Forum Moderator
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09/28/99 07:17am
>I am trying to plot a data set {x,y,z} with the color of the point calculated by Sqrt[x^2 + y^2 + z^2]. I am trying to use the Hue[h] function since I know that it is cyclic.
=====
You might try constructing your own points with color and
other directives.
Here is a random set of points:
In[10]:= xyzcoords=Table[{Random[],Random[],Random[]}, {10}]
Out[10]={{0.915568,0.459252,0.314224},{0.202207,0.638274,0.82676},{0.457012,0.316369,
0.0488907},{0.296286,0.357261,0.0308598},{0.69779,0.819632,0.854321},{
0.352389,0.0439262,0.974541},{0.455583,0.505874,0.816139},{0.0265835,
0.844555,0.287832},{0.900571,0.567331,0.530331},{0.085625,0.262297,
0.740572}}
Here is a function that matches your color function. Note
that this function will always return a result between
0 and 1 (the maximum value of x^2+y^2+z^2 is 3) as required by Hue.
In[12]:= colorf[{x_, y_, z_}]:= Sqrt[x^2+y^2+z^2]/Sqrt[3]
Here is the color value of the first point in the list.
In[13]:= colorf[ xyzcoords[[1]]]
Out[13]= 0.618578
Here is a set of graphics expressions that include a color
for each point, a PointSize increase for visibility and
the Point primitive itself.
In[17]:= xyzpoints=
Table[{Hue[colorf[xyzcoords[[i]]]],PointSize[.02], Point[xyzcoords[[i]]]}, {
i, 1, Length[xyzcoords]}]
Out[17]=
{{Hue[0.618578],PointSize[0.02],Point[{0.915568,0.459252,0.314224}]},{
Hue[0.614224],PointSize[0.02],Point[{0.202207,0.638274,0.82676}]},{
Hue[0.322149],PointSize[0.02],Point[{0.457012,0.316369,0.0488907}]},{
Hue[0.26856],PointSize[0.02],Point[{0.296286,0.357261,0.0308598}]},{
Hue[0.793426],PointSize[0.02],Point[{0.69779,0.819632,0.854321}]},{
Hue[0.598843],PointSize[0.02],Point[{0.352389,0.0439262,0.974541}]},{
Hue[0.613609],PointSize[0.02],Point[{0.455583,0.505874,0.816139}]},{
Hue[0.515373],PointSize[0.02],Point[{0.0265835,0.844555,0.287832}]},{
Hue[0.686572],PointSize[0.02],Point[{0.900571,0.567331,0.530331}]},{
Hue[0.456281],PointSize[0.02],Point[{0.085625,0.262297,0.740572}]}}
These points can displayed as follows:
In[18]:= Show[Graphics3D[xyzpoints]]
Information on graphics primitives and directives can
be found in the Mathematica Help Browser.
Tom Zeller
Forum Moderator
URL: , 
