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<TITLE>3d plot - rotation of a point (x,y,z) via RotX,RotY,RotZ</TITLE>
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<P><FONT SIZE=2 FACE="Arial">Hi,</FONT>
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<P><FONT SIZE=2 FACE="Arial">I hope someone can help me with this, but I am a bit stuck</FONT>
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<P><FONT SIZE=2 FACE="Arial">I am using two coordinate systems, </FONT>
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<P><FONT SIZE=2 FACE="Arial">1) The first is the normal OXYZ cartesian system which I setup as </FONT>
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<P><FONT SIZE=2 FACE="Arial">\pstThreeDCoor[nameX=$x_{0}$,nameY=$y_{0}$,nameZ=$z_{0}$,xMin=0,yMin=0,zMin=0,xMax=4,yMax=5,zMax=6] </FONT>
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<P><FONT SIZE=2 FACE="Arial">I name this system : ORIGINAL</FONT>
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<P><FONT SIZE=2 FACE="Arial">2) The second is the rotated system OX'Y'Z' with the same origin but setup as </FONT>
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<P><FONT SIZE=2 FACE="Arial">\pstThreeDCoor[<B>RotX=30,RotY=-15,RotZ=50</B>,nameX=$x$,nameY=$y$,nameZ=$z$,xMin=0,yMin=0,zMin=0,xMax=25,yMax=4,zMax=6]</FONT>
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<P><FONT SIZE=2 FACE="Arial">I name this system : ROT</FONT>
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<P><FONT SIZE=2 FACE="Arial">In system ORIGINAL I draw a line from the origin to the point (0,0,z) with e.g z = 3</FONT>
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<P><FONT SIZE=2 FACE="Arial">In system ROT I also draw a line from the origin to the point (0,0,z' ) with z' = 3 (via \psset{RotX=30,RotY=-15,RotZ=50} and \pstThreeDLine )</FONT></P>
<P><B><FONT SIZE=2 FACE="Arial">Question :</FONT></B>
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<P><FONT SIZE=2 FACE="Arial">I want to find the coordinates (x,y,z) in system ORIGINAL for a point (x',y',z') in system ROT </FONT>
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<P><B><FONT SIZE=2 FACE="Arial">Example</FONT></B>
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<P><FONT SIZE=2 FACE="Arial">in system ROT I have the point (x',y',z' ) = (0,0,3), but what are its coordinates (x,y,z) in system ORIGINAL</FONT>
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<P><B><FONT SIZE=2 FACE="Arial">Test I did</FONT></B>
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<P><FONT SIZE=2 FACE="Arial">I tried to use the standard 3D rotation matrices I know, and try to map this to the pst-3dplot where the rotation matrix M is used.</FONT></P>
<P><FONT SIZE=2 FACE="Arial">What I cannot figure out is the order in which the rotation operations are done. What I mean is, is that in</FONT>
<BR><FONT SIZE=2 FACE="Arial">the call to \pstThreeDCoor[</FONT><B><FONT SIZE=2 FACE="Arial">RotX=30,RotY=-15,RotZ=50</FONT></B><FONT SIZE=2 FACE="Arial">, ...... I cannot determine what the rotation sequence is </FONT>
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<P><FONT SIZE=2 FACE="Arial">RotX, RotY , RotZ or</FONT>
<BR><FONT SIZE=2 FACE="Arial">RotZ, RotY, RotX or</FONT>
<BR><FONT SIZE=2 FACE="Arial">RotY, RotZ, RotX etc</FONT>
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<P><FONT SIZE=2 FACE="Arial">I also used consequent calls to </FONT>
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<P><FONT SIZE=2 FACE="Arial">\pstRotPointIIID[RotX=30](0,0,3){\xvalb}{\yvalb}{\zvalb}</FONT>
<BR><FONT SIZE=2 FACE="Arial">\pstRotPointIIID[RotY=-15](\xvalb,\yvalb,\zvalb){\xvalb}{\yvalb}{\zvalb}</FONT>
<BR><FONT SIZE=2 FACE="Arial">\pstRotPointIIID[RotZ=50](\xvalb,\yvalb,\zvalb){\xvalb}{\yvalb}{\zvalb}</FONT>
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<P><FONT SIZE=2 FACE="Arial">to find the coordinates in this way, but no success so far</FONT>
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<P><FONT SIZE=2 FACE="Arial">The rotation matrices I use are (sort of in mathematica notation)</FONT>
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<P><FONT SIZE=2 FACE="Arial">Rotation Z-axes = </FONT>
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<BR> <FONT SIZE=2 FACE="Arial">( Cos[alpha] Sin[alpha] 0</FONT>
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<P> <FONT SIZE=2 FACE="Arial"> Sin[alpha] Cos[alpha] 0</FONT>
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<P> <FONT SIZE=2 FACE="Arial"> 0 0 1 )</FONT>
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<P><FONT SIZE=2 FACE="Arial">with alpha = RotZ</FONT>
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<P><FONT SIZE=2 FACE="Arial">Rotation X axes = </FONT>
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<P> <FONT SIZE=2 FACE="Arial">( 1 0 0 </FONT>
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<P><FONT SIZE=2 FACE="Arial"> 0 Cos[gamma] -Sin[gamma]</FONT>
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<P><FONT SIZE=2 FACE="Arial"> 0 Sin[gamma] Cos[gamma] )</FONT>
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<P><FONT SIZE=2 FACE="Arial">with gamma = RotX</FONT>
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<P><FONT SIZE=2 FACE="Arial">Rotation Y axes = </FONT>
<BR> <FONT SIZE=2 FACE="Arial">( Sin[beta] 0 Cos[beta]</FONT>
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<P> <FONT SIZE=2 FACE="Arial"> 0 1 0</FONT>
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<BR> <FONT SIZE=2 FACE="Arial">Cos[beta] 0, Sin[beta] )</FONT>
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<P><FONT SIZE=2 FACE="Arial">with beta = RotY</FONT>
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<P><FONT SIZE=2 FACE="Arial">Thanks in advance for all the help</FONT>
<BR><FONT SIZE=2 FACE="Arial">Kind regards</FONT>
<BR><FONT SIZE=2 FACE="Arial">Wim Neimeijer</FONT>
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