# [pstricks] help about frenet frame

Aydin USTUN austun at selcuk.edu.tr
Thu Dec 18 12:04:41 CET 2008

Dear all,I am trying to plot the tangent, normal, and bi-normal unit vectors at several points along the space curve. I applied the following code, but the tangent and bi-normal unit vectors point to the incorrect directions. I could not find that where is the problem? Please help.Thanks,Aydin\documentclass[12pt]{article}   % A. Ustun 19.10.2006\usepackage[latin5]{inputenc}\usepackage{pst-3dplot}\SpecialCoor\pagestyle{empty}\begin{document}\psset{arrowlength=2.5,arrowinset=0,unit=2}\begin{pspicture}(0,0)(4,4)%\psgrid(-3,-3)(3,3)\psset{Alpha=70,Beta=30}\pstThreeDCoor[linecolor=gray,linewidth=1pt,xMin=0,yMin=0,zMin=0,xMax=3,yMax=3.1,zMax=2.5]\parametricplotThreeD[plotstyle=curve,xPlotpoints=200](0,840){  t cos           t sin           t 300 div}% unit tangent vector: e1\parametricplotThreeD[plotstyle=line,arrows={->},xPlotpoints=2,yPlotpoints=4,linecolor=red](0,1)(0,660){%    f0         t      df/dt                1/||df/dt||               f0+t*e1   %%%%%%%%%     %    %%%%%%%%%    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%      %%%%%%%  u cos         t    u sin neg    1 1 300 div 2 exp add sqrt div      mul add % for x  u sin         t    u cos        1 1 300 div 2 exp add sqrt div      mul add % for y  u 300 div     t    1 300 div    1 1 300 div 2 exp add sqrt div      mul add % for z}% unit normal vector: e2\parametricplotThreeD[plotstyle=line,arrows={->},xPlotpoints=2,yPlotpoints=4,linecolor=blue](0,1)(0,660){%    f0         t      de1/dt      f0+t*e2   %%%%%%%%%     %    %%%%%%%%%     %%%%%%%  u cos         t    u cos neg     mul add % for x  u sin         t    u sin neg     mul add % for y  u 300 div     t    0             mul add % for z}% unit tangent vector: e3\parametricplotThreeD[plotstyle=line,arrows={->},xPlotpoints=2,yPlotpoints=4,linecolor=green](0,1)(0,660){%    f0         t      e1xe2                       1/||df/dt||                f0+t*e1   %%%%%%%%%     %    %%%%%%%%%            %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%      %%%%%%%  u cos         t    u sin 300 div        1 1 300 div 2 exp add sqrt div      mul add % for x  u sin         t    u cos 300 div neg    1 1 300 div 2 exp add sqrt div      mul add % for y  u 300 div     t    1                    1 1 300 div 2 exp add sqrt div      mul add % for z}\end{pspicture}\end{document}
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