<span style="font-family: Courier;">Dear all,</span><br><br style="font-family: Courier;"><span style="font-family: Courier;">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. </span><br><span style="font-family: Courier;">I could not find that where is the problem? Please help.</span><br><span style="font-family: Courier;"></span><span style="font-family: Courier;">Thanks,<br>Aydin<br><br style="font-family: Courier;"></span><span style="font-family: Courier;">\documentclass[12pt]{article}&nbsp;&nbsp; % A. Ustun 19.10.2006</span><br style="font-family: Courier;"><span style="font-family: Courier;">\usepackage[latin5]{inputenc}</span><br style="font-family: Courier;"><span style="font-family: Courier;">\usepackage{pst-3dplot}</span><br style="font-family: Courier;"><span style="font-family: Courier;">\SpecialCoor</span><br style="font-family: Courier;"><span style="font-family: Courier;">\pagestyle{empty}</span><br style="font-family: Courier;"><span style="font-family: Courier;">\begin{document}</span><br style="font-family: Courier;"><span style="font-family: Courier;">\psset{arrowlength=2.5,arrowinset=0,unit=2}</span><br style="font-family: Courier;"><span style="font-family: Courier;">\begin{pspicture}(0,0)(4,4)%\psgrid(-3,-3)(3,3)</span><br style="font-family: Courier;"><span style="font-family: Courier;">\psset{Alpha=70,Beta=30}</span><br style="font-family: Courier;"><span style="font-family: Courier;">\pstThreeDCoor[linecolor=gray,linewidth=1pt,xMin=0,yMin=0,zMin=0,xMax=3,yMax=3.1,zMax=2.5]</span><br style="font-family: Courier;"><span style="font-family: Courier;">\parametricplotThreeD[plotstyle=curve,xPlotpoints=200](0,840){</span><br style="font-family: Courier;"><span style="font-family: Courier;">&nbsp; t cos&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><br style="font-family: Courier;"><span style="font-family: Courier;">&nbsp; t sin&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><br style="font-family: Courier;"><span style="font-family: Courier;">&nbsp; t 300 div</span><br style="font-family: Courier;"><span style="font-family: Courier;">}</span><br style="font-family: Courier;"><span style="font-family: Courier;">% unit tangent vector: e1</span><br style="font-family: Courier;"><span style="font-family: Courier;">\parametricplotThreeD[plotstyle=line,arrows={-&gt;},xPlotpoints=2,yPlotpoints=4,linecolor=red](0,1)(0,660){</span><br style="font-family: Courier;"><span style="font-family: Courier;">%&nbsp;&nbsp;&nbsp; f0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; t&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; df/dt&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1/||df/dt||&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; f0+t*e1 </span><br style="font-family: Courier;"><span style="font-family: Courier;">&nbsp; %%%%%%%%%&nbsp;&nbsp;&nbsp;&nbsp; %&nbsp;&nbsp;&nbsp; %%%%%%%%%&nbsp;&nbsp;&nbsp; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; %%%%%%%</span><br style="font-family: Courier;"><span style="font-family: Courier;">&nbsp; u cos&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; t&nbsp;&nbsp;&nbsp; u sin neg&nbsp;&nbsp;&nbsp; 1 1 300 div 2 exp add sqrt div&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; mul add % for x</span><br style="font-family: Courier;"><span style="font-family: Courier;">&nbsp; u sin&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; t&nbsp;&nbsp;&nbsp; u cos&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1 1 300 div 2 exp add sqrt div&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; mul add % for y</span><br style="font-family: Courier;"><span style="font-family: Courier;">&nbsp; u 300 div&nbsp;&nbsp;&nbsp;&nbsp; t&nbsp;&nbsp;&nbsp; 1 300 div&nbsp;&nbsp;&nbsp; 1 1 300 div 2 exp add sqrt div&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; mul add % for z</span><br style="font-family: Courier;"><span style="font-family: Courier;">}</span><br style="font-family: Courier;"><span style="font-family: Courier;">% unit normal vector: e2</span><br style="font-family: Courier;"><span style="font-family: Courier;">\parametricplotThreeD[plotstyle=line,arrows={-&gt;},xPlotpoints=2,yPlotpoints=4,linecolor=blue](0,1)(0,660){</span><br style="font-family: Courier;"><span style="font-family: Courier;">%&nbsp;&nbsp;&nbsp; f0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; t&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; de1/dt&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; f0+t*e2 </span><br style="font-family: Courier;"><span style="font-family: Courier;">&nbsp; %%%%%%%%%&nbsp;&nbsp;&nbsp;&nbsp; %&nbsp;&nbsp;&nbsp; %%%%%%%%%&nbsp;&nbsp;&nbsp;&nbsp; %%%%%%%</span><br style="font-family: Courier;"><span style="font-family: Courier;">&nbsp; u cos&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; t&nbsp;&nbsp;&nbsp; u cos neg&nbsp;&nbsp;&nbsp;&nbsp; mul add % for x</span><br style="font-family: Courier;"><span style="font-family: Courier;">&nbsp; u sin&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; t&nbsp;&nbsp;&nbsp; u sin neg&nbsp;&nbsp;&nbsp;&nbsp; mul add % for y</span><br style="font-family: Courier;"><span style="font-family: Courier;">&nbsp; u 300 div&nbsp;&nbsp;&nbsp;&nbsp; t&nbsp;&nbsp;&nbsp; 0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; mul add % for z</span><br style="font-family: Courier;"><span style="font-family: Courier;">}</span><br style="font-family: Courier;"><span style="font-family: Courier;">% unit tangent vector: e3</span><br style="font-family: Courier;"><span style="font-family: Courier;">\parametricplotThreeD[plotstyle=line,arrows={-&gt;},xPlotpoints=2,yPlotpoints=4,linecolor=green](0,1)(0,660){</span><br style="font-family: Courier;"><span style="font-family: Courier;">%&nbsp;&nbsp;&nbsp; f0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; t&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; e1xe2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1/||df/dt||&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; f0+t*e1 </span><br style="font-family: Courier;"><span style="font-family: Courier;">&nbsp; %%%%%%%%%&nbsp;&nbsp;&nbsp;&nbsp; %&nbsp;&nbsp;&nbsp; %%%%%%%%%&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; %%%%%%%</span><br style="font-family: Courier;"><span style="font-family: Courier;">&nbsp; u cos&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; t&nbsp;&nbsp;&nbsp; u sin 300 div&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1 1 300 div 2 exp add sqrt div&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; mul add % for x</span><br style="font-family: Courier;"><span style="font-family: Courier;">&nbsp; u sin&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; t&nbsp;&nbsp;&nbsp; u cos 300 div neg&nbsp;&nbsp;&nbsp; 1 1 300 div 2 exp add sqrt div&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; mul add % for y</span><br style="font-family: Courier;"><span style="font-family: Courier;">&nbsp; u 300 div&nbsp;&nbsp;&nbsp;&nbsp; t&nbsp;&nbsp;&nbsp; 1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1 1 300 div 2 exp add sqrt div&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; mul add % for z</span><br style="font-family: Courier;"><span style="font-family: Courier;">}</span><br style="font-family: Courier;"><span style="font-family: Courier;">\end{pspicture}</span><br style="font-family: Courier;"><span style="font-family: Courier;">\end{document}</span><br style="font-family: Courier;"><span style="font-family: Courier;"><br></span>