SquareBentPipe.html

Square Bent Pipe

Example from the PscFunctions package

With the help of routines of the PscFunctions package one can get general parametric equations of the piecewise linear surfaces.
In the following example a parametric equation of the bent square pipe surface is generated. The frame of the surface composed from four closed rectangles located on the different planes. At first with the help of CPolyline routine we obtain equations of rectangles of the surface frame.

> restart;
with(PscFunctions):
Tr1:=CPolyline([[3,1,0],[3,1,1],[3,-1,1],[3,-1,-1],[3,1,-1],[3,1,0]],[0,1,3,5,7,8]):
Tr2:=CPolyline([[1,1,0],[1,1,1],[-1,-1,1],[-1,-1,-1],[1,1,-1],[1,1,0]],[0,1,3,5,7,8]):
Tr3:=CPolyline([[1,3,0],[1,2,1],[-1,2,1],[-1,4,-1],[1,4,-1],[1,3,0]],[0,1,3,5,7,8]):
Tr4:=CPolyline([[1,3,3],[1,2,3],[-1,2,3],[-1,4,3],[1,4,3],[1,3,3]],[0,1,3,5,7,8]):
TrspAll:=plots[spacecurve]({[Tr1(t)],[Tr2(t)],[Tr3(t)],[Tr4(t)]},t=0..8,thickness=2,axes=BOXED,color=black,numpoints=200,orientation=[30,60],labels=["X","Y","Z"]):
plots[display](TrspAll);

Equation of the ruled surface spanned the frame occupies only 5 lines. It is generated by the SPscRuled routine.

> rl7:=SPscRuled([[Tr1[1],Tr1[2],Tr1[3]],[Tr2[1],Tr2[2],Tr2[3]],[Tr3[1],Tr3[2],Tr3[3]],[Tr4[1],Tr4[2],Tr4[3]]],[[0,8],[0,8],[0,8],[0,8]],psc=true):
plot3d([rl7(u,v)],u=0..1,v=0..3,axes=BOXED,labels=["X","Y","Z"],scaling=CONSTRAINED,orientation=[40,70]);
print('x'=rl7[1](u,v));
print('y'=rl7[2](u,v));
print('z'=rl7[3](u,v));