M_2D_Letter.html

Plane Region of the M Letter

Example from the PscFunctions package

With the help of routines of the PscFunctions package it is possible to get parametric equations of plain regions with boundaries .
The following example shows how to find parametric equation of a plane region of the M letter. At the beginning we generate a parametric equation of the lower and upper boundary curves.

> with(PscFunctions):
fd1:=CPolyline([[0,0],[1,0],[1,2],[2,1],[3,2],[3,0],[4,0]]):
fu1:=CPolyline([[0,3],[1,3],[1,3],[2,2],[3,3],[3,3],[4,3]]):
plot({[fd1(t),t=0..6],[fu1(t),t=-1..7]},-1..5,-0.1..3.1,thickness=3,scaling=CONSTRAINED,color=[BLACK,BLUE]);
'xd'=fd1[1](t);
'yd'=fd1[2](t);
'xu'=fu1[1](t);
'yu'=fu1[2](t);

Then with the help of DRectDomain routine we generate parametric equation of a plane region in the shape of the letter M.

`>`	x:=t->fd1[1](t): f1:=t->fd1[2](t): f2:=t->fu1[2](t): Mletter:=DRectDomain(x,f1,f2): plot3d([Mletter(u,v),0],u=0..6,v=0..3,axes=BOXED,grid=[31,16],scaling=CONSTRAINED,orientation=[-120,30]); 'x'=Mletter[1](u,v); 'y'=Mletter[2](u,v);