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{ 3D_ELLIPSOID_SHELL.PDE
This problem constructs an elliptical shell.
It is the geometric construction only, there are no variables or equations.
}
title '3D Ellipsoid Shell'
coordinates cartesian3
definitions
ao=3.2 bo=2.2 co=1.2 { x,y,z radii - outer ellipse }
ai=3.0 bi=2.0 ci=1.0 { x,y,z radii - inner ellipse }
xc=1 yc=1 zc=1 { coordinates of ellipsoid center }
{ top half of ellipsoid surface :
the MAX function is used to ensure the surface is defined throughout all
x,y space - essentially placing a 'skirt' on the top ellipsoid surface }
outer_ellipsoid = co*sqrt( max(0,1-(x-xc)^2/ao^2-(y-yc)^2/bo^2) )
inner_ellipsoid = ci*sqrt( max(0,1-(x-xc)^2/ai^2-(y-yc)^2/bi^2) )
extrusion
surface 'outer bottom' z = zc - outer_ellipsoid
surface 'inner bottom' z = zc - inner_ellipsoid
surface 'inner top' z = zc + inner_ellipsoid
surface 'outer top' z = zc + outer_ellipsoid
boundaries
region 'outer ellipse'
start(xc+ao,yc)
arc(center=xc,yc) to (xc,yc+bo) to (xc-ao,yc) to (xc,yc-bo) to close
limited region 'inner ellipse'
layer 2 void
start(xc+ai,yc)
arc(center=xc,yc) to (xc,yc+bi) to (xc-ai,yc) to (xc,yc-bi) to close
plots
grid(x,y,z)
grid(x,y) on z=zc paintregions
grid(y,z) on x=xc paintregions
grid(x,z) on y=yc paintregions
end