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# 3d_ellipsoid_shell

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# 3d_ellipsoid_shell   { 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