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{ 3D_ELLIPSOID.PDE

 

 This problem constructs an ellipsoid.

 It is the geometric construction only, there are no variables or equations.

 

}  

title '3D Ellipsoid'

 

coordinates cartesian3

 

definitions

 a=3  b=2  c=1   { x,y,z radii }

 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 an x=0 'skirt' on the ellipsoid surface }

 ellipsoid = c*sqrt( max(0,1-(x-xc)^2/a^2-(y-yc)^2/b^2) )

 

extrusion

  surface 'bottom' z = zc - ellipsoid

  surface 'top'    z = zc + ellipsoid

 

boundaries

  region 'ellipse'

      start(xc+a,yc)

      arc(center=xc,yc) to (xc,yc+b) to (xc-a,yc) to (xc,yc-b) to close

 

plots

  grid(x,y,z)

  grid(x,y) on z=zc

  grid(y,z) on x=xc

  grid(x,z) on y=yc

 

end