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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