Create a 3D mesh of a paraboloidal region

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Marcelo hernandez 2020-1-17

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https://ww2.mathworks.cn/matlabcentral/answers/500674-create-a-3d-mesh-of-a-paraboloidal-region

编辑： Image Analyst 2020-1-17

I have a paraboloid region. I would like to plot this region and build a tetrahedron or Hexahedron mesh, for this I use:

   a = 40;
   d = 1;
   x=-40:step:40;
   y=-40:step:40;
   z=-40:step:40;
 I = 16*a^2.*y.^4+a.*y.^3.*(-32*a^2-8*d^2-8.*x.^2-8.*z.^2)+a.*y.*(32*a^2*d^2+8*d^4-8*a^2.*x.^2+2*d^2.*x.^2-10.*x.^4-8*a^2.*z.^2+2*d^2.*z.^2-20.*x.^2.*z.^2-   10.*z.^4)+y.^2.*(16*a^4-8*a^2*d^2+d^4+32*a^2.*x.^2-2*d^2.*x.^2+x.^4+32*a^2.*z.^2-2*d^2.*z.^2+2.*x.^2.*z.^2+z.^4)-(16.*a.^4.*d^2+8*a^2*d^4+d^6+20*a^2*d^2.*x.^2-   3*d^4.*x.^2-a^2.*x.^4+3*d^2.*x.^4-x.^6+20*a^2*d^2.*z.^2-3*d^4.*z.^2-2*a^2.*x.^2.*z.^2+6*d^2.*x.^2.*z.^2-3.*x.^4.*z.^2-a^2.*z.^4+3*d^2.*z.^4-3.*x.^2.*z.^4-z.^6)<= 0;

The following step is use:

[X,Y,Z] = meshgrid(x,y,z);

but the usage the memory is so large (+70 gb).

Is there another way to create geometry and meshing for this region?

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Image Analyst 2020-1-17

编辑：Image Analyst 2020-1-17

Not sure what you're looking for. I'm not sure what a "a tetrahedron or Hexahedron mesh" is. Do you have some kind of picture of it that you can post? Some guesses:

Do you want a grid of (x,y) locations where the z value is a parabola? So it's like you have a bowl sitting above (or below) the x-y plane? Because if that's so, you don't need z. The I value is the z value, which is the distance from the x-y plane.
Or do you want to do some kind of Delaunay triangulation of a set of (x,y,z) points to form a surface with a bunch of triangles on it?

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