Plot 3D surface

I have 3 vectors x, y, z and I would like to generate a 3D surface instead of having just separate points (e.g.: plot3 or scatter3). Note z is function of x and y, but I have calculated this before. I have tried to use scatteredInterpolant, meshgrid and mesh, however this creates z points in zones/areas that are supposed to be empty. How can I avoid this and just plot the surface within the z limits/boundaries?
Thanks in advance for the help!

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Hi PallaC,
Can you explain what went wrong with scatteredInterpolant, meshgrid, mesh with some snapshots or post sample values for x,y and z.
Hi Jeevan, here you can see the difference -on the mesh plot I have an additional surface part I don't want to generate (or how can I remove it?)

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2016-6-1

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2016-6-10

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