What is a z-buffer?

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Well, they are not Blitz specific. More general 3D related.

Normals are used in 3D calculations such as in checking what direction a polygon is facing - ie which way a polygon's normal is pointing.

The 'Blitz' definition is 'Recalculates all normals in a mesh. This is necessary for correct lighting if you have not set surface normals using 'VertexNormals' commands.'

In Blitz you generally use normals for lighting reasons - but you could use them for backface culling, etc too.

Here is a link regarding the z-buffer:
http://www.toymaker.info/Games/html/z_buffer.html

Blitz also has a wbuffer command. Type wbuffer into Blitz3D - click on the word, then press F1 for a bit of info.

You are best Googling your two questions as they are not Blitz-based. I believe though that there are quirks to the z-buffer in Blitz3D.