I know that a plane has a normal. But in Nehe''s lessons a vertex''s normal is mentioned? I think a vertex is a point, for example a triangle has 3 vertexes and 3 edges, why dose a vertex has a normal? Would you please tell me what is a vertex''s normal?Thanks in advance.

A vertex normal is vector (Normaly with a magnitude of 1) that points at a tangent(90 degrees) to the surface. It is primarily used in lighting calulations so that objects surfaces look smooth rather than like lots of flat triangles.

Imagine a curves surface for a moment. In a perfect world, that curved surface could be made of millions of faces to give a perfectly smooth and accurate representation of the curve. But this is not a perfect world so this is not likely to run at an acceptable rate. Now imgine the same curve, but with 3 or 4 Verticies along the curve. The normal of each verticies will be the tangent to the curve at that vertex position. Now the lighting can be calcuated to better represent the effect of the high detail curve.

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The normal of each verticies will be the tangent to the curve at that vertex position

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The normal will be the normal to the curve (i.e. to the tangent at that point), not the tangent

The vertex normal is used to determine the intensity of light at that particular vertex.

But is a vertex a point or a surface?In my opinion it is a point, but it seems to be a surface since it has a normal.

Read what Bobby-D said. A mesh is an approximation for an underlying smooth surface. A mesh is formed from faces and vertices (and edges, but you get the idea).

So yes, a vertex is a point, but it is also part of an approximation to a (smooth) surface.

Thank you.