Introduction to surface normals

To really explain how normal mapping works, we will first describe what a “normal” is, and how it is used in real-time lighting. Perhaps the most basic example would be a model where each surface polygon is lit simply according to the surface angles relative to the light. The surface angle can be represented as a line protruding in a perpendicular direction from the surface, and this direction (which is a vector) relative to the surface is called a “surface normal”, or simply, a normal.

In the image above, the left cylinder has basic flat shading, and each polygon is shaded according to its relative angle to the light source. The lighting on each polygon is constant across the polygon’s area because the surface is flat. Here are the same two cylinders, with their wireframe meshThe main graphics primitive of Unity. Meshes make up a large part of your 3D worlds. Unity supports triangulated or Quadrangulated polygon meshes. Nurbs, Nurms, Subdiv surfaces must be converted to polygons. More info
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The model on the right has the same number of polygons as the model on the left, however the shading appears smooth - the lighting across the polygons gives the appearance of a curved surface. Why is this? The reason is that the surface normal at each point used for reflecting light gradually varies across the width of the polygon, so that for any given point on the surface, the light bounces as if that surface was curved and not the flat constant polygon that it really is.

Viewed as a 2D diagram, three of the surface polygons around the outside of the flat-shaded cylinder would look like this:

The surface normals are represented by the orange arrows. These are the values used to calculate how light reflects off the surface, so you can see that light will respond the same across the length of each polygon, because the surface normals point in the same direction. This gives the “flat shading”, and is the reason the left cylinder’s polygons appear to have hard edges.

For the smooth shaded cylinder however, the surface normals vary across the flat polygons, as represented here:

The normal directions gradually change across the flat polygon surface, so that the shading across the surface gives the impression of a smooth curve (as represented by the green line). This does not affect the actual polygonal nature of the mesh, only how the lighting is calculated on the flat surfaces. This apparent curved surface is not really present, and viewing the faces at glancing angles will reveal the true nature of the flat polygons, however from most viewing angles the cylinder appears to have a smooth curved surface.

Using this basic smooth shading, the data determining the normal direction is actually only stored per vertex, so the changing values across the surface are interpolated from one vertex to the next. In the diagram above, the red arrows indicate the stored normal direction at each vertex, and the orange arrows indicate examples of the interpolated normal directions across the area of the polygon.