One advantage of tangent space normal maps is that the normals are always pointing outwards, so assuming unit length, the normal z coordinate can be reconstructed from the x and y components.

What is tangent space in computer graphics?

Tangent space is just another such coordinate system, with it's own origin. This is the coordinate system in which the texture coordinates for a face are specified. ... In most texturing only U and V change across a face tangent space can be thought of a 2D coordinate system aligned to the plane of a face.

Why are normal maps purple?

A normal map is an RGB texture, where each pixel represents the difference in direction the surface should appear to be facing, relative to its un-modified surface normal. These textures tend to have a bluey-purple tinge, because of the way the vector is stored in the RGB values.