Combining tangent space normal map is different from combining normal images. Here are some ways to combine two normal map together. The general idea is the identity normal, float3(0, 0, 1), will use the vertex default normal.

Adding

Adding two normals and preserving both details can be done this way.

finalNormal = float3(normal1.xy + normal2.xy, normal1.z * normal2.z);

finalNormal = normalize(finalNormal);

Blending

Using lerp. we can easily blend two normal

lerp(normal1, normal2, factor)

Strengthen

To make the normal map look stronger we could do

normal.xy *= strength;

normalize(normal);

This will cause any slope to bent away from the surface normal making it look steeper.

Decompress

To compress normal, it is common to copy the X value to the A channel of the image, and calculate the Z value from X and Y

In short it is to take advantage of the uncompressed A channel in DXT5 and to save an additional channel data by calculating Z during runtime.

float3 normal;

normal.xy = tex2D(normalMap, uv).ag;

normal.z = sqrt(1 ā normal.x * normal.x ā normal.y * normal.y);

which can be optimise to

normal.z = sqrt(1 ā dot(normal.xy, normal.xy));