The basic element for the deformation is the vector queried from the displacement map. This vector usually holds either a RGBA-color or a scalar color (gray level height map). We will use this vector and more precisely the sum of its components as a factor to change the vertex position. One of the common methods is to move the vertex position along its normal proportionately to the previous factor.

Fig. 3 - Displacement principle

The schema of the figure 3 can be summed up by the following relation:

where P0 is the original position of the vertex, P1 the vertex position after displacement, N the vertex normal vector, df the normalized displacement factor (i.e [0.0; 1.0]) and uf an user scaling factor. df can be get with the following relation which converts a RGB value to a grey value:

where dv is the vector fetched from the displacement map for the current processed vertex.

Now that the theory is okay, let's go to the practice...