Shadow Lines, Rotation and Density

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Shadow lines are loci of the points at which the light direction is perpendicular to the normal to the surface.

Let N be the normal to the surface at a point P and L the light direction lying on the plane tangent to the surface at P. N and L are perpendicular (NL=0).
The following illustration shows one shadow line through point P. N is the normal to the surface in P (N' is the binormal at P, P is the tangent plane at P), L is the light direction at P.



When you assign a Rotation angle a to shadow lines, you are simply rotating the light direction L on the tangent plane P:



When you have more than one shadow line (in the following illustration, for example, the Number of lines is 3), the tangent planes are obviously different:



Suppose now you move L1 and L2 to the plane defined by L and N:



The angle D is the Density value.