Polar representation of the solar intake on a plane
The 2 spheres have a diameter=1 and are touching the axis of rotation of the plane at the point (0,0,0).
The sphere perpendicular to the horizontal plane represent in a 3D polar graph, the solar intensity at a particular elevation angle. This solar intensity is measured perpendicular to the direction of the sun. We can call this sphere the solar intensity sphere.
The rotating plane (in section and in 3D) represents a building surface, inclined at a particular angle.
The solar intensity sphere is copied and rotated along the y-y axis, so that it remains perpendicular to the building surface.
The solar intake on this particular plane at a particular solar elevation and solar azimut angle is shown by the surface represented by an orange mesh. The distance from the centre point to this surface in the direction of the sun is the product of the distance to the 1st sphere by the distance to the 2nd sphere.
Another way of calculating it is to take the unit vector of the direction of the sun, multiplied by the scalar product of the direction of the sun with the zenith vector (a unit vector perpendicular to the horizontal plane), multiplied by the scalar product of the direction of the sun with the normal vector (a unit vector perpendicular to the building surface).
So that's a vector multiplied by 2 scalar products.
This surface represented by the mesh is the 3D polar representation of the instantaneous solar intake on this particular building surface, for every sun azimut and elevation.
In practice, the range of sun angles and elevations must be restricted to the actual solar path at this particular latitude.