Diametric Projections:

In this class of projections, view plane normal n = (n_x, n_y, n_z) is set so that this makes equal angles along two of the axes. In this class, only lines drawn along with the two equally foreshortened axes are scaled by the same factor. This condition may be satisfied only if the view plane normal n in any of the two directions are equal, that is n_x = | n_y |, n_x = | n_z |, or n_y = | n_z |. Figure shows a diametric projection of a cube. While the view plane is parallel to a major axis, measurements of all lines are maintained in the projection for lines that are parallel to this axis.

Figure

cos² φ+ sin ² φ sin ² θ= cos² θ

cos² φ = 1 - sin ² φ and  cos² θ = 1 - sin ² θ yields

2 sin ² θ- 2 sin⁴ θ- (1 - sin ² θ)       = 0

u = sin² θ, solution yields