Set here how a crystallographic plane is projected.
### Net

The projection net can be **Wulff** (Stereographic) or **Schmidt**
(Equivalent). In the **Wulff** projection, the point to project (above)
and the point of the sphere farther from the user (below) define a segment
that intersects the circle at a point, giving the final representation.
### Model

In both projections, a plane can always be represented by a **Pole**
or a **Trace**. The intersection of a vector normal to the plane with
the projection sphere is a point that projected gives the **Pole**
representation. The intersection of the plane with the projection sphere
is an arch that projected gives the **Trace** representation: a
circumpherence arch in the **Wulff** projection and a 4th order
conic arch in the **Schmidt** projection.

In the **Schmidt** projection, the point to project (above) is
rotated around the point of the sphere closer to the user (above),
keeping the same XY direction, until both points have the same Z
coordinate, and then divided by square root of 2, to be inside the
circle with radius R at coordinate Z, giving the final representation.

Every family of crystallographic planes or directions can be described by the intersection of the plane or direction passing through the origin O with a sphere of radius R centered at O, defining a circumpherence or a point, respectively. These in turn can be projected on the circle parallel to the screen (constant Z coordinate) that divides the sphere in half, with radius R and origin O. In GAMGI, points in the half-sphere farther from the user are hidden, so only half-circumpherences and points above are visible.

A plane can always be described by its normal vector, and a direction by its plane perpendicular, so both representations are valid for crystallographic planes and directions.

In a **Wulff** projection, angles between planes are given by
the angles between the traces, so angles are preserved. This is not
true for the **Schmidt** projection. The **Wulff** projection
is mostly used in materials science.

In a **Schmidt** projection, minor circles on the sphere are
distorted when projected but the areas are preserved. This is not
true for the **Wulff** projection. The **Schmidt** projection
is mostly used in structural geology.