# Direction Create

Set here how a crystallographic direction 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.

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.

### Model

In both projections, a direction can always be represented by a Pole or a Trace. The intersection of the direction with the projection sphere is a point that projected gives the Pole representation. The intersection of the plane normal to the direction 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.

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.