# Plane Create

- Type
- Polygon
- Projection
- View

Set here how a crystallographic plane is represented in a stereographic projection.

### Wulff, Schmidt

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.

The actual projection 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.

To select the projection to use, press Wulff or Schmidt.

### Pole, Trace

In both projections, a direction is represented by a point, a Pole, and a plane by an arch, a Trace. These are circumpherence archs, in the Wulff projection, and 4th order conic archs, 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 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.

To select the visual representation to use, press on Pole, Trace or both.
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