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.