Change here the stereographic projection for a direction or a list of directions.
To modify a direction, click over its graphic image, or write its identification
(name and number) on the
Direction entry. To modify a list of directions,
press the button
List (after creating the list of directions with
Direction->Select). Parameters for empty entries or
Local choices
remain unchanged.
To change a direction name write the new name in the
Direction entry,
followed by the direction number (GAMGI needs the number to identify the direction).
To change the name for a list of directions, press
List first
and then write the new common name in the
Name entry.
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.