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<title>GAMGI Interfaces: Plane Create</title>
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<h1>Plane Create</h1>
<div id="notebook">
<ul>
<li><a href="create_type.html">Type</a></li>
<li><a href="create_scope.html">Scope</a></li>
<li><span>Projection</span></li>
<li><a href="create_view.html">View</a></li>
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Set here how a crystallographic plane is projected.
<h3>Net</h3>
The projection net can be <b>Wulff</b> (Stereographic) or <b>Schmidt</b>
(Equivalent). In the <b>Wulff</b> 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.
<p/>
In the <b>Schmidt</b> 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.
<p/>
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.
<h3>Model</h3>
In both projections, a plane can always be represented by a <b>Pole</b>
or a <b>Trace</b>. The intersection of a vector normal to the plane with
the projection sphere is a point that projected gives the <b>Pole</b>
representation. The intersection of the plane with the projection sphere
is an arch that projected gives the <b>Trace</b> representation: a
circumpherence arch in the <b>Wulff</b> projection and a 4th order
conic arch in the <b>Schmidt</b> projection.
<p/>
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.
<p/>
In a <b>Wulff</b> projection, angles between planes are given by
the angles between the traces, so angles are preserved. This is not
true for the <b>Schmidt</b> projection. The <b>Wulff</b> projection
is mostly used in materials science.
<p/>
In a <b>Schmidt</b> projection, minor circles on the sphere are
distorted when projected but the areas are preserved. This is not
true for the <b>Wulff</b> projection. The <b>Schmidt</b> projection
is mostly used in structural geology.
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