Last Update 27/ 03/ 2001
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Interaction with this page may enhance the understanding on stereographic projection of a crystal face pole up from a projection on a sphere.
The stereographic projection is drawn on a two dimensional surface. Any face pole will be contained over a circumference or on its circle, according the respective spherical coordinates as can be observed on the right side of the figure. This circle is just the equatorial circle on the sphere.
On the left side of the figure a sphere in perspective projection can be observed, with the North pole and South pole signed by N and S, respectively. The blue curve represents the part of the sphere in front of the screen and the white curve the part behind the screen.
Points P and Q represent two crystal face poles projected on the sphere. A push and drag mouse action on the green square located in the centre of the figure will draw a line connecting points S and Q on the sphere. When this line intercepts the equatorial plane (drawn in perspective projection) a white point is drawn on the line and a little circle on the stereographic projection. On the other hand, a push and drag mouse action on the green square on the bottom of the figure will draw a line connecting points N and Q. In this case when this line intercepts the equatorial plane a white point is drawn on the line and a black point on the stereographic projection.
The equatorial plane drawn in perspective in the sphere is the stereographic projection drawn in perspective.
Any face pole on the equatorial circumference of the sphere is on the circumference of the stereographic projection, does not need to be projected.
Bibliography
1. Woolfson, M.M., X-ray Crystallography, Cambridge University Press, London, 1970.
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