How to change the centre of the stereographic projection from [001] to any [uvw]
First determine the angle, q, between the vector [uv0] and the X-axis. Then rotate the co-ordinate system by that angle such that the X-axis coincides with the vector [uv0]. Superimpose the Wulff net over the projection such that the small circle projections lie about the Y-Axis as shown.
Secondly, calculate the angle f between the vector [uvw] and the Z-axis. Then rotate around the Y-axis through this angle to bring [uvw] into the centre of the projection. The Pole of P will rotate around the small circle as shown above.
Finally, rotate the Wulff net back to its original position by reversing the first rotation.
The equation above shows how to transform the co-ordinates of the vector P in a standard [001] projections to those when the projection is centred on an arbitray pole [uvw], where q is the angle between the X-axis [100] and [uv0] and f is the angle between the Z-axis [001] and [uvw].
|
