Depending on your choice of rotation axes, only two rotations are
needed, one for the elevation of the pole and one around the gnomon for
longitude correction. These are the two that correspond to the actual
changes needed.
If you are using the three orthogonal x, y, and z axes, then three
rotations are needed. And they can tell you how to make the wedge.
Another three rotation procedure that might be easier to understand but
may not tell you how to make the wedge is this. Rotate about a
horizontal axis until the gnomon is vertical. Now rotate around the
vertical axis to include the longitude correction. Then rotate around a
horizontal axis to put the gnomon in the correct new location. I would
do this in a computer graphics situation because it only requires the
old and new position values.
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On 2023-04-04 15:54, Steve Lelievre wrote:
At a new location, a dial must end up with the style parallel to the polar axis - but how do you achieve that using a wedge? Assuming you start with the dial at the new location on a horizontal surface with the sub-stile line on the local meridian, the required sequence is to rotate it about the local vertical, then about an east-west line, and then about the vertical again. Perhaps this helps visualize it... https://youtu.be/mtEgSXJPXSw
The wedge achieves the same thing because the twisting of the dial on the wedge face corresponds to the first rotation about a vertical, it's tip angle corresponds to the east-west rotation, and the turning of the wedge corresponds to the second rotation about the vertical.
Steve
On 2023-04-04 11:59 a.m., Rod Wall wrote:
As Michael indicated in his email below: Rotating the whole dial around the
polar axis is the correct way. to adjust a local solar time dial to a different
longitude
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