Copy of 3D Trihedron
A more flexible set of axes. I will adopt this system for now.
Each axis slides along one meridian. Arrows indicate the direction of positive rotation.
I adopt the following notation:
Capital letters X, Y, Z denote the 3-dimensional vectors:
X Y Z are mutually perpendicular unit vectors forming a right-handed coordinate system.
Barred letters are projections:
are the projections of X Y Z on the view plane (the coordinates of are the ordinary GGB coordinates.)
I have begun with a coordinate-free representation. I submit without proof that the axes are bound by the following constraints:
The two constraints can also be stated this way: Let determine an ellipse with center O, major axis the unit perpendicular to , and minor axis of . Then are conjugate radii on the ellipse.
And likewise are conjugate on the ellipses determined by , respectively.
Update: So. I made that up, to respect freedom of motion. Today I find this is Gauss' Fundamental Theorem of Normal Axonometry.
This was problem #74 in Heinrich Dorrie's 100 Great Problems of Elementary Mathematics..
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Unit Sphere
[list]
Setup: http://www.geogebratube.org/material/show/id/101282
→ Trihedron:
Base Object: http://www.geogebratube.org/material/show/id/105255
Spherical Coordinates {link}
Meridian, (Horizon Points)
Latitude, (Horizon Points)