Let me begin here, and incrementally improve the representation. I don't want 3D coordinates to "happen" to me. I may pick them out of a list, but I think there is a better way. My coordinates will describe an intrinsic property of physical objects (orientation), and should be consistent from object to object. So, I have introduced coordinates in this order 1. orient an object in a natural way 2. describe that orientation with math. I call these [i]object[/i] or [i]local[/i] coordinates. Like this:
[list] [*]Declare the FRONT of the object. →The principal (facing) vector is X. [*]If the object moves forward (in X), the SIDE is the direction perpendicular to X, and also [i]lying in the plane of motion[/i]. →The second vector in the not-up plane is Y. [*]→UP is Z. [/list] By convention, we choose X Y Z by positive rotation. [b]Example 1:[/b] I stand upright and face forward. The direction I face is X. My LEFT ARM is Y, and Z is up. Now I walk around. My plane of motion on the surface of the earth is the XY plane, and Z is up. [b]Examples 2-n:[/b] Car. Airplane. Boat. Flying guitar. bicycle. sled. squirrel. ambulating cabinet. pram. poodle. moon. This is consistent with classical differential geometry, which is also to say all of classical physics (mechanics). ([i]Why?[/i]) I can always conform another representation to this system with a (series of elementary) matrix multiplication(s). So that is what I will do. ________ [b]Unit Sphere[/b] [list] [*][b] →Setup[/b] [*] Trihedron: [url]http://www.geogebratube.org/material/show/id/107064[/url] [*] Base Object:[url]http://www.geogebratube.org/material/show/id/105255[/url] [*] Spherical Coordinates {link} [*] Meridian, (Horizon Points) [*] Latitude, (Horizon Points) [/list]