I have a research project, maybe you’ll have ideas or knowledge to help me. It is about calculating distances on a sphere surface, similar to calculating navigating routes for planes on the spherical earth map (great circle lines or orthodromes)
I have a sphere with a defined radius. In front of the sphere sits another body, let s say it is a cube. The upper left corner and the lower right corner of the cube’s closest surface project themselves over the sphere surface (point A and point B). By rotating the sphere, I want to move the A into B position. How do I measure the distance between A and B on spherical surface and how do I calculate the needed rotational angle of the sphere to do that? After that I will have more points on the sphere surface and I will need to do some spherical trigonometry for calculating the surfaces (need to define some angles between sphere centrum and the points on the surface)
Any ideas how to do that?
The project is about simulating the human shoulder joint (more exactly the pathological shoulder that luxates) using a ball and socket model with the points on the sphere as anatomical landmarks and the cube as the human glene. The sphere fits perfectly the articular surface of the humeral head. The center of the sphere is always in line with the center of the cube. Somewhere on that sphere surface it is a bony defect, like a canion. When this defect is coming in contact with the anterior rim of the glenoid (the margin of the cube in my example), makes the humeral head (sphere) slip anteriorly (the center of the sphere is not anymore in line with the center of the cube).
I want to see how some anatomical landmarks (points on a sphere) come in contact with the margin of the socket.
To make the problem more dificult, the socket will not be a cube in the future, but a light concave surface with an eliptical form, as the human glenoid is.
For the beginning i need to learn how to draw other body’s projections points and lines on the sphere surface and then how to draw and measure the angles made by these points with the sphere centrum. That would help a lot!
Here are some other pictures of the anatomical model: