Tagged Questions
0
votes
0answers
59 views
two points on a unit sphere
Consider the two vectors to the points on the unit sphere,
$${\bf v}_i=(\sin\theta_i\cos\varphi_i,\sin\theta_i\sin\varphi_i,\cos\theta_i)$$
with $i=1,2$. Use the dot product to get the angle $\psi$ ...
1
vote
1answer
224 views
Coordinates of interception point Y with XY being the shortest distance of X to AB on sphere
How would one calculate the interception point $Y$ with $\overleftrightarrow{XY}$ being the shortest distance of $X$ to $\overleftrightarrow{AB}$?
This answer to the question How to find the ...
1
vote
1answer
168 views
How to scale a polyhedron contained a 3-sphere?
In the 3-sphere simulator I am building, the viewpoint is contained in the space of a 3-sphere (the surface of a 4-D hypersphere), and the user is able to navigate through it.
There are some ...
2
votes
0answers
255 views
projection of a sphere onto a plane
Consider you have a sphere centered at the origin.The sphere has a diameter of $\frac{1}{2} \sqrt{\frac{3}{2}}$. This means that the inscribed cube has an edge of 1.
Take any point from the plane ...
1
vote
1answer
241 views
Trying to pick a random point on sphere end up picking from a lune
I was inspired by this question to play around a little bit (its a weekend). I was pretty confident of my derivation and thought it might be nice to supplement it with a pretty picture. However, ...
6
votes
3answers
525 views
What is the area of the portion of 1/8 of an sphere cut off by two parallel planes?
So the problem that I'm trying to solve is as follows:
Assume 1/8 of a sphere with radius $r$ whose center is at the origin (for example the 1/8 which is in $R^{+}$). Now two parallel planes are ...
8
votes
1answer
281 views
Navigating though the surface of a hypersphere in a computer game
People in StackOverflow seems not so into this theme, so I thought I could have better luck in here.
I had the idea of an spaceship game where the world is confined in the surface of an 4-D ...
4
votes
4answers
762 views
How to find the distance between a point and line joining two points on a sphere?
How do I calculate the distance between the line joining the two points on a spherical surface and another point on same surface? I have illustrated my problem in the image below.
In the above ...
