# Tagged Questions

geometry as on the surface of a sphere, where "lines" are great circles and any pair of lines must intersect

477 views

### Uniform distribution of points on the surface of a circle around a randomly chosen point

In a Monte Carlo simulation i have encountered the following problem: given a unity vector u defining a point A on the surface of a unity sphere, i must randomly determine a new vector forming an ...
3k views

### Surface integral on a sphere using spherical coordinates

I have a question involving surface integral on a unit sphere. Suppose $s_1$ and $s_2$ are two points on a unit sphere with spherical coordinates $(\theta_1, \psi_1)$ and $(\theta_2, \psi_2)$, ...
162 views

### Name and properties of spherical polygon with small-circle sides

Just as the title says: is there a formal name for a convex polygon on a sphere, of which the vertices are connected not by great circle but by small circle segments? My end goal is to intersect two ...
310 views

### Graph Isomorphisms, Delaunay Triangulation on a sphere, and Kulikowski's Theorem

Suppose I have a collection of $n$ non-collinear points on a sphere, $\left\lbrace P_i\right\rbrace_{i=1}^n$. And I construct a mapping from this collection of points to the Delaunay Triangulation ...
162 views

### Find third geographic coordinate in triangle using spherical earth model

I'm trying to solve triangulation problems using geographic coordinates from a GPS. all calculations must use the spherical earth model (great circle distance). Given the points and lengths: Point $A$...
274 views

### Apollonius Pursuit Problem

Most references in a brief search under 'Apollonius' concern tangent circles. The problem I am interested in is the Apollonius pursuit problem. In the plane, the question concerns the point at which ...
135 views

### Real numbers mapped onto a sphere

We can compare real values if they were greater, lesser but we cannot do same for complex numbers. What if we map real values(within some small range) onto a sphere and declare each one of them as ...
407 views

### spherical triangle inequality for multiple edges

Consider a spherical triangle, with side lengths $0 \leq a,b,c \leq \pi$. In texts on spherical geometry we see proofs that $a \leq b + c$ but this inequality is unnecessarily weak, in that some sets ...
759 views

### Moving points along a curve on sphere.

I have two points on a unit sphere. I also have their coordinates. ...
490 views

### Formula for the fourth side of a spherical quadrilateral

Given two sides $a,b$ of a spherical triangle and the angle $C$ between them, the spherical law of cosines gives an elegant formula for the missing edge length $c$: \cos c = \cos a \cos b+ \sin a \...
3k views

### Angle between GPS coordinates

I realize GPS Coordinates are spherical coordinates. However I know the earth is more of an ellipsoid. I need to compute with a fairly high degree of accuracy the pitch and yaw between two objects ...
286 views

204 views

### Why do derivatives of certain equations relating to circles yield other similar equations? [duplicate]

Possible Duplicate: Why is the derivative of a circle's area its perimeter (and similarly for spheres)? We all know that the volume of a sphere is: $V = \frac{4}{3}\pi r^{3}$ and its ...
701 views

### How to project a spherical map onto a sphere / cube

I have this panorama, an spherical map from google streetview, and want to map this on a sphere/cube. Below are some examples and illustrations, i am going to implement it in c++ and are not sure ...
477 views

### Find Double of Distance Between 2 Quaternions

I want to find the geometric equivalent of vector addition and subtraction in 3d for quaternions. In 3d difference between 2 points(a and b) gives the vector from one point to another. (b-a) gives the ...
96 views

119 views

### Analytical calculation of the resulting surface between a sphere and a spherical cap from another sphere

Let's say I have one spherical cap, resulting from cutting a sphere centered at origin and with radius R1 with a plane, whose normal goes into the direction of the <...