59 views

Calulate area when two circle intersect each other [duplicate]

I have Sphere with radius R. Inside the sphere I have Two circle. One circle is fixed defined by $\alpha$. Another circle can rotate and the orientation of that circle can be defined by $\beta$. From ...
44 views

Calculate the limit of spherical cap in spherical coordinate [duplicate]

I am using spherical coordinate system $r,\theta, \phi$ like this picture. Consider I have a sphere with radius $R$, is divided into two hemisphere $S$ and $P$. With this given information I am able ...
54 views

calculate complex geometry for a dynamic system [duplicate]

Imagine a spherical ball with radius r that equally coated into two hemisphere P(grey) and S(white) is thrown at the pool. Consider the ball can float (up-down) and rotate. There is an interface ...
182 views

Area of a spherical cap across an intersection [duplicate]

I have a sphere with radius $r$ that equally divided in to two hemisphere P and S. There is a plane that separate two different zone A and B. Upper zone called A and lower zone called B. $\alpha$ is ...
71 views

calculate surface area of a spherical ball's portion [duplicate]

Imagine a spherical ball with radius r that equally coated into two hemisphere P(grey) and S(white) is thrown at the pool. Consider the ball can float (up-down) and rotate. There is an interface ...
248 views

Area of a spherical cap crossing an intersection [duplicate]

Consider the following background information: I have a sphere that equally divided in to two hemisphere P and S. There is a plane that separate two different zone. Upper zone called A and lower zone ...
87 views

How to calculate part of sphere area bounded by two planes?

Let we have two planes $p_1$ and $p_2$ that intersect by an angle $\beta$. Let $p_1$ be on distance of $a$ from the center $C$ of sphere with radius $1$ and $a<1$. Let intersection of the two ...
330 views

calculating the area on the surface os a sphere created by intersection of two spherical caps!

Consider a spherical object composed of two compartments (A and B, not necessarily hemispheres) sitting at the interface which is characterized by a plane separating 1 and 2. For this case, ...
Given two ellipses that take up regions $E_1$ and $E_2$ in $\mathbb{R^2}$, with the following properties: Centers defined in the Cartesian coordinate system $(c_1, 0)$ for $E_1$ and $(c_2, 0)$ for \$...