# Sphere¶

`Spheres`

are defined by their local coordinates and `radius`

.

## Sphere-Sphere contact¶

Todo

Something along the following lines (note that htis semsntics – negative value of distFactor – is not yet implemented): **Contact criterion for spheres:** When there is not yet contact, it will be created if \(u_n=|\curr{\vec{x}}_2-\curr{\vec{x}}_1|-|f_d|(r_1+r2)<0\), where \(f_d\) is `interaction radius`

(sometimes also called “interaction radius”). If \(f_d>0\), then \(\vec{u}_{0x}\) will be initalized to \(u_N\), otherwise to 0. In another words, contact will be created if spheres enlarged by \(|f_d|\) touch, and the “equilibrium distance” (where \(\vec{u}_x-\vec{u}_{0x}=0\)) will be set to the current distance if \(f_d>0\) is positive, and to the geometrically-touching distance if \(f_d<0\). Initial contact point is \(\vec{c}=\vec{x}_1+\left(r_1+\frac{\vec{u}_{0x}}{2}\right)\normalized{\vec{x}_2-\vec{x}_1}\).

Todo

`distFactor`

is not yet implemented as described above; some formulas mix values at different times, should be checked carefully.

Tip

Report issues or inclarities to github.