# 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