The **distance** between the origins of frame_a
and of frame_b are determined and provided at the
output signal connector **distance**. This
distance is always positive. **Derivatives** of this
signal can be easily obtained by connecting the
block
Modelica.Blocks.Continuous.Der
to "distance" (this block performs analytic differentiation
of the input signal using the der(..) operator).

In the following figure the animation of a Distance
sensor is shown. The light blue coordinate system is
frame_a, the dark blue coordinate system is frame_b, and
the yellow arrow is the animated sensor.

If the distance is smaller as parameter **s_small** (in the "advanced" menu),
it is approximated such that its derivative is
finite for zero distance. Without such an approximation, the derivative would
be infinite and a division by zero would occur. The approximation is performed
in the following way: If distance > s_small, it is computed as sqrt(r*r) where
r is the position vector from the origin of frame_a to the origin of frame_b.
If the distance becomes smaller as s_small, the "sqrt()" function is approximated
by a second order polynomial, such that the function value and its first derivative
are identical for sqrt() and the polynomial at s_small. Futhermore, the polynomial
passes through zero. The effect is, that the distance function is continuous and
differentiable everywhere. The derivative at zero distance is 3/(2*s_small).