  We propose a new paradigm for modelling and calibrating laser scanners with
rotation symmetry, as is the case for Lidars or for galvanometric laser systems
with one or two rotating mirrors. Instead of bothering about the intrinsic
parameters of a physical model, we use the geometric properties of the device
to model it as a specific configuration of lines, which can be recovered by a
line-data-driven procedure. Compared to universal data-driven methods that
train general line models, our algebraic-geometric approach only requires a few
measurements. For example, a galvanometric laser scanner with two mirrors is
modelled as a grid of hyperboloids represented by a grid of 3x3 lines,
providing a new type of lookup table: containing not more than 9 elements,
lines rather than points, where we replace the approximating interpolation with
exact affine combinations of lines. The proposed method is validated in a
realistic virtual setting. As a collateral contribution, we present a robust
algorithm for fitting ruled surfaces of revolution on noisy line measurements.
