On the angular control of rotating lasers by means of line calculus on hyperboloids

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.