  Large surveys provide numerous non-targeted observations of small bodies
(SSOs). The upcoming LSST of the Rubin observatory will be the largest source
of SSO photometry in the next decade. With non-coordinated epochs of
observation, colors, and therefore taxonomy and composition, can only be
computed by comparing absolute magnitudes obtained in each filter by solving
the phase function (evolution of brightness of the small body against the solar
phase angle). Current models in use in the community (HG, HG12* , HG1G2)
however fail to reproduce the long-term photometry of many targets due to the
change in aspect angle between apparitions.
  We aim at deriving a generic yet simple phase function model accounting for
the variable geometry of the SSOs over multiple apparitions.
  We propose the sHG1G2 phase function model in which we introduce a term
describing the brightness changes due to spin orientation and polar oblateness.
We apply this new model to 13,245,908 observations of 122,675 SSOs. These
observations were acquired in the g and r filters with the Zwicky Transient
Facility. We retrieve them and implement the new sHG1G2 model in Fink, a broker
of alerts designed for the LSST.
  The sHG1G2 model leads to smaller residuals than other phase function models,
providing a better description of the photometry of asteroids. We determine the
absolute magnitude H and phase function coefficients (G1, G2) in each filter,
the spin orientation (RA_0,DEC_0), and the polar-to-equatorial oblateness R for
95,593 Solar System Objects (SSOs), which constitutes about a tenfold increase
in the number of characterised objects compared to current census.
  The application of the sHG1G2 model on ZTF alert data using the FINK broker
shows that the model is appropriate to extract physical properties of asteroids
from multi-band and sparse photometry, such as the forthcoming LSST survey.
