Observations of the sky irradiation intensity in the visible wavelengths during a solar eclipse permit to model the Sun diameter,a key number to constrain the internal structure of our star.In this paper,we present an algorithm that takes advantage of the precise Moon topography from Lunar Reconnaissance Orbiter to compute,with a high resolution in time,the geometrical part (i.e.top-of-atmosphere,and for a given wavelength) of the sky irradiation at any given location on the Earth during these events.The algorithm is also able to model the Baily's beads.We give as an application the theoretical computation of the light curve corresponding to the solar eclipse observed at Lakeland (Queensland,North Australia)on 2012 November 13.The application to real data,with the introduction of atmospheric and instrumental passbands,will be considered in a forthcoming paper.