  Jet breaks in gamma ray burst (GRB) afterglows provide a direct probe of
their collimation angle. Modeling a jet break requires an understanding of the
"jet spreading" process, whereby the jet transitions from a collimated outflow
into the spherical Sedov-Taylor solution at late times. Currently, direct
numerical calculations are the most accurate way to capture the deceleration
and spreading process, as analytical models have previously given inaccurate
descriptions of the dynamics. Here (in paper I) we present a new,
semi-analytical model built empirically by performing relativistic numerical
jet calculations and measuring the relationship between Lorentz factor and
opening angle. We then calculate the Lorentz factor and jet opening angle as a
function of shock radius and compare to the numerical solutions. Our analytic
model provides an efficient means of computing synthetic GRB afterglow light
curves and spectra, which is the focus of paper II.
