The presence of silicate material in known rings in the Solar System raises the possibility of ring systems existing even within the snow linewhere most transiting exoplanets are found. Previous studies have shown that the detection of exoplanetary rings in transit light curves is possible, albeit challenging. To aid such future detection of exoplanetary rings, we present the Polygon+Segments model for modelling the light curve of an exoplanet with rings. This high-precision model includes full ring geometry as well as possible ring transparency and the host star's limb darkening. It is also computationally efficient, requiring just a 1D integration over a small range, making it faster than existing techniques. The algorithm at its core is further generalized to compute the light curve of any set of convex primitive shapes in transit (e.g. multiple planets, oblate planets, moons, rings, combination thereof, etc.) while accounting for their overlaps. The python source code is made available.