Satellite Coverage Analysis is a fundamental performance assessment element in remote sensing and communications services projects. Coverage is a key parameter in the constellation operation and design for missions relying on several satellites. Since coverage areas over the surface of the Earth change with time, intersecting and drifting apart, the dynamics of every satellite influence the constellation's behavior as a whole. For this reason, every configuration change, be it in the number of satellites or their relative positions, heavily impacts the cost/performance of the mission. This paper presents a constellation-to-ground coverage analysis model that enables the rapid evaluation of areas on the surface of the Earth. The method leverages geodetic projections and an oblate Earth model and uses dynamic transformation and anti-transformation techniques combined with polygon Boolean operations. Timestamped datasets are obtained to account for the dynamics of the scenario, which can be exploited in statistical coverage analysis of the constellation. Our empirical evaluations show that this approach is superior in accuracy and computation effort compared to traditional net-point techniques. While net-point approaches are at the core of state-of-the-art commercial software, they are approximate. We show that, for finer grid granularity, the netpoint schemes converge to our polygon-based results.