Many homes today are logically or physically 'zoned' based on properties such as HVACs, activities, or physical layouts. Accurately sensing the occupancy of these zones can yield energy savings, aid in automatic heating and lighting control, energy disaggregation, etc. Existing systems that attempt to sense occupancy are power consuming, non real-time, pet unfriendly and/or sensitive to ambient heat, light and air flow. In this paper, we address these by building Doorpler, a time, space and power-aware radar-based system that detects occupancy at zone transition points by sensing crossings and their direction. It detects a crossing via the Doppler Principle, and infers the direction of crossing by measuring the angle-of-arrival of the human reflection. We evaluate Doorpler by conducting a scripted study and two in-situ studies for 200 hours, collecting over 1600 doorway crossings. We obtain a precision, recall and direction accuracy of over 99% in the scripted studies, and over 95% in the in-situ studies. Our results estimate that Doorpler can fall in the energy-harvestable range of indoor environments with an average power consumption of 6.1mW. With an execution time of 13.8ms, Doorpler has the potential to enable several real-time smart home applications like smart-lighting and HVAC control.