Density scatter plots showing the distribution of projected separation with semimajor axis for different assumptions about eccentricity and inclination distributions. The solid blue line indicates 1:1 correspondence, a_proj = a. The dashed blue line shows ﹩{a}_{\mathrm{proj}}=a\cos i﹩, which is the minimum a_proj for fixed inclination and circular orbits. The distribution of a_proj with a is bimodal for fixed inclination (right column) because the apparent orbital speed of the planet has minima at both a_proj = a and ﹩{a}_{\mathrm{proj}}=a\cos i﹩, effectively piling-up planets at these four points on the orbit.