Different methods have been proposed in the literature for the calculation of phase envelopes of mixtures. The phase envelopes of even simple mixtures have at least two stationary points on the P-T plane [partial derivative P/partial derivative T = 0 at the point of maximum pressure (cricondenbar) and partial derivative T/partial derivative P = 0 at the point of maximum temperature (cricondentherm)]. Even more stationary points exist for complex mixtures. Therefore, a monotonic variation of either pressure or temperature cannot be used to trace the full phase envelope. Different methods have been proposed in the literature to help choose the right variable at the right location of the phase envelope to automatically trace the entire phase envelope. Although most methods work well for simple mixtures, many of them do not work well with wide-boiling mixtures or with mixtures that exhibit open-ended dew lines. In this article, we compare phase envelopes with space curves and show that the use of an independent variable helps trace complex phase envelopes automatically. It is shown that density is the ideal independent variable. A density-based method is developed to determine saturation points and automatically construct complex phase envelopes. The proposed method has immediate application in property programs and process simulators and was implemented in version 9.1 of NIST REFPROP property program released in May 2013.