In this paper, we introduce a wider perspective in Rotor Angle Stability (RAS) analysis, by mapping parts of state-space boundary of interest to parameter space boundary points. These points are obtained using the Time Domain Simulation (TDS), the Closest Unstable Equilibrium Point (UEP) approximation, and the Potential Energy Boundary Surface (PEBS) concepts. Then analytical parameter-space boundaries are constructed using polynomial regression model with optimal fit coefficients in least squares terms. Security boundaries constructed in this manner directly give information about critical clearing times for different faults and operating states, and are suitable as an on-line tool for transient stability assessment.