The proliferation of satellite mega-constellations for communication, navigation, and Earth observation has created an urgent need for fast, reliable, and autonomous mission planning systems. A cornerstone of this autonomy is the rapid and accurate determination of satellite-to-site visibility windows. While hybrid methods that use a geometric interval shrinking pre-filter are computationally efficient, existing implementations rely on a simplified geometric model that is not robust for all orbit-site configurations. This can lead to wrong interval shrinking results or even missed detections, a critical failure for autonomous operations. This paper presents a comprehensive interval shrinking method that corrects this fundamental flaw. We introduce a dichotomous critical angle model that accounts for all possible tangency scenarios (both acute and obtuse) between the orbit plane and the ground site’s viewing cone. This generalized model allows for the systematic classification of the problem into distinct geometric regimes. Numerical simulations, validated against STK, demonstrate that the proposed algorithm correctly identifies all visibility windows, including those completely missed by the existing method, with negligible additional computational cost. This work provides a complete, robust, and efficient algorithm that serves as a critical enabling technology for reliable autonomous mission planning and large-scale constellation analysis.