A common unwanted difficulty in treatment planning, especially in non-coplanar radiotherapy set-ups, is the potential collision of the rotating gantry with the couch and/or the patient's body. A technique and computer program that detects these and signals avoidance of such beam directions is presented. The problem was approached using analytical geometry. The separate components within the treatment room have either been measured and modelled for an Elekta linear accelerator, or read out from a Pinnacle3 treatment planning system and are represented as an integer grid of points in three-dimensional (3D) space. The module is attached to the treatment planning system and can provide rejection or acceptance of unwanted beam directions in a plan. In contrast to previous work that has only used patient models, each individual patient's outlines are considered here in their actual treatment position inclusive of any immobilization device. The extremities of the patient superiorly and inferiorly to the scanned region are simulated by an expanded version of the RANDO phantom. In this way, 'potential' collisions can be detected in addition to the certain ones. Patient position is not a limiting factor for the accuracy of the collision detection anymore, as each set-up is always created around the isocentre. Maps of allowed and forbidden zones within the treatment suite have been created by running the code for all possible gantry and couch angles for three commonly arising cases: a head and neck plan utilizing a small stereotactic collimator, a prostate plan with multileaf collimators and an abdominal plan with the lead tray attached. In the last case, the 3D map permitted significantly fewer set-up combinations. Good agreement between prediction and experiment confirmed the capability of the program and introduces a promising add-on for treatment planning.