Mid-resolution Infrared Astronomical Spectrograph (MIRADAS) is a near-infrared multi-object echelle spectrograph for Gran Telescopio de Canarias. It selects targets from a 5-arc min field of view using up to 12 deployable probe arms with pick-off mirror optics. The focal plane where the probe arms move has a diameter around 250 mm. The specific geometry of the probe arms requires an optimized collision detection algorithm for the determination of the target assignment and the trajectories determination. We present the general polygonal chain intersection algorithm, which is used to detect the possible collisions and avoid them. It is a generalization of the Polygonal Chain Intersection algortihm, allowing to work with vertical segments, providing a solution for the intersection of any class of polygons. Its use has reduced the time required to detect the collisions between 3 and 4 times compared with a naive solution when used in MIRADAS.