Schematic representation of the definition of filament segments connected to the X-ray cluster and the computation of their projected inclinations using the PHT technique. Red circles indicate the segment points [S1, S2, ..., S7] that are part of the detected filament network. Dashed magenta lines represent 0.8 and 1.2 times the r₂₀₀ around the X-ray peak, respectively. Dark red segment points [S2, S3, S4, S5], located between the dashed curves, are used to compute the mean projected inclination of the filament segment connected to the galaxy cluster (magenta ellipse). The PHT operator is centered at the position of S4, with each line representing a possible local alignment angle of the segment points, based on the positions of the points within the dashed circumference. Line thickness corresponds to the probability of alignment at that specific angle, with the thickest blue line denoting the most probable inclination angle at S4. The same procedure is applied at S2, S3 and S5 to ultimately compute the mean projected alignment angle using Eq. (2), represented as the red vector ${\widehat{v}}_{\mathit{fill}}$. The inclination angle of the X-ray cluster is represented as the magenta vector ${\widehat{v}}_x.$