Over the past few decades, the scientific community’s and industry’s interest in additive manufacturing technologies has surged. This technology is distinguished by the layer-by-layer deposition of the raw materials and the piece’s growth in a predetermined build orientation. This factor impacts the process’ overall cost, surface quality, and other crucial parameters. Numerous methods to solve competing aspects have been proposed in the literature, with the more promising that iteratively uses ray-tracing techniques. Existing algorithms iterate for each discrete element of the model’s bounding box projection onto the building platform. However, when optimisation algorithms are used on real-life industrial parts, computational time problems arise due to the high number of faces in the models. A new computational technique to determine the appropriate part orientation to reduce the support volume is proposed to address the problem. The method reduces the computational time, cycling the ray-tracing only on the triangles where the model surface is discretised. This approach has been integrated into an enhanced particle swarm optimisation algorithm to prove its efficiency. The approach is intended for industrial applications where it is necessary to handle complicated geometries quickly and efficiently to find the best orientation. Based on the computer’s resources and the complexity of the faceted model, a set of case studies with an industrial engineering significance is used to demonstrate the approach’s effectiveness.