Surface normals play a pivotal role in most shape analysis applications. As such, their accurate computation has received a considerable amount of attention over the years. In heritage sites, where entities of complex shape are prevalent, the development of reliable means to estimate them becomes even more important. When approaching the computation of normals, not only the shape complexity becomes a factor, but also the nature of the data, specifically the point density and noise level. To handle both shape and data quality-related aspects, this paper proposes a new method for the computation of surface normals, focusing on entities of complex form. We consider portable laser scanners as our data acquisition source, as such scanners offer efficient site coverage. Nonetheless, as portable scans are characterized by relatively sparse point clouds and noisy responses, their processing becomes a challenge. While existing research focused on the development of robust estimation methods, their application scope exhibited some limitations in preserving sharp features. Here, we demonstrate how the use of the <i>L₀</i> norm optimization framework, which features an inherent ability to preserve sharp transitions, with no need to introduce assumptions about the scene structure, can accommodate such a problem. Results show improved performance compared to common normal computation schemes with more reliable and accurate estimations of their form.