Revisiting the Original Vision: Digital Reconstruction of the Kosmaj Monument’s Hyperbolic Contours

This paper introduces a method for creating an accurate hyperbola through five given points in CAD environments that lack native conic tools. Unlike numerical approaches, the method relies on purely graphical procedures of defining cones through selected points and extracting their planar sections, which results in a faithfully represented conic—hyperbola. Applied on the Kosmaj Monument, an emblematic example of post-WWII Yugoslav brutalism, the approach enabled reconstruction of its contours as true hyperbolas, rather than the stylized arcs and line segments of the realized structure. Using photogrammetric data and point-cloud analysis from the previous research, the study develops an idealized digital model that resonates with the authors’ original design intent. By balancing geometric rigor with practical accessibility, the method offers advantages for heritage reconstruction, where interpretive reasoning is required. It further highlights the continued relevance of the synthetic geometry approach within standard CAD workflows for design, analysis, and education.