Approximating a spline with conics or osculating circles is

necessary because conics are well-known geometric loci that are easily constructed, whereas a spline is a complex curve not defined by a single equation. Using conics (ellipses, parabolas, hyperbolas) allows for approximating long sections of the spline with fewer elements compared to using only osculating circles, improving precision in complex surfaces. The approach with conics ensures smoother transitions and geometric continuity, reducing construction costs and simplifying the creation of innovative architectural forms. Osculating circles, while simpler, require more elements to achieve similar results. Additionally, the geometric difficulty of controlling a spline during the construction phase, related to managing control points and continually adjusting the curve, makes the use of conics even more advantageous. Conics offer greater stability and predictability in physical realization, reducing the risk of errors and improving efficiency in the construction process.

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