Karikó, Csongor CsanádValasek, GáborGünther, TobiasMontazeri, Zahra2025-05-092025-05-092025978-3-03868-269-11017-4656https://doi.org/10.2312/egp.20251026https://diglib.eg.org/handle/10.2312/egp20251026We investigate the problem of robust and real-time rendering of algebraic surfaces. We show that expressing the intersection of the ray and the algebraic surface as a single univariate polynomial is not robust in practice, comparing results between monomial, Bernstein, Lagrange, and Chebyshev basis fits. We show that fitting multiple polynomials over subintervals, such as a unit length subdivision of the ray extent within the region of interest, improves robustness at a negligible performance cost.Attribution 4.0 International LicenseCCS Concepts: Computing methodologies → Ray tracingComputing methodologies → Ray tracing10.2312/egp.202510262 pages