Since you have MatLab:
https://www.researchgate.net/publication/318476279_Algorithm_976_Bertini_real_Numerical_Decomposition_of_Real_Algebraic
_Curves_and_Surfaces/download?_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6Il9kaXJlY3QiLCJwYWdlIjoiX2RpcmVjdCJ9fQ
https://www.researchgate.net/publication/4278665_Interactive_Ray_Tracing_of_Arbitrary_Implicits_with_SIMD_Interval_Arit
hmetic/download?_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6Il9kaXJlY3QiLCJwYWdlIjoiX2RpcmVjdCJ9fQ
Bezier patches and Bernstein polynomials! :)
https://cad-conference.net/files/CAD24/CAD24_334-338.pdf
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