Topology of the Intersection of Two Parameterized Surfaces, Using Computations in 4D Space

We compute the topology of the intersection curve between two parametric surfaces, represented in the 4D parameter space. Our algorithm constructs an isotopy with a list of line segments. We certify the exactness of the topology of the curve, up to any specified precision. Our algorithm relies on injectivity criteria and efficient solvers of systems of polynomial equations, generalizing similar studies for curves in 2D and 3D.

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