Approximating implicit curves on plane and surface triangulations with affine arithmetic

• Our method is the first interval method for polygonal approximation of implicit curves that can handle triangles and so can be used for triangulated surfaces.
• Our method exploits the additional geometric information provided by affine arithmetic to avoid having to compute derivatives.
• Our method can be used for rectangular and triangular decompositions, both structured and unstructured, can use any refinement scheme that the decompositions offer, and can provide its own refinement scheme otherwise.

We present a spatially and geometrically adaptive method for computing a robust polygonal approximation of an implicit curve defined on a planar region or on a triangulated surface. Our method uses affine arithmetic to identify regions where the curve lies inside a thin strip. Unlike other interval methods, even those based on affine arithmetic, our method works on both rectangular and triangular decompositions and can use any refinement scheme that the decomposition offers.

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