PTOPO: Computing the geometry and the topology of parametric curves

We consider the problem of computing topology and describing geometry a parametric curve in R n . present an algorithm, PTOPO , that constructs abstract graph is isotopic to embedding space. Our method exploits benefits representation does not resort implicitization. Most importantly, we perform all computations parameter space implicit When parametrization involves polynomials degree at most d maximum bitsize coefficients ? then worst case bit complexity O ˜ B ( 6 + 5 4 2 ) 3 This bound matches current record for plane algebraic given form. For curves, if N = max ? { } becomes which improves state-of-the-art result, due Alcázar Díaz-Toca [CAGD'10], by factor 10 In same time complexity, obtain whose straight-line curve. However, visualizing on top construction, increases 7 curves general dimension, can also distinguish between ordinary non-ordinary real singularities determine their multiplicities expected employing algorithm Blasco Pérez-Díaz [CAGD'19]. have implemented maple curves. experiments illustrate its practical nature.