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We introduce a new method to approximate algebraic space curves. The algorithm combines a subdivision technique with local approximation of piecewise regular algebraic curve segments. The local technique computes pairs of polynomials with modified Taylor expansions and generates approximating circular arcs. We analyze the connection between the generated… (More)

We present an algorithm generating a collection of fat arcs which bound the zero set of a given bivariate polynomial in Bernstein– Bézier representation. We demonstrate the performance of the algorithm (in particular the convergence rate) and we apply the results to the computation of intersection curves between implicitly defined algebraic surfaces and… (More)

We present a new algorithm to approximate real roots of multivari-ate polynomial systems. This algorithm combines the standard subdivision technique with a new domain reduction strategy. We introduce fat spheres as multidimensional quadratic enclosures for algebraic hyper-surfaces. Then we present a local reformulation technique of the algebraic system,… (More)

The most important aim in tool path generation methods is to increase the machining efficiency by minimizing the total length of tool paths while the error is kept under a prescribed tolerance. This can be achieved by determining the moving direction of the cutting tool such that the machined stripe is the widest. From a technical point of view it is… (More)

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