By William Fulton
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The middle of classical homotopy idea is a physique of rules and theorems that emerged within the Nineteen Fifties and used to be later principally codified within the suggestion of a version type. This middle comprises the notions of fibration and cofibration; CW complexes; lengthy fiber and cofiber sequences; loop areas and suspensions; etc.
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DIFFERENTIAL TOPOLOGY AND GEOMETRY 42 A sector defined by two consecutive separatrices is • hyperbolic if none of the lines in the sector have the umbilic in their limit set; • parabolic if all curvature lines in the sector have the umbilic in their α or exclusive ω limit set; The alternative case of an elliptic sector, if all curvature lines in the sector have the umbilic in their α and ω limit set, is not generic —cf. 360]. Note that a separatrix is a line of curvature which ends at an umbilic, hence its tangent at this point is a limiting principal direction.
Pour des surfaces discrétisants des surfaces lisses dont les ridges sont connus, des exemples prouvent que notre algorithme heuristique retrouve la topologie des ridges et des ombilics. Pour des maillages reconstruits à partir de données scannées, des exemples montrent que notre algorithme retrouve des sousensembles des ridges comparables aux autres méthodes de l’état de l’art (qui utilisent des ajustements globaux), tout en améliorant les temps de calculs d’au moins un ordre de grandeur et en fournissant une méthode de filtrage plus performante.
Since we just aim at presenting the local and global structure of the medial axis, we shall follow [BGG85, GK00], but the interested reader should also consult [Yom81]. Given a closed manifold S embedded in R3 , the medial axis MA(S) consists of the points of the open set R3 \S having two or more nearest points on S. A related notion is the skeleton of R3 \S, which consists of the centers of maximal spheres included in R3 \S —maximal for the inclusion amongst such spheres. For smoothly embedded manifolds, the closure of the medial axis is actually equal to the skeleton, which is why we just refer to the medial axis in the sequel.
Algebraic Curves: An Introduction to Algebraic Geometry by William Fulton