piecewise smooth

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• Piecewise linear manifold — In mathematics, a piecewise linear (PL) manifold is a topological manifold together with a piecewise linear structure on it. Such a structure can be defined by means of an atlas, such that one can pass from chart to chart in it by piecewise… …   Wikipedia

• Piecewise linear continuation — implicial ContinuationSimplicial Continuation, or Piecewise Linear Continuation (Allgower and Georg [1] , [3] ) is a one parameter continuation method which is well suited to small to medium embedding spaces. The algorithm has been generalized to …   Wikipedia

• PDIFF — Splines are piecewise smooth, hence in PDIFF, but not globally smooth or piecewise linear, hence not in DIFF or PL. In geometric topology, PDIFF, for piecewise differentiable, is the category of piecewise smooth manifolds and piecewise smooth… …   Wikipedia

• Differential geometry of surfaces — Carl Friedrich Gauss in 1828 In mathematics, the differential geometry of surfaces deals with smooth surfaces with various additional structures, most often, a Riemannian metric. Surfaces have been extensively studied from various perspectives:… …   Wikipedia

• Holonomy — Parallel transport on a sphere depends on the path. Transporting from A → N → B → A yields a vector different from the initial vector. This failure to return to the initial vector is measured by the holonomy of the connection. In differential… …   Wikipedia

• Manifold — For other uses, see Manifold (disambiguation). The sphere (surface of a ball) is a two dimensional manifold since it can be represented by a collection of two dimensional maps. In mathematics (specifically in differential geometry and topology),… …   Wikipedia

• Maps of manifolds — A Morin surface, an immersion used in sphere eversion. In mathematics, more specifically in differential geometry and topology, various types of functions between manifolds are studied, both as objects in their own right and for the light they… …   Wikipedia

• Poisson manifold — In mathematics, a Poisson manifold is a differentiable manifold M such that the algebra of smooth functions over M is equipped with a bilinear map called the Poisson bracket, turning it into a Poisson algebra. Since their introduction by André… …   Wikipedia

• Contourlet — Contourlets form a multiresolution directional tight frame designed to efficiently approximate images made of smooth regions separated by smooth boundaries. The Contourlet transform has a fast implementation based on a Laplacian Pyramid… …   Wikipedia

• Gauss–Bonnet theorem — The Gauss–Bonnet theorem or Gauss–Bonnet formula in differential geometry is an important statement about surfaces which connects their geometry (in the sense of curvature) to their topology (in the sense of the Euler characteristic). It is named …   Wikipedia

• Line integral — Topics in Calculus Fundamental theorem Limits of functions Continuity Mean value theorem Differential calculus  Derivative Change of variables Implicit differentiation Taylor s theorem Related rates …   Wikipedia