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 maps between them. It properly contains DIFF (the category of smooth manifolds and smooth functions between them) and PL (the category of piecewise linear manifolds and piecewise linear maps between them), and the reason it is defined is to allow one to relate these two categories. Further, piecewise functions such as splines and polygonal chains are common in mathematics, and PDIFF provides a category for discussing them.
In geometric topology, PDIFF, for piecewise differentiable, is the category of piecewise-smooth manifolds and piecewise-smooth maps between them. It properly...
of smoothness at the places where the polynomial pieces connect B-spline PDIFF f ( x ) = { exp ( − 1 1 − x 2 ) , x ∈ ( − 1 , 1 ) 0 , otherwise {\displaystyle...
isomorphism of PL manifolds is called a PL homeomorphism. PL, or more precisely PDIFF, sits between DIFF (the category of smooth manifolds) and TOP (the category...
in turn contained in the category of piecewise-differentiable functions, PDIFF. In agriculture piecewise regression analysis of measured data is used to...
manifolds. These are progressively weaker structures, properly connected via PDIFF, the category of piecewise-smooth maps between piecewise-smooth manifolds...
compare source code and compiled executables. These tools include Dup and Pdiff, which compare regions of source code to determine if there are any repeated...
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