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Survey on Modeling of Human‐made Articulated Objects
Computer Graphics Forum, EarlyView.Abstract 3D modeling of articulated objects is a research problem within computer vision, graphics, and robotics. Its objective is to understand the shape and motion of the articulated components, represent the geometry and mobility of object parts, and create realistic models that reflect articulated objects in the real world.
Jiayi Liu +2 more
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Mapping Mental Models of Uncertainty to Parallel Coordinates by Probabilistic Brushing
Computer Graphics Forum, EarlyView.Abstract Through training and gathered experience, domain experts attain a mental model of the uncertainties inherent in the visual analytics processes for their respective domain. For an accurate data analysis and trustworthiness of the analysis results, it is essential to include this knowledge and consider this model of uncertainty during the ...
Gabriel Borrelli +2 more
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Piecewise constant and piecewise linear expansions
Computers & Chemistry, 1977Abstract We consider certain complete, orthonormal systems of piecewise-constant functions which include the Haar and the Walsh system as special cases. Using the properties of these systems we generate and study certain complete systems which are piecewise linear.
W.R. Madych, R.D. Larsen, E.F. Crawford
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Piecewise smooth extreme functions are piecewise linear
Mathematical Programming, 2018The infinite relaxations in integer programming were introduced by Gomory and Johnson to provide a general framework for the theory of cutting planes: the so-called valid functions, and in particular the minimal and extreme functions, can be seen as automatic rules for the generation of cuts.
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On Piecewise Linear Functions and Piecewise Linear Equations
Mathematics of Operations Research, 1980In this paper we treat of the number of solutions of certain piecewise linear (p.l.) equations and of necessary and sufficient conditions for a PL function to be a homeomorphism. The function f: Rn → Rm is PL when a finite set H of hyperplanes exists such that Rn\∪H is the disjoint union of open polyhedral sets C1, …, Cq and F ∣ C̄ (x) = Aix + bi with
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Cumulative chords,Piecewise-Quadratics and Piecewise-cubics
2006Cumulative chord piecewise-quadratics and piecewise-cubics are examined in detail, and compared with other low degree interpolants for unparameterized data from regular curves in R n , especially piecewise-4-point quadratics. Orders of approximation are calculated and compared with numerical experiments.
Ryszard Kozera, Lyle Noakes
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Piecewise fractional Brownian motion
IEEE Transactions on Signal Processing, 2005Starting from fractional Brownian motion (fBm) of unique parameter H, a piecewise fractional Brownian motion (pfBm) of parameters Hi, Ho and gamma is defined. This new process has two spectral regimes: It behaves like an fBm of parameter Ho for low frequencies and like an fBm of parameter Hi for high frequencies .When Ho = Hi, or for limit cases, pfBm ...
Perrin, Emmanuel +3 more
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From piecewise deterministic to piecewise diffusion Markov processes [PDF]
Proceedings of the 27th IEEE Conference on Decision and Control, 2003 The author presents PD (piecewise deterministic) processes as pathwise unique solutions of an Ito stochastic differential equation (SDE), driven by a Poisson random measure. Since such an SDE permits the inclusion of diffusion, this approach leads to a large variety of piecewise diffusion Markov processes, represented by pathwise unique SDE solutions. >
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Studia Scientiarum Mathematicarum Hungarica, 2004
We show that it is consistent that there is a hereditarily separable, 0-dimensional T2 space X of cardinality ω1 such that for each uncountable subspace Y of X there is a continuous bijection φ : Y → X and there is a partition (Yi)i<n of Y into finitely many pieces such that φ ↾ Yi is a homeomorphism for each i < n.
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We show that it is consistent that there is a hereditarily separable, 0-dimensional T2 space X of cardinality ω1 such that for each uncountable subspace Y of X there is a continuous bijection φ : Y → X and there is a partition (Yi)i<n of Y into finitely many pieces such that φ ↾ Yi is a homeomorphism for each i < n.
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The Piecewise Concave Function
Management Science, 1967An important function which is neither concave nor convex often arises in production and inventory models. This function is herein called piecewise concave and can be considered to be a generalization of the concave function. Essentially it is the maximum of a collection of concave functions.
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