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An Algorithm for Decomposing Multi-dimensional Non-manifold Objects into Nearly Manifold Components [chapter]

M. Mostefa Mesmoudi, Leila De Floriani, Franco Morando, Enrico Puppo
2005 Mathematics and Visualization  
In this paper we address the problem of building valid representations for non-manifold d-dimensional objects.  ...  Our approach provides a rigorous basis for designing efficient dimension-independent data structures for describing non-manifold objects.  ...  The standard decomposition is a useful basis for defining a data structure for non-manifold objects in arbitrary dimensions as described in [1] .  ... 
doi:10.1007/3-540-26808-1_4 fatcat:nax5mjztnfgndluexxsj2pfav4

Non-manifold Decomposition in Arbitrary Dimensions [chapter]

Leila De Floriani, Mostefa Mohammed Mesmoudi, Franco Morando, Enrico Puppo
2002 Lecture Notes in Computer Science  
We first introduce the notion of d-quasi-manifold complexes, then we sketch an algorithm to decompose an arbitrary complex into an assembly of quasi-manifold components abutting at non-manifold joints.  ...  In this paper we consider the problem of decomposing a nonmanifold n-dimensional object described by an abstract simplicial complex into an assembly of 'more-regular' components.  ...  Ministry of Instruction, University and Research (MIUR) "SPADA -Representation and processing of spatial data in Geographic Information Systems".  ... 
doi:10.1007/3-540-45986-3_6 fatcat:nby5mtrdlnch3cezenmf72cnji

A Decomposition-based Approach to Modeling and Understanding Arbitrary Shapes [article]

David Canino, Leila De Floriani
2011 Smart Tools and Applications in Graphics  
Modeling and understanding complex non-manifold shapes is a key issue in shape analysis and retrieval.  ...  We describe a dimension-independent algorithm to generate such decomposition.  ...  But non-manifold and non-regular objects arise in several applications.  ... 
doi:10.2312/localchapterevents/italchap/italianchapconf2011/053-060 dblp:conf/egItaly/CaninoF11 fatcat:aaj6jk7uevc4pdfravrgntbm2i

Page 422 of American Journal of Mathematics Vol. 69, Issue 3 [page]

1947 American Journal of Mathematics  
terms of 3 arbitrary vector functions of one variable; in the non-holonomic case we get only the ds* of the manifolds in. terms of an arbitrary function of two variables and some necessary and sufficient  ...  derivatives in the order B, « 7g is the “non-holonomy object ” relative to our coordinate directions, which are in the general case non-holonomic; this symbol expresses the “deviation of the commutativity  ... 

A Decomposition-based Representation for 3D Simplicial Complexes [article]

Annie Hui, Lucas Vaczlavik, Leila De Floriani
2006 Symposium on geometry processing : [proceedings]. Symposium on Geometry Processing  
It also provides a suitable basis for geometric reasoning on non-manifold shapes. We describe an algorithm to decompose a 3D simplicial complex into nearly manifold parts.  ...  The DLD data structure is based on a unique decomposition of the simplicial complex into nearly manifold parts, and encodes the decomposition in an efficient and powerful two-level representation.  ...  This decomposition is unique, since it does not make any arbitrary choice in deciding where the object has to be decomposed, and natural, since it removes singularities by splitting the complex at non-manifold  ... 
doi:10.2312/sgp/sgp06/101-110 fatcat:vtb3trtqxjhf7njjomghhyfymu

Puffini-Videv Models and Manifolds [article]

P. Gilkey, E. Puffini, V. Videv
2006 arXiv   pre-print
We present non-trivial geometric examples of Riemannian manifolds with this property.  ...  In the Riemannian setting, we give a complete characterization of such tensors; in the pseudo-Riemannian setting, partial results are available.  ...  We say that M = (V, ·, · , A) is decomposible if there exists a non-trivial orthog- onal decomposition V = V 1 ⊕ V 2 which decomposes A = A 1 ⊕ A 2 ; in this setting, we shall write M = M 1 ⊕ M 2 where  ... 
arXiv:math/0605464v1 fatcat:gwrlitl7bne6bdryxx55jcdr4q

Complex 3D General Object Reconstruction from Line Drawings

Linjie Yang, Jianzhuang Liu, Xiaoou Tang
2013 2013 IEEE International Conference on Computer Vision  
In this paper, we propose a novel approach to 3D reconstruction of complex general objects, including manifolds, non-manifold solids, and non-solids.  ...  An important topic in computer vision is 3D object reconstruction from line drawings.  ...  Decomposing line drawings of general objects A general object can be a manifold, non-manifold solid, or non-solid.  ... 
doi:10.1109/iccv.2013.181 dblp:conf/iccv/YangLT13 fatcat:vypzr6ov6jhwpb2zcj3jsmd6le

Leading infrared logarithms for the σ-model with fields on an arbitrary Riemann manifold

M. V. Polyakov, A. A. Vladimirov
2011 Theoretical and mathematical physics  
We derive non-linear recursion equation for the leading infrared logarithms (LL) in four dimensional sigma-model with fields on an arbitrary Riemann manifold.  ...  This result paves a way to the solution of the model in arbitrary number of dimensions at N-->oo  ...  The work is supported in parts by German Ministry for Education and Research (grant 06BO9012) and by Russian Federal Programme "Research and Teaching Experts in Innovative Russia" (contract 02.740.11.5154  ... 
doi:10.1007/s11232-011-0126-7 fatcat:ztjw5x2yfjhobdcwpkwrh4nini

Page 2438 of Mathematical Reviews Vol. , Issue 2004c [page]

2004 Mathematical Reviews  
decomposition in arbitrary dimensions.  ...  Summary: “In this paper we consider the problem of decomposing 68 COMPUTER SCIENCE 2438 a non-manifold n-dimensional object described by an abstract simplicial complex into an assembly of ‘more-regular  ... 

NATURAL REPRESENTATION OF SHAPES WITH SINGULARITIES

IMRE HORVÁTH, JORIS S. M. VERGEEST
1997 International journal of shape modeling  
The singularity oriented modeling is very useful in certain applications, e.g. in form-giving and styling, rapid prototyping and shape generation based on gestural devices.  ...  A shape singularity is an observable discontinuity of the boundary of an object that is featured by specific tangency and curvature characteristics.  ...  The research work reported in this paper relates to the Integrated Concept Advancement (ICA) project of the Subfaculty of Industrial Design Engineering, FDEP, of the Delft University of Technology.  ... 
doi:10.1142/s0218654397000100 fatcat:vxnkkhd3zrff5bhuyi7vjyjahm

datafold: data-driven models for point clouds and time series on manifolds

Daniel Lehmberg, Felix Dietrich, Gerta Köster, Hans-Joachim Bungartz
2020 Journal of Open Source Software  
Typically, manifold learning attempts to construct a global parametrization (embedding) of this manifold, in a space of much lower dimension than the original ambient space.  ...  point clouds to find an explicit mani-fold parametrization and to identify non-linear dynamical systems on these manifolds.  ...  In addition to non-linear dimension reduction, "Diffusion Maps" allow the user to approximate mathematically meaningful objects on manifold data, such as the Laplace-Beltrami operator (Coifman & Lafon  ... 
doi:10.21105/joss.02283 fatcat:orm4nlvgwjgxjl2m4ibrzb62fq

Page 7396 of Mathematical Reviews Vol. , Issue 2002J [page]

2002 Mathematical Reviews  
They introduce the adapted basis to these distributions and decompose all the geometric objects on J'(T,M) accordingly.  ...  Let T and M be smooth manifolds of finite dimension and con- sider the jet bundle z:J'(7,M)— T x M.  ... 

Manipulating Topological Decompositions of Non-Manifold Shapes [article]

David Canino
2016 Smart Tools and Apps for Graphics - Eurographics Italian Chapter Conference  
Many techniques for decomposing a non-manifold shape are available in the current literature, and provide a structural model, which exposes its non-manifold singularities, as well as the connectivity of  ...  Decomposing a non-manifold shape into its almost manifold components is a powerful tool for analyzing its complex structure.  ...  [DFMMP03] decompose a non-manifold shape of arbitrary dimension and not necessarily embedded in the Euclidean space as the collection of its Initial Quasi-Manifold (IQM-) components.  ... 
doi:10.2312/stag.20161359 dblp:conf/egItaly/Canino16 fatcat:mesgcjkywvhw3coxt76lbpqeta

A Dimension-Independent Data Structure for Simplicial Complexes [chapter]

Leila De Floriani, Annie Hui, Daniele Panozzo, David Canino
2010 Proceedings of the 19th International Meshing Roundtable  
We consider here the problem of representing non-manifold shapes discretized as d-dimensional simplicial Euclidean complexes.  ...  To this aim, we propose a dimension-independent data structure for simplicial complexes, called the Incidence Simplicial (IS) data structure, which is scalable to manifold complexes, and supports efficient  ...  A natural way to deal with non-manifold objects consists of decomposing them into nearly manifold components by cutting at non-manifold simplices.  ... 
doi:10.1007/978-3-642-15414-0_24 dblp:conf/imr/FlorianiHPC10 fatcat:w7acb7iwkfaeddk4pxzxuppzee

Design of globally stable controllers for a class of chaotic systems

N. Apostolou, R. E. King
2002 International Journal of Systems Science  
A simple method to design chaos suppressors for a class of chaotic systems that can be decomposed into a linear subsystem and a nonlinear subsystem whose states can be decoupled is presented.  ...  Although the dimensions of the partial state vectors ¹ 1 , ¹ 2 can be arbitrary, in all three paradigms that follow, the dimension of the invariant manifold (i.e. the order of the nonlinear subsystem 2  ...  As in Tian (1999) , the primary objective of the proposed approach is to drive the trajectory of the controlled system from any arbitrary initial state towards an invariant manifold and thereafter asymptotically  ... 
doi:10.1080/00207720210123733 fatcat:i34v6xbm6jhyjbpsm5w3xnl5x4
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