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Piecewise Rational Manifold Surfaces with Sharp Features [chapter]

G. Della Vecchia, B. Jüttler
2009 Lecture Notes in Computer Science  
We present a construction of a piecewise rational free-form surface of arbitrary topological genus which may contain sharp features: creases, corners or cusps.  ...  The surface is C s smooth, for an arbitrary value of s, except for the sharp features defined by the user. Our method is based on the manifold construction and follows the blending approach.  ...  Conclusions We presented a new construction of piecewise rational free-form surfaces with the possibility to define sharp features on it, based on the manifold construction already presented in [4] .  ... 
doi:10.1007/978-3-642-03596-8_6 fatcat:rkuvze3ol5hrtkhlnnflmz77k4

Surface Tiling with Differential Topology [article]

Herbert Edelsbrunner
2005 Symposium on geometry processing : [proceedings]. Symposium on Geometry Processing  
A challenging problem in computer-aided geometric design is the decomposition of a surface into four-sided regions that are then represented by NURBS patches.  ...  This by itself is not a new idea, but we have some novel ingredients that make this work, one being a rational notion of hierarchy that guides the construction of a simplified decomposition sensitive to  ...  They coincide with what we would intuitively refer to as ridges of the surface only if f is chosen accordingly. These ridges are round, somewhere on the scale between sharp and flat.  ... 
doi:10.2312/sgp/sgp05/009-011 fatcat:lylyhmfxanah3jnjgvkayg5iom

Bézier Triangles with G2 Continuity across Boundaries

Chang-Ki Lee, Hae-Do Hwang, Seung-Hyun Yoon
2016 Symmetry  
PN (point-normal) triangles are cubic Bézier triangles which meet at their edges to surface a triangular mesh, but this only achieves G 0 continuity.  ...  The sharpness of the blends can be controlled locally by varying the extent of these blending regions. We demonstrate the effectiveness of our technique by showing several modeling examples.  ...  surface; (e) A blended surface with sharp features.  ... 
doi:10.3390/sym8030013 fatcat:dkypdpxfavcbnngppnbpflhjqq

Manifold-based isogeometric analysis basis functions with prescribed sharp features [article]

Qiaoling Zhang, Fehmi Cirak
2019 arXiv   pre-print
The derived non-rational manifold-based basis functions are particularly well suited for isogeometric analysis of Kirchhoff-Love thin shells with kinks.  ...  We introduce manifold-based basis functions for isogeometric analysis of surfaces with arbitrary smoothness, prescribed C^0 continuous creases and boundaries.  ...  In Figure 18 the application of the manifold-based basis functions in representing a smooth surface with sharp features is demonstrated.  ... 
arXiv:1904.03258v2 fatcat:dkftcxavwvdy5hsr7n5tgtr3xm

AUTOMATIC RECONSTRUCTION OF 3D CAD MODELS FROM DIGITAL SCANS

FAUSTO BERNARDINI, CHANDRAJIT L. BAJAJ, JINDONG CHEN, DANIEL R. SCHIKORE
1999 International journal of computational geometry and applications  
The reduced mesh is interpolated with piecewise algebraic surface patches which approximate the original points.  ...  Our reconstruction approach is exible enough to permit interpolation of both smooth surfaces and sharp features, while placing few restrictions on the geometry or topology of the object.  ...  W e will instead mainly deal with objects whose boundary is a free form" surface, or a piecewise combination of smooth surfaces adjoining along sharp edges.  ... 
doi:10.1142/s0218195999000236 fatcat:e6dugdyssrhuxk4zh2ykdv2one

Support Function Representation for Curvature Dependent Surface Sampling

Maria Lucia Sampoli, Bert Jüttler
2009 Applied and Industrial Mathematics in Italy III  
Starting from the observation that triangular Bézier spline surfaces have quite simple support functions, we approximate any given free-form surface by a quadratic triangular Bézier spline surface.  ...  In many applications it is required to have a curvature-dependent surface sampling, based on a local shape analysis.  ...  Since volume data is usually sampled on a regular grid with a given step width, we often observe severe alias artifacts at sharp features on the extracted surfaces.  ... 
doi:10.1142/9789814280303_0046 fatcat:c4focpx2avay7lp253afksk4jy

Surface Reconstruction based on Self-Merging Octree with Deep Learning

Jian Lv, Xie Han, Jiajie Zheng, Fengguang Xiong, Min Pang
2019 Asian Conference on Machine Learning  
types of surfaces.  ...  In this paper, we proposed a new method named self-merging octree to reconstruct the surface of 3D Point Cloud which can be obtained by laser scanners or generated by some 3D modeling software.  ...  In 2009, Vecchia et al. constructed a manifold surface with sharp features using the principles of manifold structure and hybrid approximation Vecchia and Jüttler (2009) .  ... 
dblp:conf/acml/LvHZXP19 fatcat:3kguwhg2mnfwvav34k5uucxa4i

Page 5575 of Mathematical Reviews Vol. , Issue 99h [page]

1999 Mathematical Reviews  
It is proved that if the rotation set of a torus homeomorphism is a line segment with rational slope and contains a vector with rational coordinates, then there exists a pe- riodic point.  ...  Klaudiusz Wojcik (PL-JAGL; Krakow) 99h:58148 58F20 11M36 Pollicott, Mark (4-MANC; Manchester) ; Sharp, Richard (4-MANC; Manchester) Exponential error terms for growth functions on negatively curved surfaces  ... 

Manifold splines

Xianfeng Gu, Ying He, Hong Qin
2005 Proceedings of the 2005 ACM symposium on Solid and physical modeling - SPM '05  
As a result, our new spline surface defined over any manifold is a piecewise polynomial surface with high parametric continuity without the need for any patching and/or trimming operations.  ...  This paper presents a general theoretical and computational framework, in which spline surfaces defined over planar domains can be systematically extended to manifold domains with arbitrary topology with  ...  Furthermore, spatially varying smoothness requirements and sharp features can easily be achieved via different knot placements in the parametric domain.  ... 
doi:10.1145/1060244.1060249 dblp:conf/sma/GuHQ05 fatcat:inyekbp2gvf3tlerj6qoiv236i

Manifold splines

Xianfeng Gu, Ying He, Hong Qin
2006 Graphical Models  
As a result, our new spline surface defined over any manifold is a piecewise polynomial surface with high parametric continuity without the need for any patching and/or trimming operations.  ...  This paper presents a general theoretical and computational framework, in which spline surfaces defined over planar domains can be systematically extended to manifold domains with arbitrary topology with  ...  Furthermore, spatially varying smoothness requirements and sharp features can easily be achieved via different knot placements in the parametric domain.  ... 
doi:10.1016/j.gmod.2006.03.004 fatcat:vlkc4cify5ffjf7dflyxy36cwa

Design and Application of a Gradient-Weighted Moving Finite Element Code II: in Two Dimensions

Neil N. Carlson, Keith Miller
1998 SIAM Journal on Scientific Computing  
A catalog of inner products which occur in GWMFE is given, with particular attention paid to those involving second-order operators.  ...  These moving node methods are especially suited to problems which develop sharp moving fronts, especially problems where one needs to resolve the fine-scale structure of the fronts.  ...  We have an oriented piecewise linear GWMFE manifold u (not necessarily the graph of a function), and we wish to evaluate the surface integral (2.6) with K(u) = C(u).  ... 
doi:10.1137/s1064827594269561 fatcat:un62qlq665hubiy4m3jgdqflcu

A construction of rational manifold surfaces of arbitrary topology and smoothness from triangular meshes

Giovanni Della Vecchia, Bert Jüttler, Myung-Soo Kim
2008 Computer Aided Geometric Design  
The surface is obtained by a special manifold surface construction, which proceeds by blending together geometry functions for each vertex.  ...  Given a closed triangular mesh, we construct a smooth free-form surface which is described as a collection of rational tensor-product and triangular surface patches.  ...  First, we plan to address boundary conditions and sharp features (edges) that may be present in a given object.  ... 
doi:10.1016/j.cagd.2008.08.003 fatcat:5k6xszpzxvgrnc27hek5ck2g3a

Biorthogonal wavelets for subdivision volumes

Martin Bertram
2002 Proceedings of the seventh ACM symposium on Solid modeling and applications - SMA '02  
Sharp features and boundaries, defined by specific polygons, edges, and vertices of a lattice are explicitly represented using modified subdivision rules.  ...  Our wavelet construction based on subdivision volumes extends these concepts to trivariate geometries, such as time-varying surfaces, free-form deformations, and solid models with non-uniform material  ...  Multiple surface features can share a sharp curve inside the lattice, thus defining a non-manifold feature. Vertices can be part of a surface feature, a crease, or a dart (a fixed vertex).  ... 
doi:10.1145/566282.566296 dblp:conf/sma/Bertram02 fatcat:wojmcktwlrhzlibgrux52ajffm

Biorthogonal wavelets for subdivision volumes

Martin Bertram
2002 Proceedings of the seventh ACM symposium on Solid modeling and applications - SMA '02  
Sharp features and boundaries, defined by specific polygons, edges, and vertices of a lattice are explicitly represented using modified subdivision rules.  ...  Our wavelet construction based on subdivision volumes extends these concepts to trivariate geometries, such as time-varying surfaces, free-form deformations, and solid models with non-uniform material  ...  Multiple surface features can share a sharp curve inside the lattice, thus defining a non-manifold feature. Vertices can be part of a surface feature, a crease, or a dart (a fixed vertex).  ... 
doi:10.1145/566294.566296 fatcat:gjxa65fvr5hsdd2anuncf2ywgm

Polynomial surfaces interpolating arbitrary triangulations

S. Hahmann, G.-P. Bonneau
2003 IEEE Transactions on Visualization and Computer Graphics  
Note that this undulation problem is not particular to parametric interpolation, but also occurs with interpolatory subdivision surfaces.  ...  The previously introduced 4-split method interpolates the vertices of a 2-manifold triangle mesh by a set of tangent plane continuous triangular Bé zier patches of degree five.  ...  This work was partially supported by the European Community 5-th framework program, with the Research Training Network MINGLE (Multiresolution IN Geometric modELing, HPRN-1999-00117).  ... 
doi:10.1109/tvcg.2003.1175100 fatcat:ae54yjxy6fgprhlc2xypt4cyne
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