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Comonotone parametric C1 interpolation of nongridded data

P. Costantini, C. Manni
1996 Journal of Computational and Applied Mathematics  
We present a local scheme for constructing a C 1 interpolating function comonotone with a set of data having a tensor product topology.  ...  The constructed interpolant is a parametric surface with piecewise bicubic components which locally maintain the monotonicity of the data along curves "parallel" to the related coordinate lines.  ...  Ri,j and locally invertible. Hence ~,j is invertible since it is proper, locally invertible and invertible on the boundary (see, e.g., [1]). [] Remark 6.  ... 
doi:10.1016/s0377-0427(96)00084-2 fatcat:m5ul4pc4szb3jn35ylihr2rpk4

Surface modeling and parameterization with manifolds

Cindy Grimm, Denis Zorin
2005 ACM SIGGRAPH 2005 Courses on - SIGGRAPH '05  
There are many possible methods for mapping triangles to spheres [PH03] , we use the Gnomonic map which takes triangle edges to great circle arcs and is invertible.  ...  A third advantage is establishing correspondences between meshes of the same topology. In this case, we establish, for each mesh, a mapping from the mesh to the correct topology.  ...  We compute Euclidean barycentric coordinates for the transformed point and triangle, then map back.  ... 
doi:10.1145/1198555.1198688 dblp:conf/siggraph/GrimmZ05 fatcat:2vmogiofc5dglkc36imeoprqzi

Surface modeling and parameterization with manifolds

Cindy Grimm, Denis Zorin
2006 ACM SIGGRAPH 2006 Courses on - SIGGRAPH '06  
There are many possible methods for mapping triangles to spheres [PH03] , we use the Gnomonic map which takes triangle edges to great circle arcs and is invertible.  ...  A third advantage is establishing correspondences between meshes of the same topology. In this case, we establish, for each mesh, a mapping from the mesh to the correct topology.  ...  We compute Euclidean barycentric coordinates for the transformed point and triangle, then map back.  ... 
doi:10.1145/1185657.1185728 dblp:conf/siggraph/GrimmZ06 fatcat:sgtq2jp33fdvzibhpnwmbayxmu

Adaptive smooth surface fitting with manifolds

Cindy Grimm, Tao Ju, Ly Phan, John Hughes
2009 The Visual Computer  
We present a smooth, everywhere C k , analytic surface representation for closed surfaces of arbitrary topology.  ...  Keywords Manifolds · Surface fitting · Analytic surface Motivation We present a smooth, everywhere C k , analytic surface representation for closed surfaces of arbitrary topology.  ...  This parameterization is a C ∞ , invertible map from part of the global domain to a disk in the plane.  ... 
doi:10.1007/s00371-009-0334-4 fatcat:da4enzx32vd3palbjbg3h6noc4

SCANimate: Weakly Supervised Learning of Skinned Clothed Avatar Networks [article]

Shunsuke Saito, Jinlong Yang, Qianli Ma, Michael J. Black
2021 arXiv   pre-print
We observe that fitting a parametric 3D body model, like SMPL, to a clothed human scan is tractable while surface registration of the body topology to the scan is often not, because clothing can deviate  ...  We also observe that articulated transformations are invertible, resulting in geometric cycle consistency in the posed and unposed shapes.  ...  Parametric body models [4, 26, 43, 53, 67] body shape variations and pose-dependent shape correctives that capture non-linear body deformation and compensate for linear blend skinning artifacts [3  ... 
arXiv:2104.03313v2 fatcat:bz76iumdbzd6fn7v74tzuatfiy

T-spline Parameterization of 2D Geometries Based on the Meccano Method with a New T-mesh Optimization Algorithm [chapter]

J. I. López, M. Brovka, José María Escobar, J. M. Cascón, Rafael Montenegro
2014 Proceedings of the 22nd International Meshing Roundtable  
First, we define a parametric mapping between the input boundary of the object and the boundary of the parametric domain.  ...  We present a new method, based on the idea of the meccano method and a novel T-mesh optimization procedure, to construct a T-spline parameterization of 2D geometries for the application of isogeometric  ...  As the parametric and real meshes are topologically identical, each triangle in the physical space has its counterpart in the parametric space.  ... 
doi:10.1007/978-3-319-02335-9_4 dblp:conf/imr/LopezBECM13 fatcat:7tkzqoijxvfqlkxr73rmobsq7m

Inversion-free geometric mapping construction: A survey

Xiao-Ming Fu, Jian-Ping Su, Zheng-Yu Zhao, Qing Fang, Chunyang Ye, Ligang Liu
2021 Computational Visual Media  
AbstractA geometric mapping establishes a correspondence between two domains. Since no real object has zero or negative volume, such a mapping is required to be inversion-free.  ...  Computing inversion-free mappings is a fundamental task in numerous computer graphics and geometric processing applications, such as deformation, texture mapping, mesh generation, and others.  ...  Acknowledgements We would like to thank the anonymous reviewers for their constructive suggestions and comments.  ... 
doi:10.1007/s41095-021-0233-9 fatcat:ortfgxu6g5fz5ezmo3utdoslsq

As-rigid-as-possible shape interpolation

Marc Alexa, Daniel Cohen-Or, David Levin
2000 Proceedings of the 27th annual conference on Computer graphics and interactive techniques - SIGGRAPH '00  
These local transformations are naturally interpolated over time and serve as the basis for composing a global coherent least-distorting transformation.  ...  We present an object-space morphing technique that blends the interiors of given two-or three-dimensional shapes rather than their boundaries.  ...  Thanks to Wolfgang Müller and Jose Encarnaçaõ for their support.  ... 
doi:10.1145/344779.344859 dblp:conf/siggraph/AlexaCL00 fatcat:gvja3f5d75bjngnwh32asapqfq

Topological framework for part families

Srinivas Raghothama, Vadim Shapiro
2002 Proceedings of the seventh ACM symposium on Solid modeling and applications - SMA '02  
Every parametric family is defined by the representation-induced topological space of solids that are closed under the continuous maps in the assumed topology.  ...  We propose a formal framework for families based on the notion of topological categories.  ...  When a CSG-complex map g is also one-to-one and invertible, then g will be called CSG-complex homeomorphism.  ... 
doi:10.1145/566282.566287 dblp:conf/sma/RaghothamaS02 fatcat:iakszjipwffbnl7ibm45rgtlsq

Topological framework for part families

Srinivas Raghothama, Vadim Shapiro
2002 Proceedings of the seventh ACM symposium on Solid modeling and applications - SMA '02  
Every parametric family is defined by the representation-induced topological space of solids that are closed under the continuous maps in the assumed topology.  ...  We propose a formal framework for families based on the notion of topological categories.  ...  When a CSG-complex map g is also one-to-one and invertible, then g will be called CSG-complex homeomorphism.  ... 
doi:10.1145/566286.566287 fatcat:oqf5fejqmrhbdkv2trrmxkwuou

Geometric Texturing Using Level Sets

A. Brodersen, K. Museth, S. Porumbescu, B. Budge
2008 IEEE Transactions on Visualization and Computer Graphics  
Unlike previous approaches, we can produce topologically connected surfaces with smooth blending and low distortion.  ...  Abstract-We present techniques for warping and blending (or subtracting) geometric textures onto surfaces represented by high resolution level sets.  ...  This representation allows for robustness to topology changes during the mapping, flexibility when defining the blend of the base and texture geometry, and is amenable to high quality offset surface generation  ... 
doi:10.1109/tvcg.2007.70408 pmid:18192709 fatcat:on44ohxbtnbjldaeh7g7ke26yq

Manifold Learning for Object Tracking with Multiple Motion Dynamics [chapter]

Jacinto C. Nascimento, Jorge G. Silva
2010 Lecture Notes in Computer Science  
The inverse mappings h i = g −1 i are parameterizations of the manifold. m n Fig. 1. A manifold and its charts  ...  Instead, the algorithm can deal with arbitrary manifold topology by decomposing the manifold into multiple local models that are combined in a probabilistic fashion using Gaussian process regression.  ...  The tangent bundle T M can, if approximated by some finite set of n-dimensional tangent linear hyperplanes, form a convenient collection of local parametric domains upon which to map the manifold points  ... 
doi:10.1007/978-3-642-15558-1_13 fatcat:le2ivrnnerdonndqohwgwvhz7a

Neural Surface Reconstruction of Dynamic Scenes with Monocular RGB-D Camera [article]

Hongrui Cai, Wanquan Feng, Xuetao Feng, Yan Wang, Juyong Zhang
2022 arXiv   pre-print
Considering that the surface topology of dynamic scene might change over time, we employ a topology-aware strategy to construct the topology-variant correspondence for the fused frames.  ...  To represent and constrain the non-rigid deformations, we propose a novel neural invertible deforming network such that the cycle consistency between arbitrary two frames is automatically satisfied.  ...  Special thanks to Weiwei Xu for providing some help.  ... 
arXiv:2206.15258v1 fatcat:7vrri4jy7jdrxc5puyuklg3oee

Mesh Morphing [article]

Marc Alexa
2001 Eurographics State of the Art Reports  
Not surprisingly, morphing techniques for meshes have received a lot of interest lately. This state of the art report sums up recent developments in the area of mesh morphing.  ...  Defining such a mapping is not trivial for two main reasons. First, it requires a parametrization of the boundary representation, and second, the mapping might involve shapes with different topology.  ...  To achieve such an interior interpolation, they represent the interior of the 2D shapes by compatible skeletons and apply the blend to the parametric description of the skeletons.  ... 
doi:10.2312/egst.20011048 fatcat:zqff5om3ijecvo2l7nvo3lasae

A Meshless Method for Variational Nonrigid 2-D Shape Registration [article]

Wei Liu, Eraldo Ribeiro
2011 arXiv   pre-print
In addition, we model global shape deformation as an approximation blended from local deformation fields using partition-of-unity.  ...  The global deformation field is regularized by penalizing inconsistencies between local fields.  ...  Here, RBFs are used for blending local polynomial models instead of directly representing the shape deformation.  ... 
arXiv:1104.4168v1 fatcat:awh62ri7mffcbanwvyo35caypy
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