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Stationary binary subdivision schemes using radial basis function interpolation

Byung-Gook Lee, Yeon Ju Lee, Jungho Yoon
2006 Advances in Computational Mathematics  
A new family of interpolatory stationary subdivision schemes is introduced by using radial basis function interpolation.  ...  This work extends earlier studies on interpolatory stationary subdivision schemes in two aspects.  ...  Now, we present a stationary 2L-point interpolatory subdivision scheme using radial basis function interpolation.  ... 
doi:10.1007/s10444-004-7642-z fatcat:vhsyxd2jvvcxhd26lao7jiqtwa

Page 8452 of Mathematical Reviews Vol. , Issue 2002K [page]

2002 Mathematical Reviews  
An interpolating 4-point C? ternary stationary subdivision scheme. (English summary) Comput. Aided Geom. Design 19 (2002), no. 1, 1-18.  ...  Starting from an initial polygon, a ternary univariate stationary n-point subdivision scheme iteratively generates a sequence of refined polygons using three subdivision rules, each involving (at most)  ... 

Analysis of Univariate Nonstationary Subdivision Schemes with Application to Gaussian-Based Interpolatory Schemes

Nira Dyn, David Levin, Jungho Yoon
2007 SIAM Journal on Mathematical Analysis  
Next, a new class of interpolatory 2m-point non-stationary subdivision schemes based on Gaussian interpolation is presented.  ...  This paper is concerned with non-stationary subdivision schemes. First, we derive new sufficient conditions for C ν smoothness of such schemes.  ...  Second, in this paper, we study a new class of non-stationary interpolatory subdivision schemes, where the value at the inserted point is obtained by radial basis function (RBF) interpolation to data at  ... 
doi:10.1137/050638217 fatcat:bauycaswpzdkfm434ywlen2wge

Page 3699 of Mathematical Reviews Vol. , Issue 96f [page]

1996 Mathematical Reviews  
Sch- aback, Creating surfaces from scattered data using radial basis functions (477-496); Thomas W.  ...  Buh- mann, New developments in the theory of radial basis function interpolation (35-75); Charles K.  ... 

Nonlinear subdivision through nonlinear averaging

S. Schaefer, E. Vouga, R. Goldman
2008 Computer Aided Geometric Design  
Using our method, we can easily create stationary subdivision schemes for Gaussian functions, spiral curves, and circles with uniform parametrizations.  ...  More generally, we show that stationary subdivision schemes for e p(x) , cos(p(x)) and sin(p(x)) for any polynomial or piecewise polynomial p(x) can be generated using only addition, subtraction, multiplication  ...  Using our method, we will build simple stationary subdivision schemes for Gaussians, spirals, and circular arcs for which no known stationary linear subdivision schemes exist.  ... 
doi:10.1016/j.cagd.2007.07.003 fatcat:kdtze4qrnvchpf7txw6pp7do2q

Generalized stochastic subdivision

J. P. Lewis
1987 ACM Transactions on Graphics  
This paper describes the basis for techniques such as stochastic subdivision in the theory of random processes and estimation theory.  ...  The popular stochastic subdivision construction is then generalized to provide control of the autocorrelation and spectral properties of the synthesized random functions.  ...  One of the main computational advantages of the subdivision approach is that different resolutions (at binary orders Figure 3 : Planar quadrilateral subdivision mesh using a 4x4 neighborhood.  ... 
doi:10.1145/35068.35069 fatcat:rh3b4i7xjffediypmubnuvgqla

Introduction and Motivation [chapter]

2016 Ranking of Multivariate Populations  
This paper presents a new, volumetric subdivision scheme for interpolation of arbitrary hexahedral meshes.  ...  We address this lack of smooth, interpolatory subdivision algorithms by devising a new scheme founded upon the concept of tri-cubic Lagrange interpolating polynomials.  ...  Generally, any binary stationary subdivision scheme for solids can be written as P k+1 (z) = a(z)P k (z 2 ), z ∈ R 3 , (12) where P k (z) = µ∈Z 3 p k µ z µ is a formal generating function associated with  ... 
doi:10.1201/b19673-3 fatcat:w3h573opuzdbpnsr3c5qmjtmaa

Interpolatory, solid subdivision of unstructured hexahedral meshes

Kevin T. McDonnell, Yu-Sung Chang, Hong Qin
2004 The Visual Computer  
This paper presents a new, volumetric subdivision scheme for interpolation of arbitrary hexahedral meshes.  ...  We address this lack of smooth, interpolatory subdivision algorithms by devising a new scheme founded upon the concept of tri-cubic Lagrange interpolating polynomials.  ...  Generally, any binary stationary subdivision scheme for solids can be written as P k+1 (z) = a(z)P k (z 2 ), z ∈ R 3 , (12) where P k (z) = µ∈Z 3 p k µ z µ is a formal generating function associated with  ... 
doi:10.1007/s00371-004-0246-2 fatcat:ull3zpm5cbgbhlkluxzchd7w7m

Introduction and Motivation [chapter]

2000 Lecture Notes in Computer Science  
This paper presents a new, volumetric subdivision scheme for interpolation of arbitrary hexahedral meshes.  ...  We address this lack of smooth, interpolatory subdivision algorithms by devising a new scheme founded upon the concept of tri-cubic Lagrange interpolating polynomials.  ...  Generally, any binary stationary subdivision scheme for solids can be written as P k+1 (z) = a(z)P k (z 2 ), z ∈ R 3 , (12) where P k (z) = µ∈Z 3 p k µ z µ is a formal generating function associated with  ... 
doi:10.1007/bfb0101407 fatcat:z5lvdakwrrcjzggtbw2cq3omhi

Real-Time Collision Detection for Deformable Characters with Radial Fields

Sebastian John Friston, Anthony Steed
2018 IEEE Transactions on Visualization and Computer Graphics  
Radial fields are much more application-specific than traditional distance fields.  ...  We present radial fields: a variant of distance fields parameterised in cylindrical space, rather than Cartesian space.  ...  Space is divided using schemes such as Octree or Binary Space Partitioning trees, hashing, or simple grids. Again there is a trade-off, this time between traversal complexity, memory and cell size.  ... 
doi:10.1109/tvcg.2018.2859924 pmid:30047884 fatcat:2foj6prw25bmjma2fn7vd6c4ge

Optimising Spatial and Tonal Data for PDE-based Inpainting [article]

Laurent Hoeltgen and Markus Mainberger and Sebastian Hoffmann and Joachim Weickert and Ching Hoo Tang and Simon Setzer and Daniel Johannsen and Frank Neumann and Benjamin Doerr
2015 arXiv   pre-print
To optimise the spatial data, we use a probabilistic sparsification, followed by a nonlocal pixel exchange that avoids getting trapped in bad local optima.  ...  After this spatial optimisation we perform a tonal optimisation that modifies the function values in order to reduce the global reconstruction error.  ...  We also thank Pascal Gwosdek and Christian Schmaltz for providing the electrostatic halftoning images for us.  ... 
arXiv:1506.04566v1 fatcat:s3skqaugcjg7jplhtpu2z7p6ae

Kernel techniques: From machine learning to meshless methods

Robert Schaback, Holger Wendland
2006 Acta Numerica  
It addresses non-expert readers and focuses on practical guidelines for using kernels in applications.  ...  Kernels are valuable tools in various fields of Numerical Analysis, including approximation, interpolation, meshless methods for solving partial differential equations, neural networks, and Machine Learning  ...  Hence, such a situation is usually referred to as a stationary scheme. Thus, for a stationary setting, the basis function scales linearly with the grid width.  ... 
doi:10.1017/s0962492906270016 fatcat:hmwsgedodbfujlh6qusweugsyu

A Review of Geometric Transformations for Nonrigid Body Registration

M. Holden
2008 IEEE Transactions on Medical Imaging  
., linear elasticity and fluid flow) and basis function expansions derived from interpolation and approximation theory (e.g., radial basis functions, B-splines and wavelets).  ...  It explains the theoretical foundation of the models and classifies them according to this basis.  ...  Radial Basis Functions Radial basis functions [72] - [74] are functions of the distance between the interpolation point and basis function centre or landmark position .  ... 
doi:10.1109/tmi.2007.904691 pmid:18270067 fatcat:ij3xb2d4hfdfxa3dctj23mk4hm

DISCO: A 3D MOVING-MESH MAGNETOHYDRODYNAMICS CODE DESIGNED FOR THE STUDY OF ASTROPHYSICAL DISKS

Paul C. Duffell
2016 Astrophysical Journal Supplement Series  
Magnetohydrodynamics is implemented in DISCO using an HLLD Riemann solver and a novel constrained transport scheme which is compatible with the mesh motion.  ...  Figure 26 shows the field loop after a single orbit advected using N r =128 radial zones, using 12 different combinations of schemes (with different options for the Riemann solver, mesh motion, and  ...  The official version of DISCO therefore only performs parallel subdivision of the domain radially and vertically (in other words, = = f f f N N N G L ).  ... 
doi:10.3847/0067-0049/226/1/2 fatcat:f4nkzsldbze6dnwbys2fkklfru

IEEE Transactions on Medical Imaging

1983 IEEE Transactions on Medical Imaging  
from interpolation and approximation theory (e.g. radial basis functions, B-splines and wavelets).  ...  This results in two categories, physically based models described by partial differential equations of continuum mechanics (e.g. linear elasticity and fluid flow) and basis function expansions derived  ...  Radial basis functions Radial basis functions [72] , [73] , [74] are functions of the distance ||x − x i || between the interpolation point x and basis function centre or landmark position x i .  ... 
doi:10.1109/tmi.1983.4307623 fatcat:wtvshdv5rvg6xip6hafdfvpsaa
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