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Curve Variations in Non-Stationary Three-Point Subdivision Schemes

Kashif Rehan, Waqas Ali Tanveer
2018 Research Journal of Applied Sciences Engineering and Technology  
The new binary non-stationary three-point approximating subdivision schemes have been proposed that generate wide variations of C 1 and C 2 continuous curves using shape control parameter 0 ξ .  ...  Curve variations using the shape control parameter 0 ξ have been demonstrated by the several examples.  ...  can generate only one limiting curve with a small magnitude and no one can see significant variations ( Fig. 1) .  ... 
doi:10.19026/rjaset.15.5860 fatcat:trpy5seg3vgwtbmssuwn7n3bp4

Nonlinear subdivision through nonlinear averaging

S. Schaefer, E. Vouga, R. Goldman
2008 Computer Aided Geometric Design  
The smoothness of our nonlinear subdivision schemes is inherited from the smoothness of the original linear subdivision schemes and the differentiability of the corresponding nonlinear averaging rules.  ...  While our results are quite general, our proofs are elementary, based mainly on the observation that generic nonlinear averaging rules on a pair of real or complex numbers can be constructed by conjugating  ...  Again these rules for choosing the appropriate masks depending on the data introduce nonlinearity into the four-point scheme.  ... 
doi:10.1016/j.cagd.2007.07.003 fatcat:kdtze4qrnvchpf7txw6pp7do2q

A C6 approximating subdivision scheme

Shahid S. Siddiqi, Nadeem Ahmad
2008 Applied Mathematics Letters  
The approximating subdivision scheme, recently developed by Shahid S.  ...  It is proved that the new scheme generates C 6 curves. Its limit function has a support on [−6, 5].  ...  [5] presented a four-point approximating subdivision scheme that generates C 2 curves and is close to the interpolatory case.  ... 
doi:10.1016/j.aml.2007.07.028 fatcat:jpzypupv2beyljwxugj77btlju

Subdivision Algorithms for Motion Design Based on Homologous Points [chapter]

M. Hofer, H. Pottmann, B. Ravani
2002 Advances in Robot Kinematics  
We outline algorithms which rely on known interpolatory variational subdivision for curves and on registration techniques from Computer Vision.  ...  We present two algorithms for the interpolation of given positions of a moving body by a smooth and fair motion, such that chosen feature points of the moving system run on smooth and fair paths.  ...  Acknowledgements This work has been carried out within the K plus Competence Center Advanced Computer Vision and was funded from the K plus program.  ... 
doi:10.1007/978-94-017-0657-5_25 fatcat:i6273jq5a5dffoac5v5w747q4e

Subdivision Surfaces for Scattered-data Approximation [chapter]

Martin Bertram, Hans Hagen
2001 Eurographics  
The novelty of our scheme is that it applies subdivision only to the ordinates of control points, whereas the triangulated mesh in the plane is fixed.  ...  We propose a modified Loop subdivision surface scheme for the approximation of scattered data in the plane.  ...  Starting with a triangulated control mesh, Loop's scheme splits every triangle into four by inserting a new vertex on every edge.  ... 
doi:10.1007/978-3-7091-6215-6_7 fatcat:b5rreyfhjfdjnizamchmtdum2e

Subdivision Surfaces for Scattered-data Approximation [article]

Martin Bertram, Hans Hagen
2001 EUROVIS 2005: Eurographics / IEEE VGTC Symposium on Visualization  
The novelty of our scheme is that it applies subdivision only to the ordinates of control points, whereas the triangulated mesh in the plane is fixed.  ...  We propose a modified Loop subdivision surface scheme for the approximation of scattered data in the plane.  ...  Starting with a triangulated control mesh, Loop's scheme splits every triangle into four by inserting a new vertex on every edge.  ... 
doi:10.2312/vissym/vissym01/055-064 fatcat:soq2wf2uobbrxixf4itvvg7wau

Subdivision Beyond Smoothness [article]

Michael Hansmeyer
2010 Computational Aesthetics in Graphics  
In a first step, this paper presents modifications to the established subdivision processes' weighting schemes.  ...  This paper examines the role that subdivision processes can have in the production of form. It explores how subdivision processes can generate complex geometries from very simple input meshes.  ...  Variation based on position in the mesh's environment 2. Variation based on the mesh's topology and motives 3.  ... 
doi:10.2312/compaesth/compaesth10/075-081 fatcat:4vlysnwq2zflxhlueqrnxe2uiy

Quantify the effects of watershed subdivision scale and spatial density of weather inputs on hydrological simulations in a Norwegian Arctic watershed

Minh Tuan Bui, Jinmei Lu, Linmei Nie
2021 Journal of Water and Climate Change  
Spatial variation of streamflow was well analyzed in the fine schemes with high density of stream networks, while the coarse schemes simplified this.  ...  The watershed was discretized according to four TDA scheme scales including 200, 2,000, 5,000, and 10,000 ha.  ...  ACKNOWLEDGEMENTS The authors acknowledge the Department of Technology and Safety, University of Tromsø -The Arctic University of Norway for their financial support in this study.  ... 
doi:10.2166/wcc.2021.173 fatcat:negq6nxs65ao5ne424dc4oazqa

Smooth Interpolation of Key Frames in a Riemannian Shell Space [article]

Pascal Huber, Ricardo Perl, Martin Rumpf
2017 arXiv   pre-print
In this paper we study generalizations of interpolating splines and subdivision schemes to the Riemannian manifold of shell surfaces in which the associated metric measures both bending and membrane distortion  ...  With these building blocks at hand discrete Riemannian cardinal splines and three different types of discrete, interpolatory subdivision schemes are defined.  ...  Acknowledgement We acknowledge support by the FWF in Austria under the grant S117 (NFN) and the DFG in Germany under the grant Ru 567/14-1.  ... 
arXiv:1702.06746v1 fatcat:jbnlxqvzrzamriml2ygaxxotem

Page 1757 of Mathematical Reviews Vol. , Issue 96c [page]

1996 Mathematical Reviews  
Summary: “A four-point interpolation subdivision scheme is a new interpolation method suggested in the mid-1980s.  ...  Summary: “This paper presents a subdivision scheme on triangles that we call variable subdivision scheme.  ... 

Tuning Subdivision by Minimising Gaussian Curvature Variation Near Extraordinary Vertices

U.H. Augsdörfer, N.A. Dodgson, M.A. Sabin
2006 Computer graphics forum (Print)  
We compare our results to previous work on the tuning of these schemes and show that the coefficients derived with this method give a significantly smaller curvature variation around extraordinary vertices  ...  In our tuning method we optimise within the space of subdivision schemes with bounded curvature to minimise this variation in curvature around the extraordinary vertex.  ...  The 4-3 scheme 4-3 subdivision is an alternative to Catmull-Clark subdivision on quadrilateral meshes.  ... 
doi:10.1111/j.1467-8659.2006.00945.x fatcat:bdmmc6rm4jcnddcvo5akqvgnve

A multiresolution framework for variational subdivision

Leif Kobbelt, Peter Schröder
1998 ACM Transactions on Graphics  
a subdivision scheme.  ...  In the context of subdivision, fairing leads to special schemes requiring the solution of a banded linear system at every subdivision step.  ...  Acknowledgments We are greatly indebted to Wim Sweldens for many discussions which helped refine the wiring diagram ideas and who also pointed out the connection to cyclic reduction.  ... 
doi:10.1145/293145.293146 fatcat:c5x4vcjevjcoriuxxe57u6iote

Variational reconstruction using subdivision surfaces with continuous sharpness control

Xiaoqun Wu, Jianmin Zheng, Yiyu Cai, Haisheng Li
2017 Computational Visual Media  
Based on the new subdivision rules, a variational model with L 1 norm is formulated to find the control mesh and the corresponding sharpness values of the subdivision surface that best fits the input mesh  ...  We present a variational method for subdivision surface reconstruction from a noisy dense mesh.  ...  Acknowledgements The main idea of this paper was presented in the Computational Visual Media Conference 2017. This research was partially supported by the National Natural Science Foundation of China  ... 
doi:10.1007/s41095-017-0088-2 fatcat:dcepnplelvaa7lbtllqhv3zkre

A Univariate Symmetric C5 Subdivision Schem

Shahid S. Siddiqi, Kashif Rehan
2014 Research Journal of Applied Sciences Engineering and Technology  
The behavior of the proposed subdivision scheme has been depicted through four examples.  ...  A new univariate symmetric ternary 6-point approximating subdivision scheme has been introduced that generates the limiting curve of C 5 continuity and its limit functions has a support on (-9, 8).  ...  Moreover, the proposed scheme observes the variation diminishing property.  ... 
doi:10.19026/rjaset.7.460 fatcat:kitcbhgeqbay5ocfibmpq6jcam

Quasi 4–8 subdivision

Luiz Velho
2001 Computer Aided Geometric Design  
This paper presents a new scheme for subdivision surfaces based on four-directional meshes. It combines geometry-sensitive refinement with convolution smoothing.  ...  The scheme has a simple, efficient implementation and generates smooth well-shaped meshes.  ...  Variational schemes on irregular meshes employ a smoothing energy functional which depends on the global neighborhood structure and its geometry.  ... 
doi:10.1016/s0167-8396(01)00035-8 fatcat:jc64krgylffezlrgjoioct763q
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