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Shape-preserving interpolation by splines using vector subdivision

T. N. T. Goodman, B. H. Ong
2005 Advances in Computational Mathematics  
We give a local convexity preserving interpolation scheme using parametric 2 C cubic splines with uniform knots produced by a vector subdivision scheme which simultaneously provides the function and its  ...  This is also adapted to give a scheme which is both local convexity and local monotonicity preserving when the data values are strictly increasing in the x direction.  ...  In this paper we consider shape-preserving interpolation by a planar curve which is produced by a subdivision scheme and is also defined explicitly as a parametric 2 C cubic spline with uniform knots  ... 
doi:10.1007/s10444-005-1174-z fatcat:v4ws2zpaobgnhopm7o2vpuxmzm

Skinning cubic Bézier splines and Catmull-Clark subdivision surfaces

Songrun Liu, Alec Jacobson, Yotam Gingold
2014 ACM Transactions on Graphics  
Unfortunately such approaches do not trivially extend to deforming vector graphics, such as the cubic Bézier splines prevalent in 2D or subdivision surfaces in 3D.  ...  Directly deforming all control points Directly deforming interpolated control points Our optimized approach Original Figure 1: Splines stay splines.  ...  Authors Liu and Gingold are supported in part by the NSF (IIS-1451198) and a Google research award.  ... 
doi:10.1145/2661229.2661270 fatcat:xalv7ywga5e2tjuexxk3hirzyu

Page 1035 of Mathematical Reviews Vol. , Issue 95b [page]

1995 Mathematical Reviews  
Furthermore, the conditions under which the interpolation curves are shape-preserving or convexity-preserving are also given.” 95b:65020 65D07 Pevnyi, A. B.  ...  The same basic approach can be used for approximating either scalar or vector- valued functions.  ... 

Multiresolution Analysis [chapter]

2010 Fundamentals of Wavelets  
Multiresolution analysis has received considerable attention in recent years by researchers in the fields of computer graphics, geometric modeling and visualization.  ...  This survey chapter attempts to provide an overview of the recent results on the topic of multiresolution, with special focus on the work of researchers who are participating in the AIM@SHAPE European  ...  The intermediate shapes should preserve the appearance and the properties of the input shapes.  ... 
doi:10.1002/9780470926994.ch5 fatcat:bbd2jxurcnbz5hurv4vudpkj2y

Page 4166 of Mathematical Reviews Vol. , Issue 99f [page]

1999 Mathematical Reviews  
C') shape- preserving interpolant.  ...  These results are reviewed and applications and examples are presented.” 99f:65033 65D17 Wang, Yan Chun (PRC-SEU; Nanjing) Shape-preserving surface interpolation by piecewise quadratic parametric polynomials  ... 

A three-dimensional finite element model of human atrial anatomy: New methods for cubic Hermite meshes with extraordinary vertices

Matthew J. Gonzales, Gregory Sturgeon, Adarsh Krishnamurthy, Johan Hake, René Jonas, Paul Stark, Wouter-Jan Rappel, Sanjiv M. Narayan, Yongjie Zhang, W. Paul Segars, Andrew D. McCulloch
2013 Medical Image Analysis  
Here, we utilized a subdivision surface scheme and derived a generalization of the "local-to-global" derivative mapping scheme of cubic Hermite finite elements to construct bicubic and tricubic Hermite  ...  High-order cubic Hermite finite elements have been valuable in modeling cardiac geometry, fiber orientations, biomechanics, and electrophysiology, but their use in solving three-dimensional problems has  ...  Acknowledgments We thank Chandrajit Bajaj and Joe Warren for providing advice about subdivision surfaces.  ... 
doi:10.1016/ pmid:23602918 pmcid:PMC3660421 fatcat:74elovvkbjhjnbyiecd5ig3dhe

Page 6329 of Mathematical Reviews Vol. , Issue 97J [page]

1997 Mathematical Reviews  
This paper describes an algorithm to generate recursive subdivision surfaces that interpolate B-spline curves.  ...  Subsequent subdivisions of the modified network generate sequences of polygons each of which converges to a curve interpolated by the limit surface.  ... 

Bezier Crust on Quad Subdivision Surface [article]

Jianzhong Wang, Fuhua Cheng
2013 Pacific Conference on Computer Graphics and Applications  
Subdivision surfaces have been widely used in computer graphics and can be classified into two categories, approximating and interpolatory.  ...  Although widely used, one issue remains with the approximating schemes, i.e., the process of interpolating a set of data points is a global process so it is difficult to interpolate large data sets.  ...  Acknowledgment This work is supported by National Science Foundation of China (61020106001, 61170324), National Science Council of ROC (NSC-100-2811-E-007-021), and a joint grant of National Tsinghua University  ... 
doi:10.2312/ dblp:conf/pg/WangC13 fatcat:vedc3gu7j5denpo4yuykcoptrm

Page 8718 of Mathematical Reviews Vol. , Issue 99m [page]

1999 Mathematical Reviews  
Chernecky (Odessa) 99m:65038 65D17 65Y25 Seymour, Chris; Unsworth, Keith Interactive shape preserving interpolation by curvature continuous rational cubic splines.  ...  Summary: “A scheme is described for interactively modifying the shape of convexity-preserving planar interpolating curves.  ... 

New Algorithm for Local Shape Preservation T-Spline Surface Skinning

Wei Wang, Qinhe Fan, Gang Zhao
2018 Journal of Computer and Communications  
This paper contributes in the combination of T-Spline technology and surface skinning modeling by introducing a new algorithm for local shape preservation T-Spline surface skinning.  ...  shapes and transform the 2D design intention into 3D space.  ...  Acknowledgements The authors would like to acknowledge the support by the Natural Science Conflicts of Interest The authors declare no conflicts of interest regarding the publication of this paper.  ... 
doi:10.4236/jcc.2018.612008 fatcat:xr5n3qmbrzczvanql3fvtc6bim

Interactive Multiresolution Editing of Arbitrary Meshes

Seungyong Lee
1999 Computer graphics forum (Print)  
The result of the interpolation is mapped back to the editing area and then used to update the mesh. We adopt harmonic maps for the embedding and multilevel B-splines for the interpolation.  ...  user intended by moving an editing primitive.  ...  Acknowledgments This work was supported in part by Ministry of Information and Communication under grant 2NI9890701.  ... 
doi:10.1111/1467-8659.00329 fatcat:rbexhw2sv5e6ric74xx4mfcl4m

A survey of subdivision-based tools for surface modeling [chapter]

Ioana Boier-Martin, Denis Zorin, Fausto Bernardini
2005 Geometric and Algorithmic Aspects of Computer-Aided Design and Manufacturing  
Subdivision surfaces have emerged as a powerful representation for surface modeling and design.  ...  They address important limitations of traditional spline-based methods, such as the ability to handle arbitrary topologies and to support multiscale editing operations.  ...  Multiresolution subdivision extends the concept of subdivision by allowing detail vectors to be introduced at each level.  ... 
doi:10.1090/dimacs/067/01 dblp:conf/dimacs/Boier-MartinZB03 fatcat:5pqdfabmvzbj5aktapk2enku2u

Page 2289 of Mathematical Reviews Vol. , Issue 98D [page]

1998 Mathematical Reviews  
by means of wavelet analysis (351-358); Ewald Quak and Norman Weyrich, Spline wavelet packets on an interval (359-366); Ulrich Reif, Some new results on subdivision algorithms for meshes of arbitrary  ...  Jean Savoie and Frangois Dubeau, On optimal error bounds for spline interpolation on a uniform partition (485-490); Robert Schaback, Multivariate interpolation and approximation by trans- lates of a basis  ... 

Interpolatory rank-1 vector subdivision schemes

Costanza Conti, Georg Zimmermann
2004 Computer Aided Geometric Design  
We introduce the concepts of interpolating and data preserving vector subdivision schemes and discuss how these concepts are related.  ...  The concept of stationary scalar subdivision being interpolatory does not always extend immediately to the vector valued case.  ...  In the limit, the subdivision scheme is interpolating using piecewise linear splines with this set as knots. 4.2. A bivariate example.  ... 
doi:10.1016/j.cagd.2003.11.003 fatcat:77rrrqau5nebvb657piri5axq4


1996 International journal of shape modeling  
In this paper, we s u r v ey the diversity of shape representations ranging from the primitive polynomial to the sophisticated Non-Uniform Rational B-Spline (NURBS).  ...  By reviewing commonly used design paradigms such a s i n terpolation, approximation, interactive modi cation and variational optimization, we can also show that these conventional geometric design techniques  ...  The weighted Nu-spline obtained from (15) can be used as a shape-preserving interpolant. Derivative constraints enforce the piecewise cubic interpolant to preserve local monotonicity.  ... 
doi:10.1142/s0218654396000099 fatcat:ctnoubb7vvaubpbxuiev5dpmpe
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