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Least Squares Fitting of Piecewise Algebraic Curves

Chun-Gang Zhu, Ren-Hong Wang
2007 Mathematical Problems in Engineering  
A piecewise algebraic curve is defined as the zero contour of a bivariate spline.  ...  In this paper, we present a new method for fittingC1piecewise algebraic curves of degree 2 over type-2 triangulation to the given scattered data.  ...  Acknowledgments The authors appreciate the comments and suggestions of the anonymous reviewers. The  ... 
doi:10.1155/2007/78702 fatcat:rxnnr2njhbeqzlcssv74fe3tn4

Accurate Subcritical Damping Solution of Flutter Equation Using Piecewise Aerodynamic Function

Charles Goodman
2001 Journal of Aircraft  
Nomenclature coefficients in the rational function approximation (RFA) piecewise quadratic generalized aerodynamic force interpolation function coefficients reference length added structural damping for  ...  Lag terms are added to enable the function to be used for the entire reduced fre- 0.5 quency range.  ... 
doi:10.2514/2.2828 fatcat:sexsmbelbfgfrhxq43bagiclu4

Automatic Bayesian curve fitting

D. G. T. Denison, B. K. Mallick, A. F. M. Smith
1998 Journal of The Royal Statistical Society Series B-statistical Methodology  
Acknowledgements We thank James Bennett and the referees for their helpful comments on earlier versions of the paper and Harvard Rue and Chris Holmes for their help in some of the programming.  ...  The first author was supported by an Engineering and Physical Sciences Research Council research studentship.  ...  We choose I, = 1 and I = 2, s o h , , is a continuous quadratic piecewise polynomial, and put a Poisson prior over k with X = 1, to reflect assumed knowledge that the curves are very smooth and hence that  ... 
doi:10.1111/1467-9868.00128 fatcat:vde4eod3sneipnlcp62cnxxmkm

Page 5647 of Mathematical Reviews Vol. , Issue 99h [page]

1999 Mathematical Reviews  
To accomplish this goal, in this article the author defines a blending surface as a flexible plate having minimal curva- ture.  ...  Blending 3D surfaces in engineering requires a resultant surface that is continuous and has continuous derivatives up to a cer- tain order.  ... 

Various Types of Aesthetic Curves [article]

R.U. Gobithaasan
2013 arXiv   pre-print
The research on developing planar curves to produce visually pleasing products (ranges from electric appliances to car body design) and indentifying/modifying planar curves for special purposes namely  ...  The pattern of research in this field of study has branched to five major groups namely curve synthesis, fairing process, improvement in control of natural spiral, construction of new type of planar curves  ...  The author acknowledges Dept of Mathematics, University Malaysia Terengganu for their financial support to present and publish this paper.  ... 
arXiv:1304.7881v1 fatcat:ui3h3dulvbe5fctseioipzbtca

Page 6781 of Mathematical Reviews Vol. , Issue 91M [page]

1991 Mathematical Reviews  
, and other added nodes converging to 1 at the same rate.  ...  Curves and surfaces in CAGD ’89 (Oberwolfach, 1989). Comput. Aided Geom. Design 7 (1990), no. 1-4, 1-13.  ... 

Piecewise Polynomial Reconstruction of Scalar Fields from Simplified Morse-Smale Complexes [chapter]

Léo Allemand-Giorgis, Georges-Pierre Bonneau, Stefanie Hahmann
2017 Mathematics and Visualization  
Based on techniques borrowed from shape preserving design in Computer Aided Geometric Design, our method constructs the surface cell by cell using piecewise polynomial curves and surfaces.  ...  The benefit and limitations of using polynomials for reconstruction surfaces from topological data are presented in this paper.  ...  Instead of using discrete laplacian smoothing on the original mesh, our approach is to use piecewise polynomial curves and surfaces.  ... 
doi:10.1007/978-3-319-44684-4_9 fatcat:3j4lsiq2mnca7bwrxye3axknka

Page 3512 of Mathematical Reviews Vol. , Issue 2002E [page]

2002 Mathematical Reviews  
Examples are given of solving this prob- lem with noise added to the data using a Newton iteration with and without enforcing a descent requirement on the step size.  ...  The authors study the Bézier representation of rational curves and surfaces in R?.  ... 

Page 5332 of Mathematical Reviews Vol. , Issue 94i [page]

1994 Mathematical Reviews  
flexibility to piecewise quadratic curves and surfaces.  ...  Locally quadratic Bézier curves which globally have geometric con- tinuity G' have been constructed from control polygons [see, e.g., Curves and surfaces for computer aided geometric design, Academic Press  ... 

Variational surface modeling

William Welch, Andrew Witkin
1992 Computer graphics  
The complexity of the surface's shape may be increased by adding more control points and curves, without apparent limit.  ...  The user is free to apply control points and curves which are then available as handles for direct manipulation.  ...  To this surface, the user may freely attach a variety of features, such as points and flexible curves, which then serve as handles for direct interactive manipulation of the surface.  ... 
doi:10.1145/142920.134033 fatcat:temomk4svjd7rdz5que3csm4xa

Variational surface modeling

William Welch, Andrew Witkin
1992 Proceedings of the 19th annual conference on Computer graphics and interactive techniques - SIGGRAPH '92  
The complexity of the surface's shape may be increased by adding more control points and curves, without apparent limit.  ...  The user is free to apply control points and curves which are then available as handles for direct manipulation.  ...  To this surface, the user may freely attach a variety of features, such as points and flexible curves, which then serve as handles for direct interactive manipulation of the surface.  ... 
doi:10.1145/133994.134033 dblp:conf/siggraph/WelchW92 fatcat:uhsnw7mrkzbz3da26at4hukgam

Dense Stereo-Based Robust Vertical Road Profile Estimation Using Hough Transform and Dynamic Programming

Jae Kyu Suhr, Ho Gi Jung
2015 IEEE transactions on intelligent transportation systems (Print)  
The vertical road profile is modeled by a cubic B-spline curve, which is known to be accurate and flexible but difficult to estimate under a large proportion of outliers.  ...  To robustly estimate a cubic B-spline curve, the proposed method utilizes a two-step strategy that initially estimates a piecewise linear function and then obtains a cubic B-spline curve based on the initial  ...  The vertical road profile is modeled by a cubic B-spline curve, which is known to be accurate and flexible but difficult to estimate under a large proportion of outliers.  ... 
doi:10.1109/tits.2014.2369002 fatcat:bdvtj7apsbechoxs6j2hgnyeqa

Positive Approximation and Interpolation Using Compactly Supported Radial Basis Functions

Jinming Wu, Xiaolei Zhang, Lihui Peng
2010 Mathematical Problems in Engineering  
Numerical experiments are provided to illustrate that the proposed method is flexible.  ...  The approaches are presented to compute positive approximation and interpolation by solving the two corresponding optimization problems.  ...  The authors are very grateful to the referees for their careful reading of the manuscript and many valuable comments and remarks, which greatly improved this paper.  ... 
doi:10.1155/2010/964528 fatcat:5cxxz6xiorb6dpkizr6tmurrqm

B-spline modeling of road surfaces for freespace estimation

Andreas Wedel, Uwe Franke, Hernan Badino, Daniel Cremers
2008 2008 IEEE Intelligent Vehicles Symposium  
It is based on representing the ground plane as a parametric B-Spline surface and on robust tracking of the surface parameters using stereo disparities and a Kalman filter.  ...  The results show that in situations where a planar road assumption yields wrong results due to undulating roads, our approach is able to distinguish between free space and obstacles.  ...  The authors thank Wolfgang Förstner, Richard Steffens, Thomas Brox, and Clemens Rabe for fruitful discussions.  ... 
doi:10.1109/ivs.2008.4621254 fatcat:5r6r6pke3jaerej3rauegj2tvi

Polynomial-based non-uniform interpolatory subdivision with features control

Carolina Beccari, Giulio Casciola, Lucia Romani
2011 Journal of Computational and Applied Mathematics  
Such a fully flexible curve scheme is a fundamental step towards the construction of high-quality interpolatory subdivision surfaces with features control.  ...  In fact it generates visually-pleasing limit curves where special features ranging from cusps and flat edges to point/edge tension effects may be included without creating undesired undulations.  ...  Acknowledgements This research was supported by the University of Bologna and the University of Milano-Bicocca, Italy. The authors thank the anonymous referees for their useful suggestions.  ... 
doi:10.1016/j.cam.2010.09.014 fatcat:6r4fit44y5by3dw7zxpvmmcche
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