Filters








1,804 Hits in 5.3 sec

A new implicit representation of a planar rational curve with high order singularity

Falai Chen, Tom Sederberg
2002 Computer Aided Geometric Design  
This paper presents a new representation for the implicit equation of a planar rational curve with high order singularity by using moving curves technique.  ...  The results show that the implicit representation developed in this paper is not only more compact but also much more efficient to compute the implicit equation of the rational curve than previous methods  ...  Acknowledgement The first author is supported by the National Natural Science Foundation of China (grants 69603009 and 19971087), NKBRSF on Mathematical Mechanics (grant G1998030600) and a grant for Distinguished  ... 
doi:10.1016/s0167-8396(01)00087-5 fatcat:znftstz3xvambf2mfbxxc7iqom

Page 2843 of Mathematical Reviews Vol. , Issue 2003d [page]

2003 Mathematical Reviews  
In this paper the authors present a new representation for the implicit equation of a planar rational curve with high order singu- larity by using a moving curves technique.  ...  In this work the authors address the problem of implicitizing a planar rational curve of degree 2m that has a high order singularity.  ... 

Approximate parameterization by planar rational curves

Bert J�ttler, Pavel Chalmoviansk�
2004 Proceedings of the 20th spring conference on Computer graphics - SCCG '04  
We describe a method for approximate parameterization of a planar algebraic curve by a rational Bézier (spline) curve.  ...  rational parametric representation) into account.  ...  Acknowledgements The research of the first author was partly supported by the Fifth Framework Programme of the EU via project GAIA II (IST 2001-35512) entitled "Intersection algorithms for geometry based  ... 
doi:10.1145/1037210.1037215 dblp:conf/sccg/JuttlerC04 fatcat:xg2t2kdo7ffcfe577nog5wgesy

Approximate algebraic methods for curves and surfaces and their applications

Bert Jüttler, Pavel Chalmovianský, Mohamed Shalaby, Elmar Wurm
2005 Proceedings of the 21st spring conference on Computer graphics - SCCG '05  
We report on approximate techniques for conversion between the implicit and the parametric representation of curves and surfaces, i.e., implicitization and parameterization.  ...  It is shown that these techniques are able to handle general free-form surfaces, and they can therefore be used to exploit the duality of implicit and parametric representations.  ...  Acknowledgments This research was supported by the Austrian Science Fund (FWF) through subproject 15 of the Special Research Area (SFB) F013 "Numerical and Symbolic Scientific Computing" at Linz, and by  ... 
doi:10.1145/1090122.1090124 dblp:conf/sccg/JuttlerCSW05 fatcat:fh5552ulavfzplhhym467a27fy

Envelope computation in the plane by approximate implicitization

Tino Schulz, Bert Jüttler
2011 Applicable Algebra in Engineering, Communication and Computing  
Given a rational family of planar rational curves in a certain region of interest, we are interested in computing an implicit representation of the envelope.  ...  This connection enables us to use approximate implicitization for computing the (exact or approximate) implicit representation of the envelope.  ...  This research has been supported by the Austrian Science Fund (FWF) in the frame of the FSP S092 "Industrial Geometry", subproject 2.  ... 
doi:10.1007/s00200-011-0149-1 fatcat:owm256xwdjbbvkzqk6ttfuqpzu

Singularity Computation for Rational Parametric Surfaces Using Moving Planes

Xiaohong Jia, Falai Chen, Shanshan Yao
2022 ACM Transactions on Graphics  
loci including self-intersection curves, cusp curves and isolated singular points of the rational surface, together with the order of each singular locus.  ...  Then by substituting the parametric equation of the rational surface into this representation matrix, one can extract the singularity information from the corresponding matrix and return all the singular  ...  Yifei Chen from Institute of Mathematics, Chinese Academy of Sciences for his kind help on providing the important note on isolated singularities in algebraic geometry. he authors are also grateful to  ... 
doi:10.1145/3551387 fatcat:hvljinispjbkjn3ffuicx24psu

Computing the topology of a planar or space hyperelliptic curve [article]

Juan Gerardo Alcázar and Jorge Caravantes and Gema M. Diaz-Toca and Elias Tsigaridas
2019 arXiv   pre-print
The algorithms are based on the fact that 2D and 3D hyperelliptic curves can be seen as the image of a planar curve (the Weierstrass form of the curve), whose topology is easy to compute, under a birational  ...  We present algorithms to compute the topology of 2D and 3D hyperelliptic curves.  ...  As a brief summary of [7] , non-rational offsets of rational planar curves and some bisector curves (line/rational curve, or circle/rational curve) are planar hyperelliptic curves.  ... 
arXiv:1812.11498v2 fatcat:rubeefufvfas5lljgbczp7bgyi

A NEW APPROACH FOR SURFACE INTERSECTION

DINESH MANOCHA, JOHN F. CANNY
1991 International journal of computational geometry and applications  
Evaluating the intersection of two rational parametric surfaces is a recurring operation in solid modeling.  ...  We use this representation for inversion operation, computing the intersection of curves and surfaces and tracing the intersection curve o f t w o surfaces in lower dimension.  ...  of a cubic B ezier curve with a bicubic patch, the order of C in 10 is 54.  ... 
doi:10.1142/s0218195991000311 fatcat:tyk6ttlf6bf6vohjcg3jpphua4

A new approach for surface intersection

Dinesh Manocha, John Canny
1991 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications - SMA '91  
Evaluating the intersection of two rational parametric surfaces is a recurring operation in solid modeling.  ...  We use this representation for inversion operation, computing the intersection of curves and surfaces and tracing the intersection curve o f t w o surfaces in lower dimension.  ...  of a cubic B ezier curve with a bicubic patch, the order of C in 10 is 54.  ... 
doi:10.1145/112515.112544 dblp:conf/sma/ManochaC91 fatcat:6atp75uiyzdonnqcvyhil55rhy

Approximate Implicitization Using Monoid Curves and Surfaces

Thomas W. Sederberg, Jianmin Zheng, Kris Klimaszewski, Tor Dokken
1999 Graphical Models and Image Processing  
This paper presents an approach to nding an approximate implicit equation and an approximate inversion map of a planar rational parametric curve or a rational parametric surface.  ...  High accuracy of the approximation is achieved with a relatively small numberof low-degree curve segments or surface patches.  ...  The second author is also supported by Doctoral Science Foundation of China.  ... 
doi:10.1006/gmip.1999.0497 fatcat:zyrvkpv4ine4nfqbgkt53y3n7y

An application of fast factorization algorithms in Computer Aided Geometric Design

G. Casciola, F. Fabbri, L.B. Montefusco
2003 Linear Algebra and its Applications  
In this paper we consider a classical problem of Computer Aided Geometric Design, namely the computation of the intersection points of two planar rational parametric curves, given in Bernstein form.  ...  This also allows us to efficiently handle high degree curves. Numerical examples and comparisons with other standard intersection methods are given.  ...  precision, namely: From the implicitization of the first curve, we obtain a Bezout matrix with 8-degree polynomial entries whose coefficients are exactly representable with 20 bits.  ... 
doi:10.1016/s0024-3795(02)00469-x fatcat:z6j5cfk2pje3dablzpegi73u5a

Fast Approximate Implicitization of Envelope Curves Using Chebyshev Polynomials [chapter]

Oliver J. D. Barrowclough, Bert Jüttler, Tino Schulz
2012 Latest Advances in Robot Kinematics  
Consider a rational family of planar rational curves in a certain region of interest. We are interested in finding an approximation to the implicit representation of the envelope.  ...  Since exact implicitization methods tend to be very costly, we employ an adaptation of approximate implicitization to envelope computation.  ...  Conclusion We have presented a new implementation of approximate implicitization of envelope curves using Chebyshev polynomials.  ... 
doi:10.1007/978-94-007-4620-6_26 dblp:conf/ark/BarrowcloughJS12 fatcat:6xl36zbmkjc7rd6wmu46lrqq2i

Approximate Implicitization of Space Curves [chapter]

Martin Aigner, Bert Jüttler, Adrien Poteaux
2011 Texts & Monographs in Symbolic Computation  
The process of implicitization generates an implicit representation of a curve or surface from a given parametric one.  ...  This paper gives an brief survey of the existing techniques for approximate implicitization of hyper surfaces. In addition it describes a framework for the approximate implicitization of space curves.  ...  For instance, consider a cubic planar curve with a double point.  ... 
doi:10.1007/978-3-7091-0794-2_1 fatcat:tf25vcpwsrg5jf52ooh2lrvfde

Approximate Rational Parameterization of Implicitly Defined Surfaces [chapter]

Elmar Wurm, Bert Jüttler, Myung-Soo Kim
2005 Lecture Notes in Computer Science  
We present a method for approximate rational parameterization of algebraic surfaces of arbitrary degree and genus (or more general implicitly defined surfaces), based on numerical optimization techniques  ...  It can be used to generate local low degree approximations and rational approximations of non-parameterisable surfaces.  ...  This work was supported by the Austrian Science Fund (FWF) through subproject 15 of the Special Research Area SFB F013 "Numerical and Symbolic Scientific Computing" at Linz.  ... 
doi:10.1007/11537908_26 fatcat:okyypsyf25eghj4q72xxls3j2m

Identifying and approximating monotonous segments of algebraic curves using support function representation

Eva Blažková, Zbyněk Šír
2014 Computer Aided Geometric Design  
We use not only the primary algebraic equation of the planar curve but also (and more importantly) its implicit support function representation.  ...  We adopt a different approach, which is primarily based on the identification and approximation of smooth monotonous curve segments, which can in certain cases cross the singularities of the curve.  ...  Acknowledgement Eva Blažková was supported by the grants of Charles University Grant Agency GAUK 640212 and SVV-2013-267317.  ... 
doi:10.1016/j.cagd.2014.05.006 fatcat:mxg7xlx26faudayuok4v6qnmue
« Previous Showing results 1 — 15 out of 1,804 results