A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2004; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

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

2002
*
Computer Aided Geometric Design
*

This paper presents

doi:10.1016/s0167-8396(01)00087-5
fatcat:znftstz3xvambf2mfbxxc7iqom
*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 ...##
###
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

2004
*
Proceedings of the 20th spring conference on Computer graphics - SCCG '04
*

We describe

doi:10.1145/1037210.1037215
dblp:conf/sccg/JuttlerC04
fatcat:xg2t2kdo7ffcfe577nog5wgesy
*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 ...##
###
Approximate algebraic methods for curves and surfaces and their applications

2005
*
Proceedings of the 21st spring conference on Computer graphics - SCCG '05
*

We report on approximate techniques for conversion between the

doi:10.1145/1090122.1090124
dblp:conf/sccg/JuttlerCSW05
fatcat:fh5552ulavfzplhhym467a27fy
*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 ...##
###
Envelope computation in the plane by approximate implicitization

2011
*
Applicable Algebra in Engineering, Communication and Computing
*

Given

doi:10.1007/s00200-011-0149-1
fatcat:owm256xwdjbbvkzqk6ttfuqpzu
*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. ...##
###
Singularity Computation for Rational Parametric Surfaces Using Moving Planes

2022
*
ACM Transactions on Graphics
*

loci including self-intersection

doi:10.1145/3551387
fatcat:hvljinispjbkjn3ffuicx24psu
*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 ...##
###
Computing the topology of a planar or space hyperelliptic curve
[article]

2019
*
arXiv
*
pre-print

The algorithms are based on the fact that 2D and 3D hyperelliptic

arXiv:1812.11498v2
fatcat:rubeefufvfas5lljgbczp7bgyi
*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*. ...##
###
A NEW APPROACH FOR SURFACE INTERSECTION

1991
*
International journal of computational geometry and applications
*

Evaluating the intersection

doi:10.1142/s0218195991000311
fatcat:tyk6ttlf6bf6vohjcg3jpphua4
*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. ...##
###
A new approach for surface intersection

1991
*
Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications - SMA '91
*

Evaluating the intersection

doi:10.1145/112515.112544
dblp:conf/sma/ManochaC91
fatcat:6atp75uiyzdonnqcvyhil55rhy
*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. ...##
###
Approximate Implicitization Using Monoid Curves and Surfaces

1999
*
Graphical Models and Image Processing
*

This paper presents an approach to nding an approximate

doi:10.1006/gmip.1999.0497
fatcat:zyrvkpv4ine4nfqbgkt53y3n7y
*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. ...##
###
An application of fast factorization algorithms in Computer Aided Geometric Design

2003
*
Linear Algebra and its Applications
*

In this paper we consider

doi:10.1016/s0024-3795(02)00469-x
fatcat:z6j5cfk2pje3dablzpegi73u5a
*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. ...##
###
Fast Approximate Implicitization of Envelope Curves Using Chebyshev Polynomials
[chapter]

2012
*
Latest Advances in Robot Kinematics
*

Consider

doi:10.1007/978-94-007-4620-6_26
dblp:conf/ark/BarrowcloughJS12
fatcat:6xl36zbmkjc7rd6wmu46lrqq2i
*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. ...##
###
Approximate Implicitization of Space Curves
[chapter]

2011
*
Texts & Monographs in Symbolic Computation
*

The process

doi:10.1007/978-3-7091-0794-2_1
fatcat:tf25vcpwsrg5jf52ooh2lrvfde
*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. ...##
###
Approximate Rational Parameterization of Implicitly Defined Surfaces
[chapter]

2005
*
Lecture Notes in Computer Science
*

We present

doi:10.1007/11537908_26
fatcat:okyypsyf25eghj4q72xxls3j2m
*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. ...##
###
Identifying and approximating monotonous segments of algebraic curves using support function representation

2014
*
Computer Aided Geometric Design
*

We use not only the primary algebraic equation

doi:10.1016/j.cagd.2014.05.006
fatcat:mxg7xlx26faudayuok4v6qnmue
*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. ...
« Previous

*Showing results 1 — 15 out of 1,804 results*