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Rational offset approximation of rational Bézier curves

2006
*
Journal of Zhejiang University: Science A
*

The problem of

doi:10.1631/jzus.2006.a1561
fatcat:ttcuyiqqd5cvbb63pabe3ydk3u
*parametric*speed*approximation*of a*rational**curve*is raised in this paper. Offset*curves*are widely used in various applications. ... Based*on*the Jacobi polynomial*approximation*theory with endpoints interpolation, an algebraic*rational**approximation*algorithm of offset*curve*, which preserves the direction of normal, is presented. ... Based*on*the Jacobi polynomials*approximation*theory,*approximation*to the*parametric*speed of*rational*Bézier*curve*is given in this paper. ...##
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REPARAMETRIZATION OF NURBS CURVES

1996
*
International journal of shape modeling
*

Since

doi:10.1142/s0218654396000075
fatcat:gobceqiigneu7oualx6dgmac5i
*parametric**rational**curves*, except for straight lines, cannot be*parametrized*by arc length, we developed a numerical method of*approximating*the arc length*parametrization*function. ... In this way it was possible to obtain a good*parametrization*of a NURBS*curve*with respect to arc length. Numerical results show a good behaviour of the proposed method*on*several test*curves*. ... to obtain a NURBS*curve*, we are led to determine a (t)*approximation*by means of a*rational*function (t). ...##
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Rational Hausdorff divisors: A new approach to the approximate parametrization of curves

2014
*
Journal of Computational and Applied Mathematics
*

*Approximate*

*parametrization*problem for plane

*curves*: Given the implicit equation of a non-

*rational*real plane

*curve*C and a tolerance e > 0, decide whether there exists a

*rational*real plane

*curve*C at ...

*Approximate*

*parametrization*problem The

*approximate*

*parametrization*problem can be stated as follows (we state it for plane

*curves*, but it can be similarly stated for space

*curves*, see [25], and for surfaces ... ). • Application to the

*approximate*

*parametrization*problem: Hausdorff

*curves*Given a non-

*rational*irreducible

*curve*, the

*approximate*

*parametrization*problem consists in providing a

*rational*

*curve*being ...

##
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NURBS approximation of surface/surface intersection curves

1994
*
Advances in Computational Mathematics
*

The algebraic surfaces could be either in implicit or

doi:10.1007/bf02519033
fatcat:7a25bxucpvdtxe575tcyjvn3ie
*rational**parametric*form. ... We use iI. combination of both symbolic and numerical techniques to construct a degree bounded Ci:-continuous,*rational*B-spline f-*approximations*oheal algebraic surface-surface intersection*curves*. ...*Rational*B-spline*Approximation*of*Parametric*Space*Curves*2 The 2 Problem and the outline of the Algorithm The*Rational**Approximation*Problem Given a real intersection space*curve*se which is either ...##
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Page 4971 of Mathematical Reviews Vol. , Issue 96h
[page]

1996
*
Mathematical Reviews
*

Based

*on*the dual form, we develop geomet- ric algorithms for*approximating*a given*curve*with a G? piecewise*rational*PH*curve*. ... The spline*approximation*is both C' and G?, also optimal. The*approximation*method is very efficient as it is based*on*local Hermite interpolation and subdivision. ...##
###
Piecewise Rational Parametrizations of Canal Surfaces
[chapter]

2014
*
Lecture Notes in Computer Science
*

We also describe an algorithm for minimal bi-degree

doi:10.1007/978-3-642-54382-1_6
fatcat:oorxlgy3dzbh5ixhui3mu7l64m
*rational**parametrizations*of patches*on*canal surfaces, and show how this can be used to*parametrize*piecewise*rational*corner and edge blends. ... Canal surfaces, as envelopes of*one*-parameter families of spheres, correspond to*curves*in Minkowski space. ... There are non-*rational**curves*in R 3,1 whose canal surfaces can be*parametrized**rationally*. ...##
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Robust display of arbitrary rational parametric surfaces

1992
*
Curves and Surfaces in Computer Vision and Graphics III
*

A well-known strength of the

doi:10.1117/12.131734
fatcat:oj5wjzyk4ffxxdbb5njjgf3d5m
*parametric*representation of a*curve*or surface is the ease by which a piecewiselinear*approximation*is generated. ... Such surfaces have pole*curves*in their domain, where the denominators of the parameter functions vanish, domain base points that correspond to entire*curves**on*the surface, and other features that cause ...*approximation*of the*parametric*. ...##
###
Quadratic approximation to plane parametric curves and its application in approximate implicitization

2006
*
The Visual Computer
*

This paper applies

doi:10.1007/s00371-006-0075-6
fatcat:dk2zj6vogfggjljhbc4o64jtrq
*rational*quadratic B-spline*curves*to give a global C 1 continuous*approximation*to a large class of plane*parametric**curves*including*rational**parametric**curves*. ... Expressing complex*curves*with simple*parametric**curve*segments is widely used in computer graphics, CAD and so*on*. ... Sederberg et al. considered monoid*curves*and surfaces to find an approxi- mate implicit equation and an*approximate*inversion map of a plane*rational**parametric**curve*or a*rational**parametric*surface ...##
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C 1 Spline Implicitization of Planar Curves
[chapter]

2004
*
Lecture Notes in Computer Science
*

We present a new method for constructing a low degree C 1 implicit spline representation of a given

doi:10.1007/978-3-540-24616-9_10
fatcat:4u3yttuzczfllauw7panubicby
*parametric*planar*curve*. ... To ensure the low degree condition, quadratic B-splines are used to*approximate*the given*curve*via orthogonal projection in Sobolev spaces. ... equation and*approximate*inversion map of a planar*rational**parametric**curve*or a*rational**parametric*surface. ...##
###
An approximate algorithm to parametrize algebraic curves

2015
*
ACM Communications in Computer Algebra
*

We provide

doi:10.1145/2815111.2815130
fatcat:4nqvmi4runbith6vf3gqadsqfu
*approximate*algorithms to solve the*approximate**parametrization*problem for planar and spacial real algebraic*curves*. ... The solution we give to this problem is a global*one*, under the requirement that the Hausdorff distance between input and output*curves*is finite. ... In particular, we provide algorithms to solve the*approximate**parametrization*problem for*curves*: Given the implicit equation of a non-*rational*real*curve*C and a tolerance ϵ > 0, decide whether there ...##
###
Page 998 of Mathematical Reviews Vol. , Issue 93b
[page]

1993
*
Mathematical Reviews
*

We present a simple algorithm to compute the proper

*parametrization*of a polynomial*curve*and reduce the problem of detecting cusps in a*rational**curve*to that of a polynomial*curve*. ... Zuhe Shen (PRC-NAN) 93b:65024 65D15 41A20 41A50 Varga, Richard S. (1-KNTS-CM); Carpenter, Amos J. (1-BUTL-CS) Some numerical results*on*best uniform*rational**approximation*of x**on*[0, 1]. Numer. ...##
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Approximate Implicitization Using Monoid Curves and Surfaces

1999
*
Graphical Models and Image Processing
*

This paper presents an approach to nding an

doi:10.1006/gmip.1999.0497
fatcat:zyrvkpv4ine4nfqbgkt53y3n7y
*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. ... Furthermore, since Ps; t; u lies*on*the*curve*, it satis es the implicit a*rational**parametric**curve*of degree n. ...##
###
Page 4236 of Mathematical Reviews Vol. , Issue 95g
[page]

1995
*
Mathematical Reviews
*

(F-LILL-NA; Villeneuve d’Ascq) Characterizations of the set of

*rational**parametric**curves*with*rational*offsets. ... Summary: “The paper presents a very powerful construction for*rational**curves*and surfaces*on*quadrics. ...##
###
Page 2004 of Mathematical Reviews Vol. , Issue 99c
[page]

1991
*
Mathematical Reviews
*

*One*way to describe

*rational*

*curves*/surfaces with

*rational*off- sets is through Laguerre geometry. ... Among other results, they prove a theorem

*on*

*rational*

*parametrizations*for envelopes of natural quadrics which yields algorithms for evaluation of

*rational*

*parametrizations*of sur- faces such as canal ...

##
###
Page 6244 of Mathematical Reviews Vol. , Issue 2003h
[page]

2003
*
Mathematical Reviews
*

Summary: “Universal

*parametrizations*make it possible to find all*rational**parametrizations*and all*rational**curves**on*an implicit surface. ... The*rational**curves*and patches can be described with optimal degree as images under such a universal*parametrization*. Hence, the*rational**curves**on*the surface can be classified in a systematic way. ...
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