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An algorithm to parametrize approximately space curves

2013
*
Journal of symbolic computation
*

The

doi:10.1016/j.jsc.2013.04.002
fatcat:5ahvnkfgdje5dhbhg3sfnj5zgi
*algorithm*checks whether a planar projection of the given*space**curve*is ϵ-rational and, in the affirmative case, generates a planar*parametrization*that is lifted*to**an**space**parametrization*. ... We present*an**algorithm*such that, if a non-rational irreducible real*space**curve*is given, it computes a rational*parametrization*of*an**space**curve*that is near the input one. ... All authors belong*to*the Research Group ASYNACS (Ref. CCEE2011/R34). ...##
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Large mesh generation from boundary models with parametric face representation

1995
*
Proceedings of the third ACM symposium on Solid modeling and applications - SMA '95
*

We therefore turn our attention

doi:10.1145/218013.218097
dblp:conf/sma/KleinS95
fatcat:5sbgllvptjcanhyguolztsegha
*to*a new incremental*algorithm*for the accurate triangulation of meshes of trimmed*parametric*surfaces. ... The techniques we used*to*produce a robust implementation of this*algorithm*under finite precision arithmetic are reported. ... Acknowledgement We would like*to*thank T. Hüttner for his efforts on all the major implementation issues and the fruitful discussions that led*to*the realization of this*algorithm*. ...##
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Certified Rational Parametric Approximation of Real Algebraic Space Curves with Local Generic Position Method
[article]

2012
*
arXiv
*
pre-print

In this paper,

arXiv:1204.0905v1
fatcat:xoutidjlurbt7juc2ylsxq5qpu
*an**algorithm**to*compute a certified G^1 rational*parametric**approximation*for algebraic*space**curves*is given by extending the local generic position method for solving zero dimensional ... Thus, the method also gives a new*algorithm**to*compute the topology for*space*algebraic*curves*. ... It works well for low degree algebraic*space**curves*. In [23] , the authors present*an**algorithm**to**approximate**an*irreducible*space**curves*under a given precision. ...##
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Page 2004 of Mathematical Reviews Vol. , Issue 99c
[page]

1991
*
Mathematical Reviews
*

Summary: “

*An**algorithm*is proposed*to**approximate*planar alge- braic*curves*with G! piecewise cubic*parametric**curves*. Compared with the result of T. W. Sederberg, J. Zhao and A. K. ... Furthermore, we show how*to*compute*an**approximating*surface and put special emphasis on basic shapes used in computer-aided design. ...##
###
Approximate Implicitization of Space Curves and of Surfaces of Revolution
[chapter]

2008
*
Geometric Modeling and Algebraic Geometry
*

We present techniques for creating

doi:10.1007/978-3-540-72185-7_12
fatcat:dxx3crwxebh6zgrrfalgbfevyi
*an**approximate*implicit representation of*space**curves*and of surfaces of revolution. ... For*space**curves*, which are described as the intersection of two implicitly defined surfaces, we show how*to*generate*an**approximately*orthogonalized implicit representation. ... Acknowledgments This research has been supported by the European Commission through project IST-2001-35512 'Intersection*algorithms*for geometry based IT-applications using*approximate*algebraic methods ...##
###
Resolution Improvement of the Common Method for Presentating Arbitrary Space Curves Voxel
[article]

2018
*
arXiv
*
pre-print

Furthermore,

arXiv:1803.00073v1
fatcat:qprphbfntfbi3hdvra7jqkfn4i
*an*approach solution of voxel resolution of arbitrary*space**curve*, given in*parametric*form, is studied. ... The task of voxel resolution for a*space**curve*in video memory of 3D display is set. ... It is impossible*to*apply such*algorithms*for searching a tangent*to**an*arbitrary*space**curve*. ...##
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Specifying useful error bounds for geometry tools: an intersector exemplar

2003
*
Computer Aided Geometric Design
*

The Grandine-Klein intersector produces

doi:10.1016/s0167-8396(03)00043-8
fatcat:rttwv4avmbfknbt5ekc4rohfwi
*an**approximation*that is accurate*to*within a user-specified error bound, where that error bound is specified in parameter*space*. ... In particular, we consider the*approximation*of the intersection*curve*between two trimmed-surface patches. ... Grandine and Klein (1997) have published*an**algorithm*that computes the two*parametric*-domain representations of the intersection*curve*with a rigorously defined parameter-*space*error bound. ...##
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Certified Approximation of Parametric Space Curves with Cubic B-spline Curves
[article]

2012
*
arXiv
*
pre-print

This paper presents

arXiv:1203.0478v1
fatcat:ym7cbdlngvbqtkmkqmq2waa6ai
*an**algorithm**to*compute a certified*approximation**to*a given*parametric**space**curve*with cubic B-spline*curves*. ...*Approximating*complex*curves*with simple*parametric**curves*is widely used in CAGD, CG, and CNC. ... The authors also wish*to*thank the anonymous reviewers for their helpful comments and suggestions. ...##
###
Certified rational parametric approximation of real algebraic space curves with local generic position method

2013
*
Journal of symbolic computation
*

In this paper,

doi:10.1016/j.jsc.2013.06.004
fatcat:wyor4m7oczbt5jw5msw2wtk2w4
*an**algorithm**to*determine the topology of*an*algebraic*space**curve*and*to*compute a certified G 1 rational*parametric**approximation*of the algebraic*space**curve*is given by extending the ... The main advantage of the*algorithm*, inherited from the local generic method, is that the topology computation and*approximation*for a*space**curve*are directly reduced*to*the same tasks for two plane*curves*... All the authors would like*to*thank the anonymous referees, their suggestions improve the paper. ...##
###
Page 2843 of Mathematical Reviews Vol. , Issue 2003d
[page]

2003
*
Mathematical Reviews
*

As

*an**approximant*of /, a discrete smoothing spline belonging*to*a suitable piecewise polynomial*space*is proposed. ... Our characterization for the best geometric conic*approximation*can be applied*to*degree reduction, offset*curve**approximation*, or convolution*curve**approximation*, which are very frequently en- countered ...##
###
Piecewise Rational Parametrizations of Canal Surfaces
[chapter]

2014
*
Lecture Notes in Computer Science
*

We also describe

doi:10.1007/978-3-642-54382-1_6
fatcat:oorxlgy3dzbh5ixhui3mu7l64m
*an**algorithm*for minimal bi-degree 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*. ...*An**algorithm*for minimal bi-degree rational*parametrizations*of N (t, u) can be found in [3] . ...##
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Practical Sliced Configuration Spaces for Curved Planar Pairs

1999
*
The international journal of robotics research
*

The new

doi:10.1177/027836499901800104
fatcat:nmnxx6kagnbpnkry4mctv4ydvq
*algorithm*solves these problems by restricting the analysis*to*parts bounded by line segments and circular arcs, whereas the general*algorithm*handles rational*parametric**curves*. ... I present a practical configuration*space*computation*algorithm*for pairs of*curved*planar parts based on the general*algorithm*developed by Bajaj and me. ... The*algorithm*intersects two lines, a line and*an*arc, or two arcs*to*obtain the*parametric*boundary*curve*. ...##
###
Practical Sliced Configuration Spaces for Curved Planar Pairs

1999
*
The international journal of robotics research
*

The new

doi:10.1177/02783649922066060
fatcat:ddbed2nrfngydckz5zh5ieefni
*algorithm*solves these problems by restricting the analysis*to*parts bounded by line segments and circular arcs, whereas the general*algorithm*handles rational*parametric**curves*. ... I present a practical configuration*space*computation*algorithm*for pairs of*curved*planar parts based on the general*algorithm*developed by Bajaj and me. ... The*algorithm*intersects two lines, a line and*an*arc, or two arcs*to*obtain the*parametric*boundary*curve*. ...##
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Curve-fitting with piecewise parametric cubics

1983
*
Computer graphics
*

Our

doi:10.1145/964967.801153
fatcat:j4qhzf6kwfdrni3crrpajrc6ym
*algorithm*is*an*iterative technique that converges*to*this set of t values. Our*algorithm*is simple*to*state: Assign*an*initial*approximation**to*t for each data point. ... of closely-*spaced*points that*approximate*the desired*curve*. ...##
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Curve-fitting with piecewise parametric cubics

1983
*
Proceedings of the 10th annual conference on Computer graphics and interactive techniques - SIGGRAPH '83
*

Our

doi:10.1145/800059.801153
dblp:conf/siggraph/PlassS83
fatcat:fvue4fey45hpld5nrv76ij2gju
*algorithm*is*an*iterative technique that converges*to*this set of t values. Our*algorithm*is simple*to*state: Assign*an*initial*approximation**to*t for each data point. ... of closely-*spaced*points that*approximate*the desired*curve*. ...
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