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An algorithm to parametrize approximately space curves

Sonia L. Rueda, Juana Sendra, J. Rafael Sendra
2013 Journal of symbolic computation  
The 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).  ... 
doi:10.1016/j.jsc.2013.04.002 fatcat:5ahvnkfgdje5dhbhg3sfnj5zgi

Large mesh generation from boundary models with parametric face representation

Reinhard Klein, Wolfgang Straber
1995 Proceedings of the third ACM symposium on Solid modeling and applications - SMA '95  
We therefore turn our attention 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.  ... 
doi:10.1145/218013.218097 dblp:conf/sma/KleinS95 fatcat:5sbgllvptjcanhyguolztsegha

Certified Rational Parametric Approximation of Real Algebraic Space Curves with Local Generic Position Method [article]

Jin-San Cheng, Kai Jin, Xiao-Shan Gao, Daniel Lazard
2012 arXiv   pre-print
In this paper, 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.  ... 
arXiv:1204.0905v1 fatcat:xoutidjlurbt7juc2ylsxq5qpu

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]

Mohamed Shalaby, Bert Jüttler
2008 Geometric Modeling and Algebraic Geometry  
We present techniques for creating 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  ... 
doi:10.1007/978-3-540-72185-7_12 fatcat:dxx3crwxebh6zgrrfalgbfevyi

Resolution Improvement of the Common Method for Presentating Arbitrary Space Curves Voxel [article]

Anas M. Al-Oraiqat, E. A. Bashkov, S. A. Zori
2018 arXiv   pre-print
Furthermore, 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.  ... 
arXiv:1803.00073v1 fatcat:qprphbfntfbi3hdvra7jqkfn4i

Specifying useful error bounds for geometry tools: an intersector exemplar

C. Mow, Thomas J. Peters, Neil F. Stewart
2003 Computer Aided Geometric Design  
The Grandine-Klein intersector produces 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.  ... 
doi:10.1016/s0167-8396(03)00043-8 fatcat:rttwv4avmbfknbt5ekc4rohfwi

Certified Approximation of Parametric Space Curves with Cubic B-spline Curves [article]

Liyong Shen, Chunming Yuan, Xiao-Shan Gao
2012 arXiv   pre-print
This paper presents 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.  ... 
arXiv:1203.0478v1 fatcat:ym7cbdlngvbqtkmkqmq2waa6ai

Certified rational parametric approximation of real algebraic space curves with local generic position method

Jin-San Cheng, Kai Jin, Daniel Lazard
2013 Journal of symbolic computation  
In this paper, 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.  ... 
doi:10.1016/j.jsc.2013.06.004 fatcat:wyor4m7oczbt5jw5msw2wtk2w4

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]

Heidi E. I. Dahl
2014 Lecture Notes in Computer Science  
We also describe 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] .  ... 
doi:10.1007/978-3-642-54382-1_6 fatcat:oorxlgy3dzbh5ixhui3mu7l64m

Practical Sliced Configuration Spaces for Curved Planar Pairs

Elisha Sacks
1999 The international journal of robotics research  
The new 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.  ... 
doi:10.1177/027836499901800104 fatcat:nmnxx6kagnbpnkry4mctv4ydvq

Practical Sliced Configuration Spaces for Curved Planar Pairs

E. Sacks
1999 The international journal of robotics research  
The new 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.  ... 
doi:10.1177/02783649922066060 fatcat:ddbed2nrfngydckz5zh5ieefni

Curve-fitting with piecewise parametric cubics

Michael Plass, Maureen Stone
1983 Computer graphics  
Our 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.  ... 
doi:10.1145/964967.801153 fatcat:j4qhzf6kwfdrni3crrpajrc6ym

Curve-fitting with piecewise parametric cubics

Michael Plass, Maureen Stone
1983 Proceedings of the 10th annual conference on Computer graphics and interactive techniques - SIGGRAPH '83  
Our 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.  ... 
doi:10.1145/800059.801153 dblp:conf/siggraph/PlassS83 fatcat:fvue4fey45hpld5nrv76ij2gju
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