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Developable Strip Approximation of Parametric Surfaces with Global Error Bounds

Yong-Jin Liu, Yu-Kun Lai, Shi-Min Hu
2007 15th Pacific Conference on Computer Graphics and Applications (PG'07)  
In this work we propose a simple and efficient solution to approximate a general parametric surface with a minimum set of C 0 -joint developable strips.  ...  The key contribution of the proposed algorithm is that, several global optimization problems are elegantly solved in a sequence that offers a controllable global error bound on the developable surface  ...  Solution to Min-# problem Min-# problem approximates a given parametric curve c by a polyline p, with the minimum number of segments, such that the approximation error E(c, p) does not exceed a given tolerance  ... 
doi:10.1109/pg.2007.13 dblp:conf/pg/LiuLH07 fatcat:gg35oeyupnetzc423w7lv7l2pq

Parametric-surface adaptive tessellation based on degree reduction

Seok-Hyung Bae, Hayong Shin, Won-Hyung Jung, Byoung K. Choi
2002 Computers & graphics  
This paper presents a new parametric-surface tessellation method based on degree reduction: (1) a given parametric surface (or NURBS surface) of degrees (p; q) is decomposed into a set of Bezier surfaces  ...  Parametric-surface tessellation is one of the most important algorithms for CAGD applications.  ...  Acknowledgements The Ministry of Science and Technology of Korean government has supported the research.  ... 
doi:10.1016/s0097-8493(02)00126-7 fatcat:aowhn5exgvhovblah5lgtqafmy


1996 International journal of shape modeling  
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.  ...  Since 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.  ...  Moreover, when a badly parametrized curve is used in the construction of surfaces (cross-sectional techniques) badly parametrized surfaces are obtained.  ... 
doi:10.1142/s0218654396000075 fatcat:gobceqiigneu7oualx6dgmac5i

Step length problem for trimming curve approximation in tessellating trimmed surfaces

Shi-Nine Yang, Yung-Jen Yang
2002 Journal of Computational and Applied Mathematics  
A trimmed parametric surface is mainly composed of a surface together with trimming curves lying in D, the parametric space of the surface.  ...  By investigating the interrelation between surface tessellation and trimming curve approximation, we point out some problems on trimming curve approximation in existing trimmed surface tessellation algorithms  ...  A trimmed surface consists of two major ingredients, namely, a tensor product parametric surface and a set of properly oriented trimming curves.  ... 
doi:10.1016/s0377-0427(01)00527-1 fatcat:i2rgprblazcmnlnykuev6m53qm

A tracing method for parametric Bezier triangular surface/plane intersection

R. Sharma, O.P. Sha
2007 International journal of computer applications in technology  
Surface/plane intersection problem is a special case of surface/surface intersection, and is an active area of research across many disciplines in computer-aided geometric design.  ...  C 0 , C 1 , and C 2 ), a surface/plane intersection algorithm for parametric Bézier triangular surface over triangular domain.  ...  Intersection curves of constant Y planes with surface for a nonflat rectangular plate with one corner raised, C 2 continuous.  ... 
doi:10.1504/ijcat.2007.014557 fatcat:3iy2om4gafff3n7jn2t53s565a

Surface intersection using parallelism

Long Chyr Chang, Wolfgang W. Bein, Edward Angel
1994 Computer Aided Geometric Design  
The support of Boolean set operations in free-form solid modeling systems requires the repeated intersection of parametric surfaces.  ...  In this paper, we investigate a parallel approach to the surface intersection problem that shows, both theoretically and empirically, that with parallelism we can achieve both speed and precision simultaneously  ...  Both N(d) and cy= 1 SDV( i) are exponential functions. However, N(d) grows faster than the sum in most situations when d becomes large.  ... 
doi:10.1016/0167-8396(94)90024-8 fatcat:vzkeebfsgjeffhul4tv447g6iq

Fat Arcs for Implicitly Defined Curves [chapter]

Szilvia Béla, Bert Jüttler
2010 Lecture Notes in Computer Science  
We demonstrate the performance of the algorithm (in particular the convergence rate) and we apply the results to the computation of intersection curves between implicitly defined algebraic surfaces and  ...  rational parametric surfaces.  ...  The region described by them corresponds to a certain subset (a strip) on the parametric surface patch.  ... 
doi:10.1007/978-3-642-11620-9_3 fatcat:emacwht6lbhwbjnjbs46jq3phm

Page 1035 of Mathematical Reviews Vol. , Issue 95b [page]

1995 Mathematical Reviews  
On rational parametric curve approximation. (English summary) Free-form curves and free-form surfaces (Oberwolfach, 1992). Comput. Aided Geom. Design 10 (1993), no. 3-4, 363-377.  ...  ; Fuzhou) A class of shape-controllable C2-continuous cubic parametric spline curves.  ... 

The validity of Z-map model for mold and die machining [chapter]

Jung W. Park, Byoung K. Choi
1997 Computer Applications in Production and Engineering  
Presented in this paper are the following: evaluation of the height value of a point which is not a pre-defined grid point, exact (within machining tolerance) Zmap representation of sculptured surfaces  ...  Z-map is a special form of discrete nonparametric representation in which the height values at grid points on the xy-plane are stored as a 2D array z [ij].  ...  In the case of a ball-end milling cutter, a point on the edge curve should be mapped into a curve (e.g., a circular arc for a ball-end milling cutter) rather than a point, and the edge curve into a surface  ... 
doi:10.1007/978-0-387-35291-6_15 fatcat:yad7swlbtvegdetaoophu3lrai

5-axis local corner rounding of linear tool path discontinuities

Xavier Beudaert, Sylvain Lavernhe, Christophe Tournier
2013 International journal of machine tools & manufacture  
To obtain a smooth connection of the orientation a parametrization spline is required to link the bottom and top B-Spline parameters.  ...  The proposed corner rounding model allows to control precisely the contour and orientation tolerances in the workpiece coordinate system for 3 and 5-axis tool path.  ...  Acknowledgments This work is supported by the French Ministry of Research and the Digiteo foundation (2010-47D).  ... 
doi:10.1016/j.ijmachtools.2013.05.008 fatcat:gdmwhdov7zgqte3vgfn7n25fmy

Dual Drive Curve Tool Path Planning Method for 5-axis NC Machining of Sculptured Surfaces

Xu Rufeng, Chen Zhitong, Chen Wuyi, Wu Xianzhen, Zhu Jianjun
2010 Chinese Journal of Aeronautics  
The problem of finished surface being not first-order continuous commonly exists in machining sculptured surfaces with a torus cutter and some other types of cutters.  ...  To solve this problem, a dual drive curve tool path planning method is proposed in this article.  ...  Acknowledgements The authors would like to thank Xiong Xiyao, Lin Dong, Xu Yiping, Jiang Like, Tao Jianfeng, et al. for their help, and Changhe Aircraft Industries Group for the use of equipment.  ... 
doi:10.1016/s1000-9361(09)60245-4 fatcat:obdumleqdbaozh5abmm73py63i

Stripification of Free-Form Surfaces With Global Error Bounds for Developable Approximation

Yong-Jin Liu, Yu-Kun Lai, Shimin Hu
2009 IEEE Transactions on Automation Science and Engineering  
In this work we propose a practical and efficient solution to approximate a rectangular parametric surface with a small set of C 0 -joint developable strips.  ...  The key contribution of the proposed algorithm is that, several optimization problems are elegantly solved in a sequence that offers a controllable global error bound on the developable surface approximation  ...  Solution to Min-# Problem To find the minimum number of samples on a parametric curve c such that the resulting polyline has error no larger than a prescribed tolerance ε, the solution is as follows.  ... 
doi:10.1109/tase.2008.2009926 fatcat:4ds3y2otyjf2npyiotq5gny7sa

Parameterization and reconstruction from 3D scattered points based on neural network and PDE techniques

J. Barhak, A. Fischer
2001 IEEE Transactions on Visualization and Computer Graphics  
Such problems are particularly common with concave shapes whose parametric grid is self-intersecting, resulting in a fitted surface that considerably twists and changes its original shape.  ...  PDE parameterization yields a parametric grid without self-intersections.  ...  Fig. 2 . 2 The iso-curves of a projected object: (a) iso-u parametric curves; (b) iso-v parametric curves.affect the parametric density of the grid and the smoothness and magnitude of surface oscillations  ... 
doi:10.1109/2945.910817 fatcat:4yhrvqf3wjajjkrujnifl5i57m

P3 Bézier CAD Surrogates for Anisotropic Mesh Adaptation

Adrien Loseille, Lucien Rochery
2022 Zenodo  
Mesh generation and adaptation rely heavily on BREPs created by proprietary CAD software, piecewise parametric descriptions of geometry from which numerous problems arise: model continuity is only enforced  ...  up to a tolerance often higher than required mesh sizes, projection is costly and prone to error, derivatives — thus normals and curvature metrics — may not be well defined, unintended small features  ...  Some of the more frequent operations on these objects include evaluating a point on the surface given its parametric coordinates, projection of 3D points onto CAD edges and faces and computing derivatives  ... 
doi:10.5281/zenodo.6562423 fatcat:i24c76cmcba6ddi6irlbnx55ay

Computational Methods for Geometric Processing. Applications to Industry [chapter]

A. Iglesias, A. Gálvez, J. Puig-Pey
2001 Lecture Notes in Computer Science  
This paper offers a unifying survey of some of the most relevant computational issues appearing in geometric processing (such as blending, trimming, intersection of curves and surfaces, offset curves and  ...  surfaces, NC milling machines and implicitization).  ...  They also thank the referees for their careful reading of the initial version of the manuscript and their helpful suggestions which allowed a substantial improvement of the paper.  ... 
doi:10.1007/3-540-45545-0_81 fatcat:23zlekercnenxf7yr77kolmzr4
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