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Smooth polynomial approximation of spiral arcs

R.J. Cripps, M.Z. Hussain, S. Zhu
2010 Journal of Computational and Applied Mathematics  
By defining an objective function based on the relative error between the curvature profiles of the GCS and its Bézier approximation, a curve segment is constructed that has a monotonic curvature profile  ...  A method of constructing an approximation to a generalised Cornu spiral (GCS) arc using non-rational quintic Bézier curves matching end points, end slopes and end curvatures is presented.  ...  out his part of this research at the University of Birmingham, UK as a Post-Doctoral Research Fellow.  ... 
doi:10.1016/j.cam.2009.10.008 fatcat:rojdeosfcjfgrgo3zwosyapdxa

An Approximation of Bézier Curves by a Sequence of Circular Arcs

Taweechai Nuntawisuttiwong, Natasha Dejdumrong
2021 Information Technology and Control  
Furthermore, the result of the circular arc representationis not exceeding a user-specified tolerance.  ...  The sequenceof circular arcs represents the shape of the given Bézier curve which cannot be expressed using any other algebraicapproximation schemes.  ...  Accordingly, Bézier curves can be approximated with in a user-specified tolerance band.  ... 
doi:10.5755/j01.itc.50.2.25178 fatcat:shfsa5ewk5dtrp223sls5isduq

A NURBS transition between a Bézier curve and its control polygon

Imre Juhász
2021 Journal of Computational and Applied Mathematics  
We present a method for generating a one-parameter family of curves that produce a smooth transition between a Bézier curve and its control polygon.  ...  These curves have rational Bézier spline and NURBS representations. The method is also furnished with local shape control features. The procedure can be extended to tensor product Bézier surfaces.  ...  Acknowledgement The author would like to thank Ágoston Róth for the discussions on the topic.  ... 
doi:10.1016/j.cam.2021.113626 fatcat:sljxflmfkvasrekqs65kqrcu2y

A Review on Approaches for Handling Bezier Curves in CAD for Manufacturing

Hetal N. Fitter, Akash B. Pandey, Divyang D. Patel, Jitendra M. Mistry
2014 Procedia Engineering  
Various techniques and methodologies like curve fitting, curve manipulation, blending and merging of curves have been proposed over the years for better handling and enhancing Bezier curve use with every  ...  A review is done on various approaches for handling Bezier curve in Computer Aided Design for the purpose of manufacturing for example tool path optimization, profile design, reverse engineering, etc.  ...  If L c denotes the chord-length and L p polygon-length then arc-length of the Bezier curve is in the interval [L c , L p ] but L Grevsen J.  ... 
doi:10.1016/j.proeng.2014.12.394 fatcat:dqa53x5ijnaq5nczua5vybi7su

Comparison of Parametrically Programmed Machining with CAM System Machining for C0 Continuity Bezier Curves Based on Various Parameters

Hetal N. Fitter, Akash B. Pandey, Jitendra M. Mistry, Divyang D. Patel
2014 Procedia Engineering  
Few Bezier curve profiles have been constructed, by joining of which gives tangent continuity throughout the curve for the purpose of machining and their CNC and Parametric programs have been discussed  ...  Machining using parametric programming is judged against the CAM system for program length, machining time and accuracy through Coordinate Measuring Machine results.  ...  A cubic Bezier representation of an arc can give a minimum of tangential continuity at any point on the curve.  ... 
doi:10.1016/j.proeng.2014.12.395 fatcat:jtp5i477l5hjvfitgbduo24pk4

Interactive aesthetic curve segments

Norimasa Yoshida, Takafumi Saito
2006 The Visual Computer  
We identify the overall shapes of aesthetic curves depending on the slope of LCH α, by imposing specific constraints to the general formula of aesthetic curves.  ...  We clarify several characteristics of aesthetic curve segments. Keywords an aesthetic curve segment · logarithmic curvature histogram · the radius of curvature  ...  Thus an aesthetic curve segment has similar controllability to a Bézier curve segment of degree 2. The radius of curvature of aesthetic curves versus the arc length varies monotonously and smoothly.  ... 
doi:10.1007/s00371-006-0076-5 fatcat:xrbrp2kmkbezrhfob56cihpowy

Approximating curve by a single segment of B-Spline or Bézier curve directly in CAD environment

Mariusz Sobolak, Piotr Połowniak, Adam Marciniec, Patrycja Ewa Jagiełowicz
2020 Advances in Manufacturing Science and Technology  
AbstractThe paper presents the method of approximating curves with a single segment of the B-Spline and Bézier curves.  ...  The results show that the approximation method with Bézier curve using control points as "free" points can be applied to obtain the best results of approximation.  ...  Figure 13 . 13 The Bézier curve creating; 1-approximated circular arc, 2-Bézier curve, and 3-Bézier polygon. Figure 14 . 14 Comparison of the circle arc with the approximating Bézier curve.  ... 
doi:10.2478/amst-2019-0016 fatcat:fq63dp6a3vbu5g7rbarjgxykdi

Modelling of joining route segments of different curvature

Władysław Koc, Katarzyna Palikowska
2016 Baltic Journal of Road and Bridge Engineering  
The analysis of dynamic properties has showed an advantage of the obtained transition curve of nonlinear curvature over Bezier curves.  ...  The obtained S-shaped curves have been compared to the cubic C-Bezier curves and to the Pythagorean hodograph quantic Bezier curve using the Lateral Change of Acceleration diagram and the dynamic model  ...  It is premised that the linear curvature change on the specified transition curve length l k is obtained as a result of the assumption of two elementary boundary conditions (in the generalized approach  ... 
doi:10.3846/bjrbe.2016.01 fatcat:ww4wcusjrra5nim5apiqwzindi

The approximation of generalized Log-aesthetic curves using Quintic Bezier curves

Diya' J Albayari, R U Gobithaasan, Kenjiro T. Miura
2017 Journal of Physics, Conference Series  
The problem of this approach is that it requires a formidable size of computations due to arc length reparametrization.  ...  A viable solution is to approximate GLACs using a quintic polynomial curve in the form of Bezier using curvature error measure.  ...  Acknowledgements The authors acknowledge Ministry of Higher Education Malaysia (FRGS: 59431) for providing facilities and financial aids to carry out this research.  ... 
doi:10.1088/1742-6596/890/1/012068 fatcat:ulvd5fkcxrfvja2l7guebddefm

Real-time CNC interpolators for Bézier conics

Rida T. Farouki, Carla Manni, Alessandra Sestini
2001 Computer Aided Geometric Design  
An expression for the cumulative arc length function s(ξ ), amenable to accurate and efficient evaluation, is required in formulating real-time CNC interpolators capable of achieving a desired (constant  ...  Arbitrary conic segments can be specified in the rational Bézier form, r(ξ ) for ξ ∈ [0, 1], by control points p 0 , p 1 , p 2 and a scalar weight w 1 .  ...  Acknowledgement This work was supported in part by the National Science Foundation under grants DMI-9908525 and CCR-9902669.  ... 
doi:10.1016/s0167-8396(01)00058-9 fatcat:icic3yafrrbkjes3naxk57qvwe

Topologically Safe Curved Schematisation

Arthur van Goethem, Wouter Meulemans, Andreas Reimer, Herman Haverkort, Bettina Speckmann
2013 The Cartographic Journal  
We illustrate our framework with Bézier curves and circular arcs.  ...  We present a generic framework for topology-preserving curved schematization that allows a choice of quality measures and curve types. The framework fits a curve to every part of the input.  ...  Cubic Bézier curves In this section we show how to use our framework with Bézier curves. We describe a method to fit a Bézier curve to a chain and specify a distance measure. Distance measure.  ... 
doi:10.1179/1743277413y.0000000066 fatcat:f27bkxi6yvcsfberwuoyoyzsny

Identification and "reverse engineering" of Pythagorean-hodograph curves

Rida T. Farouki, Carlotta Giannelli, Alessandra Sestini
2015 Computer Aided Geometric Design  
certain maximum degree generate arc length estimates for PH curves exhibiting a sharp saturation as the number of sample points is increased.  ...  Methods are developed to identify whether or not a given polynomial curve, specified by Bézier control points, is a Pythagorean-hodograph (PH) curve -and, if so, to reconstruct the internal algebraic structure  ...  Acknowledgements This work was supported by the Gruppo Nazionale per il Calcolo Scientifico (GNCS) of the Istituto Nazionale di Alta Matematica Francesco Severi (IN-dAM) and by the project DREAMS (MIUR  ... 
doi:10.1016/j.cagd.2015.04.001 fatcat:ypnseflxxbbtplgvcvnot6usa4

Quasi-Aesthetic Curves in Rational Cubic Bézier Forms

Norimasa Yoshida, Takafumi Saito
2007 Computer-Aided Design and Applications  
The monotonicity of curvature of quasi-Aesthetic Curves is checked by the proposed method.  ...  We show that one Aesthetic Curve segment whose change of tangential angle is less than 90 deg. can be replaced by one quasi-Aesthetic Curve segment guaranteeing the monotonicity of the curvature in most  ...  Logarithmic Curvature Histograms A curve and its logarithmic curvature histogram are shown in Fig. 1 . Let ρ and s be the radius of curvature and the arc length, respectively.  ... 
doi:10.1080/16864360.2007.10738567 fatcat:ivxmxomfynfwrmd53hsualy7im

Optimal Sampling of Parametric Surfaces

Yufei Li, Wenping Wang, Changhe Tu
2012 Computer-Aided Design and Applications  
Then the optimal sampling of the surface is obtained by uniformly sampling the parameter domain of the optimal parameterization.  ...  We study the problem of optimally sampling parametric surfaces by means of reparameterization. A criterion is first formulated for measuring the parameterization quality of a given surface.  ...  For a parametric curve of unit arc length and over the interval 0,1 , clearly, ‖ ‖ describes the parametric speed of the curve, i.e., the change rate of its arc length with respect to the parameter .  ... 
doi:10.3722/cadaps.2012.55-60 fatcat:2rcpswrdabanpmoxqvd6wo4tta

Typeface styling with ramp responses

Jörn Loviscach
2012 ACM SIGGRAPH 2012 Posters on - SIGGRAPH '12  
Here, s total stands for the complete arc length of the curve.  ...  (As opposed to the original curve, these target curves do not need to be parameterized by arc length.)  ... 
doi:10.1145/2342896.2342933 dblp:conf/siggraph/Loviscach12 fatcat:ifnxm27zdbadlad3uaow4voax4
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