Implicitly Parametric Curve

Weihong Zhang,Zhouwang Yang,Jiangsong Deng (사)한국CDE학회 2010 한국CAD/CAM학회 국제학술발표 논문집 Vol.2010 No.8

This paper proposes a new representation method of plane curves and develops a novel model in parameterization. Implicitly parametric curve is defined on the implicit curve and has a parametric form, which combines the advantages of parametric form and implicit form. For a given curve, the conversion among the implicit representation, parametric representation and implicitly parametric representation are provided. As the application of implicitly parametric curve, a parameterization method of closed implicit curves is addressed. We provide a model to construct an implicitly parametric curve for implicit curve, which is a smooth mapping from the standard shape to the implicit curve without overlap and satisfies some constraints. The implicitly parametric curve is obtained by solving the constrained minimization problem. An approach is provided to get the parameterization based on the implicitly parametric curve. Several examples are given to illustrate the effectiveness of the parameterization method.

Utility of Parametric Curves in Image Processing Applications

Manish Dixit,Sanjay Silakari 보안공학연구지원센터 2015 International Journal of Signal Processing, Image Vol.8 No.7

Image Processing is dealing with images containing lots of points. By Interpolation of these points to form different curves are taken under consideration in this paper. The curve modification and fitting in image processing can use Bezier Curve applications in various ways and by modifying these curves better result are generated. Bezier curve and its applications have vast scope for research in image processing like curve fitting algorithm, pattern recognition and computer aided geometric design. Application of Bezier curve are widely implemented in face detection, smile detection, hand writing and digit recognition which give wide view of Bezier curves. In this paper we go through various concepts and its application which can be used in image processing for providing extra edge in this field.

Geometric Fitting of Parametric Curves and Surfaces

Ahn, Sung-Joon Korea Information Processing Society 2008 Journal of information processing systems Vol.4 No.4

This paper deals with the geometric fitting algorithms for parametric curves and surfaces in 2-D/3-D space, which estimate the curve/surface parameters by minimizing the square sum of the shortest distances between the curve/surface and the given points. We identify three algorithmic approaches for solving the nonlinear problem of geometric fitting. As their general implementation we describe a new algorithm for geometric fitting of parametric curves and surfaces. The curve/surface parameters are estimated in terms of form, position, and rotation parameters. We test and evaluate the performances of the algorithms with fitting examples.

Geometric Fitting of Parametric Curves and Surfaces

안성준 한국정보처리학회 2008 Journal of information processing systems Vol.4 No.4

This paper deals with the geometric fitting algorithms for parametric curves and surfaces in 2-D/3-D space, which estimate the curve/surface parameters by minimizing the square sum of the shortest distances between the curve/surface and the given points. We identify three algorithmic approaches for solving the nonlinear problem of geometric fitting. As their general implementation we describe a new algorithm for geometric fitting of parametric curves and surfaces. The curve/surface parameters are estimated in terms of form, position, and rotation parameters. We test and evaluate the performances of the algorithms with fitting examples.

하우스도르프 거리를 이용한 B-spline곡선의 낫 제거

오종석,윤승현 (사)한국컴퓨터그래픽스학회 2011 컴퓨터그래픽스학회논문지 Vol.17 No.3

We present a new technique for removing interior knots of parametric B-spline curves. An initial curve is constructed by continuous L∞ approximation proposed by Eck and Hadenfeld.We employ Hausdorff distance to measure the shape difference between the original curve and the initial one. The final curve is obtained by minimizing their Hausdorff distance. We demonstrate the effectiveness of our technique with experimental results on various types of planar and spatial curves. 본 논문에서는 B-spline 곡선의 낫 제거 (knot removal)를 위한 새로운 기법을 제안한다. 제안된 기법은 낫 제거 전후, 두곡선의 형상의 차이를 측정하기 위해하우스도르프 거리 (Hausdorff distance)를 이용한다. 먼저 Eck와 Hadenfeld의 연속L∞ 근사법 [1]을 이용하여 낫이 제거된 곡선을 생성한다. 수치적 최적화 (numerical optimization) 기법을 통해 생성된곡선의 제어점 위치를 조정하여, 낫 제거 전 곡선과의 하우스도르프 거리가 최소화 되도록한다. 본 논문에서는다양한형태와 차수의 곡선들 (space curves)에 대한 낫 제거 실험을 통해 제안된 기법의 효율성과 우수성을입증한다.

Real-Time Contour-Error Estimation Methods for Three-Dimensional Free-Form Parametric Curves in Contour-Following Tasks

Zhen-yuan Jia,De-Ning Song,Jian-Wei Ma,Xiao-Xuan Zhao,Ning Zhang 한국정밀공학회 2018 International Journal of Precision Engineering and Vol.19 No.2

It is crucial to control the contour error in curved contour-following tasks caused by reasons such as servo delay and external disturbance. Contour-error estimation plays as a precondition for its further control. Existing methods can hardly keep well estimation accuracy for high-speed following of free-form curves with sharp corners, especially for three-dimensional curves. Consequently, this paper presents three high-precision real-time contour-error estimation methods for spatial free-form parametric curved contour following. By generating and updating the backstepping point according to the tangential tracking error, a multiple tangential approximation method is presented first. Then, a spatial circular approximation method is given by means of approximating the actual-position nearby region of the desired contour with a spatial circle. Finally, via modification of the Newton method so as to improve its stability without sacrificing of its fast convergence property, an initial value regeneration-based Newton algorithm is proposed for contour-error estimation. All of the presented methods take both estimation precision and calculation burden into consideration, and possess their own advantages. Using these algorithms, the contour error can be rapidly estimated in vector form with a high accuracy. Simulation and experimental results demonstrate the feasibility and the superiority of the presented algorithms.

다중 파라메트릭 변환곡선 기반 선수 선형 변환기법 연구

박성우(Sung-Woo Park),김승현(Seung-Hyeon Kim),이인원(Inwon Lee) 대한조선학회 2022 大韓造船學會 論文集 Vol.59 No.1

In this paper, we propose a systematic hull form variation technique which automatically satisfies the displacement constraint and guarantees a high level of fairness. This method is possible through multiple parameter correction curves. The present method is to improve the hull form variation method based on parametric modification function and consists of two sub-categories: SAC variation and section lines modification. For SAC variation, the utilization of two B-Spline curves satisfying GC¹ condition led to the satisfaction of displacement constraint and high level of fairness at the same time. Section lines modification methods involves in using two fuctions: the first is the waterplane modification function combining two cubic splines. the other function is the sectional area modification function consisting of 2nd order polynomial over the DLWL(Design Load Waterline) and 3rd order polynomial below the DLWL, This function enables not only the fundamental U-V section shape variation but also systematically modified section lines. The present method is expected to be more useful in the hull form optimization process using CFD compared to the existing method.

다중 파라메트릭 변환곡선 기반 선수 선형 변환기법 연구

박성우,김승현,이인원 대한조선학회 2022 大韓造船學會 論文集 Vol.59 No.2

In this paper, we propose a systematic hull form variation technique which automatically satisfies the displacement constraint and guarantees a high level of fairness. This method is possible through multiple parameter correction curves. The present method is to improve the hull form variation method based on parametric modification function and consists of two sub-categories: SAC variation and section lines modification. For SAC variation, the utilization of two B-Spline curves satisfying GC1 condition led to the satisfaction of displacement constraint and high level of fairness at the same time. Section lines modification methods involves in using two fuctions: the first is the waterplane modification function combining two cubic splines. the other function is the sectional area modification function consisting of 2nd order polynomial over the DLWL(Design Load Waterline) and 3rd order polynomial below the DLWL, This function enables not only the fundamental U-V section shape variation but also systematically modified section lines. The present method is expected to be more useful in the hull form optimization process using CFD compared to the existing method.

공학적 수단에 의한 구조용 강재 보부재의 화재 시 거동평가 연구

권인규 한국방재학회 2019 한국방재학회논문집 Vol.19 No.5

A fire in a compartment results in weakness in the structural stability of elements, such as columns and beams, in a steel-framed building. In this study, to support the design of structural fire engineering in steel-framed structures, design fires, such as standard and parametric fire curves, were applied as fire sources to analytically evaluate the structural stability of a structural beam made of SS 275. The results showed that the structural stability evaluation performed by the parametric fire curve was more rational than that by the standard fire curve. 강구조 건축물에서의 화재는 구조부재의 온도를 상승시켜 내력감소를 유발시킴으로써 구조물의 안전성 확보에 치명적인 약점으로 작용할 수 있다. 따라서 본 연구에서는 향후 건축물의 공학적 내화설계의 기초 자료 확보를 목적으로 강구조 건축물에 사용되는 일반 구조용 강재인 SS 275을 적용한 보부재를 대상으로 표준화재곡선과 일정 화재구획내의 변수화재곡선에 의한 단순보와 고정보의 최대내력과 처짐을 해석적으로 도출하였으며, 그 결과 변수화재곡선에 의한 내력평가가 표준화재곡선보다 합리적임을 알 수 있었다.

Development of frequency weighting function for Asian (Korean) people in vertical whole-body vibration; in comparison with ISO 2631-1

Kun-Woo Kim,김민석,유완석 대한기계학회 2009 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.23 No.10

In the field of ‘human vibration’, until now most frequency weighting functions have been derived from particular experiments whose subjects were only Western people. However, because of inherent differences (e.g., characteristic and shape of body parts, muscular and cellular tissue) between Western people and Asian people, frequency weighting function based on Asian people is required. An experiment was carried out to develop a frequency weighting function for the Korean people in vertical whole-body vibration, and to verify whether this weighting is acceptable in practical applications in comparison with ISO 2631-1. Ten male subjects of mean weight and height were tested for a posture similar to sitting in a passenger seat (footrest, upright and placement of the palms of hands on thighs, etc.) of a car. This experiment was performed using sinusoidal excitation in the range from 2 to 250 Hz, which was a combination of onehalf and one-third octave bands at eight determined amplitudes. To guarantee the reliability and accuracy of the test, non-parametric statistics was adopted to resolve the fact that there was not enough of the sample. Furthermore, two methods were considered to make the frequency weighting function and equal sensation curves. The first method changes the amplitude at every fixed frequency, and the other assigns weighting values. Korean people showed the most sensitivity to vertical whole-body vibration at 6.3 Hz excitation, so much higher weighting factors than weighting factors of other frequencies must be assigned near that frequency.