• Korean Journal of Computational Design and Engineering
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• v.4 no.2
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• pp.127-138
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• 1999

For reverse engineering, curves and surfaces are modeled for new products by interpolating the digitized data points. But there are many measuring or deviation errors. Therefore, it is important to handle errors during the curve or surface modeling. If the errors are ignored, designer could get undesirable results. For this reason, fairing procedure with the aesthetics criteria is necessary in computer modeling. This paper presents methods of 3D NURBS curve fairing. The techniques are based on automatic repositioning of the digitized dat points or the NURBS curve control points by a constrained nonlinear optimization algorithm. The objective function is derived variously by derived curved. Constraints are distance measures between the original and the modified digitized data points. Changes I curve shape are analyzed by illustrations of curve shapes, and continuous plotting of curvature and torsion.

• Proceedings of the KSME Conference
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• 2003.04a
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• pp.1226-1233
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• 2003

Finish machining of a curved surface is often carried out by an NC system with curve interpolation in the field. This NURBS interpolation adopts a feedrate optimizing strategy based on both the geometrical information and dynamic properties. In case of a finish cut using a ball-end mill, the curve interpolator needs to take the machining process into account for more improved surface, while reducing the polishing time. In this study, the effect of low machinability at the bottom of a tool on surface roughness is also considered. A particular curve interpolation algorithm is proposed for generating feedrate commands which are able to control the roughness of a curved surface. The simulation of the machined surface by the proposed algorithm was carried out, and experimental results are presented.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2001.04a
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• pp.405-410
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• 2001

In this paper, a new parametric curve interpolator is proposed based on a 3D(3-dimensional) NURBS curve. A free curve is generally divided into small linear segments or circular arcs in CNC machining. The method has caused to a command error, the limitation of machining speed, and the irregular machining surface. The proposed real-time 3D NURBS interpolator continuously generates a linear segment within the range of allowable acceleration/deceleration in the motion controller. Therefore, the algorithm calculates the curvature and the remained distance of a command curve for the smoothing machining. It is expected to attaining high speed and high precision machining in CNC Machine Tool.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2003.06a
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• pp.162-167
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• 2003

Finish machining of a curved surface is often carried out by an NC system with curve interpolation in the field. This NURBS interpolation adopts a feedrate optimizing strategy based on both the geometrical information and dynamic properties. In case of a finish cut using a ball-end mill. the curve interpolator needs to take the machining process into account for more improved surface, while reducing the polishing time. In this study, the effect of low machinability at the bottom of a tool on surface roughness is also considered. A particular curve interpolation algorithm is proposed for generating feedrate commands which are able to control the roughness of a curved surface. The simulation of the machined surface by the proposed algorithm was carried out, and experimental results are presented.

• Korean Journal of Computational Design and Engineering
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• v.3 no.2
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• pp.113-120
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• 1998

Calculation of intersection points by two curves is fundamental to computer aided geometric design. Bezier clipping is one of the well-known curve intersection algorithms. However, this algorithm is only applicable to Bezier curve representation. Therefore, the NURBS curves that can represent free from curves and conics must be decomposed into constituent Bezier curves to find the intersections using Bezier clipping. And the respective pairs of decomposed Bezier curves are considered to find the intersection points so that the computational overhead increases very sharply. In this study, extended Bezier clipping which uses the linear precision of B-spline curve and Grevill's abscissa can find the intersection points of two NURBS curves without initial decomposition. Especially the extended algorithm is more efficient than Bezier clipping when the number of intersection points is small and the curves are composed of many Bezier curve segments.

• Korean Journal of Computational Design and Engineering
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• v.10 no.5
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• pp.303-313
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• 2005

This paper proposes a generalized NURBS model, called Volumetric NURBS or VNURBS for representing volumetric objects with multiple attributes embedded in multidimensional space. This model provides a mathematical framework for modeling complex structure of heterogeneous objects and analyzing inside of objects to discover features that are directly inaccessible, for deeper understanding of complex field configurations. The defining procedure of VNURBS, which explains two directional extensions of NURBS, shows VNURBS is a generalized volume function not depending on the domain and its range dimensionality. And the recursive a1gorithm for VNURBS derivatives is described as a computational basis for efficient and robust volume modeling. In addition, the specialized versions of VNURBS demonstrate that VNURBS is applicable to various applications such as geometric modeling, volume rendering, and physical field modeling.

• Journal of Ocean Engineering and Technology
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• v.14 no.1
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• pp.95-101
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• 2000

In general, free form design depends on B-spline which is used for the generating hull lines in most of shipyards. But, nowadays, the NURBS method is applied to free form modeling method, which is able to more flexible transformation than B-Spline, and then became industrial standard in the various field. Therefore, this method has been considerably applied in new application fields which are required free form modelling. In this paper, the program called 2DSURF with 5 modules and developed for the generation of hull lines is described. It is examined whether the program can be applied to body lines, sheer lines, and half breadth lines.

• Korean Journal of Computational Design and Engineering
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• v.11 no.6
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• pp.403-411
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• 2006

NURBS surfaces have been widely used in engineering design since it can create a smooth surface using minimal numbers of data. But deformation of the surfaces is quite difficult especially for the detailed modification. Also, NURBS surface deformation processes need many inputs, and it is not easy to be implemented in 3D virtual system. In this paper, both the surface trimming and multi-resolution surface are used for the detailed sculpting including sharp edges of NURBS surface. QuadTree is used to separate cleanly the target surface with the surface for sculpting effect. Simple user strokes are also used for the sculpting target curves and GOMS(Goals, Operators, Methods, Selection Rules) model is applied to verify the efficiency of the proposed sculpting process.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2006.05a
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• pp.457-458
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• 2006

A method for obtaining smooth, jerk bounded feed rate profile in high speed machining has been developed. This study proposes a NURBS interpolator based on adaptive feed rate control with a well developed look ahead algorithm which takes into account the machining dynamics as well. Limitation of jerk and proportional torque rate result in smoothened loads on the machine which effectively reduces excitation of the resonant frequencies of the machine. It is found that the values of the feed rate of the down stream sharp corner have profound effect on the feed rate of the upstream sharp corners. By using a windowing scheme the feed rate profile obtained after look ahead method is re-interpolated to reduce the jerk related problems. This is compared with the adaptive NURBS interpolator to show the effectiveness of the proposed method. Simulation results indicate that the consideration of 'ripple effect' is important in avoiding jerk and thereby increasing the machining accuracy.

• Journal of Korea Game Society
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• v.2 no.1
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• pp.62-68
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• 2002

This paper presents a method for tessellating trimmed NURBS surface with preserving sharp shape Although several existing approaches need a large number of triangular meshes to represent sharp shape of surface, resulting triangular meshes may not reflect sharp edges properly. In this study, we flit detect the sharp shape of NURBS surface automatically using C1 continuous condition and then use constraint Delaunay triangulation method to present exact sharp shape with the minimum triangular meshes. And we also use approximated developed surface domain as triangulation domain of rimmed NURBS surface. In this way, the shape of triangular elements on the triangular domains is approximately preserved and can avoid distortion when mapped into three-dimensional space. finally, we show examples that demonstrate the effectiveness of the proposed scheme in terms of reducing the number of triangular meshes and preserving sharp shape of surface more exactly.