• Korean Journal of Computational Design and Engineering
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• v.2 no.2
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• pp.122-129
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• 1997

Ball rolling blending is a popular technique for blending between parametric surfaces. The ball rolling blend surface is conceptually a trajectory of a ball rolling between two base sufaces. It is constructed by sweeping a circular arc along a ball contact curve pair. Since a ball rolling blend surfaces does not have a polynomial form like a Bezier surface patch, it is impossible to apply this method directly to a commercial CAD/CAM system. In this paper an algorithm is developed to approximate a ball rolling blend surface into Bezier surface patches. Least square method is applied to obtain proper Bezier surface patches under a given tolerance. The Bezier surface patches have degree three or more and guarantee VC1-continuity.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1994.10a
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• pp.719-724
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• 1994

This paper describes a hybrid surface-based method for smooth 3D surface approximation to a sequence of 2D cross sections. The resulting surface is a hybrid G $^{1}$ surface represented by a mesh of triangular and rectangular Bezier patches defined on skinning, branching, or capping regions. Each skinning region is approximated with a closed B_spline surface, which is transformed into a mesh of Bezier patches. Triangular G $^{1}$ surfaces are constructed over brabching and capping regions such that the transitions between each capping regions such that the transitions between each triangular surface and its neighboring skinning surfaces are G $^{1}$ continuous. Since each skinning region is represented by an approximated rectangular C $^{2}$ suface instead of an interpolated trctangular G $^{[-1000]}$ surface, the proposed method can provide more smooth surfaces and realize more efficient data reduction than triangular surfacebased method.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2004.05a
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• pp.44-47
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• 2004

This paper proposes an approach for composite surface reconstruction from 2D serial cross-sections, where the number of contours varies from section to section. In a triangular surface-based approach taken in most reconstruction methods, a triangular $G^{1}$ surface is constructed by stitching triangular patches over a triangular net generated from the compiled contours. In the proposed approach, the resulting surface is a composite $G^{1}$ surface consisting of three kinds of surfaces: skinned, surface is first represented by a B-spline surface approximating the serial contours of the skinned region and then serial contours of the skinned region and then transformed into a mesh of rectangular Bezier patches. On branched and capped regions, triangular $G^{1}$ surfaces are constructed so that the connections between the triangular surfaces and their neighboring surfaces are $G^{1}$ continuous. Since each skinned region is represented by an approximated rectangular $G^{2}$ surface instead of an interpolated triangular $G^{1}$ surface, the proposed approach can provide more visually pleasing surfaces and realize more efficient data reduction than the triangular surface-based approach. Some experimental results demonstrate its usefulness and quality.

• Journal of the Society of Naval Architects of Korea
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• v.34 no.4
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• pp.127-138
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• 1997

In this study, a new technique is presented, by which one can define ship hull form with full fairness from the input data of lines. For curve modeling, the de Casteljau Algorithm and Bezier control points are used to express free curves and to establish the unified curve modeling technique which enables one to convert non-uniform B-spline (NUB) curve or cubic spline curve into composite Bezier curves. For surface modeling, the mesh curve net which is required to define surface of ship hull form is interpolated by the method of the unified curve modeling, and the boundary curve segments of Gregory surface patches are generated by remeshing(rearranging) the given mesh curve net. From these boundary information, composite Gregory surfaces of good quality in fairness can be formulated.

• Journal of Korean Institute of Industrial Engineers
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• v.21 no.4
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• pp.529-540
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• 1995

The paper deals with a procedure for constructing a composite surface interpolating a polygonal curve mesh defined from 3D scattered points. The procedure consists of a poly-angulation, construction of a curve net, and interpolation of the curve net. The poly-angulation contains a stage that changes a triangular edge net obtained from a triangulation into a poly-angular edge net. A curve net is constructed by replacing edges on the edge net with cubic Bezier curves. Finally, inside of an n-sided polygon is interpolated by n subdivided triangular subpatches. The method interpolates given point data with relatively few triangular subpatches. For an n-sided polygon, our method constructs an interpolant with n subdivided triangular subpatches while the existing triangular surface modeling needs 3(n-2) subpatches. The obtained surface is composed of quartic triangular patches which are $G^1$-continuous to adjacent patches.

• Journal of the Korean Society for Precision Engineering
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• v.15 no.8
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• pp.46-59
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• 1998

This paper presents shape design, surface construction, and cutting path generation for the surface of marine ship propeller blades. A propeller blade should be designed to satisfy performance constraints that include operational speed which impacts rotations per minutes, stresses related to deliverable horst power, and the major length of the marine ship which impacts the blade size and shape characteristics. Primary decision variables that affect efficiency in the design of a marine ship propeller blade are the blade diameter and the expanded area ratio. The blade design resulting from these performance constraints typically consists of sculptured surfaces requiring four or five axis contoured machining. In this approach a standard blade geometry description consisting of blade sections with offset nominal points recorded in an offset table is used. From this table the composite Bezier surface geometry of the blade is created. The control vertices of the Hazier surface patches are determined using a chord length fitting procedure from tile offset table data. Cutter contact points and path intervals are calculated to minimize travel distance and production time while maintaining a cusp height within tolerance limits. Long path intervals typically generate short tool paths at the expense of increased however cusp height. Likewise, a minimal tool path results in a shorter production time. Cutting errors including gouging and under-cut, which are common errors in machining sculptured surfaces, are also identified for both convex and concave surfaces. Propeller blade geometry is conducive to gouging. The result is a minimal error free cutting path for machining propeller blades for marine ships.