• Korean Journal of Computational Design and Engineering
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• v.15 no.2
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• pp.115-123
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• 2010

We present an efficient algorithm for computing the Hausdorff distance between two planar curves. The algorithm is based on an efficient trimming technique that eliminates the curve domains that make no contribution to the final Hausdorff distance. The input curves are first approximated with biarcs within a given error bound in a pre-processing step. Using the biarc approximation, the distance map of an input curve is then approximated and stored into the graphics hardware depth-buffer by rendering the distance maps (represented as circular cones) of the biarcs. We repeat the same procedure for the other input curve. By sampling points on each input curve and reading the distance from the other curve (stored in the hardware depth-buffer), we can easily estimate a lower bound of the Hausdorff distance. Based on the lower bound, the algorithm eliminates redundant curve segments where the exact Hausdorff distance can never be obtained. Finally, we employ a multivariate equation solver to compute the Hausdorff distance efficiently using the remaining curve segments only.

• Korean Journal of Computational Design and Engineering
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• v.11 no.1
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• pp.20-26
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• 2006

This paper presents a procedure to compute pencil curves from a triangular mesh which is offset with the radius of a given ball-end mill. An offset triangular mesh has numerous self-intersections caused by an abundance of invalid triangles, which do not contribute to the valid CL-surface. Conceptually, we can obtain valid pencil curves by combining all intersections tying on the outer skin of the offset triangular mesh, i.e., the valid CL-surface. The underlying concept of the proposed algorithm is that visible intersections are always valid for pencil curves, because visible intersections lie on the outer skin of the offset model. To obtain the visibility of intersections efficiently, the proposed algorithm uses a graphics board, which performs hidden surface removal on up to a million polygons per second.

• Korean Journal of Computational Design and Engineering
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• v.15 no.4
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• pp.253-260
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• 2010

This paper presents algorithms for computing offsets of freeform curves. The approach first divides the original curve into several segments at the inflexion points. Based on the obtained new control polygon and its offsets, quadratic trigonometric splines are constructed to approximate the offset curves. Finally, the shape parameter value of trigonometric spline is determined to satisfy the required tolerance. The degree of the output curve is two, independent of the original curve's degree. Because of the great controllability, the proposed method can generate a completely overestimating offset curve by adjusting the value of the shape parameter, which guarantees no overcutting in NC machining. Furthermore, it also produces the lowest number of control points compared with other works.

• Journal of Computational Design and Engineering
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• v.1 no.2
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• pp.116-127
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• 2014

This paper aims to review methods for computing orthogonal projection of points onto curves and surfaces, which are given in implicit or parametric form or as point clouds. Special emphasis is place on orthogonal projection onto conics along with reviews on orthogonal projection of points onto curves and surfaces in implicit and parametric form. Except for conics, computation methods are classified into two groups based on the core approaches: iterative and subdivision based. An extension of orthogonal projection of points to orthogonal projection of curves onto surfaces is briefly explored. Next, the discussion continues toward orthogonal projection of points onto point clouds, which spawns a different branch of algorithms in the context of orthogonal projection. The paper concludes with comments on guidance for an appropriate choice of methods for various applications.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1994.04a
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• pp.691-700
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• 1994

Voronoi diagram of a set of geometric entities on a plane such as points, line segments, or arcs is a collection of Voronoi polygons associated with each entity, where Voronoi polygon of an entity is a locus of point which is closer to the associated entity than any other entity. Voronoi diagram is one of the most fundamental geometrical construct and well-known for its theoretical elegance and the wealth of applications. Various geometric problems can be solved with the aid of Voronoi diagram. For example, the maximum tool diameter of a milling cutter for rough cutting in a pocket can be easily found, and the pocketing tool path can be efficiently generated from Voronoi diagram. In PCB design, the design rule checking can be easily done via Voronoi diagram, too. This paper discusses an algorithm to construct Voronoi diagram of a simple polygon which consists of simple curves such as line segments as well as arcs in a plane with O(nlogn) time complexity by employing the divide and conquer scheme.

• Korean Journal of Computational Design and Engineering
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• v.4 no.1
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• pp.32-42
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• 1999

Approximate lofting or skinning is one of practical surface modeling techniques well used in CAD and reverse engineering applications. Presented in this paper is a method for approximately lofting a given set of curves wihin a specified tolereance. It is based on refitting input curves simultaneously on a common knot vector and interpolating them to get a resultant NURBS surface. A concept of reducing the number of interior knots of the common knot vector is well adopted to acquire more compact representation for the resultant surface. Energy minimization is newly introduced in curve refitting process to stabilize the solution of the fitting problem and get more fair curve. The proposed approximate lofting provides more smooth surface models and realizes more efficient data reduction expecially when the parameterization and compatibility of input curves are not good enough. The method has been successfully implemented in a new CAD/CAM product VX Vision? of Varimetrix Corporation.

• Korean Journal of Computational Design and Engineering
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• v.13 no.6
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• pp.450-458
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• 2008

Recently, Cartesian grid approach has been popular to generate grid meshes for complex geometries in CFD (Computational Fluid Dynamics) because it is based on the non-body-fitted technique. This paper presents a method of an octree generation and boundary cell clipping using section curves for fast octree generation and elimination of redundant intersections between boundary cells and triangles from 3D triangular mesh. The proposed octree generation method uses 2D Scan-Converting line algorithm, and the clipping is done by parameterization of vertices from section curves. Experimental results provide octree generation time as well as Cut-cell clipping time of several models. The result shows that the proposed octree generation is fast and has linear relationship between grid generation time and the number of cut-cells.

• Journal of Mechanical Science and Technology
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• v.15 no.9
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• pp.1292-1301
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• 2001

The mean-line method using empirical models is the most practical method of predicting off-design performance. To gain insight into the empirical models, the influence of empirical models on the performance prediction results is investigated. We found that, in the two-zone model, the secondary flow mass fraction has a considerable effect at high mass flow-rates on the performance prediction curves. In the TEIS model, the first element changes the slope of the performance curves as well as the stable operating range. The second element makes the performance curves move up and down as it increases or decreases. It is also discovered that the slip factor affects pressure ratio, but it has little effect on efficiency. Finally, this study reveals that the skin friction coefficient has significant effect on both the pressure ratio curve and the efficiency curve. These results show the limitations of the present empirical models, and more resonable empirical models are reeded.

• International Journal of Precision Engineering and Manufacturing
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• v.4 no.3
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• pp.20-27
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• 2003

Compensation of probe radius is required for accurate measurement in metal working industry. Compensation involves correctly measuring data on the surface in the amount of radius of the touch probe with a Coordinate Measuring Machine (CMM). Mechanical parts with free-formed curves and surfaces are complex enough so that accurate measurement and compensation are indispensable. This paper presents necessary algorithms involved in the compensation of the probe radius for free-formed curves and surfaces. Application of pillar curve is the focus for the compensation.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.11 no.5
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• pp.347-352
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• 1998

In this paper, the extraction and optimization of SPICE parameters on SONOSFET for NVSM circuit design were discussed. SONOSFET devices with different channel widths and lengths were fabricated using conventional 1.2 um n-well CMOS process. And, electric properties for dc parameters and capacitance parameters were measured on wafer. SPICE parameters for the SONOSFET were extracted from the UC Berkeley level 3 model for the MOSFET. And, local optimization of Ids-Vgs curves has carried out in the bias region of subthreshold, linear, saturation respectively. Finally, the extracted SPICE parameters were optimized globally by comparing drain current (Ids), output conductance(gds), transconductance(gm) curves with theoretical curves in whole region of bias conditions. It is shown that the conventional model for the MOSFET can be applied to the SONOSFET modeling except sidewalk effect.