• Journal of the Korean Society for Precision Engineering
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• v.15 no.11
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• pp.180-188
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• 1998

Z-map is a special form of discrete nonparametric representation in which the height values at grid points on the xy-plane are stored as a 2D array z[i.j]. While z-map is the simplest form of representing sculptured surfaces and it is the most versatile scheme for modeling nonparametric objects, its practical application in industry (eg, tool-path generation) aroused much controversy over its weaknesses ; accuracy, singularity (eg, vertical wall), and some excessive storage needs. Although z-map has such limitations, much research on the application of z-map can be found in various articles. However, research on the systematic analysis of sculptured surface shape representation via z-map model is rather rare. Presented in this paper are the following: shape modeling power of the simple z-map model, exact (within tolerance) B-map representation of sculptured surfaces which have some feature-shapes such as vertical-walls and real sharp-edges by adopting some complementary B-map models, and some application examples.

• International Journal of Precision Engineering and Manufacturing
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• v.3 no.1
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• pp.49-56
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• 2002

The Z-map is a special farm of discrete non-parametric representation in which the height values at grid points on the xy-plane are stored as a 2D array z[ij]. While the z-map is the simplest farm of representing sculptured surfaces and is the most versatile scheme for modeling non-parametric objects, its practical application in industry (eg, tool-path generation) has aroused much controversy over its weaknesses, namely its inaccuracy, singularity (eg, vertical wall), and some excessive storage needs. Much research or the application of the z-map can be found in various articles, however, research on the systematic analysis of sculptured surface shape representation via the z-map model is rather rare. Presented in this paper are the following: shape modeling power of the simple z-map model, exact (within tolerance) z-map representation of sculptured surfaces which have some feature-shapes such as vertical-walls and real sharp-edges by adopting some complementary z-map models, and some application examples.

• Proceedings of the KSME Conference
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• 2000.11a
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• pp.824-828
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• 2000

Prior to the downloading of the NC codes to a machining center, the NC tool-path can be verified in a computer. The Z-map is one of the tools for the verification of NC tool-path. The Z-map is a two dimensional array in which the height values of the Z-axis direction vectors are stored. The Z-axis direction vectors are arranged in a rectangular grid pattern on the XY plane. The accuracy of the simulation comes from the grid interval. In the rectangular Z-map, the distances between the grid points are different. The distance in diagonal direction is larger than those in X or Y axis directions. For the rendering of the Z-map, a rectangular grid is divided into two triangular facets. Depending on the selection of a diagonal, there are two different cases. In this paper, triangular Z-map, in which the Z-axis direction vectors are arranged in a triangular grid pattern on XY plane, is proposed. In the triangular Z-map, the distances between grid points are equal. There is no ambiguity to make triangular facets for the rendering.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1994.10a
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• pp.683-688
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• 1994

Recently, the Z-Map model has been used widely to represent the three dimensional geometric shape and to achieve the cross-section and point evaluation of the shape. In this paper, the CNC cutting planning and simulation modules for product with three dimensional geometric shape are realized based on the Z-Map model. The realized system has the various capabilities related to the automatic generation of tool path for the rough and finish cutting processes, the automatic elimination of overcut, the automatic generation of CNC program for a machining center and the cutting simulation. Especially, the overcut-free tool path is obtained by using the CL Z-Map models which are composed of the offset surfaces of the geometric shape of product.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.7 no.5
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• pp.38-45
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• 1998

The Z-map model which is quite similar to the non-parametric patch is widely used to describe the shape of a surface because of its simplicity. Despite the inherent advantage of z-map model. it has drawbacks that there exists difficulty in expressing the vertical walls and its related contact treatment method. In the region of vertical walls, there is a convergence problem in searching the contact point. In this study a contact point finding scheme is presented, based on the z value of the z-map model on the sheet normal direction. To show the utility of this scheme a compared with the experimental results. The effects of the Z-map grid distances and the interpolations of the inside Z-map value are also discussed.

• Journal of the Korean Mathematical Society
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• v.32 no.3
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• pp.573-582
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• 1995

J.Milnor[Mi2] has introduced the notion of directional entropy in his study of Cellular Automata. Cellular Automaton map can be considered as a continuous map from a space $K^Z^n$ to itself which commute with the translation of the lattice $Z^n$. Since the space $K^Z^n$ is compact, map S is uniformly continuous. Hence S is a block map(a finite code)[He]. (S is said to have a finite memory.) In the case of n = 1, we have a shift map, T on $K^Z$, and a block map S and they together generate a $Z^2$ action.

• KSCI Review
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• v.14 no.2
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• pp.141-146
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• 2006

In this paper, we propose a new algorithm for recovering the broken letters of relics into an original form by using Z-map and image processing. The letters of relics may have been broken by a lot of rubbed copy and a long time and tide. They need to be restored. But the manual reconstruction is a very tedious and laborious task. Thus, it is necessary to automate the restoration process. This paper presents a realistic algorithm with an application to Tripitaka Koreana by using Z-map and morphological filter.

• Journal of the Korean Society for Precision Engineering
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• v.14 no.3
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• pp.57-65
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• 1997

In this study, a cutting force in the Ball-end milling process is calculated using Z-map. Z-map can describe any type of cutting area resulting from the previous cutting geometry and cutting condition. Cutting edge of a ball-end mill is divided into infinitesimal cutting edge elements and the position of the ele- ment is projected to the cutter plane normal to the Z axis. Also the cutting area in the cutter plane is obtained by using the Z-map. Comparing this projected position with cutting area, it can be determined whether it engages in the cutting. The cutting force can be calculated by numerical integration of cutting force acting on the engaged cutting edge elements. A series of experiments such as contouring and upward/downward ramp cutting was performed to verify the calculated cutting force.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2002.05a
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• pp.551-554
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• 2002

The paper discusses new approach for machining operation simulation using enhanced Z map algorithm. To extract the required geometric information from NC code, suggested algorithm uses supersampling method to enhance the efficiency of a simulation process. By executing redundant Boolean operations in a grid cell and averaging down calculated data, presented algorithm can accurately represent material removal volume though tool swept volume is negligibly small. Supersampling method is the most common form of antialiasing and usually used with polygon mesh rendering in computer graphics. The key advantage of enhanced Z map model is that the data structure is same with conventional Z map model, though it can acquire higher accuracy and reliability with same or lower computation time. By simulating machining operation efficiently, this system can be used to improve the reliability and efficiency of NC machining process as well as the quality of the final product.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1996.04a
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• pp.125-129
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• 1996

In this study, a method is proposed for the cutting force prediction of Ball-end milling process using Z-map is proposed. Any types of cutting area generated from previous cutting process can be expressed in z-map data. Cutting edge of a ball-end mill is divided into a set of finite cutting edges and the position of this edge is projected to the cross-section plane normal to the Z-axis. Comparing this projected position with Z-map data of cutting area and determining whether it is in the cutting region, total cutting force can be calculated by means of numerical integration. A series of experiments such as side cutting and upward/downard cutting was performet to verify the simulated cutting force.