• 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.

• Journal of Korea Multimedia Society
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• v.14 no.2
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• pp.210-218
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• 2011

Generally, GIS digital map has been represented and transmitted by ASCII and Binary data forms. Among these forms, Binary form has been widely used in many GIS application fields for the transmission of mass map data. In this paper, we present a hierarchical compression technique of polyline and polygon components for effective storage and transmission of vector map with various degree of decision. These components are core geometric components that represent main layers in vector map. The proposed technique performs firstly the energy compaction of all polyline and polygon components in spatial domain for the lossless compression of detailed vector map and compress independently integer parts and fraction parts of 64bit floating points. From experimental results, we confirmed that the proposed technique has superior compressive performance to the conventional data compression of 7z, zip, rar and gz.

• 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 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 Computer Information Conference
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• 2014.07a
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• pp.201-202
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• 2014

본 논문에서는 3차원 공간을 시각적으로 표현이 가능한 MAYA의 MEL Script를 통해 미로 찾기 로봇을 3D시뮬레이션으로 구현하는 방법을 제안한다. MAYA에서는 생성된 개체에 대해 X-Y-Z 좌표정보를 적용하고 이 수치를 개체의 속성 값으로 제공한다. 이를 이용하여 랜덤한 미로 맵을 완성하기 위한 규칙으로 행렬을 생성하고 이 행렬의 인덱스와 값에 따라 X-Y-Z 좌표정보를 적용하여 개체를 생성하면 랜덤한 미로 맵이 완성된다. 그 후 길을 찾기 위한 규칙에 의해 이동하는 로봇의 X-Z좌표정보를 각 프레임 별로 저장하여 재생 시키면 미로 찾기 로봇 시뮬레이션을 눈으로 확인 가능하다. 사람이 직접 번거롭게 임의의 미로 맵 을 생성하지 않고 로봇이 없어도 간편하게 미로 찾기를 구현해 볼 수 있는 방법을 제시한다. 본 시뮬레이터는 미로 찾기 알고리즘을 테스트하는데 유용할 것이다.

• 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.

• Korean Journal of Computational Design and Engineering
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• v.8 no.4
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• pp.278-288
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• 2003

Presented in this paper is a numerical method for calculating the intersection points between Z-map vectors and the tool swept surface for circularly moving filleted-end mills. In numerically controlled(NC) machining simulation for large moulds and dies, a workpiece is frequently approximated as a set of z-axis aligned vectors, called Z-map vectors, and then the machining processes can be simulated through updating the Z-map with the intersection points. Circular motions are typically used for machining the free-form surfaces. For fast computation, we express each of intersection points with a single-variable non-linear equation and calculate the candidate interval in which the unique solution exists. Then, we prove the existence of a solution and its uniqueness in this candidate interval. Based on these properties, we can effectively apply numerical methods to finally calculate the solution of the nonlinear equation within a given precision. Experimental results are given for the case of a TV monitor and the hood of a car.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2002.10a
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• pp.616-619
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• 2002

The z-map structure is widely used for NC tool path verification as it is very simple and fast in calculation of Boolean operations. However, if the number of the x-y grid points in a z-map is increased to enhance its accuracy, the computation time for NC verification increases rapidly. To reduce this computation time, we proposed a NC verification method using 3-D graphic acceleration hardwares. In this method, the z-map of the resultant workpiece machined by a NC program is obtained by rendering tool swept volumes along tool pathos and reading the depth buffer of the graphic card. The experimental results show that this hardware-based method is faster than the conventional software-based method.

• Journal of the Korean Society for Precision Engineering
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• v.20 no.5
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• pp.47-56
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• 2003

Geometric cutting-simulation and verification play an important role in detecting NC machining errors in mold & die manufacturing and thereby reducing correcting time & cost on the shop floor. Current researches in the area may be categorized into view-based, solid-based, and discrete vector-based methods mainly depending on workpiece models. Each methodology has its own strengths and weaknesses in terms of computing speed, representation accuracy, and its ability of numerical inspection. The paper proposes a hybrid modeling scheme for workpiece representation with z-map model and discrete vector model, which performs 3-axis and 5-axis cutting-simulation via tool swept surface construction by connecting a sequence of silhouette curves.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.8 no.3
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• pp.83-91
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• 1999

In this paper, we suggest a virtual machining system that can simulate cutting forces of ball end milling at the stage of part design. Cutting forces, here, are estimated from the machanistic model that uses the concept of specific cutting farce coefficient. To this end, we need undeformed chip thickness which is used for calculating chip load. It is derived from the Z-map data of a CAD model. That is, chip load is the height difference between the cutting tool and the workpiece at an arbitrary position. The tool contact point is referred from the cutter location data. On the other hand, the workpiece height is acquired from the Z-map model of a CAD data. From the experimental verification, we can simulate machining process effectively to the slot and the side cutting of ball end mill.