Earticle

우리나라 도시계획 제도의 근간인 용도지역제는 건축자유를 기본원칙으로 하되, 공공복리를 위하여 이 자유를 일정수준 제한하는 제도이다. 따라서 용도지정은 명확한 기준에 근거하여 논리적 오류없이 지정되고, 예외는 누구나 동의할 수 있는 일부 불가피한 사례에만 적용되어야만 형평성을 인정받을 수 있다. 그러나 용도지정이 일정한 논리적 근거를 따르더라도 이를 객관적으로 검증함으로써 용도지정의 객관성과 신뢰성을 제고할 방법이 도출되지 못한 실정이다. 이에 본 연구에서는 위 문제를 해소하기 위한 하나의 방법으로서, 일종의 논리연산인 부울연산을 활용하여 용도지정의 논리적 정합성을 검토하는 방안을 제안하고자 한다. 이를 검토하고자 제주특별자치도의 관리지역 세분사례를 중심으로 도시관리계획 상 관리지역 세분 기준을 형식논리로 전개하고 GIS 상의 부울연산 기법을 활용하여 논리연산도구를 제작하였다. 이를 수행한 결과 관리지역 세분의 논리적 정합성, 논리적 오류의 원인, 그리고 그 정책적 시사점을 도출할 수 있었다.

The zoning regulation is provided to restrict the private land-use activities to a certain degree in an effort to augment the level of public interest and welfare. It thus should be based on the principles that are logically clear and consistent and are free from any defect so as to be objectively agreeable by the majority of the constituents to guarantee the societal equity. The current Korean zoning consequences, however, have been criticized by many for its lack of proper procedures and effective tools to check their qualification in terms of the aforementioned conditions despite the legally dictated statements as well as advanced spatial analysis tools. By taking Jeju Island, the globally renowned resort island of Korea, as the case area, this study tries to evaluate the methodology to check the appropriateness of the current zoning outcomes in the island on the GIS platform by using the Boolean operations.

The requirements of multi-resolution models of feature-based solids, which represent an object at many levels of feature detail, are increasing for engineering purposes, such as analysis, network-based collaborative design, virtual prototyping and manufacturing. To provide multi-resolution models for various applications, it is essential to generate adequate solid models at varying levels of detail (LOD) after feature rearrangement, based on the LOD criteria. However, the non-commutative property of the union and subtraction Boolean operations is a severe obstacle to arbitrary feature rearrangement. To solve this problem we propose history-based Boolean operations that satisfy the commutative law between union and subtraction operations by considering the history of the Boolean operations. Because these operations guarantee the same resulting shape as the original and reasonable shapes at the intermediate LODs for an arbitrary rearrangement of its features, various LOD criteria can be applied for multi-resolution modeling in different applications.

We propose a feature-based multi-resolution representation of B-rep solid models using history-based Boolean operations based on the merge-and-select algorithm. Because union and subtraction are commutative in the history-based Boolean operations, the integrity of the models at various levels of detail (LOD) is guaranteed for the reordered features regardless of whether the features are subtractive or additive. The multi-resolution solid representation proposed in this paper includes a non-manifold topological merged-set model of all feature primitives as well as a feature-modeling tree reordered consistently with a given LOD criterion. As a result, a B-rep solid model for a given LOD can be provided quickly, because the boundary of the model is evaluated without any geometric calculation and extracted from the merged set by selecting the entities contributing to the LOD model shape.

This paper describes the selective Boolean operations on non-manifold geometric models whose union and subtraction operations are communicative. These operations guarantee the same resulting shape in spite of change of the order of Boolean operations, and the integrity of the model for omission of some features. In addition, a B-rep model for a modified modeling history is obtained in a short time, as no boundary evaluation is necessary. These features enable easy implementation of multi-resolution representation of B-rep models.

In this paper, we propose multi-resolutional representation of B-rep solid models using the selective Boolean operations on non-manifold geometric models. Since the union and subtraction operations of the selective Boolean operations are commutative, the integrity of the model is guaranteed for reordering design features. A multi-resolution representation is established using a non-manifold merged set model and a feature modeling tree reordered according to some criterion of level of detail (LOD). Then, a solid model for a specified LOD can be extracted from this multi-resolution model using the selective Boolean operations.

D-클래스는 암호학 등의 보안 분야에 응용될 수 있는 가능성을 가지고 있다. 그러나 D-클래스 계산은 NP-완전 문제로서 현재 $4{\times}4$ 이하 크기의 행렬에 대한 D-클래스 만이 알려져 있어 D-클래스의 특성에 대한 연구가 제대로 이루어지지 못하고 있다. 최근 새로운 D-클래스를 얻기 위하여 보다 효율적인 D-클래스 계산에 대한 연구가 수행되었으나 아직 새로운 D-클래스를 계산할 수 있을 정도의 효율적인 연구결과는 보이지 않고 있다. 본 논문은 논리 대수의 연산 특성을 이용하여 D-클래스 계산을 보다 효율적으로 할 수 있는 수학적 이론과 방법을 제시한다.

This paper describes the Boolean and sectioning operations on pseudo-solid models. A pseudo-solid model is defined as a sheet body that looks like a solid model but cannot comprise a solid model due to tolerance. Most of CAD models imported from the other CAD system are pseudo-solid models and have to be repaired for further stolid modeling operations. However, healing a pseudo-solid model is a very tedious and cumbersome process. To solve this problem, we devised and implemented the Boolean and sectioning operations on pseudo-solid models. Using these operations, mold and die design can be performed more efficiently, as healing work is reduced greatly.