• 한국CDE학회논문집
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• 제15권3호
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• pp.178-188
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• 2010

This paper addresses the problem of determining if two surfaces intersect tangentially or transversally in a mathematically consistent manner and approximating an intersection curve. When floating point arithmetic is used in the computation, due to the limited precision, it often happens that the decision for tangential and transversal intersection is not clear cut. To handle this problem, in this paper, interval arithmetic is proposed to use, which provides a mathematically consistent way for such decision. After the decision, the intersection is traced using the validated ODE solver, which runs in interval arithmetic. Then an iterative method is used for computing the accurate intersection point at a given arc-length of the intersection curve. The computed intersection points are then approximated by using a B-spline curve, which is provided as one instance of intersection curve for further geometric processing. Examples are provided to demonstrate the proposed method.

• 한국CDE학회논문집
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• 제12권5호
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• pp.344-353
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• 2007

In this paper, we address the problem of robust geometric modeling with emphasis on surface to surface intersections. We consider the topology and the numerical accuracy of an intersection curve to find the best approximation to the exact one. First, we perform the topological configuration of intersection curves, from which we determine the starting and ending points of each monotonic intersection curve segment along with its topological structure. Next, we trace each monotonic intersection curve segment using a validated ODE solver, which provides the error bounds containing the topological structure of the intersection curve and enclosing the exact root without a numerical instance. Then, we choose one approximation curve and adjust it within the bounds by minimizing an objective function measuring the errors from the exact one. Using this process, we can obtain an approximate intersection curve which considers the topology and the numerical accuracy for robust geometric modeling.

• 한국컴퓨터그래픽스학회논문지
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• 제6권4호
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• pp.29-34
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• 2000

이 논문에서는 평행이동곡면 (surface of extrusion) 과 임의의 자유곡면 사이의 교차곡선의 구조를 분석하고 이를 계산하는 방법에 대해 설명한다. 평행이동곡면의 이동방향에 대하여 다른 곡면의 윤곽곡선 (silhouette curve) 을 구하고, 이를 평행이동곡면의 기준곡선과 교차시킴으로써 교차곡선의 구조를 분석한다. 또한, 교차곡선이 존재하는 범위와 특이점을 구함으로써 교차곡선 전체를 안정적이고 효율적으로 계산하는 알고리즘을 제시한다.

• 한국CDE학회논문집
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• 제3권2호
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• pp.113-120
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• 1998

Calculation of intersection points by two curves is fundamental to computer aided geometric design. Bezier clipping is one of the well-known curve intersection algorithms. However, this algorithm is only applicable to Bezier curve representation. Therefore, the NURBS curves that can represent free from curves and conics must be decomposed into constituent Bezier curves to find the intersections using Bezier clipping. And the respective pairs of decomposed Bezier curves are considered to find the intersection points so that the computational overhead increases very sharply. In this study, extended Bezier clipping which uses the linear precision of B-spline curve and Grevill's abscissa can find the intersection points of two NURBS curves without initial decomposition. Especially the extended algorithm is more efficient than Bezier clipping when the number of intersection points is small and the curves are composed of many Bezier curve segments.

• 한국정보처리학회논문지
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• 제4권8호
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• pp.2163-2172
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• 1997

곡면간의 교차계산은 부울연산(Boolean operations)과 조각된 곡면들을 지원하기위한 기하 모델링과 솔리드에서 사용되는 기본적인 기하학 연산이다. 본 논문에서는 두 정규화된 곡면의 교차곡선을 따라 추적하기 위한 새로운 알고리즘을 제안한다. 그러므로 본 논문에서는 계산상의 간소화와 2차 연속성을 나타낸다. 따라서, 교차 곡선의 한 점이 주어지면 이 점을 초기점으로 하여 교차 곡선의 전체 곡선을 추적한다. 그리고 각각의 교선들의 초기점들은 쿼드트리에서 DFS(Depth First Search) 기법으로 검색되고 교선은 연속적인 형태로 자연스럽게 표현된다.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제23권3호
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• pp.309-317
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• 2016

As a generalization of an inflection point, we consider a point P on a smooth plane curve C of degree m at which another curve C' of degree n meets C with high intersection multiplicity. Especially, we deal with the existence of two curves of degree m and n meeting at the unique point.

• 한국CDE학회논문집
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• 제3권2호
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• pp.127-134
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• 1998

This paper presents d new algorithm to compute the offlet curve of a given planar parametric curve. We reduce the problem of computing an offset curve to that of intersecting a surface to a paraboloid. Given an input curve C(t)=(x(t), y(t))∈R², the corresponding surface D/sub c(t)/ is constructed symbolically as the envelope surface of a one-parameter family of tangent planes of the paraboloid Q:z=x²+y²along a lifted curve C(t)=(x(t), y(t), x(t)²+y(t)²∈Q. Given an offset distance d∈R, the offset curve C/sub d/(t) is obtained by the projection of the intersection curve of D/sub c(t)/ and a paraboloid Q:z=x²+y²-d² into the xy-plane.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2003년도 학술회의 논문집 정보 및 제어부문 B
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• pp.1022-1030
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• 2003

In this paper we propose a efficient offset curve construction algorithm for $C^0$-continuous Open and Closed 2D sequence curve with line segment in the plane. One of the most difficult problems of offset construction is the loop problem caused by the interference of offset curve segments. Prior work[1-10] eliminates the formation of local self-intersection loop before constructing a intermediate(or raw) offset curve, whereas the global self-intersection loop are detected and removed explicitly(such as a sweep algorithm[13]) after constructing a intermediate offset curve. we propose an algorithm which removes global as well as local intersection loop without making a intermediate offset curve by forward tracing of tangential circle. Offset of both open and closed poly-line segment sequence curve in the plane constructs using the proposed approach.

• 한국CDE학회논문집
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• 제4권3호
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• pp.269-283
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• 1999

Surface/surface intersection is a common and important problem in geometric modeling and CAD/CAM. Several methods have been used to approach this problem. All possible intersection curves can be obtained by using the subdivision algorithm, while it requires a great deal of memory and is somewhat inefficient. The tracing algorithm is much faster than the subdivision algorithm, and can find points on the intersection curve sequentially. But, the tracing algorithm has some problems in the intersection curves on surface boundaries. In this paper, an Improved tracing algorithm that includes some ideas such as a new trace-terminating condition for the intersection curves on surface boundaries, detecting closed intersections and extension for composite surfaces is suggested. This algorithm consists of three step: generating state points for curve tracing, tracing intersection curves and sorting pieces of the intersection curves. The results of this algorithm and comparisons to the 'DESIGNBASE' and 'ACIS' system are presented.

• 전기학회논문지
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• 제56권1호
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• pp.188-196
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• 2007

In this paper we propose an efficient offset curve generation algorithm for open and closed 2D point sequence curve(PS curve) with line segments in the plane. One of the most difficult problems of offset generation is the loop intersection problem caused by the interference of offset curve segments. We propose an algorithm which removes global as well as local intersection loop without making an intermediate offset curve by forward tracing of tangential circle. Experiment in computer sewing machine shows that proposed method is very useful and simple.