• Korean Journal of Computational Design and Engineering
• /
• v.15 no.3
• /
• pp.178-188
• /
• 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.

• Korean Journal of Computational Design and Engineering
• /
• v.4 no.3
• /
• pp.269-283
• /
• 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.

• Korean Journal of Computational Design and Engineering
• /
• v.3 no.2
• /
• pp.113-120
• /
• 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.

• Korean Journal of Computational Design and Engineering
• /
• v.12 no.5
• /
• pp.344-353
• /
• 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.

• Journal of Korean Society of Transportation
• /
• v.20 no.7
• /
• pp.23-29
• /
• 2002

Five and more leg intersections have been still in operation in many urban areas. The number of conflicts in five leg intersection is more than four leg intersection. The signal timing design in the five leg intersection should be performed not only to reduce delay but also to increase safety. This paper suggests safety enhanced signal phase sequence design of a rotary with five leg intersection such as phase sequence minimizing the number of conflict points at the rotary with five leg intersections and the phase-length-design procedure by utilizing the Traffic Network Study Tool(TRANSYT). Field data was collected from Gonguptap five leg intersection in Ulsan and TRANSYT-7F was applied for signal timing design model. Optimal signal phase length and sequence of TRANSYT-7F is rearranged based on the Principal of "two moving traffic flows per phase". In conclusion, proposed signal phase design increased delay by 6.2% compared with the optimal signal phase of TRANSYT-7F. However, it could decrease the number of conflict in the five leg intersection by 61.5%.

• Korean Journal of Computational Design and Engineering
• /
• v.5 no.4
• /
• pp.336-346
• /
• 2000

This paper presents a geometric method that can detect and compute all conic sections in the intersection of two tori. Conic sections contained in a torus must be circles. Thus, when two tori intersect in a conic section, the intersection curve must be a circle as well. Circles in a torus are classified into profile circles, cross-sectional circlet, and Yvone-Villarceau circles. Based on a geometric classification of these circles, we present a procedural method that can detect and construct all intersection circles between two tori. All computations can be carried out using simple geometric operations only: e.g., circle-circle intersections, circle-line intersections, vector additions, and inner products. Consequently, this simple structure makes our algorithm robust and efficient, which is an important advantage of our geometric approach over other conventional methods of surface intersection.

• Korean Journal of Computational Design and Engineering
• /
• v.6 no.2
• /
• pp.101-110
• /
• 2001

The maximum intersection of spherical convex polygons are to find spherical regions owned by the maximum number of the polygons, which is applicable for determining the feasibility in manufacturing problems such mould design and numerical controlled machining. In this paper, an efficient method for partitioning a sphere with the polygons into faces is presented for the maximum intersection. The maximum intersection is determined by examining the ownerships of partitioned faces, which represent how many polygons contain the faces. We take the approach of edge-based partition, in which, rather than the ownerships of faces, those of their edges are manipulated as the sphere is partitioned incrementally by each of the polygons. Finally, gathering the split edges with the maximum number of ownerships as the form of discrete data, we approximately obtain the centroids of all solution faces without constructing their boundaries. Our approach is analyzed to have an efficient time complexity Ο(nv), where n and v, respectively, are the numbers of polygons and all vertices. Futhermore, it is practical from the view of implementation since it can compute numerical values robustly and deal with all degenerate cases.

• Korean Journal of Computational Design and Engineering
• /
• v.9 no.4
• /
• pp.382-386
• /
• 2004

This paper presents an algorithm for the triangular mesh intersection problem. The key aspect of the proposed algorithm is to reduce the number of triangle pairs to be checked for intersection. To this end, it employs two different approaches, the Y-group approach and the space partitioning approach. Even though both approaches have the same objective of reducing the number of triangular-triangular intersection (TTI) pairs, their inherent characteristics are quite different. While the V-group approach works by topology (reduces TTI pairs by guaranteeing no intersection among adjacent triangles), the space partitioning approach works by geometry (reduces TTI pairs by guaranteeing no intersection among distant triangles). The complementary nature of the two approaches brings substantial improvement in reducing the number TTI pairs.

• Proceedings of the KSRS Conference
• /
• 2005.10a
• /
• pp.749-752
• /
• 2005

In this paper, we introduce an Intersection Collision Avoidance (ICA) system as a convergence example of Telematics and USN technology and show several requirements for the ICA system. Also, we propose a system design that satisfies the requirements of reliable vehicular data acquisition, real-time data transmission, and effective intersection collision prediction. The ICA system consists of vehicles, sensor nodes and a base station that can provide drivers with a reliable ICA service. Then, we propose several technological solutions needed when implementing the ICA system. Those are about sensor nodes deployment, vehicular information transmission, vehicular location data acquisition, and intersection collision prediction methods. We expect this system will be a good case study applied to real Telematics application based on USN technology.

• Journal of Korean Society of Transportation
• /
• v.17 no.5
• /
• pp.79-86
• /
• 1999

Traffic jams of our country are due to the shortage of roadway as compared with the traffic, however. they are sometimes due to inconsistency of the roadway capacity. Inconsistency of the roadway capacity comes from the difference of cycle length, phase length and number of Phase between major intersection and minor intersection. Specialty increasing number of Phase due to left-turn movements bring out decrease of the arterial capacity, deterioration of the arterial offset. The Purpose of this research is to introduce and analyze the continuous flow intersection to solve the bottleneck of the major intersection. The major contents of this research introduce the concept and design consideration for the continuous flow intersection and also analyze delay, fuel consumption and emissions among multiphase intersection, grade separated intersection and continuous flow intersection. This research analyze the sensitivities according to change of the left-turn traffic volume and also evaluate the cost-effectiveness through the total cost analysis among three of them.