• 한국HCI학회:학술대회논문집
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• 2008.02a
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• pp.451-455
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• 2008

In this paper, we present how we implement the low-level, triangle intersection routine in a massively parallel fashion using n VIDIA's new GPGPU language, CUDA. Triangle intersection often becomes a computational bottleneck in the collision detection problem. Due to the relatively low bandwidth between CPU and GPU, it has been challenging to implement efficient, object-space collision detection between triangle sets. However, thanks to the improved data transmission rates in CUDA architecture, in this paper, we improved the performance of triangle intersection substantially better than the optimized CPU counterpart.

• Journal of the Korea Computer Graphics Society
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• v.17 no.3
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• pp.9-19
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• 2011

Computing triangle-triangle intersections has been a fundamental task required for many 3D geometric problems. We propose a novel robust GPU algorithm to efficiently compute intersections in a large triangle set. The algorithm has three stages:k-d tree construction, triangle pair generation, and exact intersection computation. All three stages are executed on GPU except, for unsafe triangle pairs. Unsafe triangle pairs are robustly handled by CLP(controlled linear perturbation) on a CPU thread. They are identified by floating-point filtering while exact intersection is computed on GPU. Many triangles crossing a split plane are duplicated in k-d tree construction, which form a lot of redundant triangle pairs later. To eliminate them efficiently, we use a split index which can determine redundancy of a pair by a simple bitwise operation. We applied the proposed algorithm to computing 3D Minkowski sum boundaries to verify its efficiency and robustness.

• Honam Mathematical Journal
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• v.36 no.4
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• pp.787-794
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• 2014

We prove three convex hull theorems on triangles and circles. Given a triangle ${\triangle}$ and a point p, let ${\triangle}^{\prime}$ be the triangle each of whose vertices is the intersection of the orthogonal line from p to an extended edge of ${\triangle}$. Let ${\triangle}^{{\prime}{\prime}}$ be the triangle whose vertices are the centers of three circles, each passing through p and two other vertices of ${\triangle}$. The first theorem characterizes when $p{\in}{\triangle}$ via a distance duality. The triangle algorithm in [1] utilizes a general version of this theorem to solve the convex hull membership problem in any dimension. The second theorem proves $p{\in}{\triangle}$ if and only if $p{\in}{\triangle}^{\prime}$. These are used to prove the third: Suppose p be does not lie on any extended edge of ${\triangle}$. Then $p{\in}{\triangle}$ if and only if $p{\in}{\triangle}^{{\prime{\prime}}$.

• Journal of Korean Society of Transportation
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• v.23 no.5 s.83
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• pp.73-81
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• 2005

Triangle-shaped island was been used for the exclusive separation between the right-turn and the through flow. However, in case that existing Triangle-Shaped Island is built at the intersection of narrow road. there are more possibilities of traffic collision trespassing into the opposite lane. Accordingly, separation of the opposite lane is required so as to prevent the intrusion of the large-sized (a heavy) vehicle into the opposite lane turning at the intersection. This study showed the comparison between intersection composed of existing Triangle-Shaped Island and the intersection with Drop Island is added. First of all, in the safety aspect, a method to decide location and shape of Drop Island considering turning trajectory of the large-sized (the heavy vehicle) is addressed. The guideline on the placement of drop island install location and method to decide form the consider heavy truck's turn trajectory in safety side. As a conclusion. we analyzed that drop island is relatively superior to existing Triangle-Shaped Island in terms of driver, ease of driving, driving pleasantness, pedestrian, widening and economic performance aspect.

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

• 한국HCI학회:학술대회논문집
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• 2009.02a
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• pp.469-474
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• 2009

This paper proposes an real time ray tracing system using optimized kd-tree traversal environment and ray/triangle intersection algorithm. The previous kd-tree traversal algorithms search for the upper nodes in a bottom-up manner. In a such way we need to revisit the already visited parent node or use redundant memory after failing to find the intersected primitives in the leaf node. Thus ray tracing for relatively complex scenes become more difficult. The new algorithm contains stacks implemented on GPU's local memory on CUDA framework, thus elegantly eliminate the problems of previous algorithms. After traversing the node we perform the latest CPU-based ray/triangle intersection algorithm 'Plucker coordinate test', which is further accelerated in massively parallel thanks to CUDA. Plucker test can drastically reduce the computational costs since it does not use barycentric coordinates but only simple test using the relations between a ray and the triangle edges. The entire system is consist of a single ray kernel simply and implemented without introduction of complicated synchronization or ray packets. Consequently our experiment shows the new algorithm can is roughly twice as faster as the previous.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1996.11a
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• pp.578-582
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• 1996

Verification of STL is essential in RP. In the study, triangle based non-manifold geometric modeling that can check intersection between triangles was used to vilify STL. The method proposed in this study can be applied at the most general case and very useful, but has a penalty on computing thime of O(n$^2$)

• Communications of Mathematical Education
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• v.22 no.1
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• pp.27-39
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• 2008

In this paper we study triangle's properties related with angle bisectors, perpendiculars, circumcenter using the principle of the lever. We analyze proof method using the principle of the lever, and describe how to investigate intersection of segments, how to prove equalities and inequalities using the principle of the lever in triangle.

• Journal of the Korean Association of Geographic Information Studies
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• v.10 no.3
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• pp.113-122
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• 2007

The rapid growth of aerial survey and remote sensing technology has enabled the rapid acquisition of very large amounts of geographic data, which should be analyzed using real-time visualization technology. The level of detail(LOD) algorithm is one of the most important elements for realizing real-time visualization. We chose the triangulated irregular network (TIN) method to generate normalized digital elevation model(DEM) data. First, we generated TIN data using contour lines obtained from a two-dimensional(2D) digital map and created a 2D grid array fitting the size of the area. Then, we generated normalized DEM data by calculating the intersection points between the TIN data and the points on the 2D grid array. We used constrained Delaunay triangulation(CDT) and ray-triangle intersection algorithms to calculate the intersection points between the TIN data and the points on the 2D grid array in each step. In addition, we simulated a three-dimensional(3D) terrain model based on normalized DEM data with real-time visualization using a Microsoft Visual C++ 6.0 program in the DirectX API library and a quad-tree LOD algorithm.

• Journal of Computational Design and Engineering
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• v.3 no.2
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• pp.151-160
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• 2016

Cutter-workpiece engagement (CWE) is the instantaneous contact geometry between the cutter and the in-process workpiece during machining. It plays an important role in machining process simulation and directly affects the calculation of the predicted cutting forces and torques. The difficulty and challenge of CWE determination come from the complexity due to the changing geometry of in-process workpiece and the curved tool path of cutter movement, especially for multi-axis milling. This paper presents a new method to determine the CWE for general milling processes. To fulfill the requirement of generality, which means for any cutter type, any in-process workpiece shape, and any tool path even with self-intersections, all the associated geometries are to be modeled as triangle meshes. The involved triangle-to-triangle intersection calculations are carried out by an effective method in order to realize the multiple subtraction Boolean operations between the tool and the workpiece mesh models and to determine the CWE. The presented method has been validated by a series of case studies of increasing machining complexity to demonstrate its applicability to general milling processes.