• Journal of the Korean Society for Precision Engineering
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• v.10 no.1
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• pp.89-99
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• 1993

A solid modeller was developed in this paper. Representation scheme of modelling is nonmanifold B-rep. While namy B-rep modellers use edges as basic element of modelling, this modeller is triangle-based. New modelling element, split triangle that is composed of 3 pure half-edges and has no information about the adjoining triangles, was defined to enlarge the range of representation. Corresponding algorithms for Boolean set operations were also developed.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.6 no.10
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• pp.2567-2586
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• 2012

Localization of sensor nodes is a key technology in Wireless Sensor Networks(WSNs). Trilateration is an important position determination strategy. To further improve the localization accuracy, a novel Trilateration based on Point In Triangle testing Localization (TPITL)algorithm is proposed in the paper. Unlike the traditional trilateration localization algorithm which randomly selects three neighbor anchors, the proposed TPITL algorithm selects three special neighbor anchors of the unknown node for trilateration. The three anchors construct the smallest anchor triangle which encloses the unknown node. To choose the optimized anchors, we propose Point In Triangle testing based on Distance(PITD) method, which applies the estimated distances for trilateration to reduce the PIT testing errors. Simulation results show that the PIT testing errors of PITD are much lower than Approximation PIT(APIT) method and the proposed TPITL algorithm significantly improves the localization accuracy.

• Journal of the Korean School Mathematics Society
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• v.13 no.2
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• pp.263-287
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• 2010

The purposes of the study were to investigate how children define a triangle, their reasoning types in identifying examples and non-examples of a triangle, and the relationship between their reasoning types and geometrical levels. Twenty-nine students consisted of 3th to 6th grades were involved in the study. Using the van Hiele levels of geometrical thought, children's reasoning types for identifying a figure as a triangle or non-triangle were categorized into visual reasoning, reasoning based on the figure's attributes and formal reasoning. The figure's attributes were further divided into critical and non-critical attributes. Most children identified a figure as a triangle or non-triangle based on critical attributes of the figure(e.g. closed figure, three, vertices, straight sides etc.) Some children identified a figure based on non-critical attributes of the figure(e.g. the length of the sides, the measurement of the angles, or the orientation of the figure). Particularly, some children who had lower levels of geometry identified a figure using visual reasoning, taking in the whole shape without considering that the shape is made up of separate components.

• Journal of the Korean Society for Precision Engineering
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• v.14 no.2
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• pp.136-144
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• 1997

Usually triangular patches are used to transfer geometric shape in Rapid Prototyping CAM system. STL, a list of triangles, is de facto standard in RP industry. Because STL does not have topological infoma- tion, it can cause errornous results. So STL should be verified before using. After adding support structures to anchor the part to the platform and to prevent sagging or distortion, slicing and layer by layer manufactur- ing process are done. But triangular patch is surface model and cannot provide sufficient information on geometry in the above processes. So, geometric modeling is necessary in verifying STL, adding support structures and slicing. It is natural that triangle based modeling is the best when tringular patches are used as input. Considering support structures, solid and faces coexist in RP process. Therefore non-manifold modeler is required. In this study, triangle based non-manifold geometric modeling is proposed for RP sys- tem consistent with STL input.

• Journal of Advanced Marine Engineering and Technology
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• v.21 no.5
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• pp.571-578
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• 1997

This paper presents a method for designing a control system to stand upright inverted triangle. A linearized model is obtained form the nonlinear system by Taylor series expansion and a state controller is designed based on the model. After implementing the control system which is combined control law and estimator with reference input, experiments are carried out to stand upright inverted triangle at any angluar position.

• Journal of the Korean Data and Information Science Society
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• v.18 no.3
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• pp.793-801
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• 2007

For multiply Type-II censored samples from a half-triangle distribution, the maximum likelihood method does not admit explicit solutions. In this case, we propose some explicit estimators of the location parameter in the half-triangle distribution by the approximate maximum likelihood methods. We compare the proposed estimators in the sense of the mean squared error for various censored samples.

• Journal of the Korean Data and Information Science Society
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• v.20 no.5
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• pp.961-969
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• 2009

A hybrid censoring is a mixture of Type-I and Type-II censoring schemes. This paper deals with estimation based on Type-I hybrid censored samples from the half triangle distribution. We derive some estimators of the scale parameter of the half triangle distribution based on Type-I hybrid censored samples. We compare the proposed estimators in the sense of the mean squared error for various censored samples.

• Journal of the Korean Data and Information Science Society
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• v.19 no.3
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• pp.951-957
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• 2008

We derive some approximate maximum likelihood estimators(AMLEs) and maximum likelihood estimator(MLE) of the scale parameter in the half-triangle distribution based on progressively Type-II censored samples. We compare the proposed estimators in the sense of the mean squared error for various censored samples. We also obtain the approximate maximum likelihood estimators of the reliability function using the proposed estimators. We compare the proposed estimators in the sense of the mean squared error.

• Journal of Information Processing Systems
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• v.13 no.4
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• pp.818-833
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• 2017

This paper introduces a new algorithm that renders motion blur using triangular motion paths. A triangle occupies a set of pixels when moving from a position in the start of a frame to another position in the end of a frame. This is a motion path of a moving triangle. For a given pixel, we use a motion path of each moving triangle to find a range of time that this moving triangle is visible to the camera. Then, we sort visible time ranges in the depth-time dimensions and use bitwise operations to solve the occlusion problem. Thereafter, we compute an average color of each moving triangle based on its visible time range. Finally, we accumulate an average color of each moving triangle in the front-to-back order to produce the final pixel color. Thus, our algorithm performs shading after the visibility test and renders motion blur in real time.

• 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.