• International Journal of CAD/CAM
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• 제7권1호
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• pp.91-101
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• 2007

To understand the structure of molecules, various computational methodologies have been extensively investigated such as the Voronoi diagram of the centers of atoms in molecule and the power diagram for the weighted points where the weights are related to the radii of the atoms. For a more improved efficiency, constructs like an $\alpha$-shape or a weighted $\alpha$-shape have been developed and used frequently in a systematic analysis of the morphology of molecules. However, it has been recently shown that $\alpha$-shapes and weighted $\alpha$-shapes lack the fidelity to Euclidean distance for molecules with polysized spherical atoms. We present the theory as well as algorithms of $\beta$-shape and $\beta$-complex in $\mathbb{R}^3$ which reflects the size difference among atoms in their full Euclidean metric. We show that these new concepts are more natural for most applications and therefore will have a significant impact on applications based on particles, in particular in molecular biology. The theory will be equivalently useful for other application areas such as computer graphics, geometric modeling, chemistry, physics, and material science.

• 정보처리학회논문지A
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• 제13A권3호
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• pp.267-274
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• 2006

본 논문은 주어진 자료 점들에게 가중치를 부여하여 볼륨 자료를 여러 단계별로 상세함을 표현하는 방법을 제시하고자 한다. 단계별로 상세함을 표현하기 위하여 웨이브렛 변환 과 알파쉐이프와의 관계를 얻고자 연구하였다. 산포된 자료란 자료점들 사이에 특별한 상관관계가 없는 자료들의 수집이라 정의할 수 있다. 볼륨 트라이베리에이트 공간상에 보간의 정확도는 3 차원 공간상에 흩어진 자료들의 위치정보 뿐만 아니라 자료들이 갖고 있는 값 (명암도)에도 영향을 받는다. 자료 점들에게 각각 해당되는 웨이브렛 계수를 가중치로 부여 하여 근사치의 정확도를 개선할 수 있다.

• Journal of Astronomy and Space Sciences
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• 제15권1호
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• pp.27-38
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• 1998

We discussed four different methods - the single, double and triple Gaussian fits, and the intensity weighted centroid fit - which extract rotation curves from several emis-sion lines(i.e. [OII], $H{\beta}$, [OIII], and $H{\alpha}$) of spiral galaxies. Spatial extents and the shapes of rotation curves derived through various methods applying to each emission lines of a sample galaxy UGC 11635 are all in a good agreement with one another. Linewidths of $H{\beta}$ and $H{\alpha}$ measure from rotation profiles are in a good agreement with $H{\alpha}$ linewidth of Courteau (1992). however, linewidths of [OII] seems to be much broader than $H{\alpha}$, and the profile of [OIII] does not follow the profile of $H{\alpha}$.

• 한국멀티미디어학회논문지
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• 제25권4호
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• pp.559-567
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• 2022

The optimal shipping location is determined by measuring the volume and weights of cargo shipped to non-standard cargo carriers. Currently, workers manually measure cargo volume, but automate it to improve work inefficiency. In this paper, we proposed the method of a real-time volume calculation using LiDar sensor for automating cargo measurement of non-standard cargo. For this purpose, we utilized the statistical techniques for data preprocessing and volume calculation, also used Voxel Grid filter to light weighted of data which are appropriate in real-time calculation. We implemented the function of Normal vectors and Triangle Mesh to generate surfaces and Alpha Shapes algorithms to process 3D modeling.