• International Journal of CAD/CAM
• /
• v.7 no.1
• /
• pp.91-101
• /
• 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.

• The KIPS Transactions:PartA
• /
• v.13A no.3 s.100
• /
• pp.267-274
• /
• 2006

This paper describes a method to achieve different level of detail for the given volumetric data by assigning weight for the given data points. The relation between wavelet transformation and alpha shape was investigated to define the different level of resolution. Scattered data are defined as a collection of data that have little specified connectivity between data points. The quality of interpolant in volumetric trivariate space depends not only on the distribution of the data points in ${\Re}^3$, but also on the data value (intensity). We can improve the quality of an approximation by using wavelet coefficient as weight for the corresponding data points.

• Journal of Astronomy and Space Sciences
• /
• v.15 no.1
• /
• pp.27-38
• /
• 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 $H{\alpha}$.

• Journal of Korea Multimedia Society
• /
• v.25 no.4
• /
• pp.559-567
• /
• 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.