Osman Zeki Okuyucu^*

CMES-Computer Modeling in Engineering & Sciences, Vol.133, No.3, pp. 653-671, 2022, DOI:10.32604/cmes.2022.021081

Abstract In this study, we examine the possible relations between the Frenet planes of any given two curves in three dimensional Lie groups with left invariant metrics. We explain these possible relations in nine cases and then introduce the conditions that must be met to coincide with the planes of these curves in nine theorems. More >

Afzan Adam^1,*, Abdul Hadi Abd Rahman¹, Nor Samsiah Sani¹, Zaid Abdi Alkareem Alyessari¹, Nur Jumaadzan Zaleha Mamat², Basela Hasan³

CMC-Computers, Materials & Continua, Vol.67, No.1, pp. 761-777, 2021, DOI:10.32604/cmc.2021.014599

Abstract Boundary effect in digital pathology is a phenomenon where the tissue shapes of biopsy samples get distorted during the sampling process. The morphological pattern of an epithelial layer is greatly affected. Theoretically, the shape deformation model can normalise the distortions, but it needs a 2D image. Curvatures theory, on the other hand, is not yet tested on digital pathology images. Therefore, this work proposed a curvature detection to reduce the boundary effects and estimates the epithelial layer. The boundary effect on the tissue surfaces is normalised using the frequency of a curve deviates from being a straight line. The epithelial… More >

V. Ungvichian¹, P. Kanongchaiyos¹

CMES-Computer Modeling in Engineering & Sciences, Vol.77, No.3&4, pp. 201-220, 2011, DOI:10.3970/cmes.2011.077.201

Abstract This paper describes an enhancement to Garland and Heckbert's mesh simplification method by using the principal curvatures and directions of each vertex. We calculate the values and directions, before using them to determine the absolute normal curvature in the direction of contraction, and multiplying the curvature with the edge length, the maximum absolute cosine of the angles between the edge and the normals of faces adjacent to either endpoint, and the quadric error of the collapse. We also apply penalties based on compactness and angular and dihedral deviations of the resulting faces. We have implemented these improvements and tested our… More >