Abstract
Various classification approaches have been developed for geometric form of crystals. One method involves the generation of three-dimensional (3D) models of crystals, mainly through graphical representations. However, traditional graphical representations mainly depend on symmetrical operations of crystal planes and the application of polar stereographic projections. There is still very few geometric analysis or mathematical expression for the rectangular coordinate system, implying the limited 3D visualization of crystal forms. In this paper, we present a newly geometric analysis that allows 3D visualization analysis of crystal forms and further identifies geometric relations between crystal forms. In detail, crystal models are divided in a 3D rectangular coordinate system within 47 types of geometric form into the tetrahedron, polygon (polyhedron), and cube classes. What’s more, we determine the vertex space coordinates of the 47 types of crystal form through geometric analysis and coordinate calculation of the crystal forms. Last but not least, in order to obtain 3D models of every geometric form under the automorphism of crystals, it is the convex envelope geometric polyhedron algorithm created to calculate the edges and triangular faces by WebGL technology, which makes it possible to accomplish an online interactive 3D crystallographic study system in a web-browser.
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Funding
This article is supported by Research on rapid evaluation method and technology of associated mineral resources based on data sharing and management of oil and gas exploration and development (kt2021-06–15), National Natural Science Foundation of China (No.42271014), and High level talent scientific research start-up fund project of Beibu Gulf University (19KYQD30).
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Conceptualization, H. C. and W. Y.; Data curation, H. C.; Formal analysis, H. C.; Funding acquisition, H. C. and R.W.; Investigation, H. C., W. Y. and R.W.; Methodology, H. C., W. Y. and R.W.; Project administration, H. C.; Resources, H. C. and W. Y.; Software, H. C. and W. Y.; Supervision, H. C.; Validation, H. C.; Visualization, H. C. and W. Y.; Writing – original draft, H. C.; Writing – review & editing, H. C., R.W. and Y. Li.
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Chao, H., Li, Y., Yao, W. et al. Crystal-modeler: A tool for geometric analysis and three-dimensional modeling of crystal forms based on rectangular coordinates in space. Earth Sci Inform 16, 675–693 (2023). https://doi.org/10.1007/s12145-022-00905-5
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DOI: https://doi.org/10.1007/s12145-022-00905-5