  The morphology of geological particles is crucial in determining its granular
characteristics and assembly responses. In this paper, Metaball-function based
solutions are proposed for morphological characterization and generation of
three-dimensional realistic particles according to the X-ray Computed
Tomography (XRCT) images. For characterization, we develop a geometric-based
Metaball-Imaging algorithm. This algorithm can capture the main contour of
parental particles with a series of non-overlapping spheres and refine
surface-texture details through gradient search. Four types of particles,
hundreds of samples, are applied for evaluations. The result shows good matches
on key morphological indicators(i.e., volume, surface area, sphericity,
circularity, corey-shape factor, nominal diameter and surface-equivalent-sphere
diameter), confirming its characterization precision. For generation, we
propose the Metaball Variational Autoencoder. Assisted by deep neural networks,
this method can generate 3D particles in Metaball form, while retaining
coessential morphological features with parental particles. Additionally, this
method allows for control over the generated shapes through an arithmetic
pattern, enabling the generation of particles with specific shapes. Two sets of
XRCT images different in sample number and geometric features are chosen as
parental data. On each training set, one thousand particles are generated for
validations. The generation fidelity is demonstrated through comparisons of
morphologies and shape-feature distributions between generated and parental
particles. Examples are also provided to demonstrate controllability on the
generated shapes. With Metaball-based simulations frameworks previously
proposed by the authors, these methods have the potential to provide valuable
insights into the properties and behavior of actual geological particles.
