<p class="MDPI12title"><span lang="EN-US">Algorithmic Generation of Realistic 3D Graphics for Liquid Surfaces within Arbitrary-Form Vessels in a Virtual Laboratory and Application in Flow Simulation

Hellenic Open University has developed Onlabs, a virtual biology laboratory designed to safely and effectively prepare its students for hands-on work in the university’s on-site labs. This platform simulates key experimental processes, such as 10x TBE solution preparation, agarose gel preparation and electrophoresis, which involve liquid transfers between bottles. However, accurately depicting liquid volumes and their flow within complex-shaped laboratory vessels, such as Erlenmeyer flasks and burettes, remains a challenge. This paper addresses this limitation by introducing a unified parametric framework for modeling circular cross-section pipes, including straight pipes with constant diameter, curved pipes with constant diameter and straight conical pipes. Analytical expressions are developed to define the position and orientation of points along a pipe's central axis, as well as the surface geometry of composite pipes formed by combining these elements in planar configurations. Moreover, the process of surface discretization with finite triangular elements is analyzed with the aim of optimizing their representation during the algorithmic implementation. The functions of the current length with respect to the volume of each considered container shape are developed. Finally, the methodology for handling and combining the analytical expressions during the filling or emptying of a composite pipe is explained, the filling of certain characteristic bottles is implemented, and the results of the implementations are presented. The primary goal is to enable the precise algorithmic generation of 3D graphics representing the surfaces of liquids within various laboratory vessels and subsequently the simulation of their flow. By leveraging these parametric models, liquid volumes can be accurately visualized, reflecting the vessels’ geometries and improving the realism of simulations, and the filling of various vessels can be realistically simulated.