{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:02:45Z","timestamp":1760058165211,"version":"build-2065373602"},"reference-count":13,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,3,20]],"date-time":"2025-03-20T00:00:00Z","timestamp":1742428800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computers"],"abstract":"<jats:p>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\u2019s 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 a constant diameter, curved pipes with a constant diameter and straight conical pipes. Analytical expressions are developed to define the position and orientation of points along a pipe\u2019s 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 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\u2019 geometries and improving the realism of simulations and the filling of various vessels can be realistically simulated.<\/jats:p>","DOI":"10.3390\/computers14030112","type":"journal-article","created":{"date-parts":[[2025,3,20]],"date-time":"2025-03-20T12:23:11Z","timestamp":1742473391000},"page":"112","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Algorithmic Generation of Realistic 3D Graphics for Liquid Surfaces Within Arbitrary-Form Vessels in a Virtual Laboratory and Application in Flow Simulation"],"prefix":"10.3390","volume":"14","author":[{"given":"Dimitrios S.","family":"Karpouzas","sequence":"first","affiliation":[{"name":"School of Science and Technology, Hellenic Open University, 26335 Patras, Greece"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0120-0488","authenticated-orcid":false,"given":"Vasilis","family":"Zafeiropoulos","sequence":"additional","affiliation":[{"name":"School of Science and Technology, Hellenic Open University, 26335 Patras, Greece"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0364-5966","authenticated-orcid":false,"given":"Dimitris","family":"Kalles","sequence":"additional","affiliation":[{"name":"School of Science and Technology, Hellenic Open University, 26335 Patras, Greece"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"987","DOI":"10.1021\/ed076p987","article-title":"A General Simulator for Acid-Base Titrations","volume":"76","year":"1999","journal-title":"J. Chem. Educ."},{"key":"ref_2","unstructured":"Zafeiropoulos, V., and Kalles, D. (December, January 29). Quantitative Liquid Simulation in an Interactive 3D Virtual Laboratory. Proceedings of the 22nd Pan-Hellenic Conference on Informatics, Athens, Greece."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1006\/gmip.1996.0039","article-title":"Realistic Animation of Liquids","volume":"58","author":"Foster","year":"1996","journal-title":"Graph. Models Image Process."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2182","DOI":"10.1063\/1.1761178","article-title":"Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid with Free Surface","volume":"8","author":"Harlow","year":"1965","journal-title":"Phys. Fluids"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Stam, J. (1999, January 8\u201313). Stable Fluids. Proceedings of the 26th Annual Conference on Computer Graphics and Interactive Techniques, Los Angeles, CA, USA.","DOI":"10.1145\/311535.311548"},{"key":"ref_6","unstructured":"Stam, J. (2003, January 4\u20138). Real-Time Fluid Dynamics for Games. Proceedings of the Game Developer Conference, San Jose, CA, USA."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1145\/357318.357320","article-title":"Particle Systems\u2014A Technique for Modeling a Class of Fuzzy Objects","volume":"2","author":"Reeves","year":"1983","journal-title":"ACM Trans. Graph."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Clavet, S., Beaudoin, P., and Poulin, P. (2005, January 29\u201331). Particle-Based Viscoelastic Fluid Simulation. Proceedings of the 2005 ACM SIGGRAPH\/Eurographics Symposium on Computer Animation, Los Angeles, CA, USA.","DOI":"10.1145\/1073368.1073400"},{"key":"ref_9","unstructured":"Medveck\u00fd-Heretik, J. (2018). Real-Time Water Simulation in Game Environment, Masaryk University, Faculty of Informatics."},{"key":"ref_10","unstructured":"Hass, J.R., Heil, C.E., and Weir, M.D. (2019). Thomas\u2019 Calculus: Early Transcendentals in SI Units, Pearson. [14th ed.]."},{"key":"ref_11","unstructured":"(2025, January 13). Creating a Mesh. Available online: https:\/\/catlikecoding.com\/unity\/tutorials\/procedural-meshes\/creating-a-mesh\/."},{"key":"ref_12","unstructured":"Jewell, T. (2025, January 13). How to Improve Reaction Time: Tips for Gaming and Other Sports. Available online: https:\/\/www.healthline.com\/health\/how-to-improve-reaction-time."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"101028","DOI":"10.1016\/j.gmod.2019.101028","article-title":"Liquid-Solid Interaction Sound Synthesis","volume":"103","author":"Cheng","year":"2019","journal-title":"Graph. Models"}],"container-title":["Computers"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-431X\/14\/3\/112\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:57:19Z","timestamp":1760029039000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-431X\/14\/3\/112"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,20]]},"references-count":13,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2025,3]]}},"alternative-id":["computers14030112"],"URL":"https:\/\/doi.org\/10.3390\/computers14030112","relation":{},"ISSN":["2073-431X"],"issn-type":[{"type":"electronic","value":"2073-431X"}],"subject":[],"published":{"date-parts":[[2025,3,20]]}}}