Reconstructing Dynamic 3D Models with Small Data by Integrating Position-Based Dynamics and PDE-Based Modelling

Junheng Fang, Ehtzaz Chaudhry, Andres Iglesias, Jon Macey, Lihua You and Jianjun Zhang
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Junheng Fang: The National Center for Computer Animation, Bournemouth University, Dorset BH12 5BB, UK
Ehtzaz Chaudhry: The National Center for Computer Animation, Bournemouth University, Dorset BH12 5BB, UK
Andres Iglesias: Department of Applied Mathematics and Computational Sciences, University of Cantabria, 39005 Cantabria, Spain
Jon Macey: The National Center for Computer Animation, Bournemouth University, Dorset BH12 5BB, UK
Lihua You: The National Center for Computer Animation, Bournemouth University, Dorset BH12 5BB, UK
Jianjun Zhang: The National Center for Computer Animation, Bournemouth University, Dorset BH12 5BB, UK

Mathematics, 2022, vol. 10, issue 5, 1-24

Abstract: Simulation with position-based dynamics is very popular due to its high efficiency. However, it has the weaknesses of lacking details when too few vertices are involved in simulation and inefficiency when too many vertices are used for simulation. To tackle this problem, in this paper, we propose a new method of reconstructing dynamic 3D models with small data. The core elements of the proposed approach are a curve-represented geometric model and a physics-based mathematical model defined by dynamic partial differential equations. We first use the simulation method of position-based dynamics to generate a group of keyframe poses, which are used to create the deformation animation of a 3D model. Then, wireframe curves are extracted from skin deformation shapes of the 3D model at different keyframe poses. A physics-based mathematical model defined by dynamic partial differential equations is proposed. Its closed-form solution is obtained to represent the extracted curves, which are used to reconstruct the deformation models at different keyframe poses. Experimental examples and comparisons made in this paper indicate that the proposed method of reconstructing dynamic 3D models can greatly reduce data size while keeping good details.

Keywords: reconstruction; dynamic 3D models; position-based dynamics; dynamic partial differential equation; closed-form solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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