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.
Highlights
With the rapid development of the gaming industry, the demand for a high degree of accuracy in game scenes has led to the increasing need to quickly animate more detailed 3D models
By setting the time variable involved in mathematical expressions defining dynamic 3D models to different values, some keyframes simulated by PBD can be replaced by those generated with the corresponding dynamic partial differential equation (PDE)-based modelling
We have developed a new method to reconstruct dynamic 3D models obtained from position-based dynamics simulation
Summary
With the rapid development of the gaming industry, the demand for a high degree of accuracy in game scenes has led to the increasing need to quickly animate more detailed 3D models. Since the solution to ODEs may involve complicated mathematical functions such as sine and cosine functions and/or their combinations with other mathematical functions, a single ODE patch has the potential to create a more complicated shape than polygon modelling and a single Bézier, B-spline, and NURBS patch with the same number of design variables. By setting the time variable involved in mathematical expressions defining dynamic 3D models to different values, some keyframes simulated by PBD can be replaced by those generated with the corresponding dynamic PDE-based modelling. Motivated by the above discussions, this paper will combine the fourth-order ordinary differential equation, describing the bending deformations of elastic beams, with Newton’s second law of motion, which describes the underlying physics of object movements, to achieve physics-based dynamic simulation while avoiding heavy numerical calculations of physics-based simulations.
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