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.

Online games require small data of 3D models for low storage costs, quick transmission over the Internet, and efficient geometric processing to achieve real-time performance, and new techniques of facial blendshapes to create natural facial animation. Current geometric modelling and animation techniques involve big data of geometric models and widely applied facial animation using linear interpolation cannot generate natural facial animation and create special facial animation effects. In this paper, we propose a new approach to integrate the strengths of ODE (ordinary differential equation) sweeping surfaces and Newton's second law-based facial blendshapes to create 3D models and their animation with small data, high efficiency, and ability to create special facial effects.

The emergence of position-based simulation approaches has quickly developed a group of new topics in the computer graphics community. These approaches are popular due to their advantages, including computational efficiency, controllability, stability and robustness for different scenarios, whilst they also have some weaknesses. In this survey, we will introduce the concept of the baseline position based dynamics (PBD) method and review the improvements and applications of PBD since 2018, including extensions for different materials and integrations with other techniques.

Cross-section curves play an important role in many fields. Analytically representing cross-section curves can greatly reduce design variables and related storage costs and facilitate other applications. In this paper, we propose composite generalized elliptic curves to approximate open and closed cross-section curves, present their mathematical expressions, and derive the mathematical equations of surface reconstruction from composite generalized elliptic curves. The examples given in this paper demonstrate the effectiveness and high accuracy of the proposed method. Due to the analytical nature of composite generalized elliptic curves and the surfaces reconstructed from them, the proposed method can reduce design variables and storage requirements and facilitate other applications such as level of detail.