Quasi-Static Volume Preserving Deformation Simulation
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current musculoskeletal animation systems, such as those using Position Based Dynamics (PBD) and Extended Position-Based Dynamics (XPBD), fail to effectively preserve volume during deformation, leading to unrealistic simulations and high computational costs, especially in quasi-static scenarios.
Innovation Solution
A method combining a Finite Element Method (FEM) material model with a symplectic integrator, using a mesh representation and positional constraints to estimate vertex positions, ensuring volume preservation and improved computational efficiency through iterative constraint projection and implicit integration techniques.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If Position Based Dynamics (PBD) or Extended Position-Based Dynamics (XPBD) is used to simulate soft tissue deformation, then computational efficiency is improved, but volume preservation is lost leading to unrealistic simulations
Solution Approach 1:
The patent merges PBD's efficient constraint projection approach with FEM's material model-based volume preservation by formulating FEM equations as positional constraints within the PBD framework. This combination allows the system to achieve both computational efficiency from PBD and accurate volume preservation from FEM, resolving the contradiction between productivity and reliability.
Solution Approach 2:
The patent introduces a symplectic integrator as an intermediary between the FEM material model and the PBD constraint projection. This integrator serves as a mediator that combines the benefits of both approaches, enabling volume-preserving deformation while maintaining the computational efficiency of PBD through iterative constraint satisfaction.
2Reliability
If Finite Element Method (FEM) is used to simulate solid body deformation, then volume preservation and material property control are improved, but computational cost increases and real-time simulation becomes infeasible
Solution Approach 1:
The patent segments the FEM computation by applying FEM material models only as constraint equations rather than solving the full FEM system globally. This segmentation allows volume preservation to be maintained through localized constraint projection while avoiding the high computational cost of complete FEM analysis, thus improving productivity without sacrificing reliability.
Solution Approach 2:
The patent replaces the traditional FEM mechanical solver with a constraint-based projection system. Instead of solving FEM equilibrium equations, the system uses iterative constraint projection to achieve similar volume preservation effects, substituting a computationally cheaper approach that maintains the essential mechanical behavior needed for realistic simulation.
3Reliability
If traditional FEM or FVM is used to solve deformation at mesh nodes, then realistic material behavior is achieved, but setup complexity increases and real-time simulation is not suitable
Solution Approach 1:
The patent extracts the essential volume preservation function from the complex FEM setup by formulating it as simple positional constraints. This extraction maintains accurate material behavior through constraint-based FEM equations while removing the complex global solver and setup procedures, thereby reducing device complexity and enabling real-time simulation.
4Productivity
If PBD constraint projection is used without material models, then computational speed is improved, but control over material stiffness and Poisson effect is lost
Solution Approach 1:
The patent incorporates material stiffness and Poisson's ratio as parameters within the constraint projection system. By formulating FEM equations as constraints with adjustable material parameters, the system maintains control over material properties while preserving the high simulation speed of PBD, thus resolving the contradiction between productivity and adaptability.
Data Source
AI summary
A computer-implemented method of simulating deformation of a solid body comprises: defining a mesh representation of the solid body, the mesh representation comprising a plurality of mesh elements, each mesh element defined by a plurality of vertices; receiving a material model comprising one or more material properties of the solid body; and for each of the plurality of vertices defining the plurality of mesh elements, determining a subsequent position of the vertex at a subsequent time step, wherein determining the subsequent position comprises: defining a current position and a current velocity of the vertex; defining a positional constraint of the vertex based on the material model; and computing a subsequent position of the vertex based on at least the current position, the current velocity and the positional constraint.