SOFA框架：交互式物理模拟的多模型方法

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"SOFA: A Multi-Model Framework for Interactive Physical Simulation" 这篇文档主要介绍的是SOFA框架，一个用于交互式物理模拟的多模型框架。SOFA（Simulation Open-Source Framework阿法）是一个开源项目，旨在提供一个灵活且可扩展的平台，支持多种物理模拟和计算方法，特别适用于生物力学领域的研究。在科学文献发表与传播方面，HAL（Hyper Article en Ligne）是一个多学科的开放存取档案，它允许发布和传播各种科研文献，无论这些文献是否已经出版。HAL由法国及国际的教学和研究机构，以及公共或私人研究中心贡献其研究成果。文档在HAL上的提交表明，SOFA框架的研究成果也得到了广泛的分享和认可。 SOFA框架的核心特性在于它的多模型能力，这意味着它可以处理不同类型的物理模型，如刚体动力学、流体动力学、软组织力学等。这使得SOFA成为进行复杂交互式物理模拟的理想工具，尤其在医疗、工程和游戏行业中，这些领域经常需要精确地模拟真实世界的物理行为。文档的作者包括François Faure、Christian Duriez、Hervé Delingette等人，他们都是在生物力学建模和计算机辅助技术方面有深厚研究的专家。论文中可能详细讨论了SOFA如何实现高效、实时的物理模拟，以及如何通过其插件系统来支持新模型和算法的集成。此外，还可能涉及到SOFA在软组织生物力学建模中的应用，如Yohan Payan的“Soft Tissue Biomechanical Modeling for Computer Assisted Surgery”。 SOFA框架是科学研究和工程实践中一个重要的工具，它为研究人员提供了丰富的功能来模拟和理解复杂的物理现象，特别是在生物力学和互动物理模拟的领域。其开源性质和多模型支持促进了跨学科的合作，加速了新理论和技术的发展。通过HAL这样的开放存取平台，这些研究成果得以广泛传播，对全球的科研社区产生了积极影响。

6 Authors Suppressed Due to Excessive Length

2.2 Other physical models

Research on interactive medical simulation is often limited to (bio-) mechanical as-

pects. However, an important step needs to be accomplished to better capture the

physiology of the patient. This involves integrating into the simulation more infor-

mation relevant to the procedure, which can be of different nature such as electrical

or ﬂuid.

In order to simulate ﬂuids in a free environment (like blood leaks) Smoothed-

Particle Hydrodynamics (SPH) models can be employed. This Lagrangian model

is similar to the deformable models described previously: a set of particles, with a

given mass, are linked by a force function. The method is mesh-free: at each step

of the simulation, particles are grouped by neighborhoods and attraction-repulsion

forces are computed between them. As the method relies on particles, the coupling

with deformable model can be easily done by repulsion forces (see Figure 3). More

advanced ﬂuid models, based on Eulerian approaches, were also implemented in

SOFA (see [29] for instance).

Fig. 3 Simulation of interaction between a ﬂuid model and a cloth model in SOFA.

The ﬂexible structure of Sofa allows the simulation of non-mechanical phenom-

ena such as electrical waves in cardiac electrophysiology. While this topic is a work

in progress in Sofa, different ways of modeling these electrical waves have been

implemented, namely with an eikonal approach and with monodomain cell models,

see Section 6.1.

When simulating the evolution of a physical ﬁeld deﬁned on a mesh, the state

vectors of the electric potential are placed in a new component named Electrical-

State (see Figure 4). A further extension of the framework has been to allow the

coupling between mechanical and physical model evolution.

2.3 Collision models

When a lot of primitives come into contact, collision detection and response can

become the bottleneck of a simulation. Several collision detection approaches have

been implemented: distances between pairs of geometric primitives (triangles and

spheres), points in distance ﬁelds, distances between colliding meshes using ray-

SOFA, a Multi-Model Framework for Interactive Physical Simulation 7

Fig. 4 Electrophysiology model: a dedicated component implements the propagation of the poten-

tial ﬁeld, based on the model of Monodomain Cell.

tracing [18], and intersection volume using images [3]. The collision pipeline is

described in section 4.4 with more detail.

In order to adapt the models to the data structure of the different collision algo-

rithms, a separate collision model is employed. This model is similar to an internal

model, except that its topology and its geometry are of its own and can be stored in

a data structure dedicated to collision detection. For instance, the component Trian-

gleModel is the interface for the computation of collision detection on a triangular

mesh surfaces.

If collision detection takes too much time, or if we wish to model contacts using a

small number of points, the collision mesh can be set coarser than the internal mesh.

Conversely, if precise collision detection and response between detailed surfaces is

needed, it is sometimes suitable to use more detailed mesh for collision detection.

2.4 Visual models

In the context of surgical simulation for training, to reach the state of what is often

called suspension of disbelief i.e. when the user forgets that he or she is dealing with

a simulator, there are other factors than the mechanical behavior. Realistic rendering

is one of them. It involves visually recreating the operating ﬁeld with as much de-

tail as possible, as well as reproducing visual effects such as bleeding, smoke, lens

deformation, etc. The main feature of the visual model of SOFA is that the meshes

used for the visualization can be different from the models used for the simula-

tion. The mappings described in section 2.5 maintain the coherency between them.

Hence, SOFA simulation results can easily be displayed using models much more

detailed than used for internal mechanics. They can also be rendered using external

libraries such as OGRE

and Open Scene Graph

www.ogre3d.org

www.openscenegraph.org

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SOFA框架：交互式物理模拟的多模型方法

SOFA A Multi-Model Framework for Interactive Physical Simulation 翻译

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