位置驱动的布料湿润模拟技术研究

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"基于位置的布料润湿现象模拟——研究论文" 这篇研究论文"Position-based simulation of cloth wetting phenomena"由Xuqiang Shao、Wei Wu和Baoyi Wang共同撰写，发表于一个权威的科学期刊，DOI为10.1002/cav.1788。论文主要探讨了基于位置的布料润湿现象的模拟技术，旨在通过计算方法模拟现实世界中的布料与液体相互作用的过程。这项工作由中国华北电力大学控制与计算机工程学院和北京航空航天大学虚拟现实技术与系统国家重点实验室的研究人员合作完成。在当今的计算机图形学和虚拟现实中，模拟真实世界的物理现象，如布料的湿润过程，对于提升用户体验和视觉效果至关重要。作者们的工作受到了中国国家自然科学基金（Grant/Award Number: 61502168和61472020）、河北省自然科学基金（F2016502069）、虚拟现实技术及系统国家重点实验室开放基金（BUAA-VR-16KF-03）以及中国国家863计划项目（2015AA016403）的支持。论文的摘要指出，由于基于位置的模拟方法具有高稳定性的特点，它成为解决这类复杂问题的理想选择。传统的布料模拟通常关注其几何形状和力学特性，但对液体与布料接触时的润湿行为却处理得不够精确。研究人员开发了一种新的算法，该算法能够详细模拟布料表面的湿润过程，包括液体如何在纤维间扩散、布料如何因吸水而改变形态等。这种方法不仅提高了模拟的逼真度，而且降低了计算复杂性，使得大规模的布料湿润场景能够在实时系统中得以呈现。论文可能涵盖了以下几个关键知识点： 1. **基于位置的模拟方法**：这是一种简化复杂物理现象的计算技术，它以位置信息为基础，可以有效处理物体的变形和相互作用，尤其适用于布料这类具有大量粒子和复杂交互的系统。 2. **布料润湿现象**：当液体接触到布料时，会发生润湿现象，液体会在布料纤维间扩散，改变布料的表面性质和形状。理解并模拟这种现象对于创建逼真的虚拟环境至关重要。 3. **算法开发**：研究团队设计的新型算法解决了传统方法在模拟布料湿润时的不足，提高了模拟的精度和效率，使得在虚拟环境中更真实地展现布料的动态特性成为可能。 4. **计算机图形学应用**：这种模拟技术的应用领域广泛，包括游戏开发、电影特效、虚拟现实体验等，能够提升这些领域的视觉真实感。 5. **计算效率优化**：为了实现实时的润湿效果，研究者必须优化算法，减少计算负载，确保在有限的计算资源下，模拟过程仍然流畅且准确。通过这些研究，学者们为计算机图形学领域的布料模拟提供了新的理论基础和技术手段，对于推动相关技术的发展和应用有着积极的影响。

4of16 SHAO ET AL.

where x =[x

, x

, … , x

]

is the vector of particle positions and n and m are the number of particles and constraints in

the system, respectively. The strength of each constraint is defined by the stiffness parameter 𝜅

∈[0, … , 1].

To guarantee the positions of all particles satisfying each constraint, PBD needs to find a correction vector Δx =

[Δx

, Δx

, … , Δx

]

such that C(x +Δx)=0. This equation can be approximated by

(x +Δx)≈C

(x)+∇C

(x)·Δx = 0. (2)

The correction vector Δx is restricted to be in the direction of ∇C

(x) to enforce the conservation of linear and angular

momentum

as follows:

Δx =λ

∇C

(x). (3)

Substituting Equation 3 into Equation 2 and solving for λ

and substituting it back into Equation 3 yield the final formula

for Δx as follows:

Δx =

(x)



∇C

(x)



∇C

(x), (4)

where Δx is the same for all particles. If the particles have individual masses, the PBD method weights the corrections

Δx

by the inverse masses w

= 1∕𝑚

for each particle j.

Positions are updated by solving each constraint independently one after the other, and after several iterations, the

velocity is computed as v =

Δx

Δt

. To consider the stiffness of the constraint, PBD multiplies the correction vector Δx by

1 −(1 − 𝜅

)

1∕n

in each iteration

as follows:

Δx =



1 −(1 − 𝜅

)

1∕n



Δx, (5)

where n

is the iteration number and 𝜅

is the user-defined stiffness parameter.

3.2 Water and cloth simulation

We simulate water using the position-based fluid method,

where the density constraint on every water particle i is

defined using an equation of state as follows:

density

(x)=

𝜌

− 1, (6)

where 𝜌

is the rest water density and 𝜌

is calculated by the standard SPH density estimator

as follows:

𝜌



W(x

− x

, h), (7)

where W

= W(x

− x

, h) denotes a Gaussian-like kernel with finite support radius h.

Our position-based cloth solver accepts arbitrary triangle meshes as input. The only restriction imposed on the meshes

is that each edge is shared by at most two triangles. Each vertex o f the mesh is selected as a simulated particle of the

PBD method. On the basis of the cloth simulation approach by Müller et al.,

we iteratively solve two equality constraints

stretch

and C

bend

to simulate cloth. For each edge (x

, x

), we define a stretching constraint imposed on it as follows:

stretch

, x

)=x

− x

− l

, (8)

where l

is the initial length of the edge. For each pair of adjacent triangles (x

, x

) and (x

, x

) sharing the edge

, x

), we generate a bending constraint function

bend

, x

)=acos



− x

)×(x

− x

)



− x

)×(x

− x

)



− x

)×(x

− x

)



− x

)×(x

− x

)





− 𝜑

, (9)

where the scalar 𝜑

is the initial dihedral angle between two triangles.

4 NONLINEAR CLOTH WETTING MODEL

According to Darcy's law,

the wetting of porous cloth is a complex phenomenon caused by capillary forces and gravity. In

order to simulate this phenomenon in the unified PBD framework at a macroscopic scale, we remodel the cloth simulation

particles as porous particles to hold an amount of water. Then, a nonlinear wetting model, which takes into account the

influence of gravity on water absorption, diffusion, and emission, is proposed to update the saturations of cloth particles

to visually realistically simulate cloth wetting.

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