实时布料模拟技术研究

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"实时布料模拟技术" 在计算机图形学领域，实时布料模拟是一个重要的研究方向，它涉及到了物理模拟、碰撞检测以及图形渲染等多个方面。"Real-Time Cloth Simulation"这篇论文由Robert Bargmann撰写，他在2003年的夏季以此为主题完成了他的SSC（可能是指学士或硕士毕业论文）。论文的指导老师包括了Markus Gross教授、Sabine Süssstrunk教授以及Matthias Teschner博士，分别来自ETHZ/CGL（瑞士联邦理工学院/计算图形学实验室）和EPFL/LCAV（洛桑联邦理工学院/音视频实验室），这些机构都是在计算机图形学研究领域的知名学府。论文的核心内容是基于Layered Depth Images (LDIs)的快速碰撞检测方法。LDIs是一种用于实时3D环境中的高效碰撞检测技术，通过利用深度图像来简化物体间的碰撞检测过程。作者提出了一种新的处理布料自碰撞和布料与可变形体积碰撞的策略。这种方法特别关注实时性能，目标是在保持30帧每秒（fps）的帧率下，同时进行布料的物理整合，处理布料自身的碰撞以及与可变形物体的碰撞。布料模拟的关键挑战在于如何在不影响视觉效果的前提下实现高效率的计算。传统的布料模拟算法通常需要大量的计算资源，难以满足实时性要求。Bargmann的方法试图解决这一问题，通过对布料模型的优化和碰撞检测的改进，使得模拟过程可以在较短的时间内完成，从而实现在游戏和虚拟现实应用中的流畅体验。在布料自碰撞处理上，论文可能介绍了如何避免布料内部的穿透现象，保持其物理真实感。对于布料与可变形物体的碰撞，比如人物或其他动态对象，论文可能会讨论如何准确地计算接触点，确保布料能够自然地附着或与这些物体交互，同时保持物理一致性。这篇论文对实时布料模拟进行了深入研究，为游戏开发、电影特效以及虚拟现实等领域提供了重要的理论和技术支持。通过结合高效的碰撞检测技术和优化的布料模拟算法，它为实现高质量、高帧率的布料动画提供了一个有力的解决方案。

Kinematical tracking : when a proximity is detected, one considers the

current velocities of the triangles and deduces if a collision occurred

previously.

Consistency checking and correction : previous approaches are not de-

terministic, so adding a consistency checking is necessary. It is based

on collision regions.

Except for the integration, the approaches presented here are slow and

roughly described. In our work, the collision detection uses the LDI which

allows us to perform it in real-time.

Collision Response [Hec97] (1997)

The collision response presented in this article is for instantaneous collisions

and does not consider forces involved in the collision process. These forces

are important for collisions of ﬂexible bodies, where the elasticity of the

bodies aims at bringing the bodies back to their rest state and would produce

an acceleration of the bodies. This is therefore only usable for rigid bodies.

The approach here is however similar to ours even if we deal with de-

formable objects. We must clearly make the distinction between ﬂexible

and deformable volumes in that the ﬂexible ones can change their geometry

through collision or any external force but they will return to a rest state.

Deformable models change their geometry according to a function of time

and collisions can be treated as those for the rigid bodies.

A diﬀerence with our approach is that the collision detection in this

article is supposed to detect whenever two bodies are in contact, i.e. touching

but have not penetrated each other. The way we pull a point outside of a

volume is not described.

The article ends by considering the angular velocity of the bodies. Ad-

mitting that a body always rotates around its center of mass, and knowing

the geometry of the body, one can always tell the velocity of any point of

the body. But in our case, the relative position of the points with a rotating

axe changes over time. We compute the velocity of the faces of our volumes

from the distance they traversed since their last know position. Thus, the

component of the velocity due to rotation is included.

Collision and Self-Collision Detection: Eﬃcient and Robust

Solutions for Highly Deformable Surfaces [VM95] (1998)

Self-collision is time costly and few algorithms oﬀer at the same time ac-

curacy and eﬃciency. It is probably the bottleneck of all cloth simulation

regarding computation time and no bounding volume approach can be use-

ful.

This article proposes an algorithm based on surface discretization al-

lowing to handle complex situations, including wrinkling. Throughout the

list of our selected articles, it is actually the most often used algorithm for

self-collision.

The approach is based on optimizing common collision detection tech-

niques by lowering the test number in delimiting regions that can not be

self-colliding.

Such regions have the property that the normals all their faces have a

positive dot product with some common vector. If the projection of the

border of the region onto an orthogonal plane to the common vector does

not self intersect, then the region is not self-colliding. Extensions allow also

avoiding collision tests between adjacent regions.

Finally, these properties coupled with a fast hierarchical algorithm, pro-

duces performances where the time spent on self-collision detection is pro-

portional to the number of colliding elements.

The second half of the article goes further beyond the detection of col-

lision but presents a way to react to it. This is called the orientation con-

sistency which will pull the surfaces back, once a proximity or collision is

detected, to the correct sides of the surfaces. The approach taken for this

part, is based on consistency tracking when we store the history of the

surfaces location so to remember where their last position was before the

collision.

Large Steps in Cloth Simulation [BW98] (1998)

This paper presents an approach for implementing cloth simulation. The

advantages with this method are that they allow great time steps between

two consecutive integration steps. We will not discuss this aspect here as it

is not a part of the cloth modeling we are investigating. However, there is a

paragraph on collision which is of interest for us.

For the detection phase of the collision, the authors refer to another

article of theirs [BW92] that is adequate for ﬂexible bodies as clothes are.

In the response phase, when two faces are detected to be colliding, a strongly

damped spring is inserted between them to push them apart. This response

might be of great interest for our work as we are currently setting up a

new approach for detecting self-collisions but have not thought yet of an

appropriate response.

Interactive Animation of Cloth-like Objects for Virtual Real-

ity [DMB] (2000)

In this more recent paper, a modiﬁcation to the largely used mass-spring

model for simulation cloth is presented. It introduces the implicit integration

which replaces the forces at time t by the ones at time t+dt. This alternative

allows greater stability in the system and thus larger time steps. The ﬁrst

three parts of the paper discuss the implicit integration.

The fourth part is devoted to external forces. Beginning by considering

forces induced by wind or ﬂuid ﬂows, collision is then considered.

Nevertheless, they use a voxel-discretization of the bounding-boxes ap-

proach which does not consider self-collision of the cloth. The collisions are

related to the voxels who have each of them been associated to a closest

vertex of the body. This approach is similar to ours as we use the LDI-

sticks instead of the voxels. It diﬀers in that we make a triangle association

rather than a vertex association. This diﬀerence gives us a more accurate

projection direction to pull the points out of the volume and a better com-

putation of the response. Furthermore, we are able to modify the length of

the sticks, whereas the voxels are rigid cubes, allowing us to have a more

ﬂexible proximity detection and response treatment.

Improved Collision Detection and Response Techniques for

Cloth Animation [MKE02] (2002)

This paper focuses on collision detection, self-collision detection and col-

lision response for deformable bodies. It is based on diﬀerent previous

works mainly on hierarchical bounding volumes [VT94], collision prediction

(proximities) through k-DOPs bounding volumes [KHM

98] and heuristics

[VT94]. It presents a system by merging and improving these techniques.

A k-DOP (discrete oriented polytype) is a convex polyhedron deﬁned

by k half spaces. It allows a more precise enclosure of volumes than the

traditional rectangular bounding-boxes. To perform proximity detection or

collision prediction, the k-DOP gets inﬂated in the direction of its movement.

A hierarchy is then generated within the bounding volumes by recursively

splitting it into k-DOPs, thus generating a tree data-structure until one

single polygon remains per leaf.

Collisions can then be detected by recursively traversing the inﬂated

hierarchies of two colliding bodies. When two or more candidate faces are

returned, they are passed to the collision response. Self-collision detection

proceeds in a similar way but uses also adjacency and curvature properties

of the body. The self-collision turns out to be very eﬃcient.

The idea is to preserve large time steps and stability by detecting col-

lisions before they occur. Two diﬀerent types of collisions are considered:

ﬁrstly, between two deformable faces, and secondly, between a deformable

face and a rigid environment-face. In the second case, we must consider

a transfer of momentum. The further computations for the response are

comparable with what we have presented until now and we will not discuss

them here any longer.

The results presented at the end of this paper show great eﬃciency.

However, we cannot consider the diﬀerent approaches related here as they

are not easily compatible with the architecture we are working with.

Real-time Animation of Dressed Virtual Humans [CMT02]

(2002)

This document is the ﬁrst claiming eﬀective real-time cloth-simulation. The

work presented describes rather an overall optimization than bringing new

more eﬀective integration methods or collision algorithms.

The idea here is to decrease the computations necessary for a fully

dressed human, by classifying clothes with regard to their usual behavior

when worn. The considered cloth-types are the following:

Stretch clothes : tight clothes that remain at a constant distance to the

body and for which no or few simulation is needed. The mesh of the

cloth is attached to the body.

Loose clothes : like sleeves or trousers. The tissue cannot be attached

to the body but one deﬁnes latitudes along the arm or the leg, cloth-

points can be assigned to remain on a same plane deﬁned by these

latitude. This means it is not possible any more to roll up trousers or

sleeves.

Floating clothes : the common considered cloth for simulation. The cloth

can move freely (dress, cape, etc.) still with control points attached to

thebodysotoﬁxthetissueasabeltwoulddo.

Interactive Animation of Cloth including Self Collision Detec-

tion [FGL03] (2003)

This paper is very recent and presents an interactive system for animating

cloth. It ﬁrst describes a integration method allowing large time steps while

keeping high stiﬀness of the cloth. The integration method is based on

discretizing the cloth into particles and assigning constraints to them, mainly

a minimum distance constraint preventing particles to come too close to each

other.

The minimum distance constraint will be reused in the self-collision de-

tection. Instead of correcting collisions once they occur, the constraint will

prevent them. However, a proximity test is still necessary between all par-

ticles and a hierarchical structure is implemented.

Although this approach allows very rapid computations, it still is not

robust enough and is not able to treat a collision whenever it might occur.

Also, even if computations are drastically reduced, it is indicated that over

1600 particles, the simulation slows down and the self-collision process must

be bypassed.

For the experimental part, the cloth is tested onto a static rigid volume

and there are no considerations regarding collision with deformable bodies.

Computational Aspects of Dynamic Surfaces [Bri03] (2003)

This last document is the Dissertation for the Degree of Philosophy from

Robert E. Bridson. It is the most recent document we have, dealing with

cloth simulation. Whole chapters are dedicated to integration methods,

collision detection and response, but the presented approaches aim to get

the most realistic possible simulations using often diﬀerent techniques to

achieve the necessary precision. Thus, no real-time aspect is considered

even if eﬃciency is clearly one of the most important parameters.

2.3 Summary

As we have seen, investigation on cloth modeling began in 1992, with a paper

from Baraﬀ and Witkin [BW92] where they deal with deformable ﬂexible

bodies and present approaches to detect collisions and perform eﬃcient re-

sponse.

In 1995, Volino and Thalmann [VCT95] present an approach for cloth

integration based a mass-spring system. They consider collisions and already

distinguish proximities from interferences.

Hecker then describes, in a game programming journal, an eﬃcient way

to handle collision response [Hec97]. It is on his approach that the collision

response for our system is based.

One of the ﬁrst, and nowadays one of the most widely used, self-collision

algorithm is proposed by Volino and Thalmann in 1998 [VM95]. The ap-

proach studies the curvature of the cloth and deﬁnes regions where no self-

collision can occur; collisions can then be detected by searching intersecting

regions.

The same year, Baraﬀ and Witkin [BW98] show how simulations can be

accelerated by presenting methods allowing larger time steps in the cloth in-

tegration without loosing on stability. Moreover, they consider self-collisions

and propose to separate colliding regions of a cloth by inserting small springs

between them.

In the year 2000, Meyer, Bebune, Desbrun and Barr [DMB] propose

an implicit cloth integration method, which allows to use even larger time

steps. For handling collisions, they make a voxel-discretization of the space

for fast proximities detections.

Recently, in 2002, Mezger, Kimmerle and Etzmuss [MKE02] implemented

many of the diﬀerent existing techniques in a single system. Although they

did not achieve real-time simulations, they clearly deﬁned collision handling

as being the bottleneck for interactive simulations.

The same year, Cordier and Thalmann [CMT02] showed how it is pos-

sible to optimize systems simulating a large number of clothes at the same

time, by making a distinction among the diﬀerent clothes. Clothes are sep-

arated into three categories, the stretched ones, that require few computa-

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