实时2D角色骨骼形状感知变形法：无繁琐权重选择

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本文主要探讨了2D角色形状感知骨骼变形（Shape-awareskeletaldeformationfor2Dcharacters）的一种创新方法，发表于2013年的VisComput会议，期刊引用为DOI10.1007/s00371-013-0817-1。传统的2D角色动画处理中，骨骼变形技术常常依赖于将骨骼绑定到角色形状上，这种方法需要精细的权重分配，以便控制骨骼对形状的影响，这在实际操作中往往较为繁琐。然而，该研究提出了一种新颖的策略，即通过在角色形状上传播骨骼变换。这种方法避免了先前方法中的权重选择过程，简化了工作流程。通过这种传播机制，作者能够更好地利用形状的几何特性，从而有效地防止局部形状扭曲，确保了变形过程的全局一致性。这使得变形更为精确，且在保持视觉效果自然的同时，实现了实时性，能够在动画制作中提高效率。该文章首先介绍了背景，指出2D形状变形在动画和图像编辑中的广泛应用，特别是在动态物体形状变化时。随后，文章详细阐述了作者团队开发的算法原理，如何通过骨骼的运动传递到角色表面，以及这种方法如何在保持视觉效果和谐的同时，避免了形状变形的局部偏差。实验结果显示，新方法不仅能够实时地适应角色动作，而且产生的变形效果具有很高的视觉吸引力。关键词包括形状变形（Shapedeformation）、骨骼（Skeleton）、2D角色动画（2DCharacter Animation）以及形状匹配（Shapematching），这些关键词突出了本文的核心贡献和应用领域。这项工作为2D角色动画的高效、逼真变形提供了一种新的解决方案，对于提升动画制作的质量和效率具有重要意义。

Vis Comput (2013) 29:545–553

DOI 10.1007/s00371-013-0817-1

ORIGINAL ARTICLE

Shape-aware skeletal deformation for 2D characters

Xun Wang ·Wenwu Yang ·Haoyu Peng ·

Guozheng Wang

Published online: 1 May 2013

Abstract This paper presents a skeleton-based method for

deforming 2D characters. While previous skeleton-based

methods drive the shape deformation by binding the skele-

ton to the shape, our method does so by propagating the

skeleton transformations over the shape. In this way, the

tedious process of weight selection in previous skeleton-

based methods is not required. Also, the propagation allows

us to consider the geometric characteristics of the shape

such that local shape distortion can be effectively avoided.

Experimental results demonstrate that our method allows

real-time deformation and generates visually pleasing re-

sults.

Keywords Shape deformation · Skeleton · 2D Character

Animation · Shape matching

1 Introduction

2D shape deformation is widely used in two-dimensional

animation and image editing to represent moving objects

of changing shape. Nowadays, this tool can be commonly

found in commercial software for video editing or 2D char-

acter animation [4], such as Adobe After Effects, Adobe

Flash, or Toon Boom Studio.

Recently, many deformation algorithms that allow the

user to directly manipulate a shape through a click-and-drag

interface have been introduced [8, 28]. By minimizing local

distortion of the shape, these methods can generate pleas-

ing and physically plausible deformation results. However,

X. Wang ·W. Yang (



) · H. Peng · G. Wang

School of Computer Science & Information Engineering,

Zhejiang Gongshang University, Hang Zhou, China

e-mail: wwyang@zjgsu.edu.cn

the click-and-drag interface may fail to control the natural

deformation of 2D characters that have rigid limbs such as

humans or animals (Fig. 1(b)).

For the characters that have a jointed structure, the

skeleton-based approach, which uses a skeleton to control

shape deformation, offers intuitive control as it naturally

manifests the way in which the characters deform. In a typ-

ical workﬂow, the user deﬁnes a skeleton and the system

binds the components of the character to the skeleton such

that each component will follow motions of its associated

skeleton bones: Each point on the character is transformed

by a weighted linear combination of afﬁne transformations

deﬁned by the associated bones [10]. However, binding the

character to a skeleton is not a trivial task, and a tedious

process of weight selection is typically required to obtain

satisfactory deformation results [25].

In [25], Yan et al. decompose the shape into simplices,

i.e., triangles (in 2D) or tetrahedra (in 3D), and use the skele-

ton to control the movement of simplices. In the method,

each simplex is associated with only one skeleton bone, thus

the weight selection issue is avoided. In [9, 22], the inﬂuence

weights of each bone to the shape points are computed as

discrete harmonic functions over a mesh coving the shape.

Since such weights can spread the inﬂuences of the skele-

ton bones in a topology-aware and localized manner, the

explicit binding between the shape and its skeleton is not

needed. Essentially, however, the above methods determine

the shape deformation mainly from the linear skeleton sub-

space, oblivious to the underlying geometric characteristics

of the shape, which would possibly lead to inappropriate dis-

tortion (Figs. 2 and 7).

This paper presents a shape-aware 2D skeletal deforma-

tion method that combines the skeleton-based approach and

the deformation algorithm that considers the shape rigidity.

To make the shape deform naturally relative to the skeleton,

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