# Automatic Generation of Dynamic Skin Deformation for Animated Characters

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Related Work

**Automatic rigging**, Generation and placement of an animation skeleton, is developed to avoid tedious and time-consuming manual rigging. Here, an animation skeleton typically consisting of bones and joints is used to drive the movements and deformations of skin meshes, while a curve skeleton is defined as the medial axis [2] or a curve connecting the centers of closed curves on a skin mesh.

**Geometric skin deformation methods**Linear Blend Skinning (LBS) also called skeleton subspace deformation (SSD) is the most well-known geometric skinning algorithm [11] due to its efficiency and simplicity. However, its limitations include collapsing elbow, candy-wrapper effects, and failure of secondary deformation [12]. The authors of [13] proposed one approach to address the deformation of B-spline surfaces while constraining the volume enclosed by the surface. The authors of [14] presented a novel framework to treat shapes in the setting of Riemannian geometry. A novel skinning algorithm based on linear combination of dual quaternions is presented in [15] to tackle some serious drawbacks of linear blend skinning. By introducing an extra scalar weight function per bone, a simple modification of the linear blend skinning (LBS) formulation was presented in [16] that enables stretching and twisting without changing the existing skeleton rig or bone weights. To remedy the problems like collapsing elbow and candy wrapper joint, curve skeletons along with the joint-based skeletons was used in [17] to animate the skin shape. The authors of [18] choose to pre-compute optimized center of rotation for each vertex, and use these centers to interpolate rigid transformations. The authors of [19] firstly provide one pure geometric method which could handle skin contact and muscle bulge problem in real-time, but fails to address deep self-intersections. To solve this problem, [20] use new composition operators enabling blending effects and local self-contact between implicit surfaces, as well as a tangential relaxation scheme derived from the as-rigid-as possible energy to solve the tracking problem. As above mentioned, in recent years, various geometric skinning methods have been proposed to overcome these limitations. But, in spite of its high efficiency, geometric skinning is still less capable of creating highly realistic skin deformations.

**Example-based skin deformation methods**is employed to address the realism issue of geometric skinning, by learning deformation dynamics from a set of given examples [21]. An automated framework was presented in [22] to fit the parameters of a deformation model using a set of examples consisting of skeleton configurations paired with the deformed geometry as static meshes. One parallel deformation method using the GPU fragment processors was developed by the authors of [23]. Joint weights for each vertex are automatically calculated from sample poses, thereby reducing manual effort and enhancing the quality of WPSD (Weighted Pose Space Deformation) as well as SSD (Skeletal Subspace Deformation). One data-driven technique for synthesizing skin deformation from skeletal motion was presented by the authors of [24]. Eulerian representation of skin was proposed in [25] to simulate thin hyperelastic skin that can stretch and slide over underlying body structures such as muscles, bones, and tendons. One automated algorithm, called Smooth Skinning Decomposition with Rigid Bones (SSDR), was introduced in [26] to extract the linear blend skinning (LBS) from a set of example poses. It outperforms the state-of-the-art skinning decomposition schemes in terms of accuracy and applicability. One major disadvantage of example-based skin deformation methods is the design of a sufficient set of example skin shapes in order to produce realistic skin deformations, which is often a non-trivial task in practice.

**Physics-based skin deformation methods**try to simulate the underlying physics to create more realistic skin deformations. The authors of [27] propose a method to simulate human beings based on anatomy concepts. In [28], volume preserving method was presented to avoid extra bulge or wrinkle. A comprehensive biomechanical model of the human upper body was developed in [29] that uses a coupled finite element model with the appropriate constitutive behavior to simulate biomechanically realistic flesh deformations and investigates an associated physics-based animation controller. A physically based simulation system for skeleton-driven deformable body characters is developed in [30] that gives a well-coordinated combination of a reduced deformable body model with nonlinear finite elements, a linear-time algorithm for skeleton dynamics, and explicit integration can boost simulation speed. An efficient algorithm based on a novel discretization of corotational elasticity over a hexahedral lattice is examined in [31] to achieve near-interactive simulation of skeleton driven, high resolution elasticity models, but it still need several seconds per animation frame. The authors of [32] formulate the equations of motions in the subspace of deformations defined by animator’s rig, bringing the benefits of physics-based simulation to enhance the realism of traditional animation pipelines, but need tens of seconds when simulate one normal character model. A closed-form skinning method is proposed in [33] to generate higher quality deformations than both linear and dual quaternion skinning through optimize skinning weights for the standard linear and dual quaternion skinning techniques and introducing joint-based deformers. Elastic animation editing with spacetime constraints was discussed in [34] that not only optimizes control forces added to a linearized dynamic model, but also optimizes material properties to better match user constraints and provide plausible and consistent motion. By minimizing quadratic deformation energy, built via a discrete Laplacian inducing linear precision on the domain boundary, a method was presented in [35] to design linear deformation subspaces, unifying linear blend skinning and generalized barycentric coordinates. A fast physically based simulation system for skeleton-driven deformable body characters is developed in [36] that gives a well-coordinated combination of a reduced deformable body model with nonlinear finite elements, a linear-time algorithm for skeleton dynamics, and explicit integration, to boost simulation speed. In [37], EigenSkin has been presented to correct SSD results, it achieves high frame rates per second, but constructing one proper error-optimal eigen displacement basis requires sufficient experience and background knowledge. Since it is not easy to model the different elastic behaviors of muscle, fat and skin using simple volumetric mesh, [38] introduce one novel multi-layer model to simulate them, but it fails handle collisions during fast motions. The authors of [39] present one computational model for geodesics in the space of thin shells and incorporate bending contributions into deformation energy. Besides, [40] develop a time- and space-discrete geodesic calculus to shoot geodesics with prescribed initial data, they all need heavy computation. The authors of [41] introduce model reduction into dynamic deformation simulations to achieve real-time performance at the cost of decreasing the computational accuracy and increasing the implementation complexity.

**Curve-based methods**have also been proposed for modeling and simulating 3D character models in recent years. For example, [42] proposed sweep-based human deformation. The authors of [43,44] presented a curve-based sweeping surface and dynamic skin deformation method. The authors of [45] discussed the theory, discretization, and numerics of curves which are evolving such that part of their shape, or at least their curvature as a function of arc length, remains unchanged. The authors of [46] sought congruent planar curves to generate or approximately generate a freeform surface. The authors of [1] investigated a finite difference solution to curve-based dynamic skin deformations. The authors of [47] introduce techniques for the processing of motion and animations of non-rigid shapes. Although curve-based approaches simplify physics-based skinning, analytical solutions have not yet been presented to achieve both high efficiency and good realism of physics-based skin deformations.

## 3. Overview

## 4. Identify Iso-Parametric Curves

## 5. Creating Animation Skeleton

## 6. ODE-Based Dynamic Skin Deformation

## 7. Evaluation

#### 7.1. Evaluation of Iso-Parametric Curve Identification

#### 7.2. Evaluation of Animation Skeleton Creation

#### 7.3. Evaluation of ODE Dynamic Skin Deformation

## 8. Discussion and Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 3.**Our iso-parametric curves identifying step transforms a quad mesh (

**a**) into discrete vertices on iso-parametric curves (

**b**).

**Figure 4.**Creation of the animation skeleton. (

**a**) shows one curve skeleton automatically calculated by iso-parametric curves; (

**b**) shows the minimal angle threshold between two connected line segments of a curve skeleton; (

**c**) depicts the joints between the forearm and upper arm determined by the down-sampling algorithm; (

**d**) indicates joints on the skin mesh at the starting pose; in (

**e**), the double pime symbol is used to indicate the joints of the template skeleton; (

**f**) shows the corresponding joints on the skin mesh at the ending pose; (

**g**) is the animation skeleton automatically generated for a human hand; (

**h**) shows some other human skeleton.

**Figure 5.**The models (

**a**) and (

**e**) are input as examples, intermediate models (

**b**–

**d**) are created efficiently, (

**f**) is the rendered model.

**Figure 6.**(

**a**), (

**f**), and (

**k**) are three input example poses, all the frames in (

**b**–

**e**) are in-between poses generated by the proposed approach based on (

**a**) and (

**f**), all the frames in (

**g**–

**j**) are in-between poses generated by the proposed approach based on (

**f**) and (

**k**).

**Figure 8.**Skeleton creation with different methods. (

**a**) skeleton extraction by mesh contraction [5] , (

**b**) skeleton generated by the proposed approach.

**Figure 9.**Comparison results between our automatic rigging algorithm and [3]. (

**a**) and (

**c**) show the rigged results of the proposed method, while (

**b**) and (

**d**) show the rigged results by [3]. Note the skeleton in the ears of (

**b**) actually should be the skeleton in two arms, so the skeleton in (

**b**) may not be optimal for animation purpose.

**Figure 10.**Comparison among different skin deformation methods. (

**a**) this approach, (

**b**) classic linear skinning, (

**c**) dual quaternion skinning.

**Table 1.**Runtime breakdown of our approach when it was used to automatically process the different models. Here, VI: Vertex Identifier on iso-parametric curves, SC: Skeleton Creating, SD: Skin Deformer.

Runtime (ms) | |||||
---|---|---|---|---|---|

Model | Vertices | VI | SC | SD | Total |

Cat | 7207 | 1.32 | 0.269 | 1.517 | 3.106 |

Dancer | 13201 | 2.03 | 0.431 | 2.830 | 5.291 |

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## Share and Cite

**MDPI and ACS Style**

Bian, S.; Zheng, A.; Chaudhry, E.; You, L.; Zhang, J.J.
Automatic Generation of Dynamic Skin Deformation for Animated Characters. *Symmetry* **2018**, *10*, 89.
https://doi.org/10.3390/sym10040089

**AMA Style**

Bian S, Zheng A, Chaudhry E, You L, Zhang JJ.
Automatic Generation of Dynamic Skin Deformation for Animated Characters. *Symmetry*. 2018; 10(4):89.
https://doi.org/10.3390/sym10040089

**Chicago/Turabian Style**

Bian, Shaojun, Anzong Zheng, Ehtzaz Chaudhry, Lihua You, and Jian J. Zhang.
2018. "Automatic Generation of Dynamic Skin Deformation for Animated Characters" *Symmetry* 10, no. 4: 89.
https://doi.org/10.3390/sym10040089