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  • Material-Aware Mesh Deformations

    Tiberiu Popa

    University of British ColumbiaDan Julius

    University of British Columbia

    Alla Sheffer

    University of British Columbia

    Abstract

    Most real world objects consist of non-uniform materi-als; as a result, during deformation the bending and shear-ing are distributed non-uniformly and depend on the localstiffness of the material. In the virtual environment there arethree prevalent approaches to model deformation: purelygeometric, physically driven, and skeleton based.

    This paper proposes a new approach to model deforma-tion that incorporates non-uniform materials into the geo-metric deformation framework. Our approach provides asimple and intuitive method to control the distribution ofthe bending and shearing throughout the model accordingto the local material stiffness. Thus, we are able to gen-erate realistic looking, material-aware deformations at in-teractive rates. Our method works on all types of models,including models with continuous stiffness gradation andnon-articulated models such as cloth. The material stiff-ness across the surface can be specified by the user withan intuitive paint-like interface or it can be learned from asequence of sample deformations.

    1 Introduction

    Mesh deformation is an important task in the modelingand the animation of digital models for computer graphics.Since most real world objects are made up of non-uniformmaterials, their behavior during deformation varies acrossthe surface depending on the local material properties. Ide-ally, a mesh deformation tool should satisfy the followingkey requirements: physical plausibility of the results, easeof control, efficiency, and high degree of automation. Exist-ing deformation approaches typically satisfy only a sub-setof these requirements. For example, physics based methodsprovide accurate model behavior, but they are often not in-

    e-mail: stpopa@cs.ubc.cae-mail: djulius@cs.ubc.cae-mail: sheffa@cs.ubc.ca

    Figure 1. Material-aware deformation. Thestiffness of the tentacle is set to be propor-tional to its girth (left) resulting in a spiral likeshape (right and bottom).

    tuitive to control and are usually relatively slow. Skeletondeformations are simple to control and can be implementedefficiently, but their range is typically limited to only a sub-set of models. Purely geometric deformation techniques aregeneral, efficient and intuitive to control; however they usu-ally ignore the properties of the underlying materials, andthus make it difficult to generate physically plausible defor-mations.

    In this paper we introduce material-aware mesh defor-mation, a novel technique that uses material properties toguide geometric deformations. We use these properties tocharacterize the stiffness of the surface, and hence to pro-vide continuous fine control of the surface behavior dur-ing deformation, while maintaining the efficiency, simplic-ity and control specific to geometric methods. The stiff-nesses with respect to bending and shearing are representedas scalar fields over the surface. We use these scalar fieldswithin the geometric deformation framework to distributethe deformation according to the local material propertiesto yield realistic-looking results (Figure 1). Often materi-

  • als may exhibit anisotropic stiffness, for instance articulatedmodels often have joints with only one degree of freedom.We support such anisotropic behavior by allowing three dif-ferent scalar fields for the three orthogonal axes of rotation.We are the first, to our knowledge, to support this feature.

    To control the deformation, users can specify the ma-terial properties using an intuitive paint-like interface. Bysimply marking a horses head as stiff (Figure 2(c)), we di-rect the deformation to the neck of the horse and achievemore realistic results than in Figure 2(b) where the defor-mation is distributed uniformly. Although some existinggeometric methods are capable of achieving similar results,typically they require more user effort to guide the defor-mation.

    In many situations, physically or anatomically correctdeformation samples of a given model may be available. Insuch cases our method can automatically learn the materialproperties from the sample set, thereby allowing users tocreate new deformations which are consistent with the sam-ple set. Each of the deformed sample poses contains im-plicit knowledge of a subset of the material properties. Bycombining the information from all samples, we are ableto reconstruct the scalar fields across the surface. For ad-ditional control, we also allow users to refine the acquiredfields in specific areas of interest where the desired behaviordiffers from that of the sample poses.

    Our main contribution is the introduction of a compactrepresentation for the local stiffness of a surface, and theintegration of this material stiffness into the geometric de-formation framework. Our method is linear, it is simple touse and control, and it creates realistic looking deformationsas discussed in the results section.

    The rest of this paper is organized as follows: Section 2reviews previous work on deformation techniques. Sec-tions 3 and 4 describe our deformation algorithm. Section 5explains how we extend the method to support anisotropicbehavior. Section 6 describes how material properties maybe learned by example. Section 7 presents some exampleresults. Finally, Section 8 summarizes our work.

    2 Previous work

    Researchers have addressed the problems of mesh edit-ing and deformation for over twenty years, creating an im-pressive body of literature and generating several distinctapproaches to the problem. One of the first, yet still ac-tively researched mesh deformation frameworks is that ofspace warping deformations [6, 22, 5, 8]. Since space de-formation techniques transform the underlying space, ratherthan the vertices themselves, it is not possible to incorporatemodel specific properties such as materials into these tech-niques.

    Another common approach is to use physical simulation

    (a) (b) (c)

    Figure 2. Turning a horses head: (a) originalmodel; (b) deformation using uniform mate-rial; (c) material-aware deformation using twodegrees of stiffness.

    methods [30, 29, 15, 21]. These methods naturally incor-porate the material properties and provide physically accu-rate behavior; however, they are often computationally in-tensive, and since their control parameters are typically de-rived from physical equations, they lack intuitive means ofcontrolling the results.

    For articulated models, it is common to use a skele-ton in order to simplify the task of defining the deforma-tion [9, 4, 31]. Most skeleton based deformation methodsdo not generalize to non-articulated models and often pro-vide only binary gradation of stiffness, thus limiting thetype of deformations created. In contrast, our method isnot restricted to a particular type of models and supportscontinuous control over the stiffness of the mesh providingfiner control of the deformation.

    Geometric deformation techniques [1, 26, 19, 23, 32, 14,34, 20, 33, 17, 7] that operate directly on the meshes havebecome increasingly popular in recent years. These meth-ods are both efficient and intuitive to control. However,existing geometric techniques do not capture the materialproperties of the models . Our method uses a geometric de-formation approach but introduces material awareness, intothe framework to provide greater physical plausibility. Thegeometric deformation methods most related to our workare those of Yu et al. [32], Zayer et al. [33] and Igarashiand Moskovitc [14]. Yu et al. [32] perform 3D mesh defor-mation by means of gradient manipulation. First, the posi-tions of some anchor vertices are manually modified by theuser. Next, the resulting local triangle transformations arepropagated to the rest of the mesh according to geodesic dis-tances. Finally, the new vertex positions are computed usingthe Poisson equation. Zayer et al. [33] show that propaga-tion of the transformations according to geodesic distancesis sub-optimal and suggest using harmonic fields as an al-ternative. Neither method considers material properties intheir formulation. Igarashi and Moskovitc [14] deform 2D

  • Figure 3. Algorithm flow.

    meshes using a formulation based on an earlier morphingtechnique [3]. They manipulate the triangles independentlyand then compute common vertex positions. They showearly research results for using material stiffness to controlthe deformation. A direct extension of their method to 3Dwould require a volumetric mesh, thus they acknowledgethat such an extension may be difficult.

    It is often tedious and difficult to define the exact phys-ical properties of an object. One alternative, presented bytwo recent techniques [16, 28], is to create realistic-lookingdeformations by mimicking existing physically correct ex-ample deformations. James and Twigg [16] automaticallydeduce the skeleton of an articulated model from a sam-ple set of deformed models. Using the estimated skele-ton and estimated blending weights they are able to createnew deformations consistent with the sample set. Sumner etal. [28] use the set of sample models to create feature vec-tors that span the space of meaningful deformations. Usingour method, we are able to use a set of sample poses as asource for automatically learning the stiffness of the mesh.The learned stiffness is used to create new poses consistentwith the samples. In our setting the material propertiesare derived explicitly, therefore it is very easy for artists tomodify and refine those if desired.

    3 Method overview

    We present a two-step method for 3D mesh deformationthat takes into account the intrinsic material properties ofthe model. To generate the deformation users select a smallset of triangles,

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