Transplanting and Editing Animations on Skinned MeshesYuntao [email protected] [email protected] [email protected] of Computer ScienceUniversity of Illinois at Urbana-ChampaignAbstractSkinned Mesh Animation (SMA) well approximates amesh animation with extracted bones and their transfor-mations. However, unlike skeleton, bones in SMA are notorganized in hierarchies, thus they need mesh dependenttranslation vectors which prevent other sources of motion(i.e. skeletal animations, MoCAP, SMAs etc) from being ap-plied to the skinned mesh. In this paper, we propose a newand fast method to transplant motion to skinned meshes.By efficiently solving a linear least-squares system, we cancompute new translation vectors which enable the motion towork on the skinned mesh. Based on the same idea, we havealso devised a SMA editing tool which allows users to editframes of the SMA interactively. Furthermore, the editingcan be propagated to all subsequent frames.1. IntroductionSkeletal animation is one of the most important prob-lems in computer graphics and it has received a great dealof attention from the animation community. It is the stan-dard way to do large scale character animations. As a re-sult, it is commonly used in computer game programmingand the movie industry. The strength of skeletal animationis that once the skeleton is available, the animation can beeasily manipulated and many nice approaches for skinningcan be applied. Common skinning approaches include SSD,smooth skinning, linear blend skinning [7], enveloping [12],example based methods [5, 11, 4, 9] and so on. A good sum-mary of research in this area can be found in [5, 9].James and Twigg extended approaches for skinning char-acters to the general setting of skinning mesh animations(SMA)[2]. With an input mesh animation, their method canautomatically extract a fixed number of bones from thesemeshes, as well as the transformations of these bones ineach frame. Each mesh vertex is weighted by several bones.With these weights and the bones’ per-frame transforma-tions, a skinned mesh animation can be constructed, whichwell approximates the original mesh animation.Different from the hierarchical bone structure of skeletalcharacters, in skinned meshes, there is no structure definedamong the extracted bones. As a result each bone needs itsown rotation matrix and translation vector. The translationvectors make SMA mesh dependent. Thus, we can neitherapply other sources of motion to the skinned mesh nor editthe SMA [1]. This limits the use of the SMA technique.Within our knowledge, there has been no research address-ing this problem yet.In this paper, we propose a new and fast method to trans-plant different sources of motion to skinned meshes. Thisis accomplished in three steps. First, the rotation matricesof the bones are extracted from the motion. Second, the restpose of the motion is aligned with that of the skinned mesh’sanimation, which makes the rotation matrices applicable tothe skinned mesh. Finally, new bone translation vectors arecomputed by efficiently solving a linear least-squares prob-lem. Based on the same idea, we also implemented a SMAediting tool which allows users to edit the poses in framesof the SMA interactively, and the editing can be propagatedto all subsequent frames.The rest of the paper is organized as follows: in Sec-tion 2, we will explain how to transplant motion to skinnedmeshes, then we will show how to apply the same idea toSMA editing in Section 3, results and discussion are givenin Section 4 and the conclusions are in Section 5.2. Transplant motion to skinned meshes2.1. Problem definitionSuppose we are having two different animations AaandAb, where Abis a skinned mesh animation (SMA) definedon skinned mesh Mb. If we want to apply the motion of Aato Mb, we call the problem transplanting motion to skinnedmeshes. Here, Aacan be any kind of animation, as long asit has bones and transformations defined on the bones. Forinstance, Aacan be a skeletal animation, MoCAP, SMA andFigure 2. Aligning rest poses to the same (approximately) bind pose.handradiushumerusheadroottibiafemurthoraxFigure 1. Bones mapping.so on. For simplicity, in the rest of the paper, we will illus-trate our method with Aadefined as a skeletal animation,and the method can be extended to other cases similarly.Suppose the bone set of Maand Mbare Baand Bbre-spectively. We assume that Baand Bbare similar to eachother, which is a reasonable assumption for transplantingmotion. Thus, we can manually build a bone mapping fromBbto Ba. The mapping does not need to be a one-to-onemapping, as long as the mapping is reasonable. One exam-ple that we are using is shown in Figure 1. The left skele-ton, which has 31 bones, is from the CMU motion capturedatabase1. The right skinned mesh has 11 bones. An injec-tive mapping from the skinned mesh to the skeleton can bebuilt.After setting up the bones mapping, for each bone Bibin Bb, we find its corresponding bone in Ba, suppose it isBja. Then we extract the motion from Bja’s transformationmatrices, and fit the motion to Bib. This is done in threesteps, extracting rotations, aligning the rest poses, and solv-ing translations using a linear least-squares method.2.2. Rotation extractionA transformation matrix is a four by four matrix. It con-tains rotation, translation and scaling of a bone in one frameof the animation. Rotation is defined in the upper left threeby three block of the transformation matrix and it controls1http://mocap.cs.cmu.edu/, Carnegie Mellon University (CMU) Graph-ics Lab Motion Capture Databasethe angle of the bone. So the motion of the animation is de-termined by the rotation. There are several methods to ex-tract a rotation matrix from a general matrix. In our imple-mentation, we used the polar decomposition method [10].With polar decomposition, we can extract the rotationfrom transformation matrices of Ba, we denote them as Ra.2.3. Rest pose alignmentThe rotation matrices Racannot be applied to Bbdi-rectly, because they are defined relative to the rest pose ofbones Bain animation Aa. The rest pose here means thepose in the first frame of the animation. An example of arest pose is shown in the rightmost image of Figure 2.In order to apply the rotations Rato Bb, we need to de-fine an intermediate pose, through which we can align therest poses of two animations. The intermediate pose is aconfiguration of bones, which both rest poses of two ani-mations can be