Digital animators require simple tools and techniques that allow them to create computer animations in an easy, fast and intuitive way. To perform this kind of task, several methods are available, like cagebased or skeleton-based skinning. Cages and skeletons allow animators to de ne mesh deformation in order to obtain a character pose. Both of them have di erent pros and cons, and di erent expressive power. We aim to create a new skinning technique using a skeleton/cage hybrid paradigm that merges together the expressive power of both of them, reducing the complexity of pose de nition and making the animation pipeline more simple, intuitive and straightforward.
Nowadays, computer graphics is widely used by all kinds of industries: cinematographics, videogames, engineering, medical and so on. Computer animation is one of the most important branches of computer graphics, and it makes it possible to give the idea of movement of three-dimensional characters or objects.
Artists and digital animators require powerful tools that allow them to generate computer animations in an easy, fast and intuitive way. There are several di erent kinds of techniques that allow to achieve this objective. The main technique used to perform this kind of task is called skinning and makes use of di erent structures in order to obtain mesh deformation that de nes the character poses. Two popular skinning structures are the so-called cages and skinningskeletons. A cage is an external structure that contains a three-dimensional mesh, and the deformation of such mesh is obtained by manipulating the cage vertices. A skinning-skeleton, instead, is composed of bones and/or joints and is an internal structure contained in a three-dimensional mesh. The deformation of the character mesh is obtained by applying geometric transformations to bones and joints.
Cages and skeletons have di erent expressive powers and di erent positive and negative aspects. Skeletons are usually used to perform articulation deformations, while Cages are usually used to perform volumetric deformations. This topic is discussed in details in section 2.
The de nition of character poses is a time-consuming task, and consequently animators need simple and fast techniques that allow them to simplify the animation process. For this reason we want to de ne a new skinning technique, and our aim is to create a skeleton/cage hybrid that merges the expressive power of the skeleton with the one of the cage.
At the state of the art, there are two main works that address this kind of problem but both of them need to rede ne the cage and the skeleton from scratch with some constraints. Our idea, instead, is to merge together already existing cages, with already existing skeletons, proposing an hybrid skinning paradigm. Our goal is also to develop a software tool that allows users to realize deformations using this paradigm. This tool must be fast, simple and more easy to use than other professional software used to realize deformations, like Maya or Blender. In this way, the animator is able to use at the same time both skeletons and cages to realize animations, simplifying the animation pipeline, reducing the animator workload and making the deformation process more intuitive and straightforward.
In section 3 we examine in details the related works discussed earlier, while, in section 4, the preliminary idea is explained. 2 2.1
In order to create an animation and bring a virtual character \to life" we need to produce a sequence of character poses, and we can identify several techniques used by digital animators that ful l this purpose. One of the most popular techniques is the skeleton-based or cage-based skinning.
Usually, a three-dimensional character is a polyhedral structure called mesh composed of vertices, edges and faces. The faces can be composed of triangles, quads, general polygons, or a combination of all these.
The pose of the character mesh is obtained by deforming the mesh itself, moving all its vertices and, consequently, all the faces and edges. A mesh can be composed of millions of vertices and, in order to de ne a pose, manually edit every single vertex would be an impossible task for an animator, for this reason the skinning techniques were created.
The skinning process de nes how the geometric surface of the character must
deform, i.e. how its vertices (with faces and edges) must move, according to a
function de ned by deformation primitives [
During the rigging phase, the artist speci es the in uence of every single deformation primitive on every mesh vertex de ning the so-called \weights", so that the deformation of a handle will propagate to every single vertex proportionally to the amount of in uence that the handle has on each single vertex. The skinning weights can be computed automatically by using several techniques, or can be de ned manually, with greater precision, by a rigging artist.
In synthesis, the skinning process is considered an essential task because it simpli es the whole deformation process. Indeed, it prevents digital animators from manually editing every single vertex of the mesh to make it move and allows them to simply associate a group of vertices to a single handle or multiple handles. This is necessary especially if we want to animate a very complex three-dimensional character composed of thousands or millions of vertices. For this reason it is clear that it is easier to manipulate single handles to obtain a deformation (needed to represent a pose) rather than a very large amount of vertices.
Deformations can be performed through di erent kinds of deformation primitives, and according to the structure of those primitives, we can talk of skeletons or cages, whose advantages and disadvantages must be taken into account according to the morphology of the digital character. In some contexts, the choice of a speci c handle deeply simpli es the work of the animators and enables them to improve the graphical result.
In the next paragraphs the details of cages and skeletons are discussed, and
further information about all the skinning techniques can be found in [
A skeleton is a structure contained inside the character skin. It is usually composed of bones and/or joints: the rst ones represent the rigid parts of a character and the second ones are usually placed in the character articulation. In a skeleton-based skinning setup, bones and joints can be used as handles to create the deformation and propagate it to the character skin vertices using automatically generated or manually de ned skinning weights. So, skeletons usually represent the articulated portion of a digital character. (Fig. 1)
There are several techniques that make use of skinning skeletons in order
to perform skin deformation (surveys can be found in [
Unfortunately, Linear Blend Skinning presents visual artifacts like volume loss, self-intersection and the so-called \candy-wrapper" artifact, caused by the linear interpolation of the transformation matrices.
Another popular skeleton-based skinning technique is called Dual
Quaternion Skinning [
In a cage-based skinning setup, the cage vertices can be used as handles to create the deformation and propagate it to the character skin vertices by using barycentric coordinates as weights.
The cage-based skinning deformation derives directly from the Free Form
Deformation [
Cage-based deformation, instead, is based on the concept of generalized
barycentric coordinates, through which we are able to express the position of every
character vertex in relation to its cage vertices. There are several de nitions
of barycentric coordinates such as Mean Value [
Skeletons are very useful and intuitive to use for articulated characters such as humanoids. In fact, in order to move an arm, we simply need to manipulate the single bone that represents the arm itself. Instead, using a cage, we need to move all the cage handles that envelope the arm. So, with the skeleton a single handle is needed, while, in the other case, we need to manipulate multiple handles to perform the same deformation.
Vice-versa, cages are very useful for volumetric deformation. For example, if we want to animate a bouncing ball enveloped in a square-shaped cage, we need to only move the top handles of the cage to obtain the deformation and the compression of the ball. Instead, using a skeleton, this would be a less intuitive task because the most trivial skeleton representation for a ball would be a single handle placed in the centre of it, so we need to de ne more complex and less intuitive skeletons, with extra bones and joints, to perform a similar (but not equal) deformation obtainable with a simple cage. Also, if we want to animate a breathing character, we can not accomplish this by using a skeleton. Instead, with a cage, we are able to obtain the breathing e ect by simply moving the portion of the cage de ned around the character's chest.
So, because of the di erent expressive power, the choice between a skeleton and a cage can lead to a reduction or to an increase of the rigging and skinning e orts based on the type of animation we want to realize. For this reason, the de nition of a skeleton/cage hybrid paradigm can merge together all the positive side of skeleton and cages, allowing the animator to use both of them at the same time seamlessly, simplifying and making the animation process more intuitive, and reducing the workload for a digital artist. 3
At the moment, there are two main contributions to the skeleton/cages merging for skinning purposes.
The rst one is the method proposed by Ju et al. with the cage-based
skinning templates [
In this method the skeleton is rigged to a cage and drives the motion of the cage vertices. In details, given the character mesh and a skeleton, the algorithm creates a full cage from \templates", partial cages associated to a particular skeleton part. Then, manipulating the skeleton handles, the algorithm will deform the associated cage using a particular deformation function similar (but di erent) to Linear Blend Skinning. Then the deformation will be propagated from the cage to the character skin using Mean Value Coordinates as barycentric weights.
The main purpose of this work is not to merge together the expressive power of skeleton and cages but to create volume preserving deformations using skeleton handles, overcoming the \candy-wrapper" artifact typical of the Linear Blend Skinning algorithm. (Fig. 6) So, in this case, we do not have a true skeleton/cage hybrid because it is not possible to interact directly with the cage handles to perform the deformation. In fact, to create a pose, the artist must interact only with the skeleton handles and the cage is used only the de ne the skin deformation. Also, the cage must be generated ad-hoc from the associated skeleton, so previously modelled and rigged cages can not be used. Furthermore, all the previously computed skeleton skinning weights must be dropped because the skeleton will be rigged directly to the cage vertex using a speci c function rather than directly to the character skin.
The second method is the one proposed by Jacobson et al. with the Bounded
Biharmonic Weights [
Despite the very good graphical result for the deformation (Fig. 7), the digital artist must necessarily use the bounded biharmonic as skinning weights, so previously computed or manually generated skinning weights can not be used, and all the pre-existing skeleton and cages must be rigged again with the new automatically generated weights. 4
The proposed idea is to formalize a skeleton/cage hybrid that uni es the expressive powers of the skeletons with the ones of the cages. In this way, animators have the freedom to use one kind of skinning primitive rather than the other based on the kind of pose or animation they want to achieve. In fact, as discussed earlier, for articulation deformations, like a humanoid walking or moving its arms, skeleton is the best choice. Instead, for volumetric deformations such as muscle bulging or thinning, a man breathing or a ball bouncing, cage is the best choice.
This new uni ed skinning paradigm must be weight agnostic, in fact, in order to simplify the rigging phase, we want to enable animators to use pre-existing rigged skeletons with pre-existing rigged cages, using the already de ned weights for each structure. By using this approach, in a production studio, there is no need to e ectively create a skeleton, cages or weights from scratch, but an animator can simply adapt the skinning algorithm to operate simultaneously with the previously de ned ones.
In details, if we observe the linear blending equation for skeletons (eq. 1) and the
linear blending equation for cages (eq. 3) we can observe several similarities (as
observed also in [
The idea is to formalize a skinning equation like the following one: vi0 = m X ai;j hj j=1 (4) (5) where ai;j is an\agnostic skinning weight" derived directly from the already de ned ones in the cage and in the skeleton. To do this, we need to nd a \bilateral relation" or a mapping between the cage weights and the skeleton weights, and consequently between the skeleton and the cage. In synthesis, we want to obtain a function f that, given a cage weight wcage and a skeleton weight wskel, provides an \agnostic" weight a usable on both cage and skeleton: a = f (wcage; wskel)
So, our purpose is to be able to perform a simultaneous and seamless manipulation of all the generic handles h: the manipulation of the cage handles will result in the deformation of the character and of the skeleton and, vice-versa, the manipulation of the skeleton handles will result in the deformation of the character and of the cage. For example, if the animator wants to animate a running man representing also the character's breath, he can use the skeleton handles to de ne the movements of arms and legs, while using at the same time the cage handles to represent the breathing animation. Also, we want to be able to constrain the movement of the cage based on the constraints de ned on the skeleton. In fact, if the skeleton bones are constrained to rotation only and can not be stretched, the relative portion of the cage can not be stretched either. Moreover, constraints de ned on the cage must re ect on the skeleton deformation.
In synthesis, the three main aspects we have to ful l are: { Understand how the manipulation of skeleton handles drives the motion of the cage handles. { Understand how the manipulation of cage handles drives the motion of the skeleton handles. { Choose what kind of skinning formula de nes the physical deformation of the character's skin.
The second task is the most particular because, while the skeleton movements can be reproduced by the cage, this is not true if we switch cage and skeleton. In fact, breathing, bulging or bouncing animation can not be obtained easily (if not at all) with skeletons so we have to understand how these animations obtained with cage handles a ect the skeleton handles. (Fig. 8) For the third task, instead, we have to understand if we obtain a better skin deformation by only using the skeleton-based skinning formula (eq. 1), only using the cage-based skinning formula (eq. 3) or using some form of combination of
The fundamental and novel aspect of this idea is that it does not require to de ne a totally new ad-hoc cage, or ad-hoc skeleton, and is not limited or bounded to a particular type of skinning weight. In this way, the animator can de ne poses for the animation in an intuitive way, using the appropriate type of skinning handle, avoiding the need to de ne extra bones or joints in skeletons to obtain complex animations, and streamlining and simplifying the animation pipeline.
In the nal phase of the project we plan to evaluate the usability of the developed tool, measuring the User Experience while realizing deformations and character poses. We want also to compare the UX against professional software like Maya and Blender, measuring the ease of use and the cognitive load. 5
I am Fabrizio Corda, a PhD student at the Department of Mathematics and Computer Science at University of Cagliari. My work is being conducted into the CG3HCI Lab, the Computer Graphics and Geometry Modelling supervised by the Prof. Riccardo Scateni and followed by Dr. Marco Livesu. I have started