¢¡¤£¦¥¨§¤© ¦ £ ££ !"$#&% ¥(')*¥,+-%.%/102¦ !345+¤ %. † Michael D. Smith 6 Thomas W. Sederberg Brigham Young University 798;:&<>=@?;AB< Existing computer supported cartoon inbetweening (CSCI) meth- ods often create inbetweens that are of unsatisfactory quality to professional animators or require too many time consuming adjust- ments to be economical. This paper describes skeletal interpolation a user-guided solution to the path problem in CSCI. When used within a complete CSCI system, skeletal interpolation can cut total animation production time by 75 percent or more while maintaining the artistic quality of the animation. Figure 1: The three drawings in the middle are inbetweens for the key frames indicated by black boxes on the ends. CR Categories: G.1.1 [Mathematics of Computing]: Numerical Analysis—Interpolation H.5.2 [Information Systems]: Information Interfaces and Presentation—User-centered Design I.3.5 [Comput- Most cartoon animation today is created using key frame ani- ing Methodologies]: Computer Graphics—Computational Geome- mation. Creating the inbetweens for this type of animation is a try and Object Modeling laborious and often expensive process [Durand 1991]. The goal Keywords: cartoon animation, inbetweening, interpolation, shape of computer supported cartoon inbetweening (CSCI) systems is to blending lower production costs while preserving artistic freedom. The central task of CSCI is shape blending, or gradually trans- forming one shape into another. In cartoon animation, these shapes C DFE E <>=HGJILKMAB<ONPG are either polygons, polylines or curves. Shape blending algorithms require the solution of two problems: the correspondence prob- lem and the path problem. The correspondence problem consists of Creating traditional cartoon animation is an expensive and often te- finding a continuous mapping between different shapes. This prob- dious process. In recent years, computers have played an increasing lem has been satisfactorily addressed for polygons in [Sederberg role in improving the quality of cartoon animation as well as elimi- and Greenwood 1992] and for curves in [Sederberg and Greenwood nating much of the monotony in inking, painting, and compositing 1995; Cohen et al. 1997]. individual frames of animation. However, attempts to assist in cer- The path problem, which involves defining paths of motion be- tain areas of animation such as inbetweening have enjoyed only tween points in corresponding shapes, remains an ongoing topic of moderate success. research. The purpose of this research is to create natural look- Two approaches are used to create traditional 2D animation: ing inbetweens for shapes like those found in Figure 2. Profes- straight ahead and pose-to-pose (or key frame) animation. In the sional animators remain unsatisfied with current solutions to the straight ahead approach, each frame in the animation is drawn in path problem because the results appear either “mechanical, with- succession. This method is useful in expressing randomness or out any soul” [Bluth and Goldman 2002], or “. take about the spontaneity. In key frame animation, the animator plans out the same time as drawing them by hand” [Fekete et al. 1995]. actions in a scene and draws the most significant poses to represent Motivated by these observations, we worked with traditional car- these actions. Frames called inbetweens are then drawn between toon animators to devise a paradigm that would be familiar to them, these key poses to create a smooth transition from one key frame to address their needs, and speed up overall animation production the next. Figure 1 shows several inbetweens for the two key frames time. Our resulting solution to the path problem is called skeletal marked by black boxes. This method was developed to improve the interpolation. economics of animation by having skilled animators draw the key We created a complete CSCI software package called Tween- frames and less skilled animators draw the inbetweens. It also has Maker in which we implemented and tested skeletal interpolation. the benefit of improving the timing and consistency of an animated From our experience with TweenMaker, we estimate that using sequence [Thomas and Johnston 1981]. skeletal interpolation, a CSCI system can preserve the quality of Q cartoon animation while speeding up production time by a factor of e-mail: [email protected] four. †[email protected] This paper is organized as follows. R 2 discusses advantages and disadvantages of previous solutions to the path problem in CSCI. R 3 presents skeletal interpolation as a solution to the path problem and R 4 gives details about its integration into a full CSCI system. R R 5 presents statistical and visual results, and 6 comments on these results. S T E T T =HU¤VWNPGLKM:YXZG\[]KW<ONPG :^<&G_<>`;U ?W<>` =@GL8a[bUac Solutions to the path problem in shape blending can be divided into automatic and user-guided methods. 1995] uses a global linear transformation to define paths for the inbetweens on a pair of rasterized line drawings. Unpublished solutions include Creature House’s LivingCels that automatically matches and inbetweens the curves in different key frames. This algorithm along with the others mentioned above often give pleasing results and have some useful properties. However, one side effect to these completely automatic approaches is that the results usually appear mechanical and lack expression. ¢¡ ©!#"%$&¦'¨( ¢ (a) An arm flexing using linear motion. User-guided solutions to the path problem recognize that purely au- tomatic methods are not satisfactory in many situations. [Burtnyk and Wein 1976] presents one of the first computer supported car- toon inbetweening algorithms. This approach defines 2D parameter spaces for the line segments in two drawings for which the corre- spondence problem has already been solved. The user controls a polynomial path that describes how the drawings will be distorted from one frame to the next by editing the position of inbetween frames. This method gives encouraging results but requires exten- sive user input to specify correspondences between drawings and fix distorted inbetweens. Both [Reeves 1981] and [Kort 2002] direct the motion of curves from one key frame to another through the use of paths attached (b) An arm flexing along curved paths. to points in a pair of matching curves. The curves and the paths attached to them form a patch network to which an inbetweening algorithm may be applied. While this may provide significant con- Figure 2: Two different solutions to the path problem. trol over the resulting inbetweens, the editing of each of these paths to achieve desirable results generally takes too much time to make it efficient for drawings containing more than a few curves. ¥§¦©¨ ¨ ¨ ¢ ¢¡¤£ In [Litwinowicz 1991], characters are composed of simple ge- ometric primitives such as rectangles, lines, and ellipses. These Fully automatic solutions to the path problem have uses in several primitives are arranged in a transformation hierarchy whose base areas of computer graphics. However, one critical issue that such paths are represented by splines. An animator edits the animation methods overlook in their application to CSCI is that the art of an- of a character by altering the parameters of an inbetween frame. imation does not consist of merely moving things with mathemat- The simple shapes of the character are texture mapped via Coons ical precision, but rather should “give them life” or the illusion of patches to allow a variety of similarly structured characters to use having life [Thomas and Johnston 1981]. This life is based on the the same animation data. Since there is no shape blending or mor- artistic interpretation of the animator. Since fully automatic meth- phing between different drawings, the animation consists of moving ods do not consider artistic interpretation, they are unacceptable as and distorting images in a flat plane. This results in animation that solutions to the path problem in CSCI. lacks depth and expression [Thomas and Johnston 1981; Hopper The simplest automatic solution to the path problem is to move and Gagne 1988; Bluth and Goldman 2002]. the points in a shape along straight lines to their destination posi- To provide life-like movement and artistic input for inbetweens, tion. This works satisfactorily in some simple cases, but in general [Bregler et al. 2002] captures and retargets motion from preexisting gives poor results as shown in Figure 2(a). animation. Although this process serves the objective, it does not Advances over linear interpolation include [Sederberg et al. generate new motions for which there is no existing template. 1993] where corresponding polygons are blended by interpolating There are several commercially available CSCI systems that con- their edge lengths and angles. [Johan et al. 2000] presents a method tain solutions to the path problem. Cartoon characters in Moho that extends [Sederberg et al. 1993] to shapes containing multiple [Lost Marble 2004] consist of 2D models containing a rigid skele- polygons and polylines. [Johan and Nishita 2001] continues work ton. The animator describes the motion for a character by position- on shape blending by first calculating the inbetweens for simplified ing and scaling this skeleton in different key frames which are auto- versions of two polygons and then applying the deformation to the matically inbetweened. This method allows the animator to specify original polygons. inbetweens exactly, but makes it difficult to define expressive mo- [Shapira