EUROGRAPHICS 2002 / I. Navazo Alvaro and Ph. Slusallek (Guest Editors) Short Presentations Real-time 3D Deformations by Means of Compactly Supported Radial Basis Functions Nikita Kojekine, Vladimir Savchenko , Mikhail Senin , Ichiro Hagiwara Faculty of Engineering, Tokyo Institute of Technology, 2-12-1, O-okayama, Meguro-ku, Tokyo 152-8552, Japan. Abstract We present an approach to real-time animation of deformable objects. Optimization of algorithms using compactly supported radial basis functions (CSRBF) allows us to generate deformations performed fast enough for such real-time applications as computer games. The algorithm described in detail in this paper uses space mapping technique. Smooth local deformations of animation objects can be defined by only a moderate number of control vectors and locality of deformations can be defined by radius of support. We also present examples of animations and speed benchmarks. Categories and Subject Descriptors (according to ACM CCS): I.3.7 [Computer Graphics - Three-Dimensional Graphics and Realism]: Animation 1. Introduction Many recent works have focused on using shape transforma- tion as a basic operation in computer graphics. Here, we con- sider the problem of transformation a given geometric shape into another in a continuous manner. In fact, if we want to use the method of fitting a surface into a set of control points as a design tool, it is important to assure that our fitting method does what our intuition would expect. On the other hand, we want to perform such deformations in real-time. Important examples of surface deformations have been in- vestigated during the past few years. Various strategies were proposed to minimize user interaction; however, the prob- lem of fitting a surface to a set of control points in real-time still remains a largely unsolved issue of great practical im- portance. Our main goal was to obtain an algorithm performing fast, plausible and smooth deformations. For this purpose we optimize the algorithms to reduce their computation time. For example, these algorithms can be applied, in computer Faculty of Computer and Information Sciences, Hosei University, 3-7-2 Kajino-cho Koganei-shi, Tokyo 184-8584, Japan. Moscow Institute of Physics and Technology, Kerchenskaya str., house 1"A", building 1, Moscow 113-303, Russia games. This optimization not only allows to perform com- plex deformations in real-time, but also saves memory re- quired for animation. For example, in the most popular 3D game engines (Quake, Unreal, Half-Life) for skeleton ani- mation of models all coordinates of all points of an object are stored for every frame of animation, what leads to huge amount of data stored for each model. When we use the de- scribed technique, only a small amount of additional infor- mation is needed. In this paper we propose a CSRBF-based 1 mechanism for calculating the interpolated points of a deformed surface of the animation object. This paper extends the work of Ko- jekine et al. 2 , where software tools based on CSRBFs were designed and applied for surface reconstruction of 3D geo- metric objects. The rest of the paper is organized as follows. The next sec- tion gives an overview of shape transformation techniques and of works related to animation and surface reconstruc- tion and deformation problems. In Section 3 we discuss the mathematical background of our algorithm, and in Section 4 we present the algorithm. Sections 5 and 6 show exam- ples of animation and speed benchmarks. Section 7 contains conclusions and discusses the future work. c The Eurographics Association 2002.