A Fluid Resistance Map Method for Real-time Haptic Interaction with Fluids Yoshinori Dobashi Hokkaido University Kita-ku, Kita 14, Nishi 9 Sapporo 060-0814, Japan +81.11.706.6530 doba@nis-ei.eng.hokudai.ac.jp Makoto Sato Tokyo Institute of Technology 4259 Nagatuta Yokohama 226-8503, Japan +81.45.924.5050 msato@pi.titech.ac.jp Shoichi Hasegawa Tokyo Institute of Technology 4259 Nagatuta Yokohama 226-8503, Japan +81.45.924.5050 hasegawa@pi.titech.ac.jp Tsuyoshi Yamamoto Hokkaido University Kita-ku, Kita 14, Nishi 9 Sapporo 060-0814, Japan +81.11.706.6530 yamamoto@ist.hokudai.ac.jp Mitsuaki Kato The University of Tokyo 7-3-1, Hongo, Bunkyo-ku Tokyo 113-8656, Japan +81.4.7136.3942 kato@fel.t.u-tokyo.ac.jp Tomoyuki Nishita The University of Tokyo 5-1-5, Kashiwanoha Kashiwa 227-8561, Japan +81.4.7136.3942 nis@is.s.u-tokyo.ac.jp ABSTRACT Haptic interfaces enable us to interact with a virtual world using our sense of touch. This paper presents a method for realizing haptic interaction with water. Our method displays forces acting on rigid objects due to water with a high frame rate (500 Hz). To achieve this, we present a fast method for simulating the dynamics of water. We decompose the dynamics into two parts. One is a linear flow expressed by a wave equation used to compute water waves. The other is a more complex and non- linear flow around the object. The fluid forces due to the non- linear flow is precomputed by solving Navier-Stokes equations, and stored in a database, named the Fluid Resistance Map. The precomputed non-linear flow and the linear flow are combined to compute the forces due to water. CR Categories I.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism - Animation; Virtual Reality; I.6.5 [Simulation and Modeling]: Model Development – Modeling methodologies; I.6.3 [Simulation and Modeling]: Types of Simulation - Animation. General Terms Algorithms. Keywords Virtual Reality, Haptics, Fluid Resistance, Simulation, Computational Fluid Dynamics. 1. INTRODUCTION Intuitive and natural interactions with virtual world are key mechanisms for enhanced perception of the virtual worlds. The haptic rendering is one of such technologies and many methods have been presented [16] [17] [18]. In a typical virtual reality system with a haptic interface, the user controls the movement of a virtual object using the haptic interface, and the system computes forces when the object contacts with other objects. The user can also feel the resulting forces via the haptic interface. This provides the user with a natural interactions with the virtual world. Previous methods have efficiently displayed forces between rigid objects and forces due to soft objects [3] [11] [18] [19]. In this paper, we focus on haptic interactions and rendering with fluids, especially water. In computer graphics, while several publications exist on the visual simulation of fluids such as smoke, water [5] [9] [10], there are few published techniques for the haptic interaction and rendering with fluids. Examples of the forces due to interaction with fluids are aerodynamic resistances on an airplane, hydrodynamic resistances on a ship, water buoyancy, frictional and pressure resistances with the oars of a boat, and a lure used in fishing. In this paper, we present a method for very rapidly estimating and displaying forces acting on a virtual object due to water. In the field of computational fluid dynamics and ship design engineering, researchers have developed methods to numerically estimate the resistance due to fluids by solving the Navier-Stokes equations [1] [6]. However, their estimation techniques while numerically accurate are prohibitively time consuming. This is especially true for haptic rendering, where a high frame rate is required. We additionally present a water simulation model for haptic interactions. We decompose dynamics of water into two parts, a linear flow and a non-linear flow. The linear flow is the flow far from the object. The linear flow is well approximated by wave equations derived by linearizing Navier-Stokes equations under the assumption that the flow of water is slow. However, this assumption is not valid for the flow close to the object. The flow around the object is complex and highly non-linear. This non- linear flow has to be computed by directly solving the Navier- Stokes equations, which unfortunately is compute intensive. So we precompute the non-linear flow around the object and create a database, which we call a fluid resistance map, or FRM for short. ------------------------------------------------------ Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. VRST'06, November 1–3, 2006, Limassol, Cyprus. Copyright 2006 ACM 1-59593-321-2/06/0011...$5.00.