Virtual Liquid Manipulation Using General Shape Vessel
Kenji Funahashi
Nagoya Institute of Technology
Center for Information and Media Studies
Nagoya 466-8555 Japankenji@center.nitech.ac.jp

Abstract
This paper describes a method to realize an interactive
manipulation of virtual liquid using virtual vessels which
are expressed by the general convex shape polyhedron. We
have proposed the liquid manipulation model which hassome functions to treat the relation between the volume ofliquid in a vessel and the height level of liquid surface init while it is tilted. For a general shape vessel, the look uptable to calculate the above functions is implemented. Our
system with this proposed model makes it possible to catchthe liquid using the virtual vessel, to hold the liquid in it,then to spill the liquid by tilting it. Also the system realizes the manipulation to skim the liquid from another liquidvessel.

1. Introduction
In the field of virtual reality for the recent years, many
researches such as [3] have been performed for the interactive manipulation in virtual space. In the conventional
researches, the limitation is that users can manipulate only
the solid objects under these systems.
While in the computer graphics technology, the scene
image of water current have been represented by real-time
simulation [1]. However, an interactive manipulation of thevirtual liquid is not considered in that and other studies.
In this paper, an interactive model to manipulate virtual
liquid using a virtual vessel [2] is described. The main purpose of this model is the realization of the virtual liquid manipulation, while the generation of high quality computer
graphics images or simulating the exact behavior of the liquid, are not the main.
Our system with this proposed model makes it possible
to catch the liquid using the virtual vessel, to hold the liquid
in it, then to spill the liquid by tilting it. Also the system
realizes the manipulation to skim the liquid from anotherliquid vessel.

Yuji Iwahori
Nagoya Institute of Technology
Center for Information and Media Studies
Nagoya 466-8555 Japaniwahori@center.nitech.ac.jp

2. Model for virtual liquid and vessel
2.1. Virtual liquid in virtual space
In this paper, we consider the liquid under the following
conditions.
(1) free fall condition (such as flowing water from a faucet).
(2) stay condition (such as holding water in a cup).
The proposed model represents the liquid in the condition (1) as particles. Each particle moves according to thegravity and the inertia. While, the liquid in the condition (2)is represented as volume. The exchange rate between eachcondition is assumed to be N [particles / volume].

2.2. Model of virtual vessel
A virtual vessel with convex shape is introduced to detect
the interference with liquid. Its position is represented by C,
which is the center of the sphere with radius r including it.
Its direction is represented by θ, φ and ψ, while the tilt isrepresented by θ and φ.
The functions of the vessel with the liquid are defined in
the following. The over flow point F is represented by therelative vector from the point C. When the volume of theliquid in a vessel is V (V ≥ 0), the height level of the liquidsurface H is represented by the relative distance from thepoint C. When the parameter V of the function h is overthe maximum volume Vm, H becomes Fy (Fy is defined as
the vertical coordinate of F). When the parameter H of thefunction v is under the vessel, V becomes 0. When H isabove the point F, V is taken as v(θ, φ, Fy) = Vm(θ, φ) (Fy isindependent of ψ).
F = f (θ, φ, ψ).
H = h(θ, φ,V).

(1)
(2)

V = v(θ, φ, H).

(3)

For a general shape vessel which is expressed by the generalconvex shape polyhedron, the look up table to calculate theabove functions is implemented.

Figure 1. Examples of manipulation on proposed system

3. Interaction model of liquid and vessel
3.1. Liquid in free fall condition and vessel
When the falling liquid (each particle) moves through themouth of a vessel, the status of the liquid changes from thecondition (1) to (2), and the volume of the liquid in it will
be increased according to the exchange rate N.

C language on a graphics workstation SGI O2. As shown in
Fig. 1, the user can catch the falling liquid using the virtualvessel, hold the liquid in it, then spill the liquid. Also itshows that the user can skim the liquid from another vessel.
Through this virtual liquid manipulation system in ourlaboratory, we get some positive evaluations such that “Ifeel that I really manipulate the water (liquid) using a cup.”This system can refresh its screen at 24 frames/sec. as theaverage speed for the representation of around 500 particles.

3.2. Liquid in stay condition and vessel
In this section, we describe the interaction model between a vessel and the liquid in another vessel. In the following, let each vessel be designated as vessel 1 and vessel 2 respectively, also let the symbol of each vessel be designated as subscript 1 and 2 for the distinction. When theequation (4) holds, vessel 1 and the liquid in vessel 2 areinterfered each other.
C1y − r1 < C2y + h2 (θ2 , φ2,V2 ),C2y + h2 (θ2 , φ2,V2 +Vm1 ) < C1y + F1y ,(4)(5)

where C jy is the vertical coordinate of the position C j .
When the equation (5) also holds, the situation is thatthe part of vessel 1 under the over flow point interferes withthe liquid surface of vessel 2. When it does not hold; thesituation is that the liquid in vessel 2 flows into vessel 1,
the volume of the liquid in each vessel is changed with theappropriate rate by applying the above functions [2].

5. Conclusion
In this paper, we described a method for the virtual liquid
manipulation using vessels. The experimental system cancatch the falling liquid, skim the liquid from another vessel, hold the liquid and spill it at an interactive refresh rate.
Users have an impression close to that in the real world.
The system proposed in this paper is under the stageof the realization of the basic functions, and the following
points are remained as the future subjects.
· Vessel expressed by concave polyhedron.
· Condition such as water current.
It is considered that a concave polyhedron vessel should bedivided into some neighboring convex polyhedrons, and thecurrent condition is represented as both particles and volume.

References

3.3. Spilling liquid from vessel
When the volume of liquid in a vessel is over the capacity
by the above interference or tilting it, the part of the liquidin the vessel, which is expressed using the volume, spills at
the over flow point F as particles.

4. Experimental results
Using the model mentioned above, we implemented asystem for the virtual liquid manipulation using vessels in[1] J. X. Chen, N. da Vitoria Lobo, C. E. Hughes, and J. M.
Moshell. Real-time fluid simulation in a dynamic virtual environment. IEEE Computer Graphics and Applications, 17:52–61, 1997.
[2] K. Funahashi and Y. Iwahori. Manipulation of liquid usingcases in virtual space. Proc. of IEEE Roman2000, pages 368–373, September 2000.
[3] M. Shinya and M.-C. Forgue. Laying out objects with geometric and physical constraints. The Visual Computer,11(14):188–201, 1995.