A 3D SIMULATION OF A GAME OF BILLIARDS

USING A HAPTIC DEVICE

Lucio Tommaso De Paolis, Giovanni Aloisio

Department of Innovation Engineering, Salento University, Lecce, Italy & SPACI Consortium, Italy

Marco Pulimeno

SPACI Consortium, Italy

Keywords: Computer Game, Force Feedback, Simulation, Virtual Reality.

Abstract: Performance improvements in graphics hardware and the diffusion of the low cost haptic interfaces have

made it possible to visualize complex virtual environments and provided opportunities to interact with these

in a more realistic way. In this paper a Virtual Reality application of a game of billiards is presented. By

means of a commercial haptic interface a force feedback is provided, thus rendering the interaction realistic

and exciting to the user; the introduction of the force feedback allows the user to actually feel the contact

between cue and ball. The virtual environment has been built using the development environment XVR and

rigid body dynamics have been simulated utilizing the ODE library. Since in the real game it is possible to

use the left hand when aiming and striking the ball, in the play modality it is possible to fix the cue

movement in the desired direction in order to allow a more careful aim and a more stable interaction in the

virtual environment. In addition it is possible to choose the force with which the ball is hit.

1 INTRODUCTION

The field of computer entertainment technology has

aroused a great deal of interest recently among

researchers and developers in both academic and

industrial fields as it is recognized as showing

promise in terms of generating exciting new forms

of human computer interaction.

Techniques used in computer entertainment are

also seen to translate into advances in research work

ranging from industrial training, collaborative work,

novel interfaces, novel multimedia, network

computing and ubiquitous computing.

At the same time, performance improvements

in graphics hardware and the diffusion of the low

cost haptic interfaces have made the visualization of

complex virtual environments possible and provided

us with the opportunity to interact with these in a

more realistic way.

Haptic feedback in virtual environments makes

it possible to increase the overall realism of a

simulation by improving the user experience.

Haptic interfaces in virtual environments have

been intensively studied in the past decade. Different

types of haptic interface are used in virtual games

which provide multimodal feedback creating a

deeper sense of being in control of the game, of

participation.

Players like to get some bodily feedback, be it

vibration, movement or other. Vibration is a

practical and important way of providing users with

haptic feedback. It requires a minimal interface

design and is low both in terms of complexity and

cost. Vibration feedback joysticks are widely used

input devices in current games.

Lindeman and al. investigated how vibro-tactile

feedback improves task performance (Lindeman,

Sibert, Mendez, Patil and Phifer, 2005).

Walters described the technical background of

haptics and games and shows the first steps of

integrating haptics in PC based games. He concludes

by stating that the force feedback devices are now

readily available to consumers looking for good

force response in their games (Walters, 1997).

Haptic Battle Pong is a pong clone with haptic

450

Tommaso De Paolis L., Aloisio G. and Pulimeno M. (2008).

A 3D SIMULATION OF A GAME OF BILLIARDS USING A HAPTIC DEVICE.

In Proceedings of the Third International Conference on Computer Graphics Theory and Applications, pages 450-455

DOI: 10.5220/0001097804500455

 SciTePress

control through the SensAble Phantom device. Force

feedback is used to haptically render the contact

between the ball and the paddle. Although it

provides force to the user it does not allow free

bodily action because of the device’s restrictions

(Morris and Joshi, 2004).

Jiang et al. modified Half-Life and added force

and vibration feedback. Their aim was to find out

the effectiveness of feedback in a virtual reality

training environment. The study concluded that

haptic feedback plays an important role as it reduced

the error rates of the players (Jiang, Girotra,

Cutkosky and Ullrich, 2005).

Snibbe et al. described a set of techniques for

manipulating digital media with force feedback

(Snibbe, MacLean, Shaw, Roderick, Verplank and

Scheef, 2001).

Hayward et al. provided an introduction to

haptic interfaces and a summary of devices

(Hayward, Astley, Cruz-Hernandez and Grant,

Robles-De-La-Torre, 2004).

Salisbury et al. provided a survey of some

haptic systems and discussed some haptic rendering

algorithms (Salisbury, Conti and Barbagli, 2004).

Some virtual simulations of a billiards game

have been developed with and without the force

feedback sensation.

Gourishankar presented the HAPSTICK, a high

fidelity haptic simulation of billiards game. The

system incorporates a low cost interface designed

and constructed for the haptic simulation of the

billiards game; the device allows motion in three

degrees of freedom (two rotations: pitch and yaw,

and one translation) with haptic feedback along the

translation. The game also includes an auditory

feedback (Gourishanker, 2006).

Takamura et al. presented a billiards game

simulation and the method used in this research

contributes to build a game with high reality. The

synchronization among visual, auditory and haptic

sensations are attained by SCRAME Net, a fast

network system (Takamura, Abe, Tanaka, Taki and

He, 2006).

Ciger et al. presented a virtual billiard where

ODE has been used to manage the collisions

between the billiard balls and the table; for the

collisions between the cue and any ball an own

collision detector has been created. No force

feedback is provided to the user (Ciger and Yersin,

2004).

2 DESCRIPTION OF THE

TECHNOLOGIES USED

2.1 Phantom Omni Haptic Interface

The haptic interface used in this simulation is the

PHANTOM Omni of SensAble Technologies, Inc.;

the device offers 6 degrees of freedom output

capabilities. The device specifications are reported

in Table 1.

Table 1: Specifications of Phantom Omni Haptic Interface.

Nominal Position

Resolution

~0.055 mm

Workspace > 160 w x 120 h x 70 d mm

Friction < 0.26 N

Maximum Exactable

Force

3.3 N

Continuous Exactable

Force

> 0.88 N

Stiffness

X axis > 1.26 N/ mm

Y axis > 2.31 N/mm

Z axis > 1.02 N/mm

Inertia

(apparent mass at tip)

~ 45 g

Footprint ~ 168 w x 203 d mm

Weight ~1.47 kg

Force Feedback 3 degrees of freedom (x, y, z)

Position Sensing x, y, z (digital encoders)

pitch, roll, yaw (± 5%

linearity potentiometers)

Interface

IEEE-1394

FireWire port

2.2 eXtreme Virtual Reality (XVR)

XVR is an integrated development environment for

the rapid development of Virtual Reality

applications. Using a modular architecture and a

VR-oriented scripting language, XVR content can be

embedded in a variety of container applications

making it suitable for writing content ranging from

web-oriented presentations to more complex VR

installations.

The execution environment, the web browser

plug-in and the virtual machine for this system have

been developed by PERCRO Laboratory of Scuola

S. Anna in Pisa, Italy and the XVR platform has

A 3D SIMULATION OF A GAME OF BILLIARDS USING A HAPTIC DEVICE

451

been used in many virtual reality projects

(Carrozzino, Tecchia, Bacinelli and Bergamasco,

2005).

Originally created for the development of web-

enabled virtual reality applications, XVR has

evolved in recent years into an all-around

technology for interactive applications. Beside

web3D content management, XVR now supports a

wide range of VR devices (such as trackers, 3D

mice, motion capture devices, stereo projection

systems and HMDs) and uses a state-of-the-art

graphics engine for the real-time visualization of

complex three-dimensional models, which is

perfectly adequate even for advanced off-line VR

installations.

XVR applications are developed using a

dedicated scripting language whose constructs and

commands are targeted to VR, and provide

developers with the opportunity to deal with 3D

animation, positional sounds effects, audio and

video streaming and user interaction.

In its current form XVR is an ActiveX

component running on various Windows platforms

and can be embedded in several container

applications including the web browser Internet

Explorer.

It is possible to load additional modules which

offer advanced functionalities, such as support to

VR devices, as a decision was made to keep them

separate so that web applications, which do not

usually need any of these advanced features, are not

afflicted by additional downloading times.

2.3 Open Dynamics Engine (ODE)

The Open Dynamics Engine is an open source, high

performance library for simulating rigid body

dynamics. It is a fully featured, stable, mature and

independent platform with an easy to use C/C++

API. It has advanced joint types and integrated

collision detection with friction.

ODE is useful for simulating vehicles, objects

in virtual reality environments and virtual creatures.

It is currently used in many computer games, 3D

authoring tools and simulation tools.

ODE is a free, industrial quality library for

simulating articulated rigid body dynamics. It is

good for simulating ground vehicles, legged

creatures, and moving objects in VR environments.

ODE is designed to be used in interactive or

real-time simulations and is particularly good for

simulating moving objects in changeable virtual

reality environments.

The ODE collision system provides fast

identification of potentially intersecting objects and

a non-penetration constraint is used whenever two

bodies collide; the current collision primitives are

sphere, box, capped cylinder, plane, ray, and

triangular mesh. However, it can be ignored and an

alternative collision detection can be used (Open

Dynamics Engine, http://www.ode.org).

2.4 OpenHaptics

The SensAble OpenHaptics toolkit enables software

developers to add haptics and true 3D navigation to

a broad range of applications, it can be used for

design and for games and entertainment and also for

simulation and visualization.

Using the OpenHaptics toolkit, developers can

leverage the existing OpenGL code for specifying

geometry, and supplement it with OpenHaptics

commands to simulate haptic material properties

such as friction and stiffness.

The architecture enables developers to add

functionality to support new types of shapes and it is

also designed to integrate third-party libraries such

as physics/dynamics and collision detection engines

(SensAble Technologies, http://www.sensable.com).

Figure 1: Loops of the simulation.

3 SIMULATION DESCRIPTION

The developed application is a simulation of a game

of billiards. To make the game as interactive and

realistic as possible for the user a force feedback is

provided by means of a commercial haptic interface.

In the simulation it is possible to distinguish

three different models: graphical modelling, physical

modelling and haptic modelling.

Each type of modelling can be represented by a

loop executed at a specific frequency; the XVR

application combines all the loops. This is shown in

Figure 1.

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452

3.1 Graphical Modelling

The graphical model consists of a set of 3D objects

modelled using 3D Studio and imported into the

XVR development environment where they are

managed using the XVR scenegraph.

The modelled objects are: the billiard table, the

cue, the billiard balls and the skittles. An example of

billiards with five skittles has been implemented.

XVR provides classes for the lighting, shading

and observation point (virtual camera) management;

in addition it allows the user to superimpose 2D text

onto the scene and this functionality is used in order

to provide the user with messages about the system

conditions, working modality and error states.

Three different working modalities are allowed:

 camera modality the ability to choose

the desired position of the virtual camera (no

force feedback is provided);

 positioning modality when a force

feedback is provided for the user in order to

allow the correct positioning of the billiard balls

in case of necessity or so as to decide the starting

state of the game.

 play modality when the end-effector is

mapped onto the cue and a force feedback is

provided to the user by means of the haptic

interface;

Since in the real game it is possible to use the

left hand when aiming and striking the ball, in the

play modality it is possible to fix the cue movement

in the desired direction in order to allow a more

careful aim and a more stable interaction in the

virtual environment. In addition it is possible to

choose the force with which the ball is hit.

A game situation is shown in Figure 2.

3.2 Physical Modelling

Each object of the scenegraph is modelled from the

physical point of view defining the geometry, the

mass, the inertia, the stiffness and the contact

friction with another one.

The physical modelling definition is carried out

using the functions provided by the library of rigid

bodies dynamic simulation (ODE); this library is

also used to define the dynamics for simulating the

billiard game.

The process of simulating a rigid body is called

integration. Each integration step advances the

current time by a given step size, adjusting the state

of all rigid bodies for the new time value.

The ODE integrator is very stable, but not

particularly accurate unless the step size is small.

Between each integrator step the user can call

functions to apply forces to the rigid body and the

sum of these forces will be applied to the body when

the next integrator step happens.

At each simulation step, ODE is used to check

the collisions between objects and to calculate the

forces of interaction and those applied by the user; in

addition the speed, new orientation and positioning

of the objects are computed. In this way the state of

the system is updated and a new one is provided.

Fig. 2: A game situation.

3.3 Haptic Modelling

Regarding the haptic modelling of the objects that

are present in the virtual scene, two different

solutions have been considered:

 the utilization of the HapticWeb

library of XVR;

 the utilization of the OpenHaptics

library provided with the PHANTOM Omni

haptic device.

The second solution has been chosen in this

application because it permits control at a lower

level of the haptic interface.

The cue is modelled as a rigid body and, in the

play modality, its position and orientation are linked,

using a spring-damper system, to the position and

orientation of the stylus of the haptic interface.

At each step of the simulation the forces

depending on the movement of the stylus are applied

to the cue in order to replicate it as quickly as

possible, while taking care to avoid stylus

displacement. This model is shown in Figure 3.

The user is provided with a force feedback by

means of the haptic interface and calculated

applying the proxy method (Van den Bergen, 2004).

A virtual spring-damper system links the end-

point position of the virtual cue (the proxy) to the

end-effector position of the haptic device. When the

cue is in a free space and no collision occurs, the

A 3D SIMULATION OF A GAME OF BILLIARDS USING A HAPTIC DEVICE

453

Figure: 3: Virtual coupling for the cue movement.

proxy and the end-effector position are the same, but

when the virtual cue collides with an objects in the

virtual scene, the proxy cannot enter the body and

cannot follow the position of the haptic device; so

the positions no longer match and a force is sent to

the user.

The force is calculated using (1), where x is the

distance between the end-effector and the proxy

positions, v is the velocity of the end-effector and k

and b are respectively the spring and the damper

constants (Van den Bergen, 2004).

bvkxF −−=

(1)

The described model is shown in Figure 4.

In this way the forces exercised on the cue by

the colliding objects are sent to the user by means of

the virtual coupling cue-stylus providing the force

feedback due to the impact between the cue and the

other objects.

From the haptic point of view, the scene is

rendered in two different ways: the play modality

and the positioning modality.

Figure 4: Virtual coupling for the force feedback.

In the play modality, the virtual coupling

between the end-effector of the haptic device and the

cue provides the force feedback to be sent to the user

by means of the haptic device. Figure 5 shows a

game phase using the Phantom haptic device.

In the positioning modality, used to allow the

correct positioning of the balls in case of necessity

or to decide the starting state of the game, the balls

in the scene are attracted by the cursor (end-effector

of the haptic device); in this way the selection of the

ball is made very easy.

Figure 5: A game phase.

4 CONCLUSIONS AND FUTURE

WORK

In this paper a Virtual Reality simulation of the

game of billiards is presented. In order to provide

the user with an interactive and realistic interaction a

force feedback is provided by means of the Phantom

Omni haptic interface.

The virtual environment has been built using

the development environment XVR and the rigid

body dynamics have been simulated utilizing the

ODE library.

The introduction of the force feedback makes it

possible to obtain a realistic simulation as it is

possible to strike the billiard ball and to feel the

contact between cue and ball.

The limitations of the simulation are due to the

use of a commercial haptic device which has not

been specifically designed for the game of billiards.

Because of the limited workspace of the haptic

device used, it is not possible to perform some shots,

which, in the real game, require wide movements in

order to be carried out. In addition, it is not possible

to use your left hand in order to stabilize the cue and

to obtain a more precise strike, as would happen in

GRAPP 2008 - International Conference on Computer Graphics Theory and Applications

454

the real game of billiards.

For this reason modifications have been made

to the simulation: the possibility to fix a chosen

direction to the cue during the strike has been

introduced and also the ability to decide on the force

with which to hit the billiard ball. In this way we

have tried to reduce to a minimum the limitations

that were present due to the use of a non specific

haptic device.

In the present configuration of the simulator, a

validation phase will be carried out.

In order to have a general opinion on the

project and to obtain an objective response to the

realism of the game simulator, billiard players will

be asked to try the system out. These players will

respond to a questionnaire with questions about the

game’s playability and the visual and haptic

sensations; suggestions that could help improving

the game simulation will be also asked. The results

of this survey will be used to improve the

performance of the simulator.

In order to obtain a more immersive virtual

environment and to create the illusion of a

stereoscopic image, the utilization of a pair of

shutter glasses has been scheduled; these devices are

able to display alternate frame sequencing for each

eye, thus providing stereoscopic vision.

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