LOCALIZATION IN AN INTERACTIVE SYSTEM

Juan J. Jiménez, Francisco R. Feito and Rafael J. Segura

University of Jaen, Campus Las Lagunillas s/n, Jaen, Spain

Keywords: Interaction, localization, collision detection, virtual reality, real time, tetra-tree.

Abstract: The localization of the nearest parts of an object to a device is usually solved by means of a proximity

measurement of each one of the features that form this object to the device. In order to perform this

efficiently, hierarchical decompositions of the space or of the object are used, so that the features of objects

are classified into several types of cells, usually rectangular. In this paper we propose a solution based on

the classification of a set of points located on the device in a spatial decomposition named tetra-tree. Using

this type of spatial decomposition gives us several qualitative properties that allow us a more realistic and

intuitive visual interaction. In order to show these properties we have compared an interaction system based

on tetra-trees to one based on octrees.

1 INTRODUCTION

In several virtual reality systems (Burdea and

Coiffet, 2003) it is usual for the user to move a

device through the scene, so that the user tries to

interact with the different objects that form the

virtual world. In order to do this precisely, the

system must provide the user with feedback in the

form of visual information (Sherman and Craig,

2003). This usually consists of such parts of the

object that are interacting or are going to interact.

This information could consist of the parts nearest to

the device, so that the system gives information to

the user about the interactive object features, even

before touching them. In this case the interaction

does not produce undesired effects, such as collision

response (deformation, etc.) without previous

knowledge of the area of interest.

In order to solve this problem, image-based

techniques could be used (Schneider and Klein,

2007), but these tend to be less precise. In addition,

interaction possibilities are limited due to the type of

feedback obtained.

In the case of object-based techniques, it is

habitual to use a proximity measurement from the

device to the objects, aided by a spatial

decomposition or by a bounding volume hierarchy

(Ericson, 2005), in order to classify the triangles of

the object and thereby reduce the number of features

to consider. Grids (Samet, 1990) and octrees (Ayala

et. al, 1985) are usually used for this aim, as well as

AABB-Trees (van den Bergen, 2004), OBB-Trees

(Gottschalk et. al, 1996) and Sphere-Trees

(Hubbard, 1996), among others.

Using these types of decompositions and

bounding volume hierarchies, although they are

appropriate when the device is near the object, do

not give suitable information when the device is at a

greater distance. In addition they present problems

of amplitude and continuity in relation to the

triangles displayed when the device moves.

Due to the aforementioned discussion, we will

use a spatial decomposition based on tetra-cones,

called tetra-tree (Jimenez et. al, 2006). This data

structure is constructed for each object of the scene

in pre-processing time. Simultaneously, the triangles

of the objects are classified in the tetra-cones that

from the tetra-tree of each object.

In interaction time, a set of selected and

significant points from the device are classified in

the tetra-trees of the objects, allowing us in this way

to display the triangles classified in the tetra-cones

in which these points are located. This system will

allow us to perform some operations requested by

the user, i.e. to change the amplitude (triangles to

display) by modifying the depth in the tetra-tree.

In addition this system provides us with a smooth

transition of the displayed triangles when the device

moves, in order to display (or not) the nearest

triangles. All these properties allow us to obtain a

more intuitive system and with better qualitative

properties with regard to other systems.

435

J. Jiménez J., R. Feito F. and J. Segura R. (2008).

LOCALIZATION IN AN INTERACTIVE SYSTEM.

In Proceedings of the Third International Conference on Computer Graphics Theory and Applications, pages 435-438

DOI: 10.5220/0001093604350438

 SciTePress

This paper is organized in the following way: In

the next section the use of the interaction system is

described. After that, a study of some qualitative

properties is carried out, compared with the use of a

octree. Afterwards, the time obtained by the system

is studied for different types of objects. Finally, the

main contributions of this method and the future

work to be undertaken are summarized.

2 INTERACTION SYSTEM

The virtual environment we are dealing with is

composed of objects modelled by means of triangle

meshes. The device can be a hand or a pointing

device (Figure 1). In these cases, several points have

been distributed strategically by the device, so that

they will allow us to determine the triangles of the

objects that are in relative proximity to the device.

Figure 1: Devices used and control points.

Points have been placed mainly in parts of the

device in which presumably the first contact in case

of collision will take place. We have named these

control points. For example, in the hand device

control points are necessary on the endpoint of the

fingers, on the joints and on the palm. In the

pointing device these are necessary on the part

where presumably the interaction will take place, as

well as points uniformly distributed by the device. In

the case of the pencil, only one control point has

been used on its end.

In this system we will consider two possible

situations in which we wish to obtain the triangles

related to the interaction., drawing the triangles

referred to in each case:

Expected triangles: Triangles of the object in

relative proximity to the device in movement,

without collision with the object (Figure 2.a).

Collision triangles: Triangles of the object that

the device interacts with (Figure 2.b). In this case it

is necessary to call the collision detection module in

case a suitable response is needed.

Figure 2: a) Expected triangles for interaction. b) Collision

triangles.

The collision detection module first checks the

collision of the control points with the object. In

order to do this it verifies the inclusion of these

points in each one of the triangles classified in the

tetra-cone in which the control point is included,

using the inclusion algorithm developed by (Feito et.

al, 1997), and optimized for this case, considering

the temporal and geometric coherence. Only if none

of the control points are inside the object is an

intersection test between triangles of the object and

the device required.

This system takes advantage of the temporal and

geometric coherence of the environment when the

device moves through the scene, first verifying the

inclusion of the control points in the tetra-cones in

which they were located in the previous frame, in

order not to classify these points through the

different levels of the tetra-tree. Thanks to the

coherence, most of the time the control points are in

the same tetra-cone as in the previous frame.

3 PROPERTIES OF THE

INTERACTIVE SYSTEM

The use of tetra-trees (Jimenez et. al, 2006) provides

a set of advantages with regard to other types of

spatial decompositions based on rectangular cells,

like octrees and grids, or bounding volume

hierarchies, like AABB-Trees and OBB-Trees.

These advantages are given mainly by an interactive

visualization of the triangles that take part or are

close to taking part in an interaction or manipulation

of the objects, this visualization being more intuitive

and offering a better sensation to the user with

regard to other types of decompositions.

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436

3.1 Obtaining the Triangles Related to

the Interaction

The use of tetra-trees allows us to obtain the

triangles related to an interaction, independently of

the distance of the device from the object. When the

distance increases, the number of expected triangles

diminishes, because the set of tetra-cones in which

the control points are is smaller (Figure 3).

However, the closer the device approaches, the more

related the triangles are to the future interaction.

Figure 3: When the distance increases, the number of

expected triangles diminishes.

Figure 4: In an octree there are situations in which we do

not obtain a set of triangles related to the interaction.

Nevertheless, in an octree there are cases in

which the control points are not classified (because

they are outside the bounding box) or are classified

in empty cells (without triangles, Figure 4), the

reason why this classification does not obtain a

satisfactory set of triangles related to the interaction.

This set has worse distribution in an octree, because

the cells fits deficiently to the geometry of the

object, presenting worse visual appearance.

3.2 Smooth Transition between Cells

When the device moves a change in the set of cells

in which this object has been classified takes place.

In order to obtain a more agreeable visual sensation

a smooth transition is necessary between the

triangles classified in both sets of cells, that is to say

that the set of triangles shown between two frames

has certain overlapping triangles, and that they

contain a similar number of triangles.

When using tetra-trees the transition between

cells (tetra-cones) is smooth, and discontinuity in the

set of triangles between consecutive frames is not

noticed (Figure 5). However, when using rectangular

cells as in the case of octrees, we noticed an abrupt

transition in the set of triangles between two

consecutive frames (Figure 6), either because of the

difference in the size of the cells, or because the cell

is empty (it does not contain triangles).

Figure 5: Smooth transition between cells in a tetra-tree.

Figure 6: Transition between cells in an octree.

3.3 Smooth Transition between Levels

In any given moment, the user may be interested in

modifying the level of detail for the interaction, and

displaying a greater or lesser number of triangles. In

order to do this it is necessary to increase or

diminish the level reached in the tree.

A tetra-tree has a greater set of levels than an

octree for an equal number of space subdivisions;

therefore it provides a smoother transition between

detail levels. On the other hand, in an octree this

change in the level of detail is more abrupt, and due

to the fact that the cells' form is worse adapted to the

geometry of the object, the set of triangles obtained

may be quite far from the device.

LOCALIZATION IN AN INTERACTIVE SYSTEM

437

4 TIMES STUDY

The system was implemented in C++ using gcc and

OpenGL for visualization. We used an Intel Pentium

IV-1.6 GHz processor with 1 MB in a Linux O.S..

We measured the number of frames per second

in the worst case (when collision with the objects

takes place) obtained by the interaction system for

each one of the objects of Figure 7 and the devices

of Figure 1. In this study we have included the time

consumed in obtaining the related triangles and the

collision detection time. The time needed for

visualization has not been included.

In this system the user moves both, the device

and objects freely throughout the scene. In Figure 8

we can see these times providing a real time

interaction system.

Figure 7: Objects used (f=faces): cylinder (60 f), cat (760

f), teapot (993 f), horse (7,172 f), venus (11,241 f), golf-

ball (16,205 f), dragon (201,031 f).

100

1.000

10.000

100.000

1.000.000

10.000.000

frames/sec.

hand ball-pen pen

hand

256.004 28.273 18.700 6.515 4.251 1.517 748

ball-pen

682.667 90.474 69.456 29.967 18.219 12.135 7.278

pen

1.600.036 904.737 801.411 449.498 404.875 384.285 309.049

cylinder cat teapot horse venus golfball dragon

Figure 8: Interaction times (frames/sec. in the worst case,

with logarithmic scale).

5 CONCLUSIONS

In this paper we have used a data structure for space

decomposition, especially appropriate for the

location of the parts of an object for interaction. This

data structure presents several advantages with

regard to other space decompositions and hierarchies

of bounding volumes based on rectangular cells,

mainly regarding the obtaining of the related

triangles, the accurate level of detail, and with a

better visual appearance and comfort in the

interaction.

The system obtained is able to perform an object

interaction in real time, including collision detection

with devices, by using certain control points on the

device in order to obtain the triangles related to the

interaction.

ACKNOWLEDGEMENTS

This work has been partially funded by the Ministry

of Science and Technology of Spain and the

European Union by means of the ERDF funds, under

the research projects TIN2004-06326-C03-03 and

TIN2007-67474-C03-03, and by the Consejería de

Innovacion, Ciencia y Empresa of the Junta de

Andalucía under the research project P06-TIC-

01403.

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