Elsevier

Graphical Models

Volume 73, Issue 5, September 2011, Pages 182-201
Graphical Models

Tetra-trees properties in graphic interaction

https://doi.org/10.1016/j.gmod.2011.03.003Get rights and content

Abstract

The localization of the components of an object near to a device before obtaining the real interaction is usually determined by means of a proximity measurement to the device of the object’s features. In order to do this efficiently, hierarchical decompositions are used, so that the features of the 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 situated on the device in a little-known spatial decomposition named tetra-tree. Using this type of spatial decomposition gives us several quantitative and qualitative properties that allow us a more realistic and intuitive visual interaction, as well as the possibility of selecting inaccessible components. These features could be used in virtual sculpting or accessibility tasks.

In order to show these properties we have compared an interaction system based on tetra-trees to one based on octrees.

Highlights

► Analysis of quantitative and qualitative properties of tetra-tree regarding octree. ► Spatial decomposition for localization which improves construction and interaction. ► Improving of quality, visual feed-back and precision, applicable to haptics. ► Selection of inaccessible components without accessory intersection algorithms. ► An interaction system with smooth transition between frames including large models.

Introduction

In several virtual reality systems [1] it is typical 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 the scope of this paper we refer to a device as a real or virtual object (e.g. a pen or a haptic device) used as a tool for the interaction with objects modeled by means of triangle meshes. In order to do this interaction precisely, the system must provide to the user with feed-back in the form of visual information [2]. This information may consist of the parts of the object that are going to interact or are interacting with the device, being able to select inaccessible components; so that the system gives information to the user about the object features, even before touching them. In this situation the interaction does not produce undesired effects, such as a collision response (deformation, etc.) without prior knowledge of the area of interest.

The aim of this work is to show the properties of a little-known object decomposition named tetra-tree [3], [4] in the interaction between a device and an object. This interaction concerns to interference and proximity queries with better quantitative and qualitative properties regarding traditional decompositions. The quality of the visual interaction is defined and improved by means of the techniques proposed in this paper. Construction and interaction times studies are included in order to show the improvement achieved in relation to octrees for different models (including large models) with a moderate penalty in the storage cost.

This paper is organized in the following way: next sections show the background, the motivation and main contributions. It follows with the spatial decomposition used. Then the use of the interaction system is described. After that, a study of some quantitative and qualitative properties is carried out, compared with the use of an octree for the same aim. Afterwards, the time obtained by the system is studied for different types of objects. Finally, the conclusions and the future work to be undertaken are summarized.

Section snippets

Background

In order to perform the tasks outlined in the previous section, image-based techniques could be used [5], [6], but these tend to be less accurate. In addition, interaction possibilities are limited due to the type of feed-back obtained.

In the case of object-based techniques, it is typical to use a proximity measurement from the device to the objects, aided by a spatial decomposition or by a bounding volume hierarchy [7] in order to classify the triangles of the object and thereby reduce the

Motivation and main contributions

Visual feed-back is needed in several applications for a more realistic and intuitive interaction. In some situations, accessibility to certain elements of the model is not possible [20], due to the collision of the device with the geometric model and the forces obtained, as could occur with the use of haptic devices. In this situation an accessory method for selecting inaccessible components, like the application of ray-triangle or ray-box intersection algorithms (as “pick” operations), is

Spatial decomposition

Throughout this section we will describe the spatial decomposition used, called tetra-tree [3], [4].

The general approach is similar to sector-trees (2D) and cone-trees (3D) as introduced by Chen [24] and detailed by Samet [8]. The cone-tree is analogous to a region quadtree that represents the result of recursively subdividing cones in the polar sphere into four cones of square spherical intervals. It is a boundary representation of an object’s surface where the space is treated as a polar

Interaction system

The virtual environment we are dealing with is composed of objects modeled by means of triangle meshes. The device can be a hand or a pointing device (Fig. 7). 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 moving device.

Points have been placed mainly in parts of the device in which presumably the first contact in case of collision will take place (Fig. 7

Properties of the interactive system

The use of tetra-trees 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 is more intuitive and offer a better sensation to the user with regard to other

Time study

The system was implemented in C++, using OpenGL for visualization. We used an Intel Core i7, 2.8 GHz processor with 6 GB RAM and a 64-bits Linux operating system.

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 Fig. 11 and the devices of Fig. 7. In these times we have included the time consumed in obtaining the related triangles and the collision detection time. The time

Conclusions

In this paper we have presented a data structure for space decomposition, especially appropriate for the location and selection 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, being able to

Acknowledgments

This work has been partially supported by the Consejerı´a de Innovación, Ciencia y Empresa of the Junta de Andalucı´a and the European Union (via ERDF funds) through the research Project P07-TIC-02773, and by the University of Jaén through the research Project R1/13/2010/08 sponsored by Caja Rural de Jaén.

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