Haptics has been studied as a means of providing users with natural and immersive sensations of digital content in the fields of medicine , education , entertainment , and broadcasting . Haptic interfaces allow users to touch, explore, and manipulate 3D objects in an intuitive way with realistic haptic feedback and can be applied to create touch-enabled solutions that improve learning, understanding, creativity and communication. In spite of the considerable advantages, however, haptics is still largely unfamiliar to most people, potentially due to the lack of abundant haptic interaction contents in areas of interest to the general public. Audiovisual content, on the other hand, is readily available to the general public in a variety of forms, including movies and music, because it can easily be captured using a camera or microphone and can be created by a wide range of modeling and authoring tools. Haptic content, on the other hand, has not yet reached this ease of use, as there are not many haptic cameras or microphones available and still relatively few easily-useable modeling and authoring tools for creating haptic content.
In the meantime, there are a few tools providing a graphic modeling system with force feedback in the 3D geometric model design process, including geometric modeling, sculpturing, and painting. Among them, Freeform  and ClayToolsTM  are virtual modeling and sculpturing systems that have been commercialized by SensAble Technologies. InTouch  and ArtNova  are touch-enabled 3D painting and multi-resolution modeling systems, and dAb  is a haptic painting system with 3D deformable brushes. These systems, however, use haptic technology purely as an assistant tool for effective and intuitive geometric modeling, sculpturing, and painting. Therefore, these tools cannot exactly be considered to be the haptic modeling tools according to the definitions and scopes in the following section.
Despite their lack of recognition, though, there are a few haptics-based application systems currently in use. FLIGHT GHUI Builder (FGB)  and REACHIN  Application Programming Interface (API) are both platforms that enable the development of haptic content. FGB is a tool designed specifically for the creation of graphic and haptic user, while REACHIN API is used to develop sophisticated haptic 3D applications and to provide functionalities when editing haptic data. By providing users with a set of haptic/graphic libraries and some haptics-related editing functions in haptic APIs, as in OpenHaptics Toolkit  and CHAI3D , it is possible to construct application specific haptic models. Tempkin et al.  proposed a haptic modeling system called web-based three dimensional virtual body structure (W3D-VBS). This software provides editing functions for haptic properties and can edit a variety of haptic surface properties including stiffness, friction, and damping for tissue palpation. Seo et al.  also proposed a haptic modeling system called K-Haptic ModelerTM, which provides editing functions for haptic properties by using the K-TouchTM Haptic Application Programming Interface (API)  to support the haptic user interface. Eid et al.  further suggested a haptic modeling system called HAMLAT in which the authoring tool is composed of the HAMLAT editor, the HAML engine, and a rendering engine.
Most haptic modeling systems, including HAMLAT, OpenHaptics, and K-Haptic ModelerTM, are either object or polygon-based: In the object-based modeling system, the haptic properties are applied on a whole object, while in the polygon-based system, they are applied on some parts of an object. It is therefore difficult to edit non-uniform haptic properties on only part of a surface or object. Thus, instead of applying global properties to a model, as in the object-or polygon-based approach, Kim et al. [18, 19] proposed a haptic decoration and local material editing system for enhancing the haptic realism of a virtual object. This system allows a user to paint directly on to the surface of a 3D object and to locally edit and feel haptic material properties (stiffness, friction) in a natural way.
Haptic content typically consists of computer graphic models, created using a general graphic modeler such as MAYA or 3D MAX, with the subsequent addition of haptic data. In graphic modeling, graphic content is created while the quality of work is directly verified visually. Therefore, in order to create a variety of diverse and naturally feeling haptic content, it is necessary to develop haptic modelers which are user-friendly, easy-to-use, general purpose, and efficient. The modeling software and applications must provide sufficient graphic/haptic functionality in the modeling processes, which can then provide on-line feedback of the edited haptic material properties in real time as users edit on the surface of an object. Moreover, the haptic modelers must have ample speed and memory-efficiency to ensure high productivity and to be economical.
The rest of this chapter is organized as follows. Section 2 defines the haptic modeling processes systematically and comprehensively and then summarizes their scopes. A depth image-based haptic modeling algorithm is then proposed for editing non-uniform and diverse haptic properties on the surface of a virtual object in Section 3. This proposed method stores haptic property values into six orthogonal image data structures, called haptic property images, to more efficiently and cost-effectively represent a more realistic feeling of touch. Section 4 suggests a basic framework for a haptic modeling system (a modified K-HapticModelerTM) that can create and edit haptic content for virtual objects. The final section provides conclusions and suggests future research items to improve the proposed modeling functions.
2. Haptic Modeling: defintion and scope
A. Definition of Haptic Modeling
There seems to be no formal comprehensive definition of haptic modeling and its scope, although there are many techniques for digital sculpting or performing geometric modeling with a force sensation that can be evoked by some sort of haptic device. We define haptic modeling more formally and comprehensively as follows:
Definition: Haptic modeling is a series of processes to create haptic content on graphic models that are components of virtual reality (VR), augmented reality (AR), or mixed reality (MR).
B. Scope of Haptic Modeling
The haptic modeling processes as a whole consist basically of four smaller processes: (i) acquiring haptic data and the subsequent signal/image processing, as well as data management to acquire haptic data from the physical world, (ii) geometric processing to preprocess graphic models, (iii) haptic processing to edit or to author haptic data onto a graphic model, and (iv) haptic modeling to add haptic effects into the overall graphic environment. Here, haptic data may include not only material properties (stiffness and friction), haptic texture (roughness), and force/torque histories, but also motion trajectories such as time histories of acceleration, velocity, and position. Figure 1 shows the scope of the proposed haptic modeling processes.
a. Acquiring Haptic Data
There are two processes in the acquisition stage of haptic data; (i) the acquisition of haptic data (including signal processing to get true haptic data from noisy raw signals) from the physical world through either a sensing systems or a mathematical modeling technique, and (ii) the construction of a haptic database.
To build realistic haptic contents, haptic data must first be acquired from the real world. Surface material properties (stiffness and friction), haptic texture (roughness), and force profiles of haptic widgets (buttons, sliders, joypads, etc.) can be obtained through many different kinds of physical sensors, such as a force/torque sensor to get a force/torque time history, while a user is interacting with a real physical object (e.g. physical buttons or sliders) or with a real physical scene (environment). A visual camera may also be used to acquire some of the geometric details of an object surface for haptic texture modeling with subsequent image processing.
After sensor signals are acquired, these raw signals must then be processed to derive haptically useful data. A human perception threshold may be applied in these kinds of processing. For button force history, for example, some identification process may be necessary to find out onset of sudden drop of buttoning force. Motion histories can be captured and stored by visual cameras, inertial sensors, or by motion capture systems. The motion trajectories can also be used for describing ball trajectories and hand writing trajectories. Haptic data may also be modeled by some mathematical functions. Regardless of the means of acquisition, haptic data must be stored efficiently in the memory due to the potentially large size of the dataset. Therefore, it is important to develop an efficient data base management method.
b. Preprocessing Geometric Models
The preprocessing stage requires specific geometric processing for subsequent haptic modeling. For instance, even though a geometric model may seem fine graphically, it may contain many holes, gaps, or noises that have been acquired from 3D scanners, z-CamTM, MRI, CT, etc. These can be felt haptically while users explore the graphic model to receive an unexpected haptic sensation. Therefore, these graphically-unseen-but-haptically-feelable holes, gaps, or noises must be eliminated before any material editing process can begin.
Further preprocessing may be also necessary. In most existing haptic modeling systems, a single set of haptic data is applied to the entire 3D model. However, users may want to model haptic data in one local or special area. In this case, geometric processing for dividing an object into several areas needs to be done before the haptic modeling process. Otherwise, a new method to edit non-uniform haptic properties on the surface of a virtual object should be developed.
c. Editing/Authoring Haptic Data
The editing or authoring of haptic data (surface material properties such as stiffness and frictions, force profiles of haptic widgets, etc.) is a significant part of the haptic modeling process and must be performed as intuitively and quickly as possible, similar to the geometric modeling process.
d. Adding Haptic Effects
Aside from the editing of haptic data onto graphic models, other haptic modeling processes also exist. For example, a gravity or electromagnetic effect may be applied in the whole virtual worlds to simulate weight or inter-atomic interaction force sensation when a user grabs an object or an atom (charged particle) in the gravitational or electromagnetic field. The case of automatic motion generation for a dynamically moving system is another example. If a soccer ball is kicked by an input action from the user and the user want to feel the motion trajectories of the soccer ball, the ball’s motion history must be dynamically simulated in real time by the use of numerical integration algorithms.
This chapter discusses only the modeling, more specifically, the haptic editing of graphic objects as discussed in the above step (c). Other steps will be discussed in future publications.
3. A Haptic modeling system
To edit 3D objects haptically, four steps are usually required. First, haptic modeling designers select some 3D object surfaces on which they want to assign haptic property values and, in the second step, they assign the desired haptic property values on the selected surfaces. Third, the user checks whether the touch feeling by the modeled haptic property values is realistic or not. If the feeling is not realistic or appropriate, they should adjust the values on-line by simultaneously changing the values and feeling the surface. Finally, once they are satisfied with the realistic haptic property values for the surfaces, they then store the values and chosen surfaces in a suitable format.
Depending on the method of picking out the surfaces on which the desired haptic property values are pasted, haptic modeling can be classified into three methods: (i) object-based, (ii) polygon-based, and (iii) voxel-based. The object-based haptic modeling method [14, 15] selects the entire surface of a 3D object when assigning haptic property values. Therefore, the entire surface of an object can have only a single uniform haptic property value. A glass bottle, for example, would have a single uniform haptic property value of stiffness, friction, and roughness over the entire surface. Therefore, if a 3D object consists of many parts with different haptic properties, partitioning is required in the preprocessing stage to assign different haptic property values to different parts. The polygon-based haptic modeling method  selects some parts of meshes from the whole 3D meshes comprising an object. Therefore, each mesh can have a different haptic property value. If the number of meshes is large for fine and non-uniform specifications of surface haptic properties, however, the size of the haptic property data also increases. Moreover, if a haptic modeling designer wants to model a part smaller than a mesh, subdivision is required. The object and polygon-based haptic modeling methods, therefore, usually cause difficulty when editing non-uniform haptic properties on the selected surfaces. On the other hand, the voxel-based haptic modeling method [18, 19] uses the hybrid implicit and geometry surface data representation. This method uses volumetric data representation and, therefore, in the surface selection process, the selected surfaces need to be mapped into the voxel data. Then the voxel and a single haptic property group that contains diverse haptic properties in a single data structure will be stored. However, the size of the converted volumetric data into surface data by means of a mapping function between the voxel and haptic property values is huge because the data is structured like a hash function. It subsequently needs a large amount of memory (order of N3 ) for modeling a very fine non-uniform haptic property.
In summary, for non-uniform haptic property modeling on surfaces of a virtual object, the existing methods require processes that: (i) divide a virtual object into many surfaces or component objects if a visual model consists of many components, (ii) maps between haptic property values and graphical data sets, (iii) converts data because of the dependency on data-representation, such as polygon and voxel. To avoid these additional processes in modeling non-uniform haptic properties, we propose a depth image-based haptic modeling method. In the proposed method, several two dimensional multi-layered image data structures, called haptic property images, store non-uniform and diverse haptic property values. Then, among several images, six orthogonal directional depth images of a 3D object are used to load a haptic property image that corresponds to the current haptic interaction point. Storing and loading haptic property values in this way makes the haptic modeling system more efficient and cost-effective. The proposed method therefore requires no division or partitioning of a virtual object. It is also independent of data-representation of the virtual object and, thus, is not dependent on the complexity of polygonal models.
3.1. Depth Image-based Haptic Modeling
The basic concept of the proposed depth image-based haptic modeling method is inspired by the depth image-based haptic rendering algorithm developed by Kim et al. , in which six orthogonal depth images are used for real-time collision detection and force computation. For efficiency and cost-effectiveness, the proposed method uses several layers of six orthogonal image data structures for storing and loading non-uniform and diverse haptic surface property values for the surface of a given 3D model. The six orthogonal depth images are used to identify a position in the six orthogonal image data which corresponds to the ideal haptic interaction point (IHIP), the contact point on the body, and to assign haptic properties to the position of a 3D object. One important assumption in the proposed depth image-based approach is that all points of whole surfaces in an object are mapped to certain positions among the six orthogonal images. Convex objects satisfy this assumption. Concave objects, however, need to be divided into several convex objects in the preprocessing stage, as in [21, 22].
Figure 2 shows the six orthogonal image planes for an object, which are defined at the top/bottom, left/right, and Front/rear surfaces of a bounding cube. The proposed depth image-based haptic modeling method consists of two parts: (i) an image-based modeling process and (ii) a depth image-based rendering process with the modeled image data. Two steps are therefore needed: an initialization step and a loop step. In the initialization step, a design parameter, such as image resolution, needs to be chosen carefully in order to efficiently assign the haptic property values. Depth images are then acquired from six orthogonal virtual cameras located on the bounding box surfaces, as shown in Figure 2. The haptic property images are image data structures for storing haptic property values for each pixel. In the following loop step, the location of the ideal haptic interaction point (IHIP) in the haptic property images is found by using the six orthogonal depth images in order to assign a haptic property value to a corresponding pixel in the haptic property image. It should be noted that, among the six orthogonal images, up to five haptic property images may be selected for the IHIP. Finally, pixels containing IHIP in the selected haptic property images are assigned haptic property values.
A. Initialization Step
The initialization step performs several different functions: (i) it determines six orthogonal haptic property image resolutions, (ii) it initializes six images values to zero values, and (iii) it obtains six orthogonal depth images. The haptic property image is a data structure containing a haptic property value for each pixel. It is therefore needed first in order to determine the resolution of each haptic property image. Since the haptic property image data structure contains haptic property values to describe the six orthogonal surfaces of 3D objects, haptic property images with a higher resolution are able to store finer haptic information and provide a finer touch sensation. Thus, the resolution of the haptic property image determines the quality of the detailed representation of the surfaces. Figure 3 shows several different resolutions for a haptic property image. If the resolution of the image is high, memory usage is also high, possibly creating more work for a haptic modeling designer. Therefore, the image resolution should be carefully determined to match the needs of the designer. Note that each of the six orthogonal haptic property images may all have a different image resolution, depending on the surface details and surface haptic properties.
Before obtaining the depth images, it is necessary to first create six haptic property images whose pixel values are all set to zero. The desired pixel values in the haptic property images will then be updated by assigning new haptic property values during the modeling stage in the loop process. The next step is to obtain six orthogonal depth images that have the same image resolution as the haptic property images and that have additional depth information from the virtual camera pixel planes to the surfaces of the virtual object. Note that, for simplicity, the resolution of the depth image is selected to be the same as that of a haptic property image. If the resolutions for these two images are not the same, it is necessary to first resolve the resolution difference between them.
In order to set the virtual cameras in the correct positions, a bounding box needs to be constructed. Among various boundary boxes, the axis-aligned bounding box (AABB) is used for its fast computation and direct usage of the depth image-based haptic rendering algorithm . If a virtual camera is located on the surface of the bounding box, then the surface of the object may not be captured because there is no distance between the camera and the surface. Hence, a small margin is necessary between an object and a boundary box. This bounding box with a small margin is called a “Depth workspace”. The six orthogonal side surfaces of the cube in Fig. 2 are the locations of the both the haptic property images, as well as the depth images. Figure 2 also shows the location of the six virtual cameras used to obtain the depth images, which will later be used for determining which of the haptic property images correspond to the current contact point (IHIP) during the depth image-based modeling procedure.
B. Loop Step
An important problem of the proposed depth image-based haptic modeling method is how to assign haptic property values to the pixels in the haptic property images. For this, we first need to find the pixel positions in all six orthogonal haptic property images. After finding the IHIP, which is the contact point on the surface where the Haptic Interaction Point (HIP; haptic device probe) collides with the surface of a 3D object, the IHIP position is computed in respect to the three dimensional world coordinate system, as had been done in . The corresponding position in each haptic property image can then be obtained by a simple coordinate relationship, as shown in Figure 4. The local coordinate systems of all orthogonal haptic property image planes for an object are also shown. Note that the object’s origin in the world coordinate system is located in the left-bottom-far position of an object while each image origin is located at the left-bottom.
Figure 5 shows an example of the contacted IHIP point (red spot) on the human face (just above the left eyebrow) and the associated positions in the six orthogonal depth image planes. Note that, among these six images, only three contain visible images (the three left images corresponding to the front, right side, and top views).
Second, the haptic property images that contain the IHIP need to be selected. These images are called “True Haptic Property Images.” For example, in Figure 5, it is only necessary to select three images as the True Haptic Property Images (the three left images corresponding to the front, right side, and top views). This selection process can be easily done using the six orthogonal depth images and a simple depth comparison algorithm. For example, if the depth value of the far depth image is bigger than the IHIP depth value, then the IHIP z-position is inside of the object’s front surface. In this case, the far haptic property image is not a correct True Haptic Property Image. Assume in this depth comparison that the closet depth value is zero and the farthest depth value is one. Once the True Haptic Property Images are determined, the modeling step is finished by assigning a haptic property value to one of the True Haptic Property Image positions, called the True Haptic Property Position.
So far, the method of assigning one haptic property value into a few haptic property images has been discussed. However, there are various haptic surface properties which stimulate human sense of touch, such as stiffness, damping, static or dynamic friction values in three directions. To model these diverse haptic surface properties, the proposed algorithm suggests a concept of multi-layered images, where one image layer is used to represent each haptic property. Interestingly, the proposed modeling method may very easily include some tactile sensation models in a similar way to the haptic surface property model on a per-pixel basis. In other words, vibration effects (in term of vibration time history), for example, can be assigned to each pixel or to a group of pixels of an image to render vibration effects while a user touches a point or a group of points on the surface.
The proposed algorithm is a per-pixel-based method. To assign the same haptic property values on several pixels around the True Haptic Property Position, a user needs to simply choose some surrounding pixels with a brush operation, similar to that in the Photoshop program, and then assign the desired values to the selected pixels. Even though some pixels chosen in this way may not be on the surface of a virtual object, these non-surface pixels are not haptically rendered because they are considered to be non-contacted pixels during the collision detection phase. Therefore, a process to eliminate process these non-surface pixels is not necessary.
3.2. Depth Image-based Haptic Rendering
In order to haptically render the haptic properties modeled with the proposed depth image-based haptic modeling method, it is only necessary to choose one haptic property image among the three True Haptic Property Images because of a conflict problem. This situation may be explained more clearly with an example. Figure 6 shows two haptic property images in the two dimensional view of a two dimensional object. This problem may be caused either by a difference in the image resolution of the two images, or by a difference in resolution for parts of an object. This example shows that a slope portion of the object is projected into a horizontal image with 17 pixels and, at the same time, into a vertical image with 5 pixels. In this case, a haptic property value is assigned into two images and, when rendering the assigned haptic property value, the haptic renderer cannot determine which image is to be used. Assume for example that one haptic property value are assigned to the 16-th position on the horizontal haptic property image, and another value is assigned to the 15-th position on the same image. In this case, haptic properties on this image are saved correctly; however, at the same time, the two haptic property values are to be saved in the first position on the vertical haptic property image. In this case, only the second haptic property value is saved in the vertical image in the modeling time and use of the haptic property value of the 16-th position in the horizontal image is correct. Therefore, the horizontal image must be selected.
To avoid this conflict problem, we used the contact force vector direction that can be computed in the haptic rendering process while modeling the haptic property values. As shown in Figure 7, all haptic property images have their own normal vectors. A dot product with each normal vector of a True Haptic Property Image and the contact force vector on the contacted point (i.e. IHIP) can identify only one True Haptic Property Image. For example, in Figure 7, the top image is the True Haptic Property Image because the dot product between the contact force vector and the normal vector of the top image is the smallest. When rendering, this haptic property image is identified by this simple dot product operation. For a 45 degree inclined slope, the dot product generates the same values for the two images (for example, the top and left images in Figure 6). In that case, any haptic property image can be chosen as a True Haptic Property Image.
Once the desired multiple haptic property images for various properties (stiffness, friction, etc) are constructed from the modeling process by a haptic content designer who is feeling the haptic sensation, haptic rendering for another person (such as a consumer of the modeled haptic contents) can be done, as in the usual rendering process. By a collision detection algorithm, a collision point, which is an Ideal Haptic Interaction Point (IHIP), will search a True Haptic Property Image and the corresponding pixel position in the image. Then, the modeled haptic property value is conveyed to the reaction force computation and is subsequently displayed through a force-reflecting device or tactile property display devices.
A resultant reaction force can be computed by combining the normal reaction force from the stiffness property with several horizontal haptic properties, including friction and damping, as:
where Ftotal is the total force feedback vector, and Fcomponent is each force vector generated by each haptic property. Fnormal is the normal force vector with a stiffness property that can be generated by a haptic rendering algorithm, such as a penalty method, god object, or virtual proxy algorithm. Ffrrctoin is the horizontal frictional force vector generated by the friction property on the surface. Faddtional is the force vector that is generated either by haptic textures or by any other haptic properties in a similar manner by using the proposed algorithm.
In order to calculate the normal force of the contact surface with the objects having non-uniform stiffness parameters, the haptic property image containing surface stiffness parameters is used. Once a collision is detected and the location of the IHIP is determined, the proposed algorithm reads the value of the stiffness corresponding to the surface adjacent to the IHIP by referring to the True Haptic Property Position and Image. Using the stiffness value K, the normal force of the contact surface then calculated using the spring model as
where IHIPt and HIPt describe IHIP and HIP at time t, respectively. Note that (IHIPt - HIPt ) is the contact surface normal vector.
2) Viscous Friction
The friction force is applied along the surface tangential direction. Non-uniform frictional force based on the proposed image-based representation can be computed using the following simple viscous friction model as
where Ds is the viscous damping coefficient and T is the haptic rendering rate. Similar to the previous determination of the normal contact force, once a collision is detected and the IHIP is determined, then the proposed algorithm read the viscous damping value corresponding to the IHIP position by referring the haptic property image containing the viscous damping coefficient.
Because haptic rendering should run as quickly as possible (nominally with a 1 KH rate), the proposed depth image-based haptic modeling method must also be performed very fast. On most recent PCs, one estimated time to search the True Haptic Property Image and Position using one IHIP is 0.001 msec. Larger haptic property image sizes take more time to load. Note, however, that loading haptic property images is only a one time event when the application is initialized. Therefore, the haptic property image size is not a serious problem in the proposed haptic modeling paradigm. More memory, however, is required for larger sized haptic property images.
4. Architecture of the haptic modeling System
The K-HapticModelerTM, proposed in , has been modified for this system by implementing the proposed haptic modeling algorithm. The K-HapticModelerTM provides basic file management functionalities for loading, editing, and saving 3D graphic objects as well as basic graphic model manipulation functions, such as positioning, orienting, and scaling. For haptic modeling, the K-HapticModelerTM provides haptic-specific functionalities through the Haptic User Interface (HUI) for editing surface material properties, such as stiffness, static or dynamic friction, and for editing a pushbutton force profile on a loaded graphic model. It allows users to feel, manipulate, or explore virtual objects via a haptic device.
Figure 8 shows the overall data flow for the proposed depth image-based haptic modeling and rendering. The two upper blocks in this figure represent the depth image-based haptic rendering . Note that, in the bottom blocks of this figure, the true IHIP is used both in the proposed depth image-based haptic modeling and rendering processes. For the online feeling of the modeled haptic sensation, the modeled haptic property values are used in the force computation. In order to process a 3D object with haptic properties, the XML file format is used for the entire application architecture, as outlined in Figure 9.
4.1. XML File Format
Extensible Markup Language (XML) is a simple and flexible text format derived from Solid Graphic Markup Language (SGML) (ISO 8879). It is classified as an extensible language because it allows users to define their own tags. Its primary purpose is to facilitate the sharing of data across different information systems, particularly via the Internet. The proposed haptic modeling application supports the XML file format because it provides a simple interface for dealing with many 3D objects and haptic properties. It allows users to associate meta-information (graphic and haptic information) with 3D objects without converting the representation into a particular 3D format. The tags are described in Table 1. Note that each tag is presented with its identifier (within triangular brackets) followed by the type of the data it stores (within square brackets) and a brief description. By providing access to the XML file format, we can easily save, open, and add content.
Table 1 describes the XML tag definition and description. The Level is the XML data structure hierarchy level and “Note” refers to the number of tags which can be used in each tag. For example, the <object> tag has “multiple” values, meaning that many <object> tags can exist in the <objects> tag. On the other hand, the <type> tag has a “unique” value, meaning that only one <type> tag must exist in the <object> tag. The <objects> tag is used only for notifying root node. Each object in a virtual environment has an <object> tag. “Object” can have multiple haptic properties, so that each <property> tag describes each haptic property type. The <type> tag saves the haptic property type, while the <path> tag in the <property> tag signifies a relative path for the haptic images. The “ref” attribute in the <path> tag describes which image is included among the six haptic property images. By this simple tag combination, the haptic modeling data can be easily expressed.
The proposed haptic modeling system based on the depth image-based haptic modeling method was implemented on the PHANToM Omni haptic interface  using C++ language. The computations were run on a Pentium dual core with a 1.8 GHz CPU and two gigabytes of RAM for haptic rendering, and a Geforce 9600 GT graphic card for graphic rendering. The application was multi-threaded, with the haptic force computation thread running at a higher priority with a 1 KHz rate. The graphic rendering thread ran at 60 Hz rates to display virtual objects. Figure 10 shows a GUI image of the haptic modeling system.
This system has two main functions:
To implement these two functions, image GUIs are proposed. The left images in the system, shown in Figure 10, describe the current status, stiffness status, and friction status. The current status GUI shows the area where the haptic modeling designer selected the surface to model. Therefore, after being selected, the area of current status will be updated into stiffness status or friction status.
The center area of the images shown on the right in Figure 10 indicate each haptic property value (in this figure, only stiffness and friction are shown), and brush size. The range of the brush size can be set from 1 to 10, and is editable. These GUIs are created using the Slider technique, so the haptic property values can be changed by clicking a mouse. The selected area will then be assigned by those data. After clicking the buttons in Figure 11, each haptic property will be assigned to each haptic property image. The Start button is for starting the haptic rendering process, while the reset button in the GUI is used to reset the current status images.
5. Conclusions, Discussions, and Future Works
This chapter proposes a depth image-based haptic modeling method for effectively performing haptic modeling of 3D virtual objects that provides non-uniform surface haptic property per pixel. Moreover, by adding haptic property images, we can represent diverse haptic properties in a systematic way. Even though we have focused primarily on kinesthetic haptic properties, the proposed method can also be extended for any tactile haptic modeling such as vibration, thermal, and so on. Further, this method is applicable with any geometrical data set (voxel, implicit or mathematical representation, mesh structure) because no pre-processing is required for constructing a hierarchical data structure or data conversion, making this image-based approach highly efficient.
Based on our own systematic and comprehensive definition and scope of haptic modeling, a modified K-HapticModelerTM is proposed as an intuitive and efficient system for haptic modeling of virtual objects. The proposed modified K-HapticMosdelerTM provides basic graphic file management and haptic-specific functionalities, mainly for editing surface material properties of the loaded graphic model with the use of a haptic device. The proposed system, therefore, allows users to perform haptic modeling on graphic models easily, naturally, and intuitively. We believe that any person, even those who are not familiar with haptic technology, would be able to use this system for three-dimensional haptic modeling.
Concave objects, however, cannot be properly modeled by the proposed method because some object surfaces are not visible in all haptic property images. In order to solve this problem, convex decomposition algorithms [21, 22] should be used. Those convex decomposition algorithms, however, may also create unnecessary data sets. Reducing the unnecessary data also is our future work.
The proposed modeling system is now being developed to provide more comprehensive haptic modeling capabilities in more intuitive and efficient ways. Future development will implement each stage of haptic modeling scopes. First of all, methodology for acquiring haptic data further investigated, preprocessors of acquired data, such as segmentation, grouping, and databases, will also be constructed. Furthermore, our basic haptic modeling framework will be extended by comprising various HUI to create haptic content. Finally, we hope to apply our haptic content into a wide range of applications where it may heighten realistic interactions.