Interactive Visualization of Mixed Scalar and Vector Fiel

Transcription

1 Interactive Visualization of Mixed Scalar and Vector Fiel Lichan Hong, Xiaoyang Mao: and Arie Kaufman Department of Computer Science State University of New York at Stony Brook Stony Brook, NY Abstract This paper describes an approach for interactive visualization of mixed scalar and vector fielda, in which vector icons are generated from pre-vozelized icon templates and volume-rendered together with the volumetric scalar data. This approach displays simultaneously the global structure of the scalar field land the detailed features of the vector field. Interactive visualization is achieved with incremental image update, by re-rendering only a small portion of the image wherever and whenever a change occurs. This technique supports a set of interactive visualization tools, including change of vector field visualization parameters, real-time animation of vector icons advected within the scalar field, a zooming lens, and a local probe. 1 Introduction Visualization of vector data intermixed with scalar fields, which we refer to as intermized visualization, is an important subject in applications such as computational fluid dynamic (CFD) and finite element mechanics (FEM). For example, in many CFD simulations, the quantities measured at each sample point include not only flow velocity but also scalar values, such as temperature and pressure. It can be very helpful for scientists and engineers to visualize them in a single image and thereby explore the relationship between the scalar and vector fields. Several techniques have been developed to visualize scalar and vector fields together. One approach primarily shows the vector field using geometric or volumetric primitives, and, as an additional benefit, maps the scalar data to the attributes (e.g., shape or color) of the primitives. For example, with the stream polygon approach [13], a polygon is deformed to show the vector field information, while the local scalar values *Current address: Computer Language Section, Elcctrotechnicsl Laboratory, l-l-4 Umesono, Tsukubs, Ibaraki 305, Japan. are mapped to the color of the polygon. In the virtual smoke technique [lo], a growing volume around a seed point is obtained from the vector field, while the local scalar field is mapped to the color of the volume to visualize the vector field and the local scalar values simultaneously. Another approach produces an overall intermixed picture of the scalar and vector fields, using texture filtering and volume rendering [ll, 41. Images generated by such methods tend to emphasize the global and qualitative features of the vector field but are inadequate in presenting the detailed quantitative vector field information. In this paper we describe a new approach to visualizing simultaneously the global structure of a scalar field and the detailed vector field features, in which volume rendering and conventional vector field visualization techniques, such as particle tracing, streamlines, and streamtubes, are employed. Our approach supports the following scenario. First, the volumerendered result of the scalar field is used to identify regions of interest (ROIs), such as high temperature areas in a CFD application. Then, vector icons, which are used for visualizing the detailed vector features, are generated from pre-voxelized icon templates and volume-rendered together with the scalar field to obtain an intermixed image. Thus, with the vector icons immersed in the translucent scalar data, the relationship between the scalar field and the vector field can be more easily discerned. In the case that the velocity is the only parameter that needs to be visualized, rendering time may not be a major concern because vector icons generated by the vector field can be displayed interactively using graphics hardware. However, in intermixed visualization, due to the fact that volume rendering tends to be time-consuming, new challenging problems are introduced. Generally speaking, to obtain a meaningful (See color plates, page CP-28) /95 $ IEEE 240

2 intermixed image, there are two important issues that need to be addressed: (1) finding the proper transfer functions for the scalar data, and (2) determining desired visualization parameters for the vector field (such as where to insert a particle source and how many time steps to use in generating a streamline). While how to obtain the optimal transfer functions for the scalar field is an interesting problem by itself (the issue is discussed in detail in [5] and a solution is proposed using genetic algorithms), selecting the desired vector field visualization parameters is commonly a tedious procedure. A good visualization result can usually be obtained only through trial and error. Unfortunately, in the context of volume rendering, re-rendering the whole image whenever a vector field visualization parameter is modified would be too time-consuming and non-interactive. To avoid the expensive entire image re-rendering in the trial and error process, we employ an incremental image update technique which re-computes only those pixels that are affected by a certain user operation, such as the modification of a vector field visualization parameter. With this technique, vector icons can be inserted into or deleted from the 3D scene interactively and the image is updated incrementally, thus allowing the user to try different vector field visualization parameters and obtain the intermediate visualization results interactively until a desired image is found. As a by-product, real-time animation of vector icons advetted by the vector field coupled with the translucent scalar data provides a global insight into the flow. Furthermore, using the same technique, a zooming tool and a local probe are designed, which enable the user to interactively explore the detailed information from both the scalar and vector fields within an ROI. In Section 2, we discuss the volumetric representations for the vector icons. In Section 3, we elaborate on the idea of incremental image update, and describe how to achieve interactive manipulation of the vector field visualization parameters and real-time advection of the vector icons. A zooming tool and a local probe are described in Section 4. Finally, in Section 5, we discuss some implementation issues. 2 Volumetric Representations In &term&d &u&s&on, the scalar field is represented volumetrically. However, to model the vector icons used by traditional vector field visualization techniques, such as tiny arrows and spheres, one of the following three methods can be employed: implicit surfaces, polygonal surfaces, and volumetric representations. Representing a vector icon as an implicit surface and rendering it with a ray casting technique suffers from the disadvantages that the ray-object intersection test can be computationally expensive and that not all vector icons can be easily described with implicit equations. On the other hand, using a polygon mesh to model the vector icon leads to a hybrid data structure [8, 161, and the rendering time depends on object complexity [6]. Although one may argue that, with the polygonal surface approach, graphics hardware can be used to accelerate the rendering of the vector icons, in the context of intermixed visualization, the bottleneck of the rendering time is the scalar field, not the vector icons. Therefore, we employ the volume graphics approach [6], by generating vector icons from several prevoxelized icon templates, hence obtaining a uniform data structure for both the scalar field and the vector field. The uniform data structure is then rendered with a volumetric ray casting/tracing technique [15]. Other advantages of the volume graphics approach include: insensitivity to scene and object complexity, block operations, CSG modeling, and the capability of pre-computing viewpoint-independent attributes such as antialiasing and texture [6]. A main concern of the volumetric representation has been the abasing problem caused by binary voxelization. Fortunately, with volume-sampled modeling [1 7], we can voxelize a primitive from its geometric description and convolve it with a radially symmetric 3D filter. As a result, the surface of the filtered primitive has a smoothly varying density function from the object to the empty space. Therefore, the corresponding discrete representation becomes free of object space abasing and consequently the rendered result is free of image space abasing. 3 Incremental Image Update for Interactive Control The objective of the incremental image update technique is to re-compute only those pixels on the image plane that are affected by a certain user operation, and thus save on rendering time. More specif- ically, at a certain stage of the visualization process, a desired viewpoint is obtained and further study of the flow can be continued with the static viewpoint. When the 3D scene is partially modified while a large 241

3 part of the scene remains unchanged, temporal coherence between consecutive frames can be exploited to re-render only those pixels affected by the operation, hence the rendering speed of the changed scene can be significantly accelerated. Similar ideas have been applied in medical imaging [9, 31, flow visualization [lo, 141, and volume sculpting [18]. Combined with the ray casting algorithm, the incremental image update technique can be further described as follows. Suppose in a certain instance we obtain an image by casting rays into a 3D scene consisting of several objects. With some user operation, a new object is inserted into the 3D world; hence, the image has to be updated to reflect this change. However, only a small portion of the image is usually affected by the insertion. To generate the new image, we need only to re-cast rays from those pixels that are within the projection area of the inserted object. The method of deciding which pixels should be updated is discussed in Section 5. The technique of incremental image update makes it possible for conventional vector field visualization techniques, such as particle tracing and streamtubes, to be realized interactively even in the context of volume rendering. With the particle tracing and streamtube techniques, selecting the desired vector field visualization parameters, such as seed point locations and advecting time steps, is crucial for achieving informative visualization results. In many cases, volume rendering of the scalar field may assist the user in understanding the flow patterns and hence provide a rough idea of how to choose the visualization parameters for the vector field. Once the user selects a set of vector field visualization parameters, vector icons generated by the vector field are inserted continuously into the 3D world, and only those pixels affected by the insertion are rerendered. In order to avoid occlusions and cluttering ef?&ts, the size of a vector icon, in general, tends to be relatively small with respect to the whole scene. Therefore, there are only a few pixels on the image plane that should be re-computed to reflect the insertion, and consequently the image can be incrementally updated in real-time to show the continuous insertion of vector icons. If the visualization result does not meet the user s expectation, he or she can simply delete those just-generated vector icons from the 3D scene and update the image incrementally, and then try another set of vector field visualization parameters based on the previous visualization results. This trial and error process can be repeated until the user obtains a desired visualization image. Figure 1 shows two intermixed images of temperature and air flow velocity in a CFD simulation of air flow within an air-conditioned room. The images were generated with the incremental image update technique after some trial and error iterations. The air flow velocity is visualized in Figure 1 with streamtubes which are shown as sequences of arrows. While different seed points and time steps are used to generate the streamtubes in Figure la and lb, the same transfer functions are applied for the visualization of the temperature. Figure 1: Intermixed images of temperature and air flow velocity wing different seed points and time steps for the streamtubes. A by-product of the incremental image update technique is the support for real-time animation that shows how vector icons are continuously generated distributed inside the flow. Such animation, coupled with multiple objects immersed in the translucent scalar field, provides a strong insight into the flow patterns and the correlations between the scalar and vector fields. Figure 2 shows a sequence of animation frames generated in real time with the particle tracing technique on the same CFD data set. The small spheres in the images are used to show the trace of particles inside the flow, and the same transfer functions as in Figure 1 are employed for the visualization of the temperature. 242

4 Figure 2: Four animation frames generated in realtime, with the advection of the small spheres indicating the trace of particles in the flow. 4 Zooming Tool and Local Probe With the interactive control described in Section 3, desirable images showing the global intermixed effect can be obtained by trying different vector field visualization parameters. However, to avoid mutual occlusions, vector icons can only be visualized in a very small size with respect to the size of the image. The fact that the image size is limited (no larger than the screen size) leads to a dilemma. If we want to obtain the global picture of the intermixed effect, we have to position the viewpoint far away from the scene so that we can see the whole scene, which means that vector icons such as particles and arrows will become so small that local properties such as vector direction and magnitude will be difficult to discern. If, however, we position the viewpoint close enough to a particular region in the flow so that we are able to study the local properties around that region, we will inevitably lose the global intermixed picture. Keeping several images rendered with various locations of the viewpoint will solve this problem, but the fact that expensive volume rendering of the whole image has to be performed once for each different viewpoint is undesirable. Ideally, we should be able to explore an ROI without having to pay the price of losing the global picture of the scene. Fortunately, a zooming tool based on the MagicLens [2] provides a solution. Our method shows the ROI with a zooming lens, while the rest of the image is unchanged to provide the global context. In other words, after the user positions the focus center of the zooming lens towards the ROI and specifies the size of the zooming lens, those pixels within the zooming window are re-computed with the incremental image update technique to enlarge the local features of the ROI to the level of detail that the user expects, while the pixels outside the zooming window stay the same. Therefore, with the ROI displayed in a higher level of detail than the rest of the 3D scene, the user is able to zoom into a specific region to study the local properties while still keeping the global intermixed picture. It should be noted that our zooming lens does not just magnify pixels. Instead, rays are re-cast into the 3D scene to update the pixels within the zooming window. In addition, several displaying options can be attached to the zooming lens. Besides the option of intermixing the scalar data and vector icons simultaneously, to avoid occlusions which arise naturally in intermixed visualization, the user can choose to show vector icons only, display scalar field only, or even render the scalar data with different transfer functions. Figure 3 shows a zooming lens displaying only vector icons in an intermixed context. Several streamtubes are used in Figure 3 for the visualization of the air flow velocity, and again the same transfer functions as in Figure 1 are employed to visualize the temperature. In addition, a local probe has also been designed for exploring the local properties of the flow. With an input device, such as a mouse or a spaceball, the user grabs the probe and moves it around within the trans1ucen.t scalar field to a particular point. The shape and color of the probe will be changed to reflect the local properties at the new position. In this case, updating the image can be accomplished in two steps: 1. Delete the probe at the original position (before the move). 2. Insert the probe at the new location (after the move). Only those pixels affected by these two operations should be re-rendered. A local probe tends to be relatively small in size with respect to the whole 3D scene MagicLens is.s trademark of Xerox Corporation. 243

5 rate volumetric ray tracing and radiosity, to irregular grid rendering. For our purpose, we have used the multiple volume manipulations and ray casting functionality provided by the VolVis system. Figure 3: A zooming lens displaying only vector icons is used to zoom into an ROI while keeping the global intermixed context. and the projection area of the local probe covers only a few pixels on the image plane. Consequently, interactive speed for local probing can still be achieved, even in the context of volume rendering, with the incremental image update technique. As suggested by de Leeuw and van Wijk [7], a valuebox can be attached to the local probe to show the flow data at the location of the probe. With this technique, local properties such as 3D coordinate values, velocity, tensor product, and scalar data can be provided quantitatively. Figure 4 shows a local probe (the arrow) immersed inside the translucent temperature field together with its valuebox. The same transfer functions as in Figure 1 are applied to visualize the temperature. A local probe may be used to assist the user in finding a desirable seed point. 5 Implementation and Discussion The set of interactive tools described above has been implemented in the VolVis system (version 2.0) [l] on an SGI Onyx workstation running the Irii 5.2 operating system. VolVis is a comprehensive, diversified, and high-performance volume visualization system developed at SUNY Stony Brook. It supports manipulations of multiple volumes and a variety of volume rendering algorithms, ranging from fast rough approximations, compression-domain rendering, accu- Figure 4: An arrow probe with its valuebox showing that the IocaljIow data is immersed within the tranrlucent temperature field. The techniques described in this paper can be applied to study a steady flow or an unsteady flow at a certain instant of time. For testing purposes, we have used a rectilinear data set generated from the CFD simulation of air flow within an air-conditioned room ([12] provides a detailed description of the data set). In the simulation, a heater was located at the lowerleft back corner of the room with its vent pointing up- 244

6 ward. The initial temperature in the room was 15OC, and a 3O C warm air flow was rushed from the vent of the heater during the simulation period. The CFD simulation was a 3D unsteady incompressible viscous flow computed with Boussinesq approximation. No turbulence model was used in the simulation. The simulation has two main purposes. One is to investigate how the heating effect is related to the location of the heater and the direction of the air flow coming from the vent, while the other is to explore the relationship between the comfort level in the room and the air flow velocity. An important factor that affects the comfort level is the uniform degree of temperature distribution in the room. In the CFD simulation, a total of fourteen steps are measured. At each step, the size of the data set is 41 x 41 x 41; and at every sample point, there are five floating point values representing the temperature, pressure, and air flow velocity, respectively. In thii paper, we use the flow data at the tenth simulation step to generate the pictures. Figure 5 shows the volume-rendered result of the temperature at this simulation step superimposed on a synthetically created room. Opacity and color transfer functions of the temperature are shown at the bottom of Figure 5, with the opacity transfer function above the color transfer function. The red tube above the heater shows the region of high temperature caused by the warm air flow rushing out of the heater. To obtain a uniform data structure for both scalar and vector fields, we pre-voxelize several templates of vector icons, such as a sphere and an arrow, into alias-free volumetric representations. Various orientations and sizes of vector icons can be obtained simply by scaling and rotating the corresponding templates. An isosurface extraction technique of VolVis [l], which calculates the ray-object intersection point analytically by using the t&near interpolation function and the parametric equation of the ray, is used to reconstruct the vector icons in the rendering phase. To compute the image area affected by the insertion or deletion of a vector icon, various methods of different efficiencies can be used. In our case, since the image area affected usually covers only a few pixels, we simply project the bounding box of the vector icon in the object space onto the image plane and scan convert the projection area to determine which pixels should be re-rendered. Figure 5: Volume rendering of the temperature field at the tenth simulation step superimposed on a synthetically created room. The techniques we describe in this paper can be considered as a general approach towards intermixed visualization. To illustrate our methods, we have implemented two vector field visualization techniques: streamtubes and particle tracing. The idea of streamtubes has evolved from that of streamlines, and multiple streamtubes together provide very useful information about the global flow patterns. However, with the traditional streamtube technique, the sources and destinations of the streamtubes are difficult to discern. This could be a major concern in intermixed visualization in particular, where using color mapping to show the streamtube directions may no longer be effective due to the color contribution of the scalar field between the streamtubes and the viewpoint. Therefore, we have implemented a variant of the streamtube technique. Hereby we attach a cone on top of a cylinder to construct an arrow at each time step. A streamtube is obtained by the concatenation of multiple arrows, with each arrow rotated and scaled to reach the next advetted position. Thus, the direction of the streamtube can be visualized by the orientations of the arrows. In addition, the local vector magnitude can be shown by the length of each arrow. In Figure la, the image is generated with three streamtubes, which start close to the vent of the heater, using ten time steps. Figure 245

7 lb uses four streamtubes, with the seed points located near the ceiling, using twenty time steps. The local pressure is mapped to the color of the arrows. Notice that, compared to Figure 5, different transfer functions for the temperature are applied in Figure 1 to highlight the ROIs in the flow. In our implementation of particle tracing, a particle is modeled as a tiny sphere, with the flexibility that the radius and color are free for mapping local parameters. The trace of particles is achieved when tiny spheres, generated by the vector field, are inserted into the flow continuously and the image is updated in realtime. In Figure 2, we show four frames of a real-time animation generated by the particle tracing technique. To achieve the zooming effect with a zooming lens, instead of relocating the image plane and re-rendering those pixels within the zooming window, we simply keep the same image plane and decrease the spacing between consecutive rays to update the pixels within the zooming lens, and thus a high resolution viewing is applied to the ROI. In Figure 3, the zooming lens is used to zoom into an area close to the ceiling, with the vector icons magnified two times relative to the original picture. By turning off the volume rendering of the temperature within the zooming lens, the local pressure can be visualized by the color of the vector icons without the cornpositing effects of the translucent temperature. For a local probe, any complicated vector icon such as the one described in [7] can be used. In our implementation, we have designed an arrow probe with the direction and magnitude showing the local velocity at the current position, and the attached valuebox displaying the local scalar, vector, and tensor product quantities. In Figure 4, the arrow probe is placed at the high temperature area close to the vent. The depth of the probe and the dominating vector component at the current position can be understood precisely from the valuebox. 6 Concluding Notes The primary contribution of this paper is in intermixed visualization. In our approach, vector icons used by conventional vector field visualization techniques are generated as volume graphics representations, and volume rendered together with the volumetric scalar data to show the global structure of the scalar field and the detailed features of the vector data within a single image. Temporal coherence between consecutive frames is exploited with the incremental image update technique to design a set of interactive visualization tools, which allows the user to interactively try different vector field visualization parameters in the trial and error process of obtaining an informative visualization image. Other tools provide the capabilities to observe the real-time animation of vector icons advected within the translucent scalar field and to explore a particular ROI with a zooming lens and a local probe. Interactive speed is achieved by rerendering only a small portion of the image affected by the user s interaction, rather than the entire image. In this paper, Figures 1, 2, 3, and 4 were generated within a couple of seconds after the volume rendered image of the temperature had been obtained. A typical visualization procedure using this set of tools could be as follows. First, choose a desirable viewing angle and render the scalar field. Then, explore an ROI using the arrow probe, and find the proper locations for inserting seed points. Next, try either particle tracing or streamtubes with different visualization parameters. Finally, use the zooming lens to study the detailed local flow properties. Although the user s interaction supported by the incremental image update technique has its limitations (for example, the viewpoint has to be fixed and only a small portion of the image can be updated at one instance to allow interactivity), this set of tools can be very useful during the trial and error visualization stages. To this end, our techniques can be considered to be complementary to other techniques for the visualization of mixed scalar and vector fields, and have the potential of being applied for other visualization purposes. In addition, note that the scalar field to be visualized can either exist separately as a sampled data set or be derived from the vector field. With conventional vector field visualization techniques, only a selected part of the vector field (those areas through which the vector icons pass) can be visualized. It may be helpful to derive the vector magnitude as a scalar field, and use our techniques to visualize it together with the vector icons to provide a global insight into the vector field. We are currently implementing other vector field visualization techniques, and experimenting with our tools on other flow data sets. Another direction of future research will be how to achieve the most informative mapping from the flow data to the attributes 246

8 of the vector icons. For example, in intermixed visualization, mapping a parameter to the color of a vector icon may not be a good choice because of the compositing effect of the volume renderer, although the zooming lens tool provides a partial solution to this problem. Acknowledgments This work has been supported by the National Science Foundation under grant CCR and by the Department of Energy under the CS grant. Special thanks to Issei Fqjishiro, Taosong He, Claudio Silva, and Sidney Wang for helpful discussions. We would also like to thank Hideo Miyachi of Kubota Graphics Technology, Inc. in Tokyo for providing us with the CFD data,set and valuable comments. VolVis can be obtained by sending to volvisqcs.sunysb.edu. References R. Avila, T. He, L. Hong, A. Kaufman, II. Pfister, C. Silva, L. Sobierajski, and S. Wang, VolVis: A Diversified Volume Visualization System. In R. Bergeron and A. Kaufman (eds.), Proceedings Visualization 94, 31-38, Washington D. C., October IEEE Computer Society Press. [31 M. Cohen, J. Painter, M. Mehta, and K. Ma, Volume Seedlings. Proceedings of 1992 ACM Symposium on Interactive 3D Graphics, E. Bier, M. Stone, K. Pier, W. Buxton, and T. DeRose, Toolglass and Magic Lenses: The See- Through Interface. In Proceedings of SIGGRAPH 93, 73-80, August R. Crawfis and N. Max, Texture Splats for 3D Scalar and Vector Field Visualization. In G. Nielson and D. Bergeron (eds.), Proceedings VisuaE itation 93, , San Jose, CA, October IEEE Computer Society Press. T. He, L. Hong, A. Kaufman, and H. Pfister, Generating Transfer Functions Using Genetic Algorithms. Technical Report, TR , Computer Science Department, SUNY Stony Brook. Submitted for publication. A. Kaufman, D. Cohen, and R. Yagel, Volume Graphics. IEEE Computer, 26, 7 (July 1993), W. de Leeuw and J. van Wijk, A Probe for Local Flow Field Visualization. In G. Nielson and D. Bergeron (eds.), Proceedings Visualization 93, 39-45, San Jose, CA, October IEEE Computer Society Press. [8] M. Levoy, A Hybrid Ray Tracer for Rendering Polygon and Volume Data. IEEE Computer Graphics and Applications, 10,3 (March 1990), [9] K. Ma, M. Cohen, and J. Painter, Volume Seeds: A Volume Exploration Technique. The Journal of Visualization and Computer Animation, 2, 4 (1991), [lo] K. Ma and P. Smith, Virtual Smoke: An Interactive 3D Flow Visualization Technique. In A. Kaufman and G. Nielson (eds.), Proceedings Visualization 92, 46-53, Boston, MA, October IEEE Computer Society Press. [ll] N. Max, R. Crawfis, and D. Williams, Visualizing Wind Velocities by Advecting Cloud Textures. In A. Kaufman and G. Nielson (eds.), Proceedings Visualization 98, , Boston, MA, October IEEE Computer Society Press. [12] H. Miyachi, A Note on Interactive Flow Visualization with Graphics Supercomputers. In Proceedings NICOGRAPH 90, November (In Japanese) [13] W. Schroeder, C. Volpe, and W. Lorensen, The Stream Polygon: A Technique for 3D Vector Field Visualization. In L. Rosenblum, G. Nielson (eds.), Proceedings VisuaZization 91, , San Diego, CA, October IEEE Computer Society Press. [14] H. Shen and C. Johnson, Differential Volume Rendering: A Fast Volume Visualization Technique for Flow Animation. In R. Bergeron and A. Kaufman (eds.), Proceedings Visualization 94, , Washington D. C., October IEEE Computer Society Press. [15] L. Sobierajski and A. Kaufman, Volumetric Ray Tracing Symposium on Volume Visualization, ACM Press, October [16] T. van Walsum, A. Hin, J. Versloot, and F. Post, Efficient Hybrid Rendering of Volume Data and Polygons. In A. Hin and F. Post (eds.), Advances in Scientific Visualization, Springer-Verlag, [17] S. Wang and A. Kaufman, Volume-Sampled 3D Modeling. IEEE Computer Graphics and Applications, 14, 5 (September 1994), [18] S. Wang and A. Kaufman, Volume Sculpting. Proceedings of 1995 ACM Symposium on Interactive 3U Graphics,