Sort-free Transparent Isosurface Visualization ofTetrahedral Volume Data
Asuka Sugiyama 1, Kyoko Hasegawa 2, Susumu Nakata 2, Satoshi Tanaka 2
1

1Graduate School of Information Science and Engineering, Ritsumeikan University, Japan
2
College of Information Science and Engineering, Ritsumeikan University, Japan

Introduction

In the fields of science, engineering and medicine, there arestrong demands of visualizing varieties of simulation data.
Simulation data are often tetrahedral volume data. Therefore,
comprehensible and precise visualization of tetrahedral volumedata is important, it helps us to understand three-dimensionalstructures of simulation targets and simulation results.
Recently, we proposed the “particle-based surface rendering(PBSR)” [1]. It is a kind of point rendering that is suitable forvisualizing isosurfaces and boundaries of volume data. The
PBSR is executed by following three steps (see Fig.1). The firststep is to generate particles on a polygon mesh uniformly (step1). We repeat the particle generation LR times to prepare LR
independent particles groups. We call LR a “repeat level”. The
second step is to project particles of each generated group to theimage screen. At that time, for each group, each pixel stores acolor of the particle nearest to the camera position (step 2). We
repeat step 2 LR times and create LR statistically independentimages. The third step is to make an average image of the LR
images created in step2 (step 3). In executing these three steps,
we need not sort rendering primitives (particles in the PBSR)
along the line of sight, so we can visualize large-scale data
quickly. We are also free from rendering artefact coming fromthe sorting error. Furthermore, it is easy to realize fusedvisualization, for example, fusions of isosurface–isosurface andisosurface-volume, where volumes are rendered with the“particle-based volume rendering (PBVR)” [2, 3, 4].

2

Application of the PBSR to tetrahedral volumedata

In order to apply the PBSR to isosurface visualization oftetrahedral volume data, we extract isosurfaces with themarching tetrahedrons algorithm. The combination of themarching tetrahedrons algorithm and the PBSR enables flexible
and precise isosurface visualization. Marching tetrahedrons
algorithm is a tetrahedral extension of the marching cubes
algorithm for cubic volume data. Polygons are extracted fromvolume data by comparing a given isovalue with voxel values.
Once a polygon mesh is created, we can execute the steps of
the PBSR described in the above. Particles should be madedistributed uniformly on each polygon. Particle density isdetermined from user-specified opacity based on the following
formula:      
Here n is the total number of particles, s is the particle crosssection, and S is the total area of the polygon mesh.

3Experiments

We show results of our new application of the PBSR thesetargets on tetrahedral volume data.
3.1

Static volume data
Fig. 2 is the result of visualizing one isosurface of simulated
tetrahedral temperature volume in a six-cylinder engine. We cansee the isosurface is visualized properly.

Fig. 1. Steps of the PBSR
In this paper, first, we apply the PBSR to tetrahedral volume
data, which has not been done so far. Next, we propose twokinds of fused visualization for tetrahedral data: (1) Isosurfacevolume-boundary fusion, expressing key voxel values withisosurfaces, broad overview with a volume, and exterior
appearance with a boundary surface. (2) Fusion of isosurfaces atdifferent time slices, which can intersect with each other incomplicated manners.

Fig. 2. Visualizing one isosurface with the PBSR 
Number of cells: 282,128
Number of polygons: 34,041

Fig. 3 is a result of the fused visualization. An important
isosurface (blue, the same isosurface as Fig. 2) and theboundary-surface (gray,    , 81,590 polygons) are
visualized with the PBSR, and broad overview with the PBVR
together. It successfully demonstrates simultaneous visualizationof surfaces and a volume at one time.

Fig. 5. Partial enlargement of Fig. 4.

4Fig. 3. Surface-volume fused visualization

Time series of volume data
Fig. 4 is the fused visualization of isosurfaces at different
time slices and boundary-surface (gray). Colors of isosurfaceschanges from blue to red as time develops according to therainbow color rule. Time development of stress volume insurgery simulation is clearly visualized within one static image.
Note that isosurfaces at different time slices may intersect witheach other. But use of the PBSR makes us avoid from rendering
artefact in spite of their complicated intersections (Fig. 5).

Conclusions

We combined the PBSR and the marching tetrahedrons
algorithm to execute comprehensible and precise isosurface
visualization of tetrahedral volume data. We also demonstrated(1) fusion of multiple isosurfaces, a volume, and boundary
surfaces, and (2) fusion of complicatedly intersecting
isosurfaces at different time slices. In any case, we have notseen any rendering artefact that often appears in the traditionaltransparent rendering methods. The PBSR for tetrahedral
volume data is beneficial to analyze varieties of tetrahedral
simulation data in scientific, engineering, and medical fields.

3.2

Acknowledgements
We express our thanks to Prof. K. Koyamada, Prof. H.
Tanaka, N. Sakamoto, K. Tagawa for their valuable suggestions.
We also thank Prof. H. Okuda who provided us the simulation
data of the engine.

References
[1]

[2]

[3]

[4]

Fig. 4. Fused visualization of isosurfaces atdifferent time slices.

S. Tanaka, K. Hasegawa, Y. Shimokubo, T. Kaneko, T. Kawamura,S. Nakata, S. Ojima, N. Sakamoto, H. T. Tanaka, and K.
Koyamada, “Particle-Based Transparent Rendering of Implicit
Surfaces and its Application to Fused Visualization", EuroVis
2012, Vienna (Austria), June 5–8, 2012 (accepted).
Naohisa Sakamoto, Jorji Nonaka, Koji Koyamada, Satoshi Tanaka
Volume, ”Rendering Using Tiny Particles, ” IEEE International
Symposium on Multimedia, pp.734-737, 2006.
Koji Koyamada, Naohisa Sakamoto and Satoshi Tanaka, “AParticle Modeling for Rendering Irregular Volumes”, Proceedingsof the International Conference on Computer Modeling andSimulation (UKSIM 2008), Cambridge, England, April 1 3, 2008,
pp.372-377, 2008.
Naohisa Sakamoto, Koji Koyamada, Ayumu Saito, Akinori
Kimuraand Satoshi Tanaka, ”Multi-Volume Rendering Using
Particle Fusion, ”IEEE VGTC Pacifc Visualization Symposium
2008, Kyoto, Japan, March 5-7, 2008.