Transparent Visualization for
Implicit Surface considered Texture
Takehiko Kitagawa 1, Satoshi Tanaka 2, Susumu Nakata 2 and Kyoko Hasegawa 2
1

1

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

Introduction

In the field of computer graphics, implicit surface
techniques have been developing to visualize smooth surfaces
precisely. Recent development of reconstructing an implicit
surface from 3D point cloud also makes the techniques to growimportance [1].
On the other hand, in medical, scientific and other fields,
precise and comprehensible transparent visualization is required
to investigate complex inner structures and positional relation of
3D objects. The particle-based surface rendering (PBSR) [2] hasbeen developed so satisfy such requirements. The PBSR is amethod for transparent rendering using opaque particles andprobabilistic determination of surface opacity. So far, renderingcolors used in the PBSR has been determined by hand or with acolor transfer function. For realistic visualization, however,texture mapping should also be useful. The target of this paper isto develop a particle-based texture mapping technique in theframework of the PBSR.
Fig.1. The process of the particle-base surface rendering.
2

Particle-Based Surface Rendering (PBSR) ofImplicit Surfaces

2.1

Implicit Surface
Implicit surfaces enable compact expression of complex
3D objects. An implicit surface is defined as a zero isosurface ofa proper scalar filed F(x,y,z). A usual way to execute its
transparent rendering is to decompose it into many small
polygons, e.g., triangles. The polygons are sorted along the lineof sight and dawn one by one, beginning from the farthest one
from the eye position. This rendering scheme, however, requires
computing time proportional to n log n with n the number ofpolygons. Besides rendering artifact often appears because of
sorting errors coming from finiteness of polygon widths.
Particle Base Surface Rendering
In our approach, we use the PBSR to visualize implicit
surface transparently. The PBSR is a kind of point rendering
using opaque particles and probabilistic determination of surface
opacity. It enables high-quality transparent rendering andflexible fused visualization of different types of objects, e.g.,surface-volume fusion.
The PBSR is executed, following the three steps below: 1.
particle generation, 2. particle projection, and 3. determinationof pixel values as averages of created multiple statisticallyindependent images. In the particle generation, opaque particles
are generated on curved surface uniformly. In the particle
projection, first, the generated particles are randomly divided
into LR groups. (Below we call LR “repeat level”.) Then the Zbuffer algorithm is executed to create a single image for eachparticle group. Finally, in the determination of pixel values,
images of all the particle groups are averaged to calculate thefinal pixel values. Fig.1 illustrates the process of the PBSR
explained here.

3Mapping Texture to the Curve Surfac e

The target of this paper is to propose texture mapping within
the framework of the PBSR. The ordinary texture mapping is
executed in units of polygons. In the PBSR, since its rendering
primitives are particles, the texture mapping should also be donein units of particles. Then particles become colored. Applying
the colored particles to the PBSR algorithm realizes transparent
rendering of implicit surfaces.
The way to map image colors to particles is illustrated in
Fig.2. Fig.2a is the case of the orthogonal projection, and Fig.2b
the perspective projection. In any case, we consider a straightline starting from each particle. An image color at anintersection point between the line and the texture image isassigned to the particle.

2.2(a)(b)
Fig.2. (a) Texture mapping by parallel projection, (b) texture
mapping by perspective projection.

4Experiments

Fig.3 is a simple example of our particle-based transparent
texture mapping. A transparent giraffe pattern is mapped to alemon shape using the parallel projection. A transparent section
image, which is also visualized with the PBSR, is fused with theboundary surface of the lemon. We can see that the proposed
texture mapping method works well, enabling us to see inside
the boundary surface to which a texture image is mapped. Fig.4
is a more complex example. The transparent texture of a humanface is mapped to a human-head surface. A transparent skullvolume, which is visualized with the particle-based volume
rendering (PBVR) [3], is fused with the face. We can see
positional relations of eyes, a mouth, etc. on the face surface
with those in the skull volume.
(d)

(a)

(b)

Fig.4. Transparent visualization of a human head surface towhich a facial image is mapped by the perspective
projection. A transparent skull volume is also fused. (a)Surface. (b) A facial image. (c) Skull volume. (d) Fusedimage.

(c)
5(d)
Fig. 3. Transparent visualization of a lemon shape to which
a giraffe pattern is mapped by the parallel projection. A
transparent section image is also fused. (a) Surface. (b) A
giraffe pattern. (c) Section image. (d) Fused image.

Conclusion

In this paper we have proposed s particle-based transparent
texture mapping method for precise transparent rendering ofimplicit surfaces. We have demonstrated the method using
parallel and perspective projections of a texture image to theparticles. We have also demonstrated mixed use of our texture
mapping with the fused visualization, which is a unique featureof the PBSR.
Our method proposed here is applicable to polygon models
as well as the implicit surface model. Once particles aregenerated on each polygon, our method becomes executable.
We plan to apply our method to digital archiving of cultural
heritages for which polygon models exist. For example, we aregoing to visualize complex 3D inner structures of Funeboko
float for the Gion Festival in Kyoto, Japan. Many high-quality
photographs taken during the real festival are available astexture images. Created contents should be suitable for, e.g., adigital museum in a virtual space of the Internet.

References

(a)

(b)

(c)

[1]

Y. Ohtake， A. Belyaev， M. Alexa， G. Turk and H.-P. Seidel :Multi-level Partition of Unity Implicits， ACM Transactions onGraphics， Vol.22， No.3， pp.463-470，2003.

[2]

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.

[3]

K. Koyamada, N. Sakamoto, and S. Tanaka, "A particle modelingfor rendering irregular volumes," In Proc. UKSIM, 2008 (2008),
pp. 372–377.