11

Rendering Animation of Lace Curtain Using
BRDF/BTDF and Motion Physical Characteristics
Based on a Subjective Impression
Kensuke Tobitani

Atsushi Ishida

Lisa Park

Reseach Center for Kansei Value Creation
Kwansei Gakuin University
Hyogo, Japan
Email:tobitani@kwansei.ac.jp

School of Science and Technology
Kwansei Gakuin University
Hyogo, Japan
Email: atsushi.ishida@kwansei.ac.jp

School of Science and Technology
Kwansei Gakuin University
Hyogo, Japan
Email: lpark@kwansei.ac.jp

Sousuke Kaji

Eriko Aiba

School of Science and Technology
Kwansei Gakuin University
Hyogo, Japan
Email: skaji@kwansei.ac.jp

The National Institute of Advanced Industrial Science and Technology
Reseach Center for Kansei Value Creation / Kwansei Gakuin University
Osaka, Japan
Email: aiba.eriko@aist.go.jp

Aya Shiraiwa

Noriko Nagata

Reseach Center for Kansei Value Creation
Kwansei Gakuin University
Hyogo, Japan
Email:shiraiwa.aya@kwansei.ac.jp

Reseach Center for Kansei Value Creation
Kwansei Gakuin University
Hyogo, Japan
Email:nagata@kwansei.ac.jp

Abstract—The need for rendering woven fabrics arises frequently in computer graphics. Woven fabrics have a specific appearance, luster, and transparency. A BRDF model is well known
as the basic technology employed for expressing the appearance ofa woven fabric. In order to represent the transparency of a woven
fabric, a BTDF (bidirectional transmittance distribution function)model is required in addition to the BRDF model. Additionally,
rendering fabric motion properties is also significant to enhance
the texture of materials in animations. In this paper, we propose
a new method to render woven fabrics that have both realistic
appearance and motion.

I.

I NTRODUCTION

The need for rendering woven fabrics arises frequently
in computer graphics [1]. Woven fabrics have a specificappearance, luster, and transparency. A BRDF (Bidirectional
Reflectance Distribution Function) model [2] is well known as
the basic technology employed for expressing the appearanceof a woven fabric. In order to represent the transparency ofa woven fabric, a BTDF (Bidirectional Transmittance Distribution Function) model is required in addition to the BRDF
model. In this paper, we propose rendering methods for woven
fabrics, particularly transparent fabrics such as lace, based on
a BTDF model and applying the BTDF model to a real-timerendering algorithm. Additionally, rendering fabric motion
properties is significant in enhancing the texture of materials
in animations [3]. Therefore, we performed an experiment toevaluate subjective impressions about relationships between
the optic and the motion properties, and to estimate thedynamic properties directly from the optic properties.
©QCAV2013

63

II.

R ELATED WORKS

Computer graphics(CG) is used in a number of different
fields including TV, film production, commercial message,
and web contents. In particular, there is a growing need forestablishing the digital archive of various merchandise becauseof the rapid spread of the Internet. The curtain catalog is atypical example. Development of a curtain catalog is expensive
because of the many kinds of color, pattern, and material.
Additionally, static impressions of a curtain catalog will differ
from reality because of the change of color and transparency
in placing a curtain to a window. It is necessary to express thechange of texture of a curtain due to the actual illumination
condition to show the difference from reality.
BRDF is commonly used for the texture expression of
woven cloth. The Cook-Torrance model [6] is representativeof a physically-based BRDF model. In addition, Ashikhmin etal. generated microfacet-based BRDF and modeled satin andvelvet cloth [7]. However, they were not concerned with thelight transmission characteristics of woven cloth. By contrast,
Stam et al. proposed a bidirectional reflectance model anda bidirectional transmittance model to show human skin [8].
Bousquet et al. focused attention on bidirectional reflectancemodel and bidirectional transmittance of leaves and compared
the measured BRDF and BTDF of leaves with a proposed
BRDF and BTDF model [9]. Takeda et al. focused attention on
Noh costume and estimated the microfacet surface geometryof woven fabrics in considering regular transmission characteristics [10][11]. None of this research, however, was concernedwith any of the transmission characteristics of woven clothother than the regular transmission direction. Woven cloth,such as lace curtains, express the characteristic transparencyof soft light. In order to show the characteristic transparency,
it is necessary to model the optical property by considering
not only the transmission of light but also its light-scattering
properties [12].
In this paper, we measure the transmission characteristics
and light-scattering property of two different woven cloths
and propose a transmission approximate model based on themeasurements.
III.

light to the intensity of incident light. BTDF is given by thefollowing formula;

BT DF (θt , ϕt , θi , ϕi ) =Lt (θt , ϕt , θi , ϕi )Li (θi , ϕi ) cos θi(1)Here, Li (θi , ϕi ) is the intensity of incident light from thedirection of the light source, and Lt (θt , ϕt ) is the intensity oftransmitted light to the direction of view point. As shown in
Fig.2, the transmitted light to yarn is scattering into the yarn.

R ENDERING OF WOVEN CLOTH USING BRDF AND
BTDF

A. Measurement of BRDF and BTDF of woven cloth
We measured the BTDF of the two woven fabrics by usinga BRDF instrument (OGM-3 [4]), which consists of a fixed
digital camera, a movable light source (metal halide), and a
movable sample plate. 2400 points per cloth were measured
by repositioning the lamp and the plate. As shown in Fig.1,
we made the following observations: (1) a woven fabric has
the property of bidirectional transmittance and scattering and(2) transmitted light consists of two components, diffusionaland directional transmission.
Fig. 2.

The light through the yarn

As a result of the measurement as shown in Fig.1, we
found that transmitted light consists of a diffuse transmittancecomponent (scattering light) and a directional transmittancecomponent (specular transmittance light). Based on the above
understanding, we propose a new BTDF model for woven
clothes. This model includes a diffuse transmittance component and a directional transmittance component, each ofwhich is expressed by the Henyey-Greenstein function [5]. The
Henyey-Greenstein function is a scattered model that explains
the dispersion of dust in the galaxy. This function was applied
to the scattering of yarn with following formula.

(a) Material A

ph(θ) =

1 − g24π(1 + g 2 − 2gcosθ)1.5(2)Here, g ∈ [−1, 1] is a weighting factor that decides thephase of scattering. For g positive, the scattering peaks inthe forward scattering direction. For g negative, the scatteringpeaks in the backward scattering direction. Thus, we give adefinition of the intensity of light transmitted to an arbitrary
view direction.
(b) Material B

Iout (θt ) = ID + kd Iin exp(−τ )phdif f (θt )ρ +ks Iin exp(−τ )phspec (θt )ρ
Fig. 1.

(3)

Comparison of two woven fabrics.

B. BTDF model and parameter estimation
1) Proposed BTDF model: In order to render high-quality
images of various woven cloths at low computational cost, theuse of a standardized BTDF model is essential to represent
the measurement data within a few parameters. In general,
the transmittance property of an object can be described by
BTDF, which is defined as a ratio of the intensity of transmitted

64

Here, Iout (θt ) is the light intensity transmitted, Iin is thelight intensity, ID the light intensity transmitted by the gaps
in woven cloth, kd is the diffusional transmittance coefficient,exp(−τ ) is the absorption coefficient, τ is the optical depth(filar width), phdif f (θt ) is the Henyey-Greenstein function
for the diffusional transmitted light, ρ is the filar density, ks
is the directional transmittance coefficient, and phspec (θt ) is
the Henyey-Greenstein function for the directional transmitted
light.

2) Estimation method of parameters: In order to apply
the proposed model to the measurement data, a method forautomatic estimation of parameters is required. We estimate
the parameters by using the Levenberg-Marquardt algorithm(LMA). LMA is one of the optimization algorithms that is
applied to various problems. To apply optimization to vast
amounts of the measured BTDF data is necessary to estimate
high-quality appearance. However, the way is not efficientbecause computation time cost is huge. Because we optimize
these parameters by 40 points, which appropriately represents
a diffuse transmittance component and a directional transmittance component in the measured BTDF data.

3) Comparison between the measured BTDF and the modeled BTDF: The comparison between the measured BTDF andthe result of fitting the BTDF model by estimation parameters
is shown in Fig.3. The model assumes that the size of the warp
yarn and the weft yarn is the same. In comparing the proposedmodel to the measured value, we found that the peak of the
specular transmittance of the model was in agreement with themeasured value, and the curve of the diffuse transmittance ofthe model also corresponded with the measured value.

To estimate them by M numbers of input data the merit
function is given by the following formula.

E(p) =F ∑∑rfTp rf p(4)

f =1 p∈ΩHere,rf p = Iout (θt ) − Iout (θt ; af p )(5)where p is the estimated parameter vector, F is the numberof input data, and Ω is the target data aggregate.
Based on the merit function estimates parameters, where
the parameter vector defines pk in case of k, we use the merit
function in equation 4.

Fig. 3.

Comparison between measured BTDF and modeled BTDF.

C. Rendering with the modeled BTDF
E(pk ) =F ∑∑(rfkp )T rf p

k = 1, 2, ..., M(6)

f =1 ∈Ω

Here, rfkp is the residual vector based on equation 5 in caseof k. Then the updated parameters by LMA is given by thefollowing formula.

pk+1 = pk − (JkT Jk + λk I)−1 JkT rk

D. Real-time rendering of the BTDF
(7)

Here is


..
.



 k 
T

Jk = δrk /δpk
, rk =  rf p ..
.

The results of rendering based on the measured BTDF andthe modeled BTDF are presented in Figs.4 and 5. Both therendering algorithms are implemented as shader plug-ins forMaya. In both images, we can observe that the transmission
factor differs according to the position of the curtains, andthe resulting shadows display uneven shading. These results
demonstrate that the modeled BTDF is as effective in depicting
the transmission property as is the measured BTDF.

(8)

A real-time rendering algorithm of this BTDF model was
implemented by using a combination of OpenGL and Nvidia’Cg. The algorithm was programmed using texture sampling bymeans of an LUT, which was constructed as a two-dimensional
bitmap image translated from the four-dimensional BTDF data
(Fig.6). The transmitted and reflected light obtained from the
LUT, the background light defined by cube mapping, and atexture element were added during rendering.
IV.

E STIMATION PHYSICAL CHARACTERISTIC OF WOVEN
CLOTH FROM SUBJECTIVE IMPRESSION

where the λk is the stabilization parameter to hold divergence and I is the unit matrix. Iterating to the converseis necessary since the minimum is at best only a statisticalestimate of the parameters.

65

A. Experiment of impression evaluation
We performed an experiment to evaluate subjective impressions about relationships between the optic and the motion

Fig. 4.

Rendering of images with the measured BTDF

Fig. 5.

Rendering of images with the modeled BTDF(a) Light intensity/bend and the thickness of warp

Fig. 6. Lookup table as bitmap image translated from measured BTDF data.

properties, and estimated the dynamic properties from the optic
properties directly. The experiment was performed by using ten
evaluative word pairs. All evaluative words were adjectives
related to the optic and motion properties (e.g., pliable or
stiff, heavy or light, and so on). Experimental stimuli wereeight curtain animations that differed in values of bend andshear. We adopted Scheffe’s paired comparison method as anexperimental method. Participants were required to compare
eight paired curtain animations with each evaluative word pairs
on a five-point scale. The participants were seven men andthree women in their twenties.
B. Measurement of BRDF, BTDF and KES of woven cloth
We measured the optic and motion properties of the three
woven fabric samples. For optical properties, BRDF and BTDF

66(b) Light intensity and the thickness of the weft

Fig. 7.

Relationship between optic and motion properties.

were measured by using a BRDF instrument, OGM-3. For motion properties, bend, shear, and compression were measured
by using a handle instrument, KES (Kawabata Evaluation

System).
C. Relationship between optics and motions
The results of the experiment on impression evaluation
revealed the impressions of flexibility (pliable or stiff) andweight (heavy or light) are influences on the characteristics ofcurtain motion. The impressions of flexibility and of weight
depend on the bend and the rate of specular reflection. For
flexibility, curtain motions were evaluated as more stiff bypeople when the value of bend and rate of specular reflection
were also higher. For weight, curtain motions were evaluatedas lighter when the value of bend was lower and rate ofdiffuse transparency was higher. The value of bend increased
in proportion to the thickness of warp. The specular reflectanceand the directional transmittance decreased in proportion to thethickness of weft, as shown Fig.7.

(a) Stiﬀ and heavy impression. Both warp and weft are thick, the specular
reﬂectance is high and the directional transmittance is low.

D. Rendering animations
We performed the rendering of animations with different
subjective impressions by using Maya’ shader plug-ins, andcompared in Fig.8. The rendering environments are a 3.40 GHz
Intel Core i7 processor, 16 GB of RAM, and nVIDIA Quadro
4000 graphics processor.
V.

C ONCLUSIONS

We have proposed a BTDF model and two algorithms
for both the off-line and real-time rendering of woven fabrics. Furthermore, the results of the evaluation on subjective
impression showed the possibility of estimating the dynamic
properties by the optic properties more directly. The rendering
animation with the new method, which adopted the evaluationsof subjective impressions, enhanced both realistic appearance
and motion. We are planning to generate a catalog of curtain
animations that can express various types of woven fabrics
under arbitrary light conditions.

(b) Pliable and middle weight impression.
The middle appearance of (a) and (c).

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Fig. 8. The results of curtain animations with different subjective impressions.
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