AN INTERACTIVE METHOD FOR REFRACTIVE WATER

CAUSTICS RENDERING USING COLOR AND DEPTH

TEXTURES

Nuttachai Tipprasert

Department of Computer Engineering,Faculty of Engineering,Chulalongkorn University 254 Phyathai Road, Patumwan,

Bangkok Thailand. 10330

Pizzanu Kanongchaiyos

Department of Computer Engineering,Faculty of Engineering,Chulalongkorn University 254 Phyathai Road, Patumwan,

Bangkok Thailand. 10330

Keywords: global illumination, caustics, natural phenomena, color texture, depth texture, interactive rendering.

Abstract: Realistic rendering of underwater scenes is one of the most anticipated research topics in computer graphics.

Caustics are the important component enhancing the realism of this kind of scenes. Unfortunately, rendering

caustics is a time consuming task. As a result, most existing algorithms cannot handle this at interactive rate.

In recent years, volumetric texture based rendering algorithms have been proposed. They can render the

underwater scene with caustics in real-time. However, these algorithms require large amount of memory

and are restricted to non-complex scene. In this paper we present a new interactive caustics rendering

algorithm which require less memory usage. In our proposed method, we represent each object as a pair of

color and depth texture. Color texture is used to store the object image viewed from viewing rays which

refracted at water surface. We calculate the light intensity distribution on this image and store the result

back to the color texture. The depth texture is used in the intensity calculation process to improve accuracy

of the caustics patterns. Our experiment shows that proposed algorithm can handle complex underwater

scene with caustics at interactive time rate. While using a pair of color and depth in stead of volumetric

texture, we can reduce memory usage significantly.

1 INTRODUCTION

Research in the filed of realistic natural phenomena

rendering is one of the most important subjects in

computer graphics. Of all research topics, the

realistic rendering of scene with water is one of the

most anticipates research topics in this filed. To

enhance the realism of this kind of scene, caustics

rendering is one of the most important aspect that

must be taken into account. But the rendering

process of this phenomenon involves many path

tracings and intersection tests. As a result, the

rendering of a realistic water scene seems to be more

suitable for off-line rendering rather than real-time

rendering. However, there are many applications,

such as video games and virtual realities which

require realistic real-time rendering of such a scene.

Therefore, the traditional rendering algorithm cannot

be employed at these applications.

To reduce the computation cost, the volumetric

texture based caustics rendering algorithm has been

proposed (Iwasaki, 2003, Iwasaki, 2005). This

technique use volumetric textures to represent the

objects in the scene and perform the intersection test

on these textures instead. Even though the algorithm

can achieve interactive rendering capability, it

requires a lot of memory. As a consequence, these

techniques are limited to a simple scene that doesnot

have many objects.

Due to this limitation, we introduce a new

interactive method for rendering underwater scene

with caustics as viewed from above water. Our

technique requires less memory usage. In our

proposed method, the objects are represented by one

pair of color and depth texture .These textures are

used in both caustics casting and refracted objects

rendering processes to enhance the performance.

Color texture is used to store the object image

423

Tipprasert N. and Kanongchaiyos P. (2006).

AN INTERACTIVE METHOD FOR REFRACTIVE WATER CAUSTICS RENDERING USING COLOR AND DEPTH TEXTURES.

In Proceedings of the First International Conference on Computer Graphics Theory and Applications, pages 423-428

DOI: 10.5220/0001355404230428

 SciTePress

viewed from viewing rays which refracted at water

surface. The depth texture is used to represent 3D

position of each pixel in color texture. The algorithm

is accelerated by performing intersection and

computing intensity distribution on texture-space in

stead of object-space. We are able to show that this

technique can generate complex underwater scene

with caustics at interactive time-rate.

The remainder of this paper is organized as

follows: Next section, we will briefly discuss the

related work. In section 3, a main concept of our

rendering strategy will be presented. Section 4 our

sample results are shown and then we gave the

conclusion and future work in section 5.

2 RELATED WORK

In the past few decades, many algorithms have been

developed to simulate global illumination effects

such as caustics. (Arvo, 1986; Jensen, 1996;

Guenther, 2004; Trendall, 2000; Wald, 2002;

Wyman, 2004) Even though these techniques can

render realistic caustics, they require long

computational time or require special hardware

setting. Recently, Shah et al. (Shah, 2005) presented

real-time caustics rendering algorithm based on

backward ray-tracing. In order to speed up the

algorithm, they created position texture and used it

to store 3D world coordinate of each object in the

scene, then, perform the intersection tests in the

image-space. The caustics pattern is rendered by

using point primitive. Though, the main concept of

their algorithm similar to our work, the whole idea

has so many differences in details. Besides, their

algorithm suffers from alias problem, just like any

other image-space algorithms.

There are several methods that developed for

underwater caustics rendering. Stam (Stam, 1996)

simulated underwater caustics by generating caustics

textures and mapping them onto objects in the scene,

Crespo (Crespo, 2004) has proposed a method that

was extended from this concept and implemented it

on programmable graphics hardware, although these

methods can simulate underwater caustics in real-

time, the results are not visually correct due to the

fact that they perform light intensity distribution

calculation on flat surface. Watt (Watt, 1990)

introduced underwater caustics rendering algorithm

using backward beam-tracing, which was extended

from the algorithm originally proposed by Heckbert

(Heckbert, 1984). Rather than tracing individual

light rays, the backward beam-tracing traces light

beam that emerge from light source and then refracts

them at each polygons of water mesh. The caustics

patterns are generated by accumulated light intensity

that each receiver polygons receives from each

participated light beam. Though the beautiful images

of underwater scene can be generated from this

algorithm, the computation time is also extremely

long. The main problem about beam-tracing based

caustics rendering algorithm is the intersection test

between light beam and diffuse receiver. Nishita and

Nakamae (Nishita, 1994) solved this problem by

subdividing light beam and using scan-line

algorithm to determine intersection point. Their

algorithm was then improved by Iwasaki et al.

(Iwasaki, 2002). In the following works, Iwasaki et

al. applied volume rendering technique to handle the

case where the observers are above the water

(Iwasaki, 2003). Their proposed method creates slice

image of each receiver object in which the caustics

pattern that cast on these objects can be depicted by

performing the intersection test of light beam on

these images. They continue working on this method

by presenting the extended algorithm for casting

caustics from arbitrary refractive medium (Iwasaki,

2005). By performing intersection test on the

collection of slice images instead of object mesh, the

computation time is greatly reduced. However, these

algorithms require large amount of texture

memories; as a consequence, they are not suitable

for using with complex scene.

To address this problem, our algorithm replaces

the usage of volumetric texture by using a pair of

color and depth texture. Our algorithm can display

refractive caustics due to water surface at interactive

frame-rate and requires much less memory usage

than the previously proposed beam-tracing based

interactive caustics rendering techniques.

3 RENDERING ALGORITHM

In this section we give a description of our new

algorithm. First we present the general idea of fast

intersection test by using a combination of depth

texture and reference planes (3.1). Next, we describe

how to render underwater scene with caustics. In this

step, the color texture then comes into play (3.2).

Finally, the discussion on rendering refracted

underwater scene is given (3.3).

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3.1 General Idea of Fast Intersection

Test Technique

In order to optimize the rendering speed of caustics

rendering algorithm, the method for testing

intersection between light beam and objects must be

improved. Iwasaki et al. (Iwasaki, 2003) solved this

problem by using volumetric textures. In their

proposed method, the volumetric textures are created

by projecting a part of objects images that lie

between two adjacent virtual planes onto one of

these planes. They referred to these virtual planes as

“Sampling Plane”. The sampling plane is used in the

intersection test step to determine the intersection

point of light beam and viewing ray at receiver

geometry. Because the number of sampling plane for

each objects are much less than the number of

polygons, the iteration steps required for finding

intersection point are extremely reduced.

Nevertheless, this algorithm still has a memory

usage problem because large amount of texture

memory is required to store these images. We

observed that if we line up these images in the

correct order from back to front and look straight

through them, these images will appear as one

complete image. From this observation, we realize

that only one color texture is sufficient to represent a

diffuse object. However, the use of single 2D image

to represents 3D object data cannot conserve

volumetric property of the object. If we estimate

intersection point by testing intersection on this

image, the result may be undesirable. The ray may

“early hit” the image plane or “lately miss” the

actual intersection point (see figure 1). We solve the

problem mention above via the use of depth texture

and Reference Planes. In the proposed method, the

depth texture is used to store 3D position of each

pixel of object geometry and the reference planes is

the plane which virtually slices along some given

major axe of object.

In the intersection test step, we use these

reference planes for indexing texture value. When a

ray intersects with the reference plane, the

intersection point (x, y, z) is then transform into

texture space coordinate (x’, y’, z’). The x’ - and y’ -

coordinate are used to index appropriate entry of the

depth texture and the resultant value is compared

against value of z’. If the differences of this two

values are less than some specific threshold, this

intersection point is then accepted (see figure 4).

Normally, this acceptance threshold should be the

distance between two reference planes. Otherwise,

some undesirable result might occur.

From this proposed algorithm, the intersection

test can be done at interactive time-rate and does not

require extra memory usage as it did in the previous

method. In the upcoming sections, we will show

how this technique can be used in underwater

caustics rendering process.

3.2 Rendering Caustics

The caustics pattern are formed by multiple refracted

light rays converge to single point on diffuse object

geometry. In our proposed algorithm, we emulate

this behavior by representing water surface as

triangular mesh. When the incident light rays

intersect with each water triangle, they create

refracted light beam called illumination volume.

Next, we find intersection area of each illumination

volume and object geometry and compute light

intensity for each of them. The intensity of

intersection area can be computed from radiant

equation:

= Φ

/ (A

* cos(θ

)) (1)

where Φ

is the total flux that arriving

intersection area A

and θ

is the angle between the

refracted light ray and the normal of intersection

area. The value of Φ

in equation (1) can be

obtained by finding total flux Φ

that pass through

Figure 2: Diagram of our intersection test algorithm. The

opaque line represent reference planes, dash line represent

acceptance range of each reference plane and gray curve

represent object surface. From this image, the intersection

point that will be accepted is the second point.

Figure 1: Incorrect intersection estimation. (a) The

incoming ray hit image plane early. Figure (b) show the

case where the ray is misses the actual intersection point.

AN INTERACTIVE METHOD FOR REFRACTIVE WATER CAUSTICS RENDERING USING COLOR AND DEPTH

TEXTURES

425

water triangle. When light travels through water,

some of its energy are absorbed. Thus, the

relationship between Φ

and Φ

can be written as:

= Φ

* exp(-K*d) (2)

where K is the absorption coefficient and d is the

distant light travels through the water. Let I

incident light intensity. By substituting equation (1)

with equation (2) and representing Φ

in term of I

we get:

= I

* ((A

* cos(θ

) / (A

* cos(θ

)) * exp(-K*d)

(3)

where A

is an area of water triangle and θ

is an

incident light angle. By accumulating the intensity

of each participated intersection area, caustics

pattern can be depicted. Finally, the final color of

each pixel on diffuse receiver is computed from this

equation:

= I

* I

+ I

(4)

where I

is the final color of the object I

diffuse light intensity and I

is ambient light

intensity.

In order to cast caustics pattern onto receiver

geometry by the method mentioned above, the

intersection test problem must be addressed. We use

the fast intersection test strategy described in the

previous section to handle the case. To find the

intersection area, we first create depth texture and

reference planes. In the process of depth texture and

reference planes creation, we first specify the

bounding box of an object. This bounding box is

also used to define orthogonal view-volume which

will be used in the next step. We must align this

bounding box by setting the front side of the box

perpendicular to the refracted viewing ray (see

figure 3). Then we create depth textures by

rendering diffuse object using orthographic

projection. We only store the position of each vertex

and copy them to the depth texture. The reference

planes are determined by slicing the bounding box

along the refracted viewing ray. The number of

sliced planes is specified by user.

After the depth texture and reference planes are

created, we move to the next step; caustics

rendering. In our proposed method, we first create

diffuse image of the receiver by taking the refracted

viewing ray into account as in the case of depth

texture. We call this image a Diffuse Map and store

it into color texture. Next, we find the intersection

area between each illumination volume and each

reference plane. We then draw intersection triangle

of each area to a color texture called Caustics Map

by using additive blending function. The color of

each triangle vertex is determined by calculating

intensity at the intersection point. After the

intersection triangle is rasterized, we transform each

of their pixels into the depth texture space. The

transformed coordinate of this pixel will be used to

index the value of depth texture. This indexed value

is then compared with pixel’s transformed z

coordinate. If the differences of these two values are

less than specific threshold, we accept this pixel;

otherwise, we discard it. After we finish with

caustics map creation, we then multiply it with

diffuse map to obtain final result. This result is then

stored back to the diffuse map. The overall processes

of caustics rendering are visualized in the figure 4.

By using this proposed method the image of

underwater caustics can be generated at interactive

time-rate. In order to create complete underwater

scene as viewed from the above water, there is one

problem unsolved, that is, refracted underwater

image rendering. Unfortunately, current real-time

refracted image rendering method such as

environment mapping cannot be applied to our

algorithm. This limitation comes from the fact that

our algorithm create object image by using

orthographic projection. If we directly apply these

images to water vertex as environment textures, the

resulting image may be undesirable. Therefore, new

techniques for handling refracted image of

underwater scene created by our algorithm must be

proposed. This technique will be described in details

in the upcoming subsection.

Figure 3: Reference plane alignment.

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3.3 Rendering Underwater Image as

Viewed from Above Water

In this section, we describe the method for rendering

complete underwater scene with caustics as viewed

from above water.

In order to render the refracted image of under

water objects, our method applies the concept of ray-

tracing and texture mapping (see figure 5). The

proposed method begins by calculating the viewing

vectors from view point to each fragment of water

triangle. Next, we generate refracted viewing ray at

the water surface. After that, the viewing ray is

traced and checked for the intersection point. The

intersection test is performed by using our proposed

reference plane and depth texture strategy. The final

color of water fragment is specified by transforming

the intersection point to texture space and obtaining

color from diffuse map.

4 IMPLEMENTATION AND

RESULTS

There are so many fragment operations involved in

our algorithm; as a result, it cannot be applied to the

fixed function operation on traditional graphics

hardware. By taking an advantage of

programmability on this day GPU, we can perform

caustics rendering using our algorithm at interactive

time-frame. We test our idea by implementing our

proposed algorithm on 2.8 GHz Pentuim IV desktop

with Geforce 6800 128 Mb GPU. The test programs

are written in C++ using OpenGL API. Figure 6

show the image of underwater teapot and dolphin.

All images are rendered at resolution of 512 x 512

pixels. Average rendering time of our program is

about 2.2 fps depend on number of reference plane.

The sample images indicated that our algorithm

can cast caustics on arbitrary objects. Two images

on figure 6(b) are rendered by using different

number of reference plane. Although the reference

plane of these two images is 10 times differing, the

differences on the resulting image are hardly

noticeable. It can be concluded that, in some objects

small, number of reference plane are sufficient to

create realistic result.

All sample programs can run in interactive time-

rate. Although in this version of our program, we

have not yet shown dynamic scene, such a case

would not be prone to any problem from our

algorithm, because in this version both color and

depth textures are recreated at each frame.

By comparing with previously proposed

volumetric texture based method (Iwasaki, 2003;

Iwasaki, 2005), the recreation of volumetric texture

can cause a problem. And by using only single pair

of color and depth texture to represent an object, the

required memory usage from the previously

proposed method can be reduced significantly. As a

result, our algorithm is not restricted to a simple

scene.

5 CONCLUSION AND FUTURE

WORK

We have presented a new method for interactive

rendering underwater scene with caustics. With our

proposed method, the problem of complex scene in

previous method (Iwasaki, 2003) has been solved.

The main limitation of our algorithm is it can

only handle refractive caustics and underwater

images. Thus, it cannot be used to generate complete

ure 5: Refraction ma

techni

ue.

Figure 4: Caustics rendering process. In figure (a), the

triangle represents intersection area for each reference

plane. Only accepted fragments of each intersection

triangle are drawn to the caustics map. In figure (b), the

final image is computed by multiplying diffuse map and

caustics ma

AN INTERACTIVE METHOD FOR REFRACTIVE WATER CAUSTICS RENDERING USING COLOR AND DEPTH

TEXTURES

427

water-side scene. In order to create realistic water-

side scene, the reflective caustics due to water

surface and reflective image of objects must be

taken into consideration. The casting process of

reflective caustics is somewhat different from

refractive caustics, thus, this algorithm must be

extended in order to handle such an effect in future

work. Furthermore, we want to find the optimization

method for this proposed algorithm. From our

observation, the LOD method may be used to apply

with our reference plane algorithm by using less

slice plane at the distance object. The work on

applying this concept is still in development.

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Figure 6: Results from our algorithm. Figure (a) show under water teapot. Figure (b) compare two dolphin images which

rendered by using different number of reference plane. Image on the left was rendered at average 2.2 fps with 50

reference planes. Image on the right was rendered at average 10.7 fps with 5 reference planes.

(a)

(b)

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