Eurographics Workshop on Natural Phenomena (2007)D. Ebert, S. Mérillou (Editors)

Expressive Illumination of Foliage Based on Implicit Surfaces

Thomas Luft Michael Balzer Oliver Deussen

University of Konstanz, Germany

Abstract

This paper presents an approach for vivid representations of foliage based on implicit surfaces. It approximatesthe complex lighting interaction within the foliage and enables a clear illustration of its general shape and localdensity, thus supporting the three-dimensional depth cue of the viewer. Due to its straightforward implementationas a preprocessing step that only adjusts the normal vectors of the geometry, this method has no additional memoryrequirements during the rendering process, and is especially applicable to real-time visualizations.

Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Computational Geometryand Object Modeling I.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism

(a) standard local illumination

(b) expressive illumination based on implicit surfaces

Figure 1: The characteristics of foliage are lost by usingstandard local illumination. In contrast, the approach pre-sented in this paper accentuates the general structure andthe local density of the foliage, resulting in vivid and ex-pressive representations that are also easily applicable tothe real-time rendering of large scenes.

1. Introduction

While for most real-time applications in computer graph-ics it is sufficient to use simple models of plants and treesbased on billboards, the demand for highly realistic and de-tailed representations steadily increased over the last years.This is reasoned by the availability of sophisticated mod-eling techniques [DL05], and of graphics hardware that isable to render even large plant and tree populations in real-time [DHL∗98,DCDS05,CCDH05]. Areas of application arevisualization tasks in landscaping, architecture, and ecosys-tem simulations.

Realistic plant models are characterized by a high com-plexity with a large number of vertices that is far beyond theaverage of actual models in computer graphics. For example,a simple scrub in an existing plant model library [GOS06]consists of approximately 30 000 vertices, and a tree oftenconsists of more than 200 000 vertices. This high complex-ity is especially caused by the necessarily accurate modelingof the foliage, whereby a significant simplification of the finebranches and leaves would result in visual artifacts.

These delicate and homogeneous foliage structures neces-sitate a sophisticated rendering with regard to their light-ing and shading. By simply using standard local illumina-tion, information about the general shape and the local den-sity of the foliage is lost and the foliage appears as a ‘leafcloud’ without any three-dimensional cue. The qualitativeoptimal solution is to use global illumination models to ob-

c© The Eurographics Association 2007.

T. Luft et al. / Expressive Illumination of Foliage Based on Implicit Surfaces

tain vivid representations. The disadvantages of global mod-els are their computational expensiveness, which disqualifiesthem for real-time calculations, and their additional mem-ory requirements and non-interactivity if they are applied asa preprocessing step. Especially the additional memory re-quirements are a pitfall for the representation of large sceneswith a high number of different plant models that are essen-tial for realistic landscaping and ecosystem visualizations.

This paper presents an approach for vivid representationsof foliage based on implicit surfaces. It approximates thecomplex lighting interaction within the foliage and enablesa clear illustration of the general shape and the local densityof the foliage, thus supporting the three-dimensional depthcue of the viewer. Due to its straightforward implementationas a preprocessing step that only adjusts the normal vectorsof the geometry, this method has no additional memory re-quirements during the rendering process, and is especiallyapplicable to real-time visualizations. Furthermore, it maybe applied to photorealistic as well as non-photorealistic vi-sualizations, which both benefit from the modified normalvector information.

Section 2 discusses related work, explains the conceptof implicit surfaces, and clarifies the used standard localillumination model. Section 3 introduces the approach offoliage illumination based on implicit surfaces. Section 4presents results for the application to photorealistic and non-photorealistic rendering, and Section 5 concludes the paperwith a discussion of the presented approach.

2. Background

2.1. Related Work

A method that resembles global illumination effects for real-time rendering is Precomputed Radiance Transfer [SKS02].It computes soft shadows and interreflections of objectsin low-frequency lighting environments and representsthem using low-order spherical harmonics. A light simu-lation system based on hierarchical radiosity is presentedin [SSBD03]. Using instantiated geometry and precise phasefunctions as scene description, this system allows the effi-cient computation of a radiosity solution for complex botan-ical scenes. Another method that enhances the display ofspatially complex scenes by providing additional contrastis Ambient Occlusion [PG04, Bun05]. This method deter-mines the percentage of the hemisphere above an objectpoint that is not occluded by other parts of the object.The difference between the two methods is that [PG04] isimplemented as a preprocessing step, and the results arestored in textures which are evaluated in the fragment shader,whereas [Bun05] computes the ambient occlusion directly inthe fragment shader.

A much more sophisticated parametric model for ren-dering plant leaves that achieves excellent visual results,is introduced in [WWD∗05]. Here leaves are described in

terms of spatially-variant bidirectional reflectance and trans-mittance functions that are extracted from real leaves. Forthe final illumination computation, this method extends Pre-computed Radiance Transfer for additionally handling high-frequency sunlight. The disadvantage of this method isits computational expensiveness, and more importantly, theenormous additional memory requirements, which disquali-fies it for the real-time rendering of large scenes.

A dedicated approach for the real-time rendering of treesand other plants has been presented in [HPAD06]. In thiswork an approximation of ambient occlusion is computedby using simple spherical or ellipsoidal occluders that areevaluated at runtime. However, the presented results are sub-optimal, since especially the general shape of the foliage isnot adequately reflected.

A very early work considering the illumination of trees ispresented in [RB85]. This rendering approach is based onparticle systems that are shaded by considering the parti-cle position within the tree boundary. The authors use dif-ferent schemes to approximate the shadowing of the parti-cles: a light-independent scheme for the ambient, and a light-dependent scheme for the diffuse lighting term.

In addition to photorealistic rendering, illumination infor-mation is also important for non-photorealistic rendering.Especially the representation of homogeneous leaf structuresbenefits from an adapted illumination that reduces the vi-sual complexity of the representations and allows more ab-stract rendering styles. [KMN∗99, DS00] are discussing theabstract rendering of vegetation and similar objects, therebyfocussing on the simplification and abstraction of the com-plex geometry, while preserving details to emphasize struc-ture and lighting. An approach that abstracts complex ge-ometry by additionally using implicit surfaces is proposedin [LD06]. Here implicit surfaces are used for a rigid sim-plification as a modeling step thereby enabling a clear repre-sentation of the three-dimensional structure of the objects.

2.2. Illumination Model

For the real-time rendering we assume a standard local illu-mination model [FvFH97] that computes the local illumina-tion I at a point p by

I = Iaka +∑i

IiSi

[kd(~N ·~L)+ ks(~V ·~R)n

]. (1)

The ambient reflection is denoted by the term Iaka with Iaas the intensity of the ambient light, assumed to be constantfor all objects, and ka as the ambient reflection coefficient.Furthermore, for each light source i the diffuse and specularreflection is added, which is multiplied with the intensity Iiof that particular light source and the corresponding shad-owing term Si. Thereby kd and ks specify the diffuse andspecular reflection coefficient, ~N denotes the normal vector,~L the vector to the light source i, ~V the vector to the viewpoint, and ~R the reflection vector of the light source i.

c© The Eurographics Association 2007.

T. Luft et al. / Expressive Illumination of Foliage Based on Implicit Surfaces

2.3. Implicit Surfaces

Following the Metaball concept presented in [MI87,Wat00],an implicit surface s is described by a set of generator pointsP, whereby each generator point pi ∈ P has a radius of in-fluence ri. The influence of a single generator point pi at apoint q is described by a density function Di(q) defined as

Di(q) =

(

1−(‖q−pi‖

ri

)2)2

, if ‖q− pi‖< ri

0, if ‖q− pi‖ ≥ ri

. (2)

The summation of the density function for all generatorpoints forms the density field F as

F (q) = ∑i

Di(q)− τ (3)

with τ ≥ 0. Thus, the implicit surface s with F (q) = 0 is de-fined as those points q where the sum of the density valuesof all generators equals the threshold τ . Note that any vec-tor norm can be used for the distance computation in Equa-tion 2. For all examples in this paper, the Euclidian norm isused. Figure 2 shows an implicit surface defined in R2 bytwo generator points and a threshold of τ = 0.3.

Figure 2: An implicit surface defined in R2 by two genera-tor points p1 and p2 with radii of influence r1 and r2 and athreshold of τ = 0.3.

The general shape of an implicit surface can be influencedby the global threshold τ in Equation 3. Greater values de-scribe a closer modulation of the implicit surface to its gen-erator set. Values of τ > 1 result in surfaces that do not nec-essarily enclose the generator set.

The extraction of implicit surfaces is performed by aMarching Cube algorithm [LC87] or one of its derivatives.The result is a polyline in 2D or a triangle mesh in 3D, whichapproximates the implicit surface at a regular grid with a userspecified resolution.

3. Contribution

The main concern when visualizing complex plant models,either as photorealistic or non-photorealistic representations,is the rendering of the foliage. Sophisticated global illumina-tion models are appropriate for off-line rendering, whereas

real-time rendering demands fast approximations withoutevaluating object interactions at runtime. The issue of sim-ply applying standard local illumination is the loss of foliagecharacteristics given by its general shape and local density.This is caused by the fine and complex structure of branchesand leaves that is perceived as a noisy ‘leaf cloud’ due to thelack of light interaction between the foliage components.

An appealing and vivid rendering of foliage requires aclear representation of its general shape and local density.Implicit surfaces offer a powerful abstraction for represent-ing amorphous object sets. They extract the basic shape ofa given object set based on the density distribution of thecontained primitives. The here presented approach utilizesimplicit surfaces in two different ways to adjust the illumina-tion of the foliage. First, it modifies the ambient term of theused local illumination model to approximate ambient occlu-sion effects by directly evaluating the density field formedby the generator set. The result are darkened parts withinthe foliage. Second, it realigns the normal vectors of the fo-liage vertices based on the implicit surface. Here the resultis an illumination that emphasizes the general shape of thefoliage and reduces the lighting-induced noise within the fo-liage renderings. Both methods are implemented as a prepro-cessing step, and the storage of the results within the normalvector information of the geometry enables an efficient real-time rendering without additional memory requirements.

Section 3.1 explains the generation of implicit surfacesfrom foliage geometry and its parameters. These implicitsurfaces are utilized to extract density information for theambient reflection, which is described in Section 3.2, andto realign the normal vectors of the vertices for diffuse andspecular reflection as described in Section 3.3.

3.1. Implicit Surface Generation

The set of generator points P of the implicit surface s is de-rived from the set of primitives of the given foliage geome-try G that consists of points, triangles, quads or other shapes.Therefore, a generator point pi is added to P for each geo-metric primitive gi ∈ G. The spatial position of pi is givenby the center of mass of gi. The radius of influence ri of thegenerator point pi is defined by a user specified global pa-rameter ρ , so that each generator point has the same radiusof influence. Figure 3 illustrates this implicit surface adap-tation, whereby 3(a) shows the tree with its given foliagegeometry, and Figures 3(b) to 3(d) show corresponding im-plicit surfaces with varying degrees of modulation.

The shape of the implicit surface can be adjusted by theglobal parameters ρ and τ . The parameter ρ defines the ra-dius of influence ri of each generator point pi ∈ P of the im-plicit surface s. This controls the degree of abstraction of thefoliage, whereby small values generate more details withinthe implicit surface, and high values amplify more the over-all shape of the foliage. The second parameter τ defines the

c© The Eurographics Association 2007.

T. Luft et al. / Expressive Illumination of Foliage Based on Implicit Surfaces

(a) given foliage geometry (b) ρ = 18,τ = 7

(c) ρ = 25.5,τ = 20 (d) ρ = 33.5,τ = 50

Figure 3: Simplification and abstraction of a given foliagegeometry by implicit surfaces with varying degrees of mod-ulation specified by the parameters ρ and τ .

threshold for the implicit surface s within the density fieldformed by the generator set P as described in Section 2.3. Itinfluences the distance of the implicit surface to the gener-ator points, causing a closer modulation. Experience provedthat the interactive specification of these parameters is nec-essary due to the broad variety of plant models. Values thatprovide adequate results can be automatically specified withregard to the size of the model, but only user-driven fine tun-ing offers the best results.

Although sophisticated methods exist for the evaluationof the density field and the generation of the implicit sur-face, these computations are very time-consuming. Due tothe homogeneous distribution of the leaves, this issue can beresolved by randomly selecting just a fraction of the geomet-ric primitives of the foliage as generator points, thereby pro-ducing very similar results compared to the implicit surfacethat would be generated by using all leaves of the foliage.

3.2. Density-based Ambient Reflection

By examining foliage in nature, a gradual darkening fromthe outer to the inner parts of the foliage is observed. Thisambient occlusion effect can be approximated for real-timerendering by utilizing an implicit function that is derivedfrom the foliage model. Therefore, the density field of thecorresponding set of generator points is directly evaluated.High values within this density field indicate dark areas of

the foliage, whereas low density values indicate areas thatare near the boundary of the foliage with more incident light.This method is also applicable to other parts of the geometrythat is covered by foliage geometry, e.g. the trunk and thebranches of the tree.

Having a set of generator points P, which is derived fromthe foliage geometry G and forms the density field F , anambient reflection coefficient kav is generated for each ver-tex v ∈ G by determining the density value dv = F (v), andmapping dv to kav ∈ [0..1] by the following transfer function:

kav =

1, dv ≤ 0

kamin +(

1− kamin

)(1− dv

dmin

)n, 0 < dv < dmin

kamin , dv ≥ dmin(4)

Thereby kamin ≥ 0 defines the minimum ambient reflectioncoefficient that is used for all density values above a cho-sen lower bound dmin. These areas characterize the core ofthe foliage where no variant ambient lighting is observed.For density values between zero and dmin, the exponent n in-fluences the gradient from maximum to minimum ambientreflection. Values of n < 1 result in a slower darkening fromthe outer to the inner parts of the foliage, whereas valuesof n > 1 generate a more rapid darkening. The influence ofthese three parameters that allow for an accurate adjustmentof the ambient reflection is illustrated in Figure 4. An exam-ple for a rendering using only the with this method computedambient reflection coefficients is given in Figure 5(a).

Figure 4: Dependency of the ambient reflection coefficientkav on the density value dv according to Equation 4 for thethree different exponents n = 1

3 , n = 1, and n = 3.

At the end of the preprocessing step, the ambient reflec-tion coefficients are encoded within the normal vector infor-mation of the vertices. Therefore, the normal vector of eachvertex is scaled by the corresponding ambient reflection co-efficient, which enables an effective interpolation and has noadditional memory requirements. At runtime, a simple ver-tex shader program decodes the normal vector to extract theambient reflection coefficient, and re-scales the normal vec-tor for further reflection computations, e.g. the diffuse andspecular reflection term in Equation 1.

c© The Eurographics Association 2007.

T. Luft et al. / Expressive Illumination of Foliage Based on Implicit Surfaces

(a) ambient (b) diffuse/specular (c) ambient, diffuse/specular

(d) ambient, diffuse/specular, shadow (e) ambient, diffuse/specular, shadow, textures (f) standard local illumination model

Figure 5: Illumination components for the photorealistic rendering of foliage with the here presented method based on implicitsurfaces. For comparison, the same model has been rendered with the standard local illumination model.

3.3. Normal Vector Realignment for Diffuse/SpecularReflection

To accentuate the general shape of the foliage it is necessaryto reduce the noisiness of the diffuse and specular reflection.According to the standard local illumination given in Equa-tion 1, the computation of the diffuse and specular reflectionis based on the normal vector ~N. The random orientation ofthe leaves in the foliage causes also a random alignment ofthe corresponding normal vectors that is responsible for thenoisy reflection. Thus, it is necessary to realign the normalvectors of the foliage vertices to reduce this effect.

A naive method is to realign the normal vectors accordingto a bounding ellipsoid. The drawback is the disregarding ofthe general shape of the foliage that is determined by its mainbranches. A much better method to approximate the shape ofthe foliage is to utilize implicit surfaces as already shown inFigure 3. Here the simplified shape is perfectly modulated to

the general shape of the foliage, whereby the degree of thismodulation can easily be adjusted.

The realignment of the normal vectors is applied for eachvertex v of the foliage geometry. Therefore, the vertex vs ofthe implicit surface is determined that has the minimal Eu-clidian distance to v. The new normal vector ~N′ of v is thenset to the normal vector ~Ns of vs. Alternatively, ~N′ is com-puted as a linear combination of the original normal vector~N of v and ~Ns. For all examples in this paper ~N = ~Ns is used.The result of this normal vector realignment for the diffuseand specular reflection is presented in Figure 5(b).

4. Results

Photorealistic Rendering: Having approximated ambientocclusion information and realigned normal vectors for eachvertex, these two effects are now combined (Figure 5(c)) andadditionally enriched with shadow (Figure 5(d)) and texture

c© The Eurographics Association 2007.

T. Luft et al. / Expressive Illumination of Foliage Based on Implicit Surfaces

(Figure 5(e)) information. The benefit of this implicit surfacebased method becomes evident when comparing the finalresult with a standard local illumination (Figure 5(f)). Thegeneral shape and the local density of the foliage is clearlyaccentuated, and the rendering is more vivid and realistic.Another direct comparison between a photo of a tree and asimilar tree model is given in Figure 6. Again, the tree modelis rendered using standard local illumination and the implicitsurface based method. More examplesare given in Figure 8.

(a) standard (b) photo (c) presented method

Figure 6: Comparison between the standard local illumina-tion, a photo of a similar tree, and the presented method.

Non-Photorealistic Rendering: The method presented inthis paper is also adaptable as an abstraction mechanism fornon-photorealistic rendering, and especially rendering tech-niques that rely on normal vector information benefit di-rectly. For example, image space filters that detect discon-tinuities in the normal buffer in order to produce line draw-ings, e.g. [ST90], fail for complex botanical objects, if theyare applied to the original normal vectors. Again, the reasonis the spatially high signal frequency contained in the nor-mal buffer resulting in cluttered artifacts as shown in Fig-ure 7(a). In contrast, in Figure 7(b) these image space fil-ters achieve simplified results by using the realigned normalvectors. Furthermore, the extracted ambient occlusion that iscoded in the normal vector length suppresses interior detailsof the foliage, which in turn results in a reproduction of thecharacteristic features of the foliage topology with a reducedcomplexity as shown in Figure 7(c). This abstraction mech-anism serves for numerous image-space algorithms, see Fig-ure 8 for examples. In comparison to existing works that con-sider line drawing simplification [BTS05, GDS04, WM04],the advantage of the here presented method is its implemen-tation as a preprocessing step, and the fact that it requiresno additional memory and computation time during ren-dering. Other non-photorealistic rendering techniques thataim at producing an abstract shading, such as cartoon shad-ing [Dec96] or watercolor representations [LD06], also ben-efit from the method presented in this paper. A smooth andclear shading is achieved, which faithfully resembles the ab-straction process that is usually performed by an artist. Thisallows the direct use of plant models that have been createdfor photorealistic rendering without an additional modelingeffort. More examples for the application of this technique inthe field of non-photorealistic rendering are presented in Fig-ure 8, using the watercolor approach presented in [LD06].

(a) standard (b) realigned (c) realigned & scaled

Figure 7: Application to non-photorealistic rendering. Toprow: Normal buffer; normal vectors are mapped to RGBcolor space. Bottom row: Edge detection filter applied to thenormal map.

5. Discussion

This paper presents an approach for the expressive illumi-nation of foliage that is applicable to photorealistic as wellas non-photorealistic representations. The usage of implicitsurfaces for the abstraction and simplification of the foliagegeometry enables the modification of the normal vector in-formation of the vertices. Therefore, the darkening of the in-ner parts of the foliage is approximated by the density fieldof the implicit function, and the general shape of the foliageis accentuated by realigning the normal vectors to the im-plicit surface. The degree of abstraction of an implicit sur-face can be influenced directly by two parameters that de-scribe its modulation to the given foliage geometry. Due tothe variety of the individual plant models, it is difficult tofind general settings. Therefore, these two parameters haveto be interactively adjusted by the user.

The implementation as a preprocessing step and the en-coding of the results within the normal vector informationof the vertices allow for an efficient storage, interpolation,and rendering without additional memory requirements. Thecorresponding, very simple, decoding method for the nor-mal vectors can be implemented in a vertex shader therebyproducing only a minor computational overhead during ren-dering. These attributes are advantageous for the real-timevisualizations of large-scale ecosystems.

The approximation of ambient occlusion effects is not re-stricted to the vertices of the foliage, rather it also allows toadequately modify branches or other objects that are coveredby the foliage. Furthermore, it is possible to compute the im-plicit surface for a plant population, which in turn allows toincorporate static object-to-object interactions between theindividuals. An exemplary result is a small tree that is nat-

c© The Eurographics Association 2007.

T. Luft et al. / Expressive Illumination of Foliage Based on Implicit Surfaces

urally darkened by a nearby large tree due to the ambientocclusion effects. Nevertheless, such a scenario cannot becombined with instancing—a common technique to presentlarge tree populations—since the normal vector modificationof the foliage is thereby computed individually for each tree.

Admittedly, the implementation as a preprocessing stepdoes not permit dynamic object to object interactions. Al-though dynamic scenes are possible using Precomputed Ra-diance Transfer [SKS02], it is not adequate for complexscenes due to high computational effort and memory require-ments. Likewise, a correct global illumination simulation isnot applicable to scenes with thousands or even millions ofplant models because of tremendous computational effort. Incomparison to ambient occlusion [PG04], the here presentedmethod is an effective and easy to implement approximation,especially appropriate to amorphous object sets.

References

[BTS05] BARLA P., THOLLOT J., SILLION F.: Geomet-ric clustering for line drawing simplification. In Pro-ceedings of the Eurographics Symposium on Rendering(2005), pp. 183–192.

[Bun05] BUNNELL M.: Dynamic ambient occlusion andindirect lighting. In GPU Gems 2. Addison-Wesley, 2005,pp. 223–233.

[CCDH05] COLDITZ C., COCONU L., DEUSSEN O.,HEGE H.-C.: Real-time rendering of complex pho-torealistic landscapes using hybrid level-of-detail ap-proaches. In Proceedings of the 6th International Con-ference for Information Technologies in Landscape Archi-tecture (2005), pp. 97–106.

[DCDS05] DIETRICH A., COLDITZ C., DEUSSEN O.,SLUSALLEK P.: Realistic and interactive visualizationof high-density plant ecosystems. In Proceedings of theEurographics Workshop on Natural Phenomena (2005),pp. 73–81.

[Dec96] DECAUDIN P.: Cartoon looking rendering of 3DScenes. Research Report 2919, INRIA, June 1996.

[DHL∗98] DEUSSEN O., HANRAHAN P., LINTERMANN

B., MECH R., PHARR M., PRUSINKIEWICZ P.: Realisticmodeling and rendering of plant ecosystems. In Proceed-ings of ACM SIGGRAPH (1998), pp. 275–286.

[DL05] DEUSSEN O., LINTERMANN B.: Digital De-sign of Nature: Computer Generated Plants and Organ-ics. Springer-Verlag, 2005.

[DS00] DEUSSEN O., STROTHOTTE T.: Computer-generated pen-and-ink illustration of trees. In Proceed-ings of ACM SIGGRAPH (2000), pp. 13–18.

[FvFH97] FOLEY J. D., VAN DAM A., FEINER S. K.,HUGHES J. F.: Computer Graphics: Principles and Prac-tice in C. Addison Wesley, 1997.

[GDS04] GRABLI S., DURAND F., SILLION F.: Densitymeasure for line-drawing simplification. In Proceedingsof Pacific Graphics (2004), pp. 309–318.

[GOS06] GREENWORKS ORGANIC SOFTWARE:Homepage of the Xfrog modeling software.http://www.greenworks.de, 2006.

[HPAD06] HEGEMAN K., PREMOŽE S., ASHIKHMIN

M., DRETTAKIS G.: Approximate ambient occlusion fortrees. In Proceedings of the Symposium on Interactive 3DGraphics and Games (2006), pp. 87–92.

[KMN∗99] KOWALSKI M. A., MARKOSIAN L.,NORTHRUP J. D., BOURDEV L., BARZEL R., HOLDEN

L. S., HUGHES J.: Art-based rendering of fur, grass,and trees. In Proceedings of ACM SIGGRAPH (1999),pp. 433–438.

[LC87] LORENSEN W. E., CLINE H. E.: Marching cubes:A high resolution 3D surface construction algorithm. InProceedings of ACM SIGGRAPH (1987), pp. 163–169.

[LD06] LUFT T., DEUSSEN O.: Real-time watercolor il-lustrations of plants using a blurred depth test. In Pro-ceedings of NPAR (2006), pp. 11–20.

[MI87] MURAKAMI S., ICHIHARA H.: On a 3D displaymethod by metaball technique. Transactions of the Insti-tute of Electronics, Information and Communication En-gineers J70-D, 8 (1987), 1607–1615. In Japanese.

[PG04] PHARR M., GREEN S.: Ambient occlusion. InGPU Gems. Addison-Wesley, 2004, pp. 279–292.

[RB85] REEVES W., BLAU R.: Approximate and prob-abilistic algorithms for shading and rendering structuredparticle systems. In Proceedings of ACM SIGGRAPH(1985), pp. 312–322.

[SKS02] SLOAN P.-P., KAUTZ J., SNYDER J.: Precom-puted radiance transfer for real-time rendering in dy-namic, low-frequency lighting environments. In Proceed-ings of ACM SIGGRAPH (2002), pp. 527–536.

[SSBD03] SOLER C., SILLION F. X., BLAISE F., DER-EFFYE P.: An efficient instantiation algorithm for simulat-ing radiant energy transfer in plant models. ACM Trans-actions on Graphics 22, 2 (April 2003), 204–233.

[ST90] SAITO T., TAKAHASHI T.: Comprehensible ren-dering of 3-D shapes. In Proceedings of ACM SIGGRAPH(1990), pp. 197–206.

[Wat00] WATT A.: 3D Computer Graphics. Addison-Wesley, 2000.

[WM04] WILSON B., MA K.-L.: Rendering complexityin computer-generated pen-and-ink illustrations. In Pro-ceedings of NPAR (2004), pp. 129–137.

[WWD∗05] WANG L., WANG W., DORSEY J., YANG X.,GUO B., SHUM H.-Y.: Real-time rendering of plantleaves. ACM Transactions on Graphics 24, 3 (2005), 712–719.

c© The Eurographics Association 2007.

T. Luft et al. / Expressive Illumination of Foliage Based on Implicit Surfaces

Figure 8: Photorealistic and non-photorealistic representations of single plant models and of a complex scene.

c© The Eurographics Association 2007.