Realistic Rendering of Plant Leaves

Realistic Rendering of Plant LeavesSuddha Kalyan BasuMay9,2006AbstractThis paper discusses a geometric and optical model for realistic real-istic of plant leaves.We have used a model for deformable thin shells torepresent the naturally curved shape of leaves and its dynamic reponse toimpulse,shear and stress.The optical model uses a simple BRDF func-tion,combined with a transparency map for each leaf.We show that weare able to generate realistic images,without having to model complexspatially varying BRDF functions on the leaf surfaces.1Modeling Leaves as a Thin ShellLeaves,unlike other deformable objects like cloth,rubber,have an undeformed curved shape.There has been lots of research into modeling deformable objects in the recent past,where materials like cloth have been modeled as a layout of triangulated tiles,where the dihedral angles at the edges between the tiles change.There are mainly two kinds of deformations:1.Intrinsic:Shear,Stress.Membrane deformations:Modeled using a spring-mass system.Preserves areas and lengths over the triangulated surface.2.Extrinsic:Beam bending(isometric).Modeled using torsional energies(and torques)on edges.Preserves shape of the model.11.1Energy Calculation The energy operator should be invariant over rigid body transformations.Flex-ural energy,W B ,or the bending potential is calculated using the derivative of the Gauss map ,also interpreted as the local curvature at a point on the surface.Membrane energy,W M ,is a measure of the sum of local changes in length and changes in area over the surface.Figure 1:Bending,Shear and Stress are not affected by rigid-bodynate frame.Typically,this hasn tensors.For example,shellhe second fundamental forms 17ormed configurations (pulling to the undeformed configura-Terzopoulos et al.introduced o the graphics community 25.orial expressions over smooth discretize to carry out the nu-e a discrete constitutive model tors over piecewise-linear sur-nts and our discrete treatment e same.However,the resulting discrete approach.derivative of the Gauss map ‡:e local curvature at a point onng energy is an extrinsic mea-n the shape operator evaluated med surfaces.We express this 25,our membrane and bending en-.The stiffness coefficients of the ctly carry over to the shell model.num plate is knowing the stiffness e to the unit sphere,mapping each ormal.or cloth simulations could not capture this behavior,wh earlier work on shell simulation required significant imp mentation and expertise (see also the color plate).difference as the squared difference of mean curvature :[Tr (ϕ∗S )−Tr (¯S )]2=4(H ◦ϕ−¯H )2,where ¯S and S are the shape operators evaluated over undeformed and deformed configurations respectively;li wise ¯H and H are the mean curvatures;ϕ∗S is the pull-ba of S onto ¯Ω,and we use Tr (ϕ∗S )=ϕ∗Tr (S )=Tr (S )◦ϕH ◦ϕfor a diffeomorphism ϕ.This measure is extrinsic sees only changes in the embedding of the surface in R This measure is invariant under rigid-body transformatio this ensures conservation of linear and angular momentu Integrating (1)over the reference domain we find the co tinuous flexural energy R ¯Ω4(H ◦ϕ−¯H )2d ¯A .Discretiz the integral over the piecewise linear mesh that represe the shell (see the appendix for a derivation),we express o discrete flexural energy as a summation over mesh edgW B (x )=∑e (θe −¯θe )2 ¯e /¯h e ,where θe and ¯θe are correspondi complements of the dihedral angle the deformed and undeformed confiuration respectively,and ¯h e is a third of the average of heights of the two triangles incident to the edge e (see the a pendix for another possible definition of ¯h e ).A contempo neous development (published in this volume)has arrived a similar formula:Bridson et al.6treat the bending and wr c The Eurographics Association 2Figure 2:Leaf deformation as a response to an impulse W M = e k M ∆l 2W B = e k B (θe −¯θe )2W =W B +W Mwhere,W is the total energy,k M is the stiffness of membrane edges and k B is the flexural stiffness.2Figure3:Leaf deformation as a response to an impulse2Rendering Plant LeavesPlant leaves are composed of semitransparentfianicfibres present on skins and leaves exhibit sub-surface scattering and other complex optical prop-erties.Photorealistic images of plant leaves cannot be accomplished by plain texture mapping,as the appearance of the surface is often quite‘hard’.We need to model properties like translucency,BRDF,BTDF,glossiness and sub-surface scattering.It has been studied from real data that leaves have spatially varying BRDF and BTDF functions.Also,properties like subsurface scattering is pretty complicated to model accurately,more so,for a generalized model.Figure4:Plant leaves:Calathea Zebrina and Aglaonema2.1Transparency mapWe generate the transparency map from the leaf texture simplefiltering tech-niques to get a map as shown in Figure6.2.2BRDF and ScatteringWe use the Henyey-Greenstein model for scattering of light on the leaf surface. This is a much simpler model as compared to the complex6-D spatially variant BRDF and BTDF functions used in earlier works.3Figure5:Transparency maps used to get softer shadows on leaves.43ResultsFigure7:Hypoestes Phylostachya.Figure8:Aglaonema.4Conclusion and Future WorkWhile there has been a lot of research into the rendering of plant leaves and modeling optical properties,we require a more elaborate geometrical model of the leaf to be integrated with it.Also,real-time rendering of plant leaves is still a challenging area.While there have been several methods implementsed using GPU accelerated techniques,they are based on approximations and are able to model only specific properties.In our experiments we have modeled household plants and shrubs with palm-sized leaves.We also need a generalized model for rendering of a larger variety of leaves,such as cactii,conifers and hairy plants.5Figure 9:Fittonia Verschaffeltii and Calathea Zebrina (on a simulated water surface).5AcknowlegementsI must thank Prof Dinesh Manocha and Prof.Ming Lin,for providing me guidance for this project.I must also thank all my colleagues for their valuable feedbacks and ideas.I am grateful to Nikunj Raghuvanshi,for helping me generate the final images.I have used the POV-Ray v3.6(Persistence-of-Vision Ray)software to render the scenes.Its free and available for download at .References1.“Chaotic Dynamics of Falling Disks”,Stuart B.Field,M.Klaus,M.G.Moore,and Franco Nori,Nature 388,252,1997.2.“Discrete Shells”,Eitan Grinspun,Anil Hirani,Mathieu Desbrun and Peter Schrder,Eurographics/SCA 2003.3.“Efficient Animation of Point-Sampled Thin Shells”,Martin Wicke,Denis Steinemann,Markus Gross in Proceedings of EUROGRAPHICS 2005.4.“Point Based Animation of Elastic,Plastic and Melting Objects”,Matthias Mller,Richard Keiser,Andrew Nealen,Mark Pauly,Marc Alexa,Markus Gross in Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation 2004.5.Lifeng Wang and Wenle Wang and Julie Dorsey and Xu Yang and Baining Guo and Heung-Yeung Shum,”Real-Time Rendering of Plant Leaves”,ACM Trans.Graph ’05.6.Baranoski,G.V.G.,and Rokne,J.2002.Light Interaction with Plants.SIGGRAPH ’02Course Notes.67.Pat Hanrahan,Wolfgang Krueger,Reflection from layered surfaces dueto subsurface scattering,Proceedings of the20th annual conference on Computer graphics and interactive techniques,p.165-174,September1993 8.Jacquemoud,S.,and Ustin,S.2001.Leaf optical properties:A state ofthe art.In Proc.8th Int.Symp.Physical Measurements and Signatures in Remote Sensing,223–232.7。