Approach to Modeling and Virtual-reality-based Simulation for Plant Canopy Lighting

Transcription

1 Chn. Geogra. Sc (4) DOI: /s x Approach to Modelng and Vrtual-realty-based Smulaton for Plant Canopy Lghtng WANG Haopeng 1, 2, 3, ZHAO Ka 2, SONG Fengbn 2 (1. Department of Computer, Avaton Unversty of Ar Force, Changchun , Chna; 2. Northeast Insttute of Geography and Agroecology, Chnese Academy of Scences, Changchun , Chna; 3. Graduate Unversty of the Chnese Academy of Scences, Bejng , Chna) Abstract: Over the past 20 years, sgnfcant progress has been made n vrtual plant modelng correspondng to the rapd advances n nformaton technology. Vrtual plant research has broad applcatons n agronomy, forestry, ecology and remote sensng. As many bologcal processes are drven by lght, t s the key for vrtual plant to estmate the lght absorbed by each organ. Ths paper presents the radance equaton sutable for calculatng sun and sky lght ntercepted by plant organs based on the prncples of the nteracton between lght and plant canopy frstly; analyzes the process prncples of plant canopy prmary lghtng based on ray castng and projecton secondly; descrbes the multple scatterng of plant lghtng based on Monte Carlo ray tracng method and on the radosty method thrdly; and confrms the research wth 3D vsualzaton based on Vrtual Realty Modelng Language (VRML) fnally. The research s the prmary work of dgtal agrculture, and mportant for montorng and estmatng corn growth n Northeast Chna. Keywords: vrtual plant canopy; lght modelng; radatve modelng; Vrtual Realty Modelng Language (VRML) 1 Introducton The bologcal processes of plants occur at the level of organs (leaf, bud, nternode, and frut). Plant canopy structure plays a key role n radatve scatterng and absorpton, and affects the modelng based on remote-sensng sgnal or nformaton (Guo and L, 2001; Song et al., 2003). Over the past 20 years, sgnfcant progress has been made n vrtual plant modelng correspondng to the rapd advances n nformaton technology. Research results of vrtual plant have been wdely appled n agronomy, forestry, ecology and remote sensng. Modelng of plant growth should be started wth the functonng of plant organs wthn the canopy. An effcent approach Functonal-structural plant model (FSPM) (Humberto et al., 2004) conssts n modelng the canopy as a populaton of nteractng plants and a plant as a set of nteractng organs. Ths approach performs n two parts: 1) combnng a functon of plant organ growth wth a 3D descrpton of ther geometry; 2) modelng wth radatve varables based on ths approach, whch characterzes each ndvdual organ (Dng et al., 2002; Zhao et al., 2001). The plant growth s acted by four external envronment forces (lght ntensty I, temperature T, sol water H and nutrents N) and two nternal forces (respraton consumpton and dark respraton acton). And the lghtng s the prmary factor for plant growth process. Lghtng models can estmate the radatve fluxes receved by each organ va modelng the radatve exchanges between plant organs. The models nvolve the characterzaton of nteractons (reflecton, transmsson, absorpton) between lght and organs, and the ntegraton of these sub-processes. The complexty of ths ntegraton depends on the approxmaton of the structural descrpton for plant and lghtng. Many methods have been used to descrbe 3D canopy structure explctly as a set of geometry elements (Shen et al., 2005; Wu and Nu, 2008). The progress n computer scence and technology (Dgtal Image Processng, Vrtual Realty, etc.) Receved date: ; accepted date: Foundaton tem: Under the auspces of Natonal Hgh-Tech Research and Development Program of Chna (863 Program) (No. 2006AA10Z227), the Eleventh Fve-year Plan of Jln Provnce Educatonal Offce (No. 2007[456]) Correspondng author: WANG Haopeng. E-mal: wngrocc@emal.jlu.edu.cn

2 Approach to Modelng and Vrtual-realty-based Smulaton for Plant Canopy Lghtng 375 has motvated to model radatve transfer wthn a canopy structure explctly. Ths paper wll present the radance equaton sutable for calculatng sun and sky lght ntercepted by plant organs; analyze the process prncples of plant canopy prmary lghtng; descrbe the multple scatterng of plant lghtng; and confrm the research wth 3D vsualzaton based on Vrtual Realty Modelng Language (VRML). The research s of mportance for dgtal agrculture, and montorng and estmatng corn growth n Northeast Chna. 2 Radance Equaton Dsregardng artfcal lghtng scenaros, the sun and the sky are the prmary lght sources for the plant growth process. Solar radaton ntercepted by an organ may come drectly from the sky hemsphere and ndrectly from the scatterng of other organs. The dstrbuton of prmary lght wthn the canopy depends on the structure of the canopy and on the angular dstrbuton of radance characterzng the sky hemsphere. The lght ntercepted by an organ s partally absorbed and partally scattered (reflected and transmtted). The proporton of these two parts of lght vares sgnfcantly wth the wavelength dues to the leaf type, state and age. They have been accurately smulated by the prospect model. The angular dstrbuton of the reflected and transmtted lght are descrbed by, respectvely, the bdrectonal reflectance dstrbuton functon (BRDF) and the bdrectonal transmttance dstrbuton functon (BTDF). Because lght can vary spatally and temporally wth a hgh frequency due to the movements of plants, the sun and clouds, the organ responses to lght present strongly non-lnear. The soluton of the radance equaton s the feld of radance LP (, ω r ) over the set of surfaces descrbng the canopy, at a tme t and for the wavelength λ, to calculate drectly the absorbed energy or rradance from ths feld of radance. The qualty of radaton scattered from a surface element S and ntercepted by another surface element S j depends on BRDF or BTDF of S j as well as on the relatve postons and orentaton of S and S j. Ths dependency s quantfed by the radance equaton. The reflectance and transmttance propertes of leaf surface are descrbed by BRDF fr(x, θ, φ; θr, φr) and BTDF ft(x, θ, φ; θr, φ r) (Huang et al., 2006; Zhang and Wu, 2006): A σ s f r(x, θ, φ; θr, φr) = γ(x) + 2πσ + σ a s 2 tan a 2 m(x) ρs (x) e 4 2 r m (1) cosθ cosθ cos α 4 π (x) 1 ( σa+ σs)( h+ δ(x)) B σ s ft(x, θ, φ; θt, φt) = e + π 2πσa + σs (2) where A and B are constants, x=(x, y) s the poston on the leaf surface, ( θ, φ ) and ( θr, φ r) descrbe the reflect drectons, δ (x) s a functon that descrbes local thckness varatons n dfferent parts of the leaf, ρ s (x) s the dffuse reflectance. The other three parameters are: the absorpton coeffcent σ a and scatterng coeffcent σ s of nsde of the leaf, and the leaf thckness h. The radance equaton s numercally solved by ntegratng t over space, drecton, tme and wavelength. The radance equaton does not take other radatve processes such as fluorescence and polarzaton nto account because ther quanttatve contrbuton to the agronomcal condtons. Equaton (3) and Equaton (4) express the radance scattered by a surface element S at a pont P n a drecton ω r as a functon of the radance comng n at pont P from all the drectons ω (Fg. 1). The radance comng n at pont P can be decomposed n the contrbuton of prmary lght ( L 1 ( P, ω r )) and the lght scattered by sol and other organs toward drecton PL ( ( P, ω r )) based on Equaton x (1) and Equaton (2) are descrbed as: 1 L( P, ωr ) = f (, r ) (, )cos d ω ωr 0 r ω ω LPω θ ω + < (3) f ( ω, ω ) LPω (, )cosθdω ω ω > 0 r ωs ω > 0 r t x L ( P, ωr) = f ( s, r) (, )cos d ωs ωr 0 r ω ω L P ωs θωs+ < f ( ω, ω ) L( P, ω )cosθω d t s where ω s the set of drectons n whch there s a free path between P and the top of the canopy; ω s s the set of drectons n whch there s not a free path; dω s an elementary sold angle around the drecton ω; r r s s (4) θ s the angle between ω and the normal n to S at pont P; and f r and f t are the BRDF and the BTDF, respectvely, of S at the pont P. Shaded crcle sectors correspond to the sold angle through whch P s drectly lt by the sky (Fg. 1).

3 376 WANG Haopeng, ZHAO Ka, SONG Fengbn canopy from the poston of the lght source. The apparent surface depends on the orentaton of S relatve to ω and on the possble shadng due to other surfaces. It can be estmated by ray castng or by projecton (Benes and Cordoba, 2003). Fg. 1 Radatve budget of a plant organ at pont P 3 Prmary Lght 3.1 Prncple of plant canopy lghtng If there s a drect path from the pont P to the top of canopy n the drectonω, calculatng the prmary lghtng of a set of surfaces requres: 1) drectonal samplng of the sky hemsphere; 2) spatal samplng of the plant surfaces; and 3) determnng ( P, ω r ) for each element wthn the sample. For the source-based approach, the samplng s done by followng the propagaton of lght from sampled drectons over the sky hemsphere and determnng the surface element ht by each lght ray. For the recpent-based approach, the samplng s performed by followng the nverse sense of lght propagaton from the surface elements of nterest to the sky hemsphere (Lu et al., 2003; Zhang and Zhao, 2007). The samplng of the sky hemsphere reles on a dscretzaton n sold angle elements ω, so that the radance wthn ω s assumed constant. The approxmaton of the contnuous sky hemsphere s regarded as a fnte set of punctual collmated lght sources. Because the dmensons of a plant canopy are small compared to the dstance to the lght sources, any extended lght source can be approxmated as a set of punctual lght sources, so that the approach s very general (Wang et al., 2005). An effectve descrpton of prmary lght s that as the rradance of a surface s the sum of the contrbuton for each ndvdual source, the calculaton of prmary lght starts from a sngle source. The rradance of a surface S due to the lght comng from a sngle drecton s proportonal to the apparent surface S, whch s the sur- * face that would be seen by an observer lookng at the 3.2 Ray castng The source-based approach conssts of several castng rays from the lght source to the canopy. Rays cast from ponts stochastcally sampled on a plane above the canopy. The propagaton of a ray stops when t ntersects an element (Fg. 2). S * s proportonal to the number of rays caught by S. Fg. 2 Lght ntercepton usng the source-based approach by ray castng For the recpent-based approach, rays are cast from ponts randomly sampled on the surfaces of the organs * of nterest n the drecton ω. S s proportonal to the number of rays startng from S and reachng the sky hemsphere (Fg. 3). Fg. 3 Lght ntercepton followng the recpent-based approach by ray castng The second method for the source-based approach conssts of projectng the element on a dscretzed screen located above the canopy and normal to the d-

4 Approach to Modelng and Vrtual-realty-based Smulaton for Plant Canopy Lghtng 377 recton of lght (Fg. 4). Shaded elements are determned by applyng the Z-buffer algorthm, whch conssts of updatng a pxel of the dscretzed screen wth the dentfer of the closest element to the screen (Mchael et al., * 2001). S s proportonal to the number of pxels covered by the projecton of S. Ths method s very effcent n terms of speed and accuracy, but may suffer from naccuraces when the resoluton of the dgtzed screen s coarse regardng the projecton of S, e.g., for small elements. Fg. 5 Lght ntercepton followng recpent-based approach by hemsphercal projecton Fg. 4 Lght ntercepton usng source-based approach by parallel projecton In the recpent-based approach, the rradance due to the whole sky hemsphere s calculated for each S. A hemsphercal projecton centered on a pont P of S provded an mage where each pxel corresponds to a sold angle (Fg. 5). An empty pxel corresponds to a drecton n whch the sky lght reached pont P drectly. The rradance at pont P s calculated by summng the rradances due to the sky radances assocated to each empty pxel. To get the rradance of S, the method s appled for several ponts P over S. 4 Multple Scatterng of Lght Estmated multple scatterng requres solvng the radance equaton (Deng et al., 2004). As ths equaton s set at one pont, ntegraton over all surfaces s requred. Two approaches enable ths ntegraton: the Monte Carlo method and the radosty method. 4.1 Monte Carlo method For descrbng and nterpretng the nteractve process between lght and leaf commendably, Monte Carlo method (Chen and Xu, 2000) s the core of the arthmetc for smulaton models n computer. Stochastc ray tracng reles on the Monte Carlo method to solve the requred mult-dmensonal ntegrals. It conssts of calculatng the path and nteractons wth surfaces of a large sample number of photons, untl they ext the canopy or they are absorbed by surfaces. Monte Carlo models enable smulatons for nearly any type of lght source, canopy structure and optcal propertes of organ. They enable the smulaton of a large set of varables, such as fluxes over ndvdual organs, canopy BRDF, and the radance dstrbuton at dfferent levels wthn the canopy. And more, they enable the separaton of the contrbuton of the dfferent orders of scatterng to the radatve varables. In the paper, combnng the BRDF and Monte Carlo Model, the transport of lght wthn a canopy s descrbed as: y, z S E L ( y, z) = L ( y, z) + fr ( x, y, z) λ λ λ x S Gxy (, ) Lλ ( xy, )dx (5) where L ( y, λ z) s the spectral radance exchanged at pont y n drecton yz, L E ( y, z ) λ s the spectral radance emtted at the pont y n the drecton of z, frλ ( x, y, z) s the BRDF at the pont y, whch gves the proporton of lght of wavelength λ comng from x and reflected n the drecton xy and Gxy (, ) s a geometrcal term takng nto account the vsblty between x and y and the proporton of energy exchan-

5 378 WANG Haopeng, ZHAO Ka, SONG Fengbn ges between those two ponts. Results from Monte Carlo method are statstcal estmates of mean values. The numercal varance assocated wth an estmated varable depends on the number of photons that contrbute to ths result. To get low varances for such surfaces requres ether to prvlege these surfaces by usng the recpent-based approach or to trace a large number of rays n the case of the source-based approach, and estmatng the varance on each result at the end of a smulaton. To reach an expected accuracy, the smulaton should be performed by teratons, varances beng estmated at the end of each step. Satsfyng rradance estmaton for a large number of organs requres tracng a large number of rays, whch mples very long smulaton tme on usual computer. The Monte Carlo method enables one n prncple to deal wth any knd of BRDF/BTDF at the organ level. However, for ansotropc BRDF, samplng the drecton of scatterng s often a tme-consumng procedure. And, t requres accurately descrbng the 3D shape of leaves to avod numercal artefacts. Then, due to computatonal complexty, the case of ansotropc BRDF has seldom been addressed n radatve smulatons on plant canopes, and leaves are generally consdered b-lambertan, stem and other organs are Lambertan. 4.2 Radosty-based method The radosty-based method s based on the assumptons that surfaces are Lambertan or b-lambertan and radatve fluxes over an element are constant. Ths enables the radance equaton to be approxmated as a system of lnear equatons (Wu and Wang, 2002). The radosty equaton expresses the radant exstence or radosty B over a surface S as a functon of the reflecton and the transmsson of the ncomng lght. Ths ncomng lght s expressed as a lnear combnaton of the radostes B j of the other surfaces. The coeffcents of ths lnear combnaton are called form factors and represent the proporton of energy scattered by a surface S j that reached a surface S. A form factor between S j and S s calculated by ntegraton over the two surfaces. In detal: 1) If there are no surfaces between them, a standard numercal ntegraton can be performed. If S and S j are polygons, an analytcal formulaton of the form factor has been establshed. 2) If there are occlusons, the contrbutons from free paths between S and S j need to be determned and calculatons are more complex. These calculatons are usually smplfed by calculatng the form factor between S j and an elementary surface located at the centre of S. Ths method s called the method of pont-surface form factor. The rradance of a surface S due to multple scatterng s calculated n two parts: 1) the energy comng from all the organs far from S s estmated statstcally from the feld of mean fluxes provded by the Scatterng by Arbtrarly Inclned Leaves (SAIL) multlayer model (Ca and Shao, 2007); 2) the contrbuton of close organs s calculated by the classc radosty method. The partton between close and far surfaces from S s realzed by a sphere (dameter of sphere s chosen by the user) centered on S. 5 VRML-based Vsualzaton Dynamc lghtng of vrtual plants has manly been acheved for photosynthess estmaton usng projecton, quas Monte Carlo or radosty methods. 3D vsualzaton for dynamc lghtng of vrtual plants s lkely to be further developed, manly due to the recent avalablty of sutable modelng tools, e.g., platforms of open L-system models (Chen and Robert, 2003) and VRML (En-M and Tsuyosh, 2003). 5.1 Bref overvew of VRML VRML s one of Web3D technologes, whch are used to delver nteractve 3D objects and worlds across the Internet. VRML s a hgh-performance language for 3D vsualzaton on the WWW (World Wde Web). As a programmng language and lbrary for 3D computer graphcs, VRML has many functons such as shadng, settng objects, projecton, and texture mappng. Vrtual realty worlds can be easly bult on the WWW wth ths technology. VRML 1.0 was ntroduced n 1994 and VRML 2.0 (97) wth more dynamc and nteractve functons was made n GeoVRML and X3D are successful verson of VRML. VRML 2.0 s used n the work of vsualzaton n ths paper (Song and Deng, 2006). 5.2 VRML geometrc and photometrc declaraton VRML allows developers to specfy dynamc 3D objects and scenes through whch users can navgate wth the help of VRML browser. From the VRML 2.0 nodes (Wang and Zhao, 2007), we extract the rght nodes to be consdered n the vsualzaton procedure lsted n Table 1.

6 Approach to Modelng and Vrtual-realty-based Smulaton for Plant Canopy Lghtng 379 Table 1 VRML nodes for VR-based smulaton for plant canopy lghtng Node type Node Functon Shape node Lght node Group node IndexedFaceSet, Appearance, Coordnate, Color, Normal, Materal, ImageTexture, and PxelTexture SpotLght, PontLght, and DrectonLght Group, Transform, InLne, and LOD Other node VewPont, and WorldInfor Descrbng the geometry and photometry of the envronment Specfyng common lghts characterstcs Modelng vrtual plants and vrtual plant communty Extendng vsualzaton capabltes 5.3 Vsualzaton of VRML-based lghtng models An deal mplementaton of the VRML-based lghtng models permts to combne materal propertes of the objects, such as colors and textures, wth the envronment. The characterstc of VRML for lghtng model s ts capablty to nvaldate the lght nfluence on Shape node by settng ts appearance feld or the materal feld of the Appearance node to NULL (the default value). Common geometrc descrpton of VRML 2.0 can be done by usng Shape nodes and Geometrc nodes assocated appearance descrptor. The more general one s IndexedFaceSet, whch allows to descrbng set of smple surfaces. It specfes the surfaces by gvng ther vertces, and by declarng connectons between them. The RGB components of the surfaces can be declared by a Materal node. The color feld specfes RGB components for each vertex (colorpervertex feld set to TRUE) or each surface ( colorpervertex set to FALSE). Another possblty s to use texture feld of the Appearance node (Detrch et al., 2004; Zeng and Dng, 2003; Cyrl et al., 1998). In ths case the fnal RGB color of projected pxels (I RGB ) s the combnaton of color specfcaton of IndexedFaceSet node and Texture of the Appearance node (Table 2). Texture type Table 2 Fnal RGB color of projected pxels (I RGB ) I RGB (color feld s specfed) I RGB (color feld s not specfed) No texture I RGB =I CRGB I RGB =(1,1,1) Intensty texture I RGB =I T I CRGB I RGB =(I T, I T, I T ) Intensty & alpha I RGB =I T I CRGB I RGB =(I T, I T, I T ) RGB I RGB =I TRGB I RGB =I TRGB RGB & alpha I RGB =I TRGB I RGB =I TRGB Notes: I CRGB represents color extracted from vertex color nterpolaton or from materal surface color; I T descrbes texture color If appearance or materal are specfed, the ntermedate dffuse factor of objects (O DRGB ) can be obtaned (Table 3). Table 3 Intermedate dffuse factor of objects (O DRGB ) Texture type O DRGB (color feld s specfed) O DRGB (color feld s not specfed) No texture O DRGB =I CRGB O DRGB =I DRGB Intensty texture O DRGB =I T I CRGB O DRGB =I T I DRGB Intensty & alpha O DRGB =I T I CRGB O DRGB =I T I DRGB RGB O DRGB =I TRGB O DRGB =I TRGB RGB & alpha O DRGB =I TRGB O DRGB =I TRGB Fgure 6 s the VRML-based 3D vsualzaton of lght envronment for vrtual vegetaton canopy. Fg. 6 VRML-based 3D vsualzaton of plant canopy lghtng from parallel angle (a) and overlook angle (b) 6 Conclusons and Prospect The development of 3D modelng of plants by provdng an explct descrpton of the canopy geometry and by requrng the dstrbuton of lght energy on each plant

7 380 WANG Haopeng, ZHAO Ka, SONG Fengbn organ has motvated the vrtual realty smulaton development of a surface-based model for lght envronment. To study bologcal processes senstve to PAR and UV radaton, multple scatterng may be neglected allowng for fast calculatons even on large 3D structures. The smulaton of processes dependng on nfrared radaton or located n shaded zones has to take nto account the multple scatterng of lght between organs. Radosty-based method s convenent and effectve, because of the dssocaton of geometrc and radatve calculatons. However, the pont-surface method s not approprate for the calculaton of form factors when surfaces are very close. Ths makes t dffcult to estmate lght condtons n some specfc plant parts. VRML s an effectve language for 3D vsualzaton for plant canopy lghtng models. VRML fle flows permt to nteract effcently wth others VRML tools currently, lke browsers. Ths permts to easly generate nput 3D llumnated envronments, and to produce fles, at every stage of the bologcal process. These fles are ndependent from system, and vewable on common computers. The research frst presents the radance equatons whch serve for calculatng sun and sky lght ntercepted by plant organs, especally n the condton of UV or PAR radatons, and the equatons can be appled accurately. The second work s to analyze the process prncples of plant canopy prmary lghtng based on ray castng and projecton. Based on ths analyss, the modelng of lght for vrtual plant canopy can be realzed effectvely. The last work, VRML-based smulaton, s the key for 3D vsualzaton of the lght for vrtual plant canopy n the computer. The future researches are: 1) How to descrbe the 3D plant structure n the most effcent way, knowng that the more accurate ths descrpton s, the more accurate the calculaton wll be, but also the more ntensve the collaboratve computaton task. 2) How to approach a surface-based model that takng nto account the exact geometry of the canopy based on remote-sensng nformaton. 3) How to use these models or methods to mprove the knowledge of the lnk between radatve and structural propertes of a canopy and data acqured by satelltes. Those wll be contrbutory to the research on more effcent VR-based smulaton of plant n dgtal agrculture. References Benes B, Cordoba J A, Modelng vrtual gardens by autonomous procedural agents. Theory and Practce of Computer Graphcs, 15(2): Ca Bofeng, Shao Xa, Leaf area ndex petreval based on remotely sensed data and PROSPECT + SAIL model. Remote Sensng for Land & Resources, 2007(2): (n Chnese) Chen Langfu, Xu Xru, The smulaton usng Monte Carlo method n vegetaton canopy remote sensng. Progress n Geography, 19(1): (n Chnese) Chen Phoebe Y-Png, Robert M Colomb, Database technologes for L-System smulatons n vrtual plant applcatons on bonformatcs. Knowledge and Informaton Systems (5): Cyrl Kardassevtch, Mathas Pauln, Jean Perr Jessel et al., A herarchcal radosty platform usng effcent data structures and VRML 97. Computer Networks and ISDN Systems (30): Deng Ruru, Tan Guohang, Lu Qnhuo et al., B-drectonal reflectance model of canopy and sol based on mult-scatterngs. Journal of Remote Sensng, 8(3): (n Chnese) Detrch A, Wald I, Wagner M et al., VRML scene graphs on an nteractve ray tracng engne. Vrtual Realty, 21(4): Dng Welong, Zhao Xng, Xong Fanlun et al., Progresses n modelng and software development of vrtual plant. PR & AI, 15(4): (n Chnese) En-M Lm, Tsuyosh Honjo, Three-dmensonal vsualzaton forest of landscapes by VRML. Landscape and Urban Plannng, 63(3): Guo Yan, L Baoguo, New advances n vrtual plant research. Chnese Scence Bulletn, 46(11): Huang Janx, Wu Bngfang, Tan Ychen et al., Crop canopy BRDF smulaton and analyss usng Monte Carlo method. Transactons of the CSAE, 22(6): 1 6. (n Chnese) Humberto N de Mesquta Jr, Tmothy J Malthus, Marsa D et al., Structural-functonal model to remote sensng of vegetaton physognomes seasonal varaton based on lfe form. 4th Internatonal Workshop on Functonal-Structural Plant Models, Lu Qang, Chen Langfu, Lu Qnhuo et al., A radaton transfer model to predct canopy radaton n thermal nfrared band. Journal of Remote Sensng, 7(3): (n Chnese) Mchael Wand, Matthas Fscher, Ingmar Peter et al., The randomzed Z-Buffer algorthm: Interactve renderng of hghly complex scenes. In: Sggraph 2001 Conference Proceedngs. Log Angeles. Shen Yan, Nu Zheng, Mao Qlong et al., Theoretcal smu-

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