Quasi-Monte Carlo simulation of the light environment of plants.

The distribution of light in the canopy is a major factor regulating the growth and development of a plant. The main variables of interest are the amount of photosynthetically active radiation (PAR) reaching different elements of the plant canopy, and the quality (spectral composition) of light reaching these elements. A light environment model based on Monte Carlo (MC) path tracing of photons, capable of computing both PAR and the spectral composition of light, was developed by Měch (1997), and can be conveniently interfaced with virtual plants expressed using the open L-system formalism. To improve the efficiency of the light distribution calculations provided by Měch's MonteCarlo program, we have implemented a similar program QuasiMC, which supports a more efficient randomised quasi-Monte Carlo sampling method (RQMC). We have validated QuasiMC by comparing it with MonteCarlo and with the radiosity-based CARIBU software (Chelle et al. 2004), and we show that these two programs produce consistent results. We also assessed the performance of the RQMC path tracing algorithm by comparing it with Monte Carlo path tracing and confirmed that RQMC offers a speed and/or accuracy improvement over MC.

[1]  Mathias Disney,et al.  Monte Carlo ray tracing in optical canopy reflectance modelling , 2000 .

[2]  Przemyslaw Prusinkiewicz,et al.  Modeling and simulation of the interaction of plants with the environment using l-systems and their extensions , 1998 .

[3]  Wolfgang Jank,et al.  Quasi-Monte Carlo sampling to improve the efficiency of Monte Carlo EM , 2004, Comput. Stat. Data Anal..

[4]  I. R. Johnson,et al.  Plant and Crop Modelling: A Mathematical Approach to Plant and Crop Physiology , 1990 .

[5]  James Arvo,et al.  Particle transport and image synthesis , 1990, SIGGRAPH.

[6]  Donald P. Greenberg,et al.  Modeling the interaction of light between diffuse surfaces , 1984, SIGGRAPH.

[7]  Jim Hanan,et al.  Lighting virtual crops: the CARIBU solution for open L-systems , 2004 .

[8]  Pierre L'Ecuyer,et al.  Good Parameters and Implementations for Combined Multiple Recursive Random Number Generators , 1999, Oper. Res..

[9]  Radomír Mech,et al.  Visual models of plants interacting with their environment , 1996, SIGGRAPH.

[10]  P. Prusinkiewicz,et al.  3D Architectural Modelling of Aerial Photomorphogenesis in White Clover (Trifolium repens L.) using L-systems , 2000 .

[11]  Przemyslaw Prusinkiewicz,et al.  The L-system-based plant-modeling environment L-studio 4.0 , 2004 .

[12]  H. Jensen.  Realistic Image Synthesis Using Photon Mapping , 2001 .

[13]  S. Ustin,et al.  LEAF OPTICAL PROPERTIES: A STATE OF THE ART , 2000 .

[14]  Przemyslaw Prusinkiewicz,et al.  L-systems: from the Theory to Visual Models of Plants , 2001 .

[15]  J. Hammersley.  SIMULATION AND THE MONTE CARLO METHOD , 1982 .

[16]  Michael D. McCool,et al.  Stratified Wavelength Clusters for Efficient Spectral Monte Carlo Rendering , 1999, Graphics Interface.

[17]  Alan Watt,et al.  3D Computer Graphics , 1993 .

[18]  Leonidas J. Guibas,et al.  Robust Monte Carlo methods for light transport simulation , 1997 .

[19]  Peter Shirley,et al.  Fundamentals of computer graphics , 2018 .

[20]  P. Prusinkiewicz,et al.  ART AND SCIENCE OF LIFE: DESIGNING AND GROWING VIRTUAL PLANTS WITH L-SYSTEMS , 2004 .

[21]  H. Faure.  Discrépance de suites associées à un système de numération (en dimension s) , 1982 .

[22]  P. Prusinkiewicz,et al.  Virtual plants: new perspectives for ecologists, pathologists and agricultural scientists , 1996 .

[23]  J. Halton.  On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals , 1960 .

[24]  B. Andrieu,et al.  Simulation of the three-dimensional distribution of the red:far-red ratio within crop canopies. , 2007, The New phytologist.

[25]  Philippe Martin,et al.  A Model of Light Scattering in Three-Dimensional Plant Canopies: a Monte Carlo Ray Tracing Approach , 2007 .

[26]  Paul S. Wang,et al.  Distribution Ray Tracing: Theory and Practice , 1992 .

[27]  Art B. Owen,et al.  Quasi-Monte Carlo Sampling by , 2003, SIGGRAPH 2003.

[28]  François X. Sillion,et al.  An efficient instantiation algorithm for simulating radiant energy transfer in plant models , 2003, TOGS.

[29]  S. Jacquemoud,et al.  Leaf BRDF measurements and model for specular and diffuse components differentiation , 2005 .

[30]  Ferenc Szidarovszky,et al.  Modeling uncertainty : an examination of stochastic theory, methods, and applications , 2002 .

[31]  Radomír Mech,et al.  L-studio/cpfg: A Software System for Modeling Plants , 1999, AGTIVE.

[32]  A. Marshak,et al.  Calculation of canopy bidirectional reflectance using the Monte Carlo method , 1988 .

[33]  D. Greer,et al.  Photoinhibition of photosynthesis in intact kiwifruit (Actinidia deliciosa) leaves: Changes in susceptibility to photoinhibition and recovery during the growth season , 1992, Planta.

[34]  R. Cranley,et al.  Randomization of Number Theoretic Methods for Multiple Integration , 1976 .

[35]  Jim Hanan,et al.  A canopy architectural model to study the competitive ability of chickpea with sowthistle. , 2008, Annals of botany.

[36]  James T. Kajiya,et al.  The rendering equation , 1998 .

[37]  Bruno Andrieu,et al.  The nested radiosity model for the distribution of light within plant canopies , 1998 .

[38]  B. Andrieu,et al.  Modelling the light environment of virtual crop canopies , 2007 .

[39]  Pierre L'Ecuyer,et al.  Recent Advances in Randomized Quasi-Monte Carlo Methods , 2002 .

[40]  Alexander Keller.  Quasi-Monte Carlo Methods in Computer Graphics: The Global Illumination Problem , 1995 .

[41]  R. R. Coveyou.  Monte Carlo Principles and Neutron Transport Problems , 1971 .

[42]  Isao Kiuchi,et al.  Mean value results for the approximate functional equation of the square of the Riemann zeta-function , 1992 .

[43]  H. T. Breece Iii,et al.  Bidirectional scattering characteristics of healthy green soybean and corn leaves in vivo. , 1971, Applied optics.

[44]  Kadi Bouatouch,et al.  Nested radiosity for plant canopies , 1998, The Visual Computer.

[45]  I. Sobol.  On the distribution of points in a cube and the approximate evaluation of integrals , 1967 .