Free Standard AU & NZ Shipping For All Book Orders Over $80!
Register      Login
Functional Plant Biology Functional Plant Biology Society
Plant function and evolutionary biology
Shopping Cart: ( empty )
You are here: Home > Journals > FP > FP08082
RESEARCH ARTICLE
Contents Vol 35(10)

Quasi-Monte Carlo simulation of the light environment of plants

Mikolaj Cieslak A E F , Christiane Lemieux B , Jim Hanan C and Przemyslaw Prusinkiewicz D
+ Author Affiliations
- Author Affiliations

A The University of Queensland, School of Physical Sciences, Qld 4072, Australia.

B Department of Statistics and Actuarial Science, University of Waterloo, ON N2L 3G1, Canada.

C The University of Queensland, Centre for Biological Information Technology, Qld 4072, Australia.

D Department of Computer Science, University of Calgary, AB T2N 1N4, Canada.

E The Horticulture and Food Research Institute of New Zealand Limited, Palmerston North Research Centre, Palmerston North 4474, New Zealand.

F Corresponding author. Email: cieslak@maths.uq.edu.au

This paper originates from a presentation at the 5th International Workshop on Functional–Structural Plant Models, Napier, New Zealand, November 2007.

Functional Plant Biology 35(10) 837-849 https://doi.org/10.1071/FP08082
Submitted: 17 March 2008  Accepted: 22 September 2008   Published: 11 November 2008

Abstract

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.

Additional keywords: light simulation, open L-system, PAR, path tracing, red/far red ratio, (randomised) quasi-Monte Carlo sampling, variance reduction, virtual plant modelling.


Acknowledgements

We thank Michael Chelle for help with operation of his radiosity program and useful discussions, and Alla Seleznyova for help with the construction of the kiwifruit model. We also gratefully acknowledge the support of this research by the Natural Sciences and Engineering Research Council of Canada (MC, CL, and PP), the Horticulture and Food Research Institute of New Zealand Limited (MC) and the ARC Centre for Complex Systems at the University of Queensland (MC).


References


Arvo J, Kirk D (1990) Particle transport and image synthesis. Computer Graphics 24, 63–66.
| Crossref | GoogleScholarGoogle Scholar | open url image1

Bousquet L, Lachérade S, Jacquemoud S, Moya I (2005) Leaf BRDF measurements and model for specular and diffuse components differentiation. Remote Sensing of Environment 98, 201–211.
| Crossref | GoogleScholarGoogle Scholar | open url image1

Breece H, Holmes R (1971) Bidirectional scattering characteristics of healthy green soybean and corn leaves in vivo. Applied Optics 10, 119–127. open url image1

Chelle M, Andrieu B (1998) The nested radiosity model for the distribution of light within plant canopies. Ecological Modelling 111, 75–91.
| Crossref | GoogleScholarGoogle Scholar | open url image1

Chelle M , Andrieu B (2007) Modelling the light environment of virtual crop canopies. In ‘Functional–structural plant modelling in crop production’. (Eds J Vos, L Marcelis, P de Visser, P Struik, J Evers) pp. 75–89. (Springer-Verlag: Berlin)

Chelle M, Andrieu B, Bouatouch K (1998) Nested radiosity for plant canopies. The Visual Computer 14, 109–125.
| Crossref | GoogleScholarGoogle Scholar | open url image1

Chelle M , Hanan J , Autret H (2004) Lighting virtual crops: the CARIBU solution for open L-Systems. In ‘Proceedings of the 4th international workshop on functional–structural plant models’. p. 194. (UMR AMAP: Montpellier, France)

Chelle M, Evers J, Combes D, Varlet-Grancher C, Vos J, Andrieu B (2007) Simulation of the three-dimensional distribution of the red : far-red ratio within crop canopies. New Phytologist 176, 223–234.
| Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Cici S, Adkins S, Hanan J (2008) A canopy architectural model to study the competitive ability of chickpea and sowthistle. Annals of Botany 101, 1311–1318.
| Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

CIE-110 (1994) ‘Spatial distribution of daylight – luminance distributions of various reference skies.’ (Commission Internationale de l’Eclairage: Vienna)

Cieslak M (2004) ‘QuasiMC user’s manual.’ (University of Calgary: Calgary, Canada)

Cieslak M , Seleznyova AN , Hanan J (2007) Virtual kiwifruit: modelling annual growth cycle and light distribution. In ‘Proceedings of the 5th international workshop on functional–structural plant models’ pp. 46-1–46-2. (Print Solutions Hawke’s Bay Limited: Napier, New Zealand)

Cranley R, Patterson T (1976) Randomization of number theoretic methods for multiple integration. SIAM Journal on Numerical Analysis 13, 904–914.
| Crossref | GoogleScholarGoogle Scholar | open url image1

Disney M, Lewis P, North P (2000) Monte Carlo ray tracing in optical canopy reflectance modelling. Remote Sensing Reviews 18, 163–196. open url image1

Evans G , McCool M (1999) Stratified wavelength clusters for efficient spectral Monte Carlo rendering. In ‘Proceedings of the graphics interface 1999 conference’. pp. 42–49. (Canadian Human-Computer Communications Society: Kingston, CA)

Faure H (1982) Discrépance de suites associées à un système de numération. Acta Arithmetica 61, 337–351. open url image1

Gautier H, Měch R, Prusinkiewicz P, Varlet-Grancher C (2000) 3D Architectural modelling of aerial photomorphogenesis in white clover (Trifolium repens L.) using L-systems. Annals of Botany 85, 359–370.
| Crossref | GoogleScholarGoogle Scholar | open url image1

Goral C, Torrance K, Greenberg D, Battaile B (1984) Modeling the interaction of light between diffuse surfaces. Computer Graphics 18, 213–222.
| Crossref | GoogleScholarGoogle Scholar | open url image1

Govaerts Y (1996) A model of light scattering in three-dimensional plant canopies: a Monte Carlo ray tracing approach. PhD thesis, Université Catholique de Louvain, Louvain-la-Neuve, Belgium.

Greer D, Laing W (1992) Photoinhibition of photosynthesis in intact kiwifruit (Actinidia deliciosa) leaves: changes in susceptibility to photoinhibition and recovery during the growth season. Planta 186, 418–425.
| Crossref | GoogleScholarGoogle Scholar | open url image1

Halton JH (1960) On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numerische Mathematik 2, 84–90.
| Crossref | GoogleScholarGoogle Scholar | open url image1

Jacquemoud S , Ustin S (2001) Leaf optical properties: a state of the art. In ‘Proceedings 8th international symposium physical measurements and signatures in remote sensing’. pp. 223–232. (CNES: Aussois, France)

Jensen H (2001) ‘Realistic image synthesis using photon mapping.’ (A K Peters: Natick, MA, USA)

Kajiya JT (1986) The rendering equation. Computer graphics (SIGGRAPH ’86 conference proceedings) 20, 143–150.
| Crossref |
open url image1

Karwowski R , Prusinkiewicz P (2004) The L-system-based plant-modelling environment L-studio 4.0. In ‘Proceedings of the 4th international workshop on functional–structural plant models’. pp. 403–405. (UMR AMAP: Montpellier, France)

Karwowski R , Lane B (2007) ‘LPFG User’s manual.’ (University of Calgary: Calgary, Canada)

Keller A (1996) Quasi-Monte Carlo methods in computer graphics: the global illumination problem. Lectures in Applied Mathematics 32, 455–469. open url image1

Korobov NM (1959) The approximate computation of multiple integrals. Doklady Akademii Nauk SSSR 124, 1207–1210. open url image1

L’Ecuyer P (1999) Good parameters and implementations for combined multiple recursive random number generators. Operations Research 47, 159–164.
| Crossref |
open url image1

L’Ecuyer P , Lemieux C (2002) Recent advances in randomized quasi-Monte Carlo methods. In ‘Modeling uncertainty: an examination of stochastic theory, methods, and applications’. (Eds M Dror, P L’Ecuyer, F Szidarovszky) pp. 419–474. (Kluwer Academic Publishers: Boston)

Měch R (1997) Modeling and simulation of the interaction of plants with the environment using L-systems and their extensions. PhD thesis, University of Calgary, Calgary, Canada.

Měch R , Prusinkiewicz P (1996) Visual models of plants interacting with their environment. In ‘SIGGRAPH ’96: Proceedings of the 23rd annual conference on computer graphics and interactive techniques’. pp. 397–410.

Měch R , James M , Hammel M , Hanan J , Prusinkiewicz P , Karwowski R , Lane B (2005) ‘CPFG Vesion 4.0 user’s manual.’ (University of Calgary: Calgary, Canada)

Owen AB (2003) Quasi-Monte Carlo sampling. In ‘Monte Carlo tay tracing: SIGGRAPH 2003 Course 44’. (Ed. HW Jensen) pp. 69–88. (SIGGRAPH)

Prusinkiewicz P (2004) Art and science for life: designing and growing virtual plants with L-systems. Acta Horticulturae 630, 15–28. open url image1

Prusinkiewicz P , Hanan J , Hammel M , Měch R (1997) L-systems: from the theory to visual models of plants. In ‘Plants to ecosystems. Advances in computational life sciences’. (Ed. MT Michalewicz) pp. 1–27. (CSIRO Publishing: Melbourne)

Prusinkiewicz P , Karwowski R , Měch R , Hanan J (2000) L-studio/cpfg: a software system for modeling plants. In ‘Proceedings of applications of graph transformations with industrial relevance’. pp. 457–464. (Springer-Verlag: Berlin)

Room P, Hanan J, Prusinkiewicz P (1996) Virtual plants: new perspectives for ecologists, pathologists and agricultural scientists. Trends in Plant Science 1, 33–38.
| Crossref | GoogleScholarGoogle Scholar | open url image1

Ross J, Marshak A (1988) Calculation of canopy bidirectional reflectance using the Monte Carlo method. Remote Sensing of Environment 24, 213–225.
| Crossref | GoogleScholarGoogle Scholar | open url image1

Rubinstein R (1981) ‘Simulation and the Monte Carlo method.’ (John Wiley & Sons Inc.: New York)

Shirley P , Wang Y (1992) Distribution ray tracing: theory and practice. In ‘Proceedings of the 3rd Eurographics rendering workshop’. pp. 33–44. (Consolidation Express: Bristol, England)

Shirley P , Ashikhmin M , Gleicher M , Marschner S , Reinhard E , Sung K , Thompson W , Willemsen P (2005) ‘Fundamentals of computer graphics.’ (A K Peters: Wellesley, MA, USA)

Sobol’ IM (1967) The distribution of points in a cube and the approximate evaluation of integrals. U.S.S.R. Computational Mathematics and Mathematical Physics 7, 86–112.
| Crossref | GoogleScholarGoogle Scholar | open url image1

Soler C, Sillion F, Blaise F, de Reffye P (2003) An efficient instantiation algorithm for simulating radiant energy transfer in plant models. ACM Transactions on Graphics 22, 204–233.
| Crossref | GoogleScholarGoogle Scholar | open url image1

Spanier J , Gelbard E (1969) ‘Monte Carlo principles and neutron transport problems.’ (Addison-Wesley: Reading, MA, USA)

Thornley JHM , Johnson IR (1990) ‘Plant and crop modelling.’ (Oxford University Press: Oxford)

Veach E (1997) Robust Monte Carlo methods for light transport simulation. PhD thesis, Stanford University, Stanford, CA, USA.

Watt A (2000) ‘3D Computer graphics.’ (Addison-Wesley: Reading, MA, USA)