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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.

For pesticides to effectively manage pests, they must first be deposited on the target (typically a plant surface) in a manner in which the active ingredient(s) can be readily taken up by the target organism. A plant architectural model that enables the location of various plant components in 3-D space combined with a particle trajectory model has been used to study the interception of spray droplets by various vegetative elements. Results from the simulation are compared with wind tunnel studies of glyphosate deposition on cotton (Gossypium hirsutum L. var. Sicala), sow thistle (Sonchus oleraceus L.) and wild oats (Avena ludoviciana Durieu). An air induction flat fan nozzle (AI110015 at 500 kPa pressure) and an extended range flat fan nozzle (XR11002 at 280 kPa pressure) were predicted to have similar glyphosate deposition on cotton and sow thistle plants, whereas the extended range nozzle resulted in higher deposit on wild oats. Spray deposition (µg cm−2) on wild oat plants at the 5-leaf stage was more than double the amount of deposition on sow thistle or wild oat plants at the 2-leaf stage. The model was in good agreement with the experimental data except that it tended to over predict deposition on sow thistle plants.

In this paper we present a method for modeling herbaceous plants, suitable for generating realistic plant images and animating developmental processes. The idea is to achieve realism by simulating mechanisms which control plant growth in nature. The developmental approach to the modeling of plant architecture is extended to the modeling of leaves and flowers. The method is expressed using the formalism of L-systems.

Graphical applications of L-systems are not limited to fractals and plants. In this chapter we outline some of the lesser known ones.

According to the rules introduced in the previous chapter the turtle interprets a character string as a sequence of line segments, connected “head to tail” with each other. Depending on the segment lengths and the angles between them, the resulting line self-intersecting or not, can be more or less convoluted, with some segments drawn many times and others made invisible, but it always remains just a single line.

Although the developmental surface models discussed in the previous chapter allow for specifying closed polygons, the basic supporting structure is still limited to trees (in the graph-theoretic sense). An extension of L-systems to maps [104] (planar graphs with cycles which partition the plane into regions) is termed map L-systems [62,90,16,55,53].

This chapter presents bibliographical remarks which focus on plant modelling and growth simulation for computer graphics purposes. An emphasis is put on the applications of L-systems.

Vegetation type and structure can play an important role in determining the amount of spray that reaches a target as well as the amount of spray moving away from a treated area. In this paper droplet trajectory models and plant architecture models are combined using three-dimensional computer modeling techniques to develop a probabilistic model of turbulence-related spray transport around various plant architectures. The plant architecture model utilises a set of growth rules expressed in the Lindenmayer systems (L-systems) formalism linked to a C++ environmental program to determine the interception of spray droplets by the various vegetative elements. Algorithms have also been introduced to investigate the influence of droplet splash on spray deposition

Models of cotton plant architecture expressing several physiological hypotheses about plant resource use and responses to damage are incorporated in the traditional research cycle to investigate the phenomena of compensation for defoliation. Two separate approaches to modelling the uptake and allocation of carbon are used: a detailed bottom-up physiology model expressing ideas about local control, and a top-down, canonical approach where qualitative knowledge about plant responses to defoliation are modelled as yows between plant physiological compartments. The two models provide contrasting methods for developing explanations for the underlying pattern of responses observed in the plants.

A model of the transport process that follows the progress of digesta successively through the small intestine of a monogastric is investigated. The process is multi-phase and multi-constituent, as described in detail by Bastianelli et al. [J. Anim. Sci., 74:1873–1887, 1996]. The model describes the movement of marker substances that are used to obtain data on the interactions between the intestinal sections and digesta with differing levels of soluble fibre. A multi-stage process is modelled by a set of coupled first order linear differential equations. Solutions of steady and initial value problems provide information on the transfer rates of the processes. Properties of the solutions as functions of system parameters are examined.

Using models of frangipani, cotton and birch plants, this paper shows how physiology can be included in structural plant models through local plant component resource modelling, crop level modelling and canonical mathematical modelling at the level of the individual plant. These simulations are more than just pictorial representations of these plants, and more than just three-dimensional structural representations changing over time. They respond to their environment as they grow, which is achieved by including aspects of physiology in the models. However, they do not require detailed and complex quantitative understanding of the individual plant's physiology. This paper demonstrates the possibility of constructing such adaptive virtual plant simulations, with environmentally sensitive complex emergent structure, by modelling physiology in simple, yet effective ways.

This paper presents a spatial simulation model of above-ground morphogenesis in a gramineous crop, grain sorghum (Sorghum bicolor (L.) Moench). Functions and parameters describing structural development were obtained from three-dimensional (3D) measurements of plants made at intervals during their development. The functions were expressed as specifications of morphogenesis in the L-system formalism and the specifications were interpreted by specialised software to create 3D virtual sorghum plants. Using the length and height of the collar of an early leaf as initial states, realistic images were generated of the lengths and shapes of subsequent leaves. The approach captures the dynamic interaction between partitioning and morphogenesis and presents the complex results as images that aid rapid interpretation.