3. Amapmod-et-de-la-géométrie-par-digitalisation, Guide de l'utilisateur. INRA-PIAF Clermont-Ferrand (France)

M. Allen, P. Prusinkiewicz, and T. Dejong, Using L-systems for modeling source-sink interactions, architecture and physiology of growing trees: the L-PEACH model, New Phytologist, vol.117, issue.3, pp.869-880, 2005.
DOI : 10.1111/j.1469-8137.2005.01348.x

T. Alméras, Acquisition de la forme des axes ligneux d'un an chez trois variétés d'abricotier: confrontation de données expérimentales à un modèle biomécanique, 2001.

T. Alméras, J. Gril, and E. Costes, Bending of apricot tree branches under the weight of axillary growth: test of a mechanical model with experimental data, Trees, vol.16, issue.1, pp.5-15, 2002.
DOI : 10.1007/s00468-001-0139-1

T. Alméras, E. Costes, and J. Salles, Identification of Biomechanical Factors Involved in Stem Shape Variability between Apricot Tree Varieties, Annals of Botany, vol.93, issue.4, pp.455-68, 2004.
DOI : 10.1093/aob/mch054

P. Ancelin, T. Fourcaud, and P. Lac, Modelling the biomechanical behaviour of growing trees at the forest stand scale. Part I: Development of an Incremental Transfer Matrix Method and application to simplified tree structures, Annals of Forest Science, vol.61, issue.3, pp.263-275, 2004.
DOI : 10.1051/forest:2004019

URL : https://hal.archives-ouvertes.fr/hal-00883851

S. Benzing, Patterns of vegetative and reproductive growth in apple (Malus x domestica Borkh, 1999.

E. Costes and P. Lauri, Processus de croissance en relation avec la ramification sylleptique et la floraison chez le pommier, Architecture des arbres fruitiers et forestiers'. (Ed. J Bouchon) pp 41-50. (INRA Editions, 1995.

E. Costes and Y. Guédon, Modelling Branching Patterns on 1-year-old Trunks of Six Apple Cultivars, Annals of Botany, vol.89, issue.5, pp.513-524, 2002.
DOI : 10.1093/aob/mcf078

URL : https://hal.archives-ouvertes.fr/hal-00827468

E. Costes, P. Lauri, and J. Lespinasse, Modélisation de la croissance et de la ramification chez quelques cultivars de Pommier, 1995.

E. Costes, D. Fournier, and J. Salles, apricot trees, The Journal of Horticultural Science and Biotechnology, vol.75, issue.5, pp.510-529, 2000.
DOI : 10.1080/14620316.2000.11511277

URL : https://hal.archives-ouvertes.fr/hal-00830071

E. Costes, P. Lauri, and J. Régnard, Tree Architecture and Production, Horticultural Reviews, vol.32, pp.1-60, 2006.
URL : https://hal.archives-ouvertes.fr/hal-01377095

E. Costes, H. Sinoquet, J. Kelner, and C. Godin, Exploring Within-tree Architectural Development of Two Apple Tree Cultivars Over 6 Years, Annals of Botany, vol.91, issue.1, pp.91-104, 2003.
DOI : 10.1093/aob/mcg010

URL : https://hal.archives-ouvertes.fr/hal-00826993

J. Crabbé and J. Escobedo-alvarez, Activités méristématiques et cadre temporel assurant la transformation florale des bourgeons chez le Pommier, 1991.

G. Deckmyn, S. Evans, and T. Randle, Refined pipe theory for mechanistic modeling of wood development, Tree Physiology, vol.26, issue.6, pp.703-717, 2006.
DOI : 10.1093/treephys/26.6.703

J. Durand, Y. Guédon, Y. Caraglio, and E. Costes, Analysis of the plant architecture via tree-structured statistical models: the hidden Markov tree models, New Phytologist, vol.10, issue.3, pp.813-825, 2005.
DOI : 10.1111/j.1469-8137.2005.01405.x

URL : https://hal.archives-ouvertes.fr/hal-00017402

S. Fine, Y. Singer, and N. Tishby, The hierarchical hidden Markov model: Analysis and applications, Machine Learning, vol.32, issue.1, pp.41-62, 1998.
DOI : 10.1023/A:1007469218079

M. Fournier, Mécanique de l'arbre sur pied: maturation, poids propre, contraintes climatiques dans la tige standard, 1989.

M. Fournier, B. Chanson, D. Guitard, and T. B. , M??canique de l'arbre sur pied : mod??lisation d'une structure en croissance soumise ?? des chargements permanents et ??volutifs. 1. Analyse des contraintes de support, Annales des Sciences Foresti??res, vol.48, issue.5, pp.513-525, 1991.
DOI : 10.1051/forest:19910503

M. Fournier, B. Chanson, D. Guitard, and T. B. , M??canique de l'arbre sur pied : mod??lisation d'une structure en croissance soumise ?? des chargements permanents et ??volutifs. 2. Analyse tridimensionnelle des contraintes de maturation, cas du feuillu standard, Annales des Sciences Foresti??res, vol.48, issue.5, pp.527-573, 1991.
DOI : 10.1051/forest:19910504

H. Gautier, R. Mech, P. Prusinkiewicz, and C. Varlet-grancher, 3D Architectural Modelling of Aerial Photomorphogenesis in White Clover (Trifolium repens L.) using L-systems, Annals of Botany, vol.85, issue.3, 2000.
DOI : 10.1006/anbo.1999.1069

C. Godin, Representing and encoding plant architecture: A review, Annals of Forest Science, vol.57, issue.5, pp.413-438, 2000.
DOI : 10.1051/forest:2000132

URL : https://hal.archives-ouvertes.fr/hal-00883351

C. Godin and Y. Caraglio, A Multiscale Model of Plant Topological Structures, Journal of Theoretical Biology, vol.191, issue.1, pp.1-46, 1998.
DOI : 10.1006/jtbi.1997.0561

URL : https://hal.archives-ouvertes.fr/hal-00827484

C. Godin, E. Costes, and H. Sinoquet, A Method for Describing Plant Architecture which Integrates Topology and Geometry, Annals of Botany, vol.84, issue.3, pp.343-357, 1999.
DOI : 10.1006/anbo.1999.0923

URL : https://hal.archives-ouvertes.fr/hal-00827477

Y. Guédon, Estimating Hidden Semi-Markov Chains From Discrete Sequences, Journal of Computational and Graphical Statistics, vol.12, issue.3, pp.604-639, 2003.
DOI : 10.1198/1061860032030

Y. Guédon, D. Barthélémy, Y. Caraglio, and E. Costes, Pattern Analysis in Branching and Axillary Flowering Sequences, Journal of Theoretical Biology, vol.212, issue.4, pp.481-520, 2001.
DOI : 10.1006/jtbi.2001.2392

J. Hanan and P. Room, Practical aspects of virtual plant research, Plants to ecosystems'. (Ed. Michalewicz MT) pp, pp.28-45, 1997.

J. Hanan and A. Hearn, Linking physiological and architectural models of cotton, Agricultural Systems, vol.75, issue.1, pp.1-31, 2002.
DOI : 10.1016/S0308-521X(01)00114-7

R. Hangarter, Gravity, light and plant form, Plant, Cell and Environment, vol.20, issue.6, pp.796-800, 1997.
DOI : 10.1046/j.1365-3040.1997.d01-124.x

C. Jirasek, P. Prusinkiewicz, and B. Moulia, Integrating Biomechanics into Developmental Plant Models Expressed using L-systems, 2000.

R. Karwowski and P. Prusinkiewicz, Design and Implementation of the L+C Modeling Language, Electronic Notes in Theoretical Computer Science, vol.86, issue.2, pp.134-152, 2003.
DOI : 10.1016/S1571-0661(04)80680-7

J. Kelner, AIP AGRAF: Pour l'élaboration de la composition et l'aptitude à l'utilisation des grains et des fruits, 2000.

A. Lakso, L. Grappadelli, J. Barnard, and M. Goffinet, An expolinear model of the growth pattern of the apple fruit, Journal of Horticultural Science, vol.70, issue.3, pp.389-394, 1995.
DOI : 10.1080/14620316.1995.11515308

P. Lauri, From tree architecture to tree training -An overview of recent concepts developed in apple in France, Journal of the Korean Society for Horticultural Science, vol.43, pp.782-790, 2002.

P. Lauri, E. Térouanne, and J. Lespinasse, Relationship between the early development of apple fruiting branches and the regularity of bearing???An approach to the strategies of various cultivars, Journal of Horticultural Science, vol.72, issue.4, pp.519-549, 1997.
DOI : 10.1080/14620316.1997.11515539

A. Lindenmayer, Mathematical models for cellular interactions in development I. Filaments with one-sided inputs, Journal of Theoretical Biology, vol.18, issue.3, pp.280-315, 1968.
DOI : 10.1016/0022-5193(68)90079-9

G. Lopez, R. Favreau, C. Smith, E. Costes, P. Prusinkiewicz et al., Integrating simulation of architectural development and source-sink behaviour of peach trees by incorporating Markov chains and physiological organ function sub-models into L- PEACH, 2008.

C. Massonnet, Variabilité architecturale et fonctionnelle du système aérien chez le pommier (Malus x Domestica Borkh.) : comparaison de quatre cultivars par une approche de modélisation structure-fonction, 2004.

J. Matsuzaki, M. Masumori, and T. Takeshi, Phototropic bending of non-elongating and radially growing woody stems results from asymmetrical xylem formation, Plant, Cell & Environment, vol.31, issue.5, pp.646-653, 2007.
DOI : 10.1007/s10086-004-0639-x

R. Mech and P. Prusinkiewicz, Visual models of plants interacting with their environment, Proceedings of the 23rd annual conference on Computer graphics and interactive techniques , SIGGRAPH '96, pp.397-410, 1996.
DOI : 10.1145/237170.237279

C. Murray, A RELATIONSHIP BETWEEN CIRCUMFERENCE AND WEIGHT IN TREES AND ITS BEARING ON BRANCHING ANGLES, The Journal of General Physiology, vol.10, issue.5, pp.725-729, 1927.
DOI : 10.1085/jgp.10.5.725

K. Niklas, Plant biomechanics. An engineering approach to plant form and function, 1992.

C. Pradal, F. Boudon, C. Nouguier, J. Chopard, and C. Godin, PlantGL: A Python-based geometric library for 3D plant modelling at different scales, Graphical Models, vol.71, issue.1, 2007.
DOI : 10.1016/j.gmod.2008.10.001

URL : https://hal.archives-ouvertes.fr/inria-00191126

P. Prusinkiewicz, Modeling of spatial structure and development of plants: a review, Scientia Horticulturae, vol.74, issue.1-2, pp.113-149, 1998.
DOI : 10.1016/S0304-4238(98)00084-3

P. Prusinkiewicz and A. Lindenmayer, The algorithmic beauty of plants, 1990.
DOI : 10.1007/978-1-4613-8476-2

P. Prusinkiewicz, L. Mündermann, R. Karwowski, and B. Lane, The use of positional information in the modeling of plants, Proceedings of the 28th annual conference on Computer graphics and interactive techniques , SIGGRAPH '01, pp.289-300, 2001.
DOI : 10.1145/383259.383291

P. Prusinkiewicz, R. Karwowski, L. B. Vos, L. De-visser, P. Struick et al., The L+C plant-modelling language. In 'Functional-structural plant modeling in crop production'. (Eds, pp.27-42, 2007.

M. Renton, P. Kaitaniemi, and H. J. , Functional???structural plant modelling using a combination of architectural analysis, L-systems and a canonical model of function, Ecological Modelling, vol.184, issue.2-4, pp.277-298, 2005.
DOI : 10.1016/j.ecolmodel.2004.10.008

M. Renton, J. Hanan, and K. Burrage, Using the canonical modelling approach to simplify the simulation of function in functional-structural plant models, New Phytologist, vol.86, issue.76, pp.845-857, 2005.
DOI : 10.1111/j.1469-8137.2005.01330.x

M. Renton, Y. Guédon, C. Godin, and E. Costes, Similarities and gradients in growth unit branching patterns during ontogeny in 'Fuji' apple trees: a stochastic approach, Journal of Experimental Botany, vol.57, issue.12, pp.3131-3143, 2006.
DOI : 10.1093/jxb/erl075

URL : https://hal.archives-ouvertes.fr/hal-00120198

V. Segura, C. Denancé, C. Durel, and E. Costes, Wide range QTL analysis for complex architectural traits in a 1-year-old apple progeny, Genome, vol.50, pp.159-171, 2007.

H. Sinoquet, P. Rivet, and C. Godin, Assessment of the three-dimensional architecture of walnut trees using digitising., Silva Fennica, vol.31, issue.3, pp.265-73, 1997.
DOI : 10.14214/sf.a8525

URL : https://hal.archives-ouvertes.fr/hal-00827488

K. Shinozaki, K. Yoda, K. Hozumi, and T. Tira, A quantitative analysis of plant form ? the pipe model theory. (i) basic analyses, Japanese Journal of ecology, vol.14, pp.97-105, 1964.

M. Suzuki and T. Hiura, Allometric differences between current-year shoots and large branches of deciduous broad-leaved tree species, Tree Physiology, vol.20, issue.3, pp.203-209, 2000.
DOI : 10.1093/treephys/20.3.203

J. Taylor-hell, Biomechanics in botanical trees, 2005.

D. Thornby, M. Renton, and H. J. , Using Computational Plant Science Tools to Investigate Morphological Aspects of Compensatory Growth, Computational Science -Iccs, pp.708-717, 2003.
DOI : 10.1007/3-540-44864-0_73

R. Wang, W. Hua, Z. Dong, Q. Peng, and H. Bao, Synthesizing trees by plantons, The Visual Computer, vol.22, issue.3, pp.238-248, 2006.
DOI : 10.1007/s00371-006-0002-x

J. White, The Plant as a Metapopulation, Annual Review of Ecology and Systematics, vol.10, issue.1, pp.109-154, 1979.
DOI : 10.1146/annurev.es.10.110179.000545