💻 Coffee 3D Architectural Modeling

Virtual Coffee Plants: From Architecture to Function

Comprehensive guide to 3D modeling of coffee plants — from architectural reconstruction and functional-structural plant models to finite element analysis for harvest optimization and light interception simulations for agroforestry systems.

3 CoffePlant3D Modules [1][4][8]
2-20% FEM Vibration Error [5][9]
14% Shade Tree aPAR Reduction [7]
17-month OpenAlea Plant Age [2][10]

The Importance of 3D Plant Modeling

Accurate model of structural elements is necessary to model the foliage and fruit distributions in cultivated plants, both of them being key parameters for yield prediction [1][4][8].

Plant architecture can be described at various degrees of detail [1][8]. The level of details in architectural data collection could vary, simplifying the data collection when plants get older and because of the high time cost required [1][4][8].

3D modeling of coffee plants serves multiple purposes [1][2][3][4][5][6][7][8][9][10]:

  • Yield prediction: Modeling foliage and fruit distributions for accurate yield forecasting [1][4][8]
  • Photosynthesis estimation: Correlating 3D architecture with plant carbon assimilation [2][10]
  • Light interception: Simulating PAR absorption in monoculture and agroforestry systems [3][6][7]
  • Mechanical harvesting: Finite element analysis of branch vibration for harvest optimization [5][9]
  • Biomass allocation: Understanding intraspecific variability in resource partitioning [2][10]

The coffee tree architecture, described as Roux's model, is characterized by a continuous growth and dimorphic axes [1][8].

Key References

  • CoffePlant3D: Rakocevic et al. [1][4][8]
  • OpenAlea: Rakocevic et al. 2022 [2][10]
  • MAESTRA: Charbonnier et al. 2014 [3][7]
  • FEM 2025: Federal University of Lavras [5][9]
  • VPlants: Rakocevic et al. 2013 [6]

Coffee Plant Architecture

Roux's model and architectural decomposition scales

Architectural Decomposition

Three scales of decomposition are used to reconstruct coffee plant architectures [1][4][8]:

Plant Scale

Whole plant architecture and topology

Axes Scale

Orthotropic trunk and plagiotropic branches (1st, 2nd, 3rd order)

Metamer Scale

Individual internode + leaf + axillary bud units

Botanical Model

The coffee tree architecture follows Roux's model, characterized by [1][8]:

Key Architectural Relationships

The number of metamers of the 2nd order axes was shown to be linearly proportional to that of the orthotropic trunk [1][4][8].

This ratio of metamer emission rhythm between the orthotropic trunk and plagiotropic axes represents the pillar of botanical events in C. arabica development and was central in modeling approaches, especially to reconstruct missing data [1][4][8].

CoffePlant3D: Dedicated Coffee Reconstruction Software

A software integrating mathematical, computational, and statistical methods for accurate 3D coffee reconstruction [1][4][8]

CoffePlant3D

Three interconnected modules ranging from user interface to input of information related to plant, field and productivity [1][4][8]:

AmostraCafe3D

Function: Inclusion of missing data at metamer scale

Receives MTG with mixed levels of detail and performs reconstruction of missing data [1][4][8]

VirtualCafe3D

Function: Geometrical correction of axes orientation and leaf pair position and orientation [1][4][8]

Cafe3D

Function: Visualization of the 3D plant structure [1][4][8]

AmostraCafe3D

Missing Data Reconstruction

When coffee plants were sampled under mixed levels of details, the MTG needed to be topologically complemented by AmostraCafe3D [1][4][8].

Attributes Considered for Each Metamer
  • Leaf presence/absence
  • Branching presence/absence
  • Berry presence/absence
  • Internode length [1][4][8]
Probability Generation

Probabilities were generated based on properties of completely measured axes classified in the same cluster, attributing presence/absence at each node along partially measured 2nd order axes [1][4][8].

Random Selection

Probabilities were randomly chosen by running the 'choice' function, which uses the Mersenne twister as the core generator [1][8].

VirtualCafe3D

Geometrical Correction

After clustering the branches by their position along the orthotropic axis (considering 40 cm-thick layers), the 2nd order axes were filled by metamer number based on [1][4][8]:

  • Length probability of each internode
  • Defined regression coefficients
Synchronization Rule

It was assumed that the second order axes have the same phyllochron with 3rd, 4th and 5th order axes. A linear model was applied, permitting synchronization to the emitted metamer number in partially measured axes [1][8].

Index Generation Rule
y = (a - b) + x, if a > b;
y = x - (b - a), if a < b and x > (b - a);
y = 1, if x < (b - a)
Cafe3D

3D Visualization

If the leaf length and width were defined, the reproduction of individual 3D coffee leaf was constructed on 16 triangles, performed by reduction of leaf length and width equally [1][4][8].

Leaf Visualization

Individual leaves are reconstructed with accurate geometry based on measured dimensions.

Berry Distribution Modeling

The number of berries per metamer was modeled as a Gaussian function within a specific zone along the plagiotropic axes [1][4][8].

G(x) = a · exp(-(x - b)²/(2c²)) for 0 ≤ x ≤ n

Linear Regression Coefficients

Coefficient of the linear regressions between the number of metamers and the length of orthotropic and plagiotropic axes [1][8]

Production Year Variable Planting Pattern & Density
Q10 (6000/ha) Q6 (10,000/ha) R10 (6000/ha) R6 (10,000/ha)
1st year Metamer number 1.124 1.000 0.871 0.974
Length of 2nd order axes 1.033 0.891 0.828 0.960
2nd year Metamer number 0.959 1.138 0.895 0.930
Length of 2nd order axes 0.794 0.859 0.931 0.798
6th year Metamer number 0.956 0.868 0.887 0.793
7th year Metamer number 0.905 0.930 0.894 0.705

OpenAlea: Functional-Structural Plant Modeling

Non-destructive coffee plant architecture coding, reconstruction and plant photosynthesis estimations using OpenAlea platform [2][10]

Study Parameters

  • Plants: 17-month-old C. canephora (Robusta clones 'A1' and '3V'; Conilon clones '14' and '19') [2][10]
  • Conditions: Non-limiting soil, water and mineral nutrients [2][10]
  • Virtual orchard: Low leaf area index, light not limiting in early development [2][10]

Photosynthesis Parameters

3D reconstructions and inclusion of parameters calculated from light response curves allowed estimation of [2][10]:

  • Dark respiration (Rd)
  • Maximum rate of carboxylation of RuBisCO
  • Photosynthetic electron transport
  • Instantaneous and daily plant photosynthesis

Key Findings

  • Robusta vs Conilon: Robusta assimilated more CO2 at plant and orchard scale, produced higher total biomass [2][10]
  • Correlation factors: Lower plant daily photosynthesis and total biomass correlated to higher Rd in Conilon [2][10]
  • Architectural traits: Leaf inclination, size and allometry most highly correlated with plant assimilation and biomass [2][10]
  • Biomass partitioning: Higher leaf biomass allocation in '19' Conilon than in young Robusta plants, indicating intraspecific variability [2][10]
  • Root distribution: Variation in relative distribution of root biomass and root volume reflected clonal variation in soil occupation [2][10]
Implications: Relevant differences at subspecific levels indicate high potential of C. canephora to cope with drought events expected with climate change. The methodology has potential for other crops and tree species [2][10].

MAESTRA: Light Interception in Agroforestry Systems

3D light interception model applied to coffee agroforestry systems with heterogeneous canopy layers [3][7]

Coffee-Flux Observatory, Costa Rica

  • Location: Central Valley, Aquiares coffee farm
  • Altitude: 1,000 m
  • Climate: Tropical humid, no dry season
  • Coffee: Coffea arabica cv. Caturra
  • Shade trees: Erythrina poepigiana (low density, free-growing)
  • Area: 6 km² Rainforest Alliance certified farm

Model Validation

  • APAR validation: Successful validation at coffee plant scale using transient-state whole tree chamber [3]
  • Plot scale validation: Successful validation at plot scale with eddy-covariance measurements [3]
  • Parameterization: Based on field inventories, structural measurements (leaf area per tree, leaf angles), and leaf-scale gas exchange [3]

Key Results

14%

Shade trees (9% cover) reduced aPAR in coffee by 14% annually [7]

20%

Shade trees increased fraction of diffuse irradiance below their crown [7]

35%

Incident PAR absorbed by soil due to inter-row spaces [7]

Prospective Simulations

Applications: MAESTRA can be used to design new agroforestry systems to optimize light absorption, canopy temperature, carbon assimilation and transpiration [3][7].

Three-Dimensional Scanning and Finite Element Analysis (2025)

Computational modeling of coffee branches using scanning techniques and experimental validation through modal analysis [5][9]

Methodology

  • Mechanical properties: Specific gravity and elastic modulus obtained in laboratory [5][9]
  • Geometric models: 3D scanning of coffee branches [5][9]
  • Analysis method: Finite Element Method (FEM) for static and dynamic behavior [5][9]
  • Validation: Experimental modal analysis tests [5][9]

Equation of Motion (MDOF System)

[m]{ẍ(t)} + [c]{ẋ(t)} + [k]{x(t)} = {F(t)}

where [m] = mass matrix, [c] = damping matrix, [k] = stiffness matrix

Modal Analysis (Undamped Free Vibration)

([k] - ω²[m]){Φ} = {0}

Results

  • 2-20% Vibration frequency variation between simulations and experimental tests [5][9]
  • Statistical analysis found no significant differences [5][9]
  • Methodology validated for predicting static and dynamic behaviors of plagiotropic branches [5][9]

Applications

  • Harvest optimization: Vibration analysis for mechanized coffee harvesting [5][9]
  • Damage prevention: Identify excitation frequencies that optimize fruit detachment while minimizing plant damage
  • Previous applications: Similar FEM studies on tomatoes, kiwifruit, and sugarcane [9]

Previous Coffee FEM Studies

  • Pereira et al.: 3D models of coffee fruits at different ripeness stages [9]
  • Melo et al.: FEM analysis of plagiotropic branches (Catuaí Vermelho) for natural frequencies and vibration modes [9]

VPlants: Foliage Modeling and Light Partitioning

Protocol for foliage modeling and light partitioning in Coffea arabica using VPlants software [6]

Methodology

  • Virtual coffee trees reconstructed using partial morphological data
  • AmostraCafe3D and VirtualCafe3D modules
  • VPlants software for final reconstruction

Analyses

  • Leaf area size
  • STAR (Silhouette to Total Area Ratio)
  • Transmitted PAR in different horizontal layers
  • Validation against field measurements
Source: 7th International Conference on Functional Structure Plant Models, 2013 [6]

Berry Distribution Modeling

Gaussian function for berry distribution along plagiotropic axes [1][4][8]

Gaussian Model
G(x) = a · exp(-(x - b)²/(2c²)) for 0 ≤ x ≤ n

where a = maximum productivity value, b = position index, c = spread parameter

Final Berry Distribution
f(x) = G(x) + (Nb(i) - G(i))

where Nb(i) = number of berries on the boundaries

Berry Number Calculation
B(i) = Ceil((Nb · Vi)/∑Vi)

where Ceil = ceiling function, Nb = total berry number, Vi = number of berries in each node

Validation: The measured and computed sum of berries of the 2nd order axes were compared using the whole dataset regardless of planting pattern (square vs rectangular) and density, showing good agreement [1][8].

Timeline of Coffee 3D Modeling Research

2011

Rakocevic & Androcioli: Morphophysiological characteristics of Coffea arabica in different arrangements - 3D virtual plant approach [1]

2013

VPlants protocol for foliage modeling and light partitioning in Coffea arabica [6]

2014

Charbonnier et al.: MAESTRA light interception modeling in coffee agroforestry systems [3][7]

2022

Rakocevic et al.: OpenAlea functional-structural plant modeling for C. canephora photosynthesis estimation [2][10]

2025

Three-Dimensional Scanning and Computational Simulation of Coffee Tree Branches - Finite Element Analysis [5][9]

Key Publications on Coffee 3D Modeling

CoffePlant3D: Reconstructing coffee plants in 3D

Rakocevic M., et al. (2011). Coffee Science [1][4][8]

Three modules (AmostraCafe3D, VirtualCafe3D, Cafe3D); linear proportionality between orthotropic trunk and plagiotropic branch metamers; Gaussian berry distribution; validation across datasets.

View Abstract
Correlating C. canephora 3D architecture to plant photosynthesis

Rakocevic M., et al. (2022). Tree Physiology 43(4):556-574 [2][10]

OpenAlea platform; 17-month Robusta vs Conilon; leaf inclination/size/allometry correlated with assimilation; Rd differences; intraspecific biomass partitioning; high potential for drought adaptation.

View Abstract
Three-Dimensional Scanning and Computational Simulation of Coffee Tree Branches

(2025). Agriculture 15(13):1326 [5][9]

Finite Element Method; 3D scanning; vibration frequency error 2-20%; modal analysis validation; applications for mechanized harvesting optimization.

View Abstract
MAESTRA light modeling in coffee agroforestry

Charbonnier F., et al. (2014). World Congress of Agroforestry [3][7]

14% aPAR reduction from 9% shade tree cover; 20% diffuse irradiance increase; 35% soil PAR absorption; negative exponential with shade density; prospective simulations for system design.

View Abstract
VPlants foliage modeling protocol

Rakocevic M., et al. (2013). 7th FSPM Conference [6]

Virtual coffee trees from partial data; AmostraCafe3D + VirtualCafe3D; leaf area, STAR, transmitted PAR validation.

View Abstract
View All Publications →

References

Peer-reviewed sources and authoritative references cited in this research

[1] Rakocevic, M., & Androcioli Filho, A. (2011). Morphophysiological characteristics of (Coffea arabica L.) in different arrangements: Lessons from a 3D virtual plant approach. Coffee Science, 5(2), 154–166. UFLA
[2] Rakocevic, M., de Souza, G.A.R., & Campostrini, E. (2022). Correlating Coffea canephora 3D architecture to plant photosynthesis at a daily scale and vegetative biomass allocation. Tree Physiology, 43(4), 556-574. doi:10.1093/treephys/tpac138 PMID:36519756
[3] Charbonnier, F., Le Maire, G., Dreyer, E., Casanoves, F., Christina, M., Dauzat, J., Eitel, J.U.H., Vaast, P., Vierling, L.A., Van den Meersche, K., Harmand, J.M., & Roupsard, O. (2014). Using the MAESTRA model to simulate light interactions and photosynthesis in a heterogeneous agroforestry system under alternative density. 3rd World Congress of Agroforestry. Cirad
[4] Rakocevic, M., Matsunaga, F.T., & Guédon, Y. (2023). Accurate model of structural elements for coffee foliage and fruit distributions. ScienceOpen. ScienceOpen
[5] Three-Dimensional Scanning and Computational Simulation of Coffee Tree Branches. (2025). Agriculture, 15(13), 1326. doi:10.3390/agriculture15131326
[6] Rakocevic, M., Matsunaga, F.T., Costes, E., Tosti, J.B., Guédon, Y., De Cassia Santin, L., & Johann, A.L. (2013). Protocol for foliage modeling and light partitioning in Coffea arabica. 7th International Conference on Functional Structure Plant Models. AGRIS
[7] Charbonnier, F., Le Maire, G., Dreyer, E., Casanoves, F., Christina, M., Dauzat, J., Eitel, J.U.H., Vaast, P., Vierling, L.A., Van den Meersche, K., Harmand, J.M., & Roupsard, O. (2014). The end of the sun/shade dichotomy in AFS: mapping of plant light budgets in multistrata heterogeneous plots. 3rd World Congress of Agroforestry. AGRIS
[8] Rakocevic, M., et al. (2023). Accurate model of structural elements is necessary to model the foliage and fruit distributions. HAL INRAE. hal-02640747
[9] Federal University of Lavras. (2025). Three-Dimensional Scanning and Computational Simulation of Coffee Tree Branches. MDPI Agriculture. MDPI Open Access
[10] Rakocevic, M., de Souza, G.A.R., & Campostrini, E. (2022). Correlating Coffea canephora 3D architecture to plant photosynthesis. NIH PubMed. PMID:36519756

* Additional references available in the complete Publications Database. All sources are peer-reviewed.