# The Simulation of the Apple Tree Form's Effects on Its Photosynthetic Efficiency

Lin Hu, Guomin Zhou, Yun Qiu

► To cite this version:

Lin Hu, Guomin Zhou, Yun Qiu. The Simulation of the Apple Tree Form's Effects on Its Photosynthetic Efficiency. 4th Conference on Computer and Computing Technologies in Agriculture (CCTA), Oct 2010, Nanchang, China. pp.138-145, 10.1007/978-3-642-18354-6_19. hal-01563421

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# The simulation of the Apple tree form's effects on its photosynthetic efficiency

HU Lin, ZHOU Guomin, QIU Yun

Agricultural Information Institute of CAAS, Beijing, P.R. China

**Abstract.** the form of the Apple tree is decided by the organ position of the tree, it affects not ONLY the relationship between the vegetative growth and the fruit production, but also the fruit quality. In this research, the continuous growth for 3 years was gotten with polhemus fastrak, and the apple tree model was built in the POV-ray to simulate the interception of the sunlight. A mathematic model was built between the form and the photosynthetic efficiency, the growth as the index of the form while the interception of the light as the index of the photosynthetic efficiency. Utilizing this model to analyses the effects of the form on the apple tree's photosynthetic efficiency, this result show a reference for the apple trees management.

**Keywords:** apple trees, light, intercept ratio, mathematic model, fine management, simulate

## 1 Introduction

The study of plant architecture emerged as a new scientific discipline some 30 years ago. Plant architecture is a term applied to the organization of plant components in space which can change with time (2007, Daniel Barthelemy). Plant architecture is introduced into the research of the apple tree (2003, E. Costes). One of the researches is about the interactions between light and vegetation (2005, Rodrigo A.). The geometrical structure of the vegetation canopy, i.e. the location, shape and orientation of the apple tree elements determine the light distribution in the canopy (2005, J. Phattaralerphong). Many methods for the measurement of canopy geometry may involve direct measurement or may be inferred from radiation measurement using light sensor. Of the direct measurements, current induction in magnetic fields is the most convenient one.

In this paper, we use a polheumes fastrak to measure the parameters of the apple tree structure, such as the node, internodes, orientation angle, etc. the measured data was used to descript the apple tree in POV-Ray (Persistence of Vision Ray-Tracer). POV-Ray is a high-quality, freely available ray-tracing software package that is available for PC, Macintosh and UNIX platforms. POV-Ray is used in every industry widely, such as chemistry, art painting, architecture, agriculture, remote sensing and medicine. We simulate the light transfer in the crown, and evaluate the affection of the apple tree architecture on the interception of the sunlight.
## 2 Materials and Methods

The test area is located at the Fruit Research Institute of Chinese Academy of Agricultural sciences (Figure1).

The apple tree is HuaHong, a variety of Fuji apple, bred by the institute own self.
We began this project form 2006, for about 4 years.

<figure><img src="image_2.png" /><figcaption>Fig. 1. Agricultural Fruit Research Institute</figcaption></figure>

The data of the apple tree was measured with polhemus fastrak (1988, H. Sinoquet), the error is 1 mm per meter in theory, but it could be about 1 cm outside for the wind and other elements.

### 2.1 Topology and Geometry

The apple tree's structure is describing as module which can be divided in detail into two components, i.e. stem and bud. A bud develops into a flower or a branch.

We define the Apple tree structure with key points which can be divided into two kinds. One is the form key point and the other is the functional key point.

The form key point (Figure 2) is such a point which decide the apple tree form, if use a single sentence to descript, that is such a point it is not in the straight branch, or branch direction is horizontal or vertical (1999, C. Godin).

These important points can be measured by polhemus fastrak.

<figure><img src="image_3.png" /><figcaption>Fig. 2. The form key points</figcaption></figure>
## 2.2 Data structure

The point data is described with five items, i.e. point type, point-function, pre-point, next-point and the current point orientation (x, y, z, r), as table 1.

<table><caption>Table 1. the description of a point</caption><thead><tr><td>type</td><td>func</td><td>Pre</td><td>Next</td><td>orient</td></tr></thead><tbody><tr><td>fruit</td><td>Func</td><td></td><td></td><td></td></tr><tr><td>Leaf</td><td>form</td><td></td><td></td><td></td></tr><tr><td>Bud</td><td></td><td></td><td></td><td></td></tr><tr><td>branch</td><td></td><td></td><td></td><td>(x,y,z,r)</td></tr></tbody></table>

It is very convenient to conscript the apple tree structure in such a topology (Figure3), and can be implemented in computer language easily.

<figure><img src="image_4.png" /><figcaption>Fig. 3. Tree topology</figcaption></figure>

## 2.3 Apple tree simulate

The apple tree data took with polhemus fastrak is stored in data file. The 3d apple tree is implemented by POV-ray with the data reformatted from point data to triangle data with python.

Python is a very popular script language (2010, python development team), is used in many industry. We use python to write the measured data according to the POV-ray format.

POV-ray is ray trace software, a POV-ray file mainly include an object, lights and camera.

The apple tree POV-ray file includes the sun, the camera and the tree, the tree is composed by meshes (2005, Loch B.), and the mesh is compound by triangles.

The frame of the POV-ray program is as the follow:
sunpos (Year, Month, Day, Hour, Minute, Lstm, LAT,
LONG).
Camera{ persp|ortho
location <> direction <> right x
up y
}

//object 00001
#declare color = <a, b, c, 0>;
#declare layercolor = <0, 0, 0>;
#declarephong = 0;
#declare phong_size = 0;
#declare image_map = "D"
#declare bump_map = "Cdefault.png"
#include "materials.inc"
#declare Object1Material = Material0000
#declare Object1 = mesh {
smoothTriangle{<x1,y1, z1>, <x2, y2, z2>, <x3, y3,
z3>, <x4, y4, z4>, <x5, y5, z5>, <x6, y6, z6> }
........
smoothTriangle{<xn+1,yn+1,zn+1>, <xn+2, yn+2, zn+2>,
<xn+3, yn+3, zn+3>, <xn+4, yn+4 zn+4>, <xn+5, yn+5,
zn+5>, <xn+6, yn+6, zn+6> }
}

//object 00002
//same as the object1

One object is an internodes, every (x, y, z) is measured with polhemus fastrak.

In order to simulate the light interception of the apple tree (2005, D. A. King), we calculate the statistical parameters based on the data measured with polhemus fastrak (2005, C. Bassette). The stem length, the probability of the branch and the leaf, the average of the radius of the stem and the branches, etc...we model a virtual apple tree using the statistic parameters (2002, D. A. Pouliot), and the demonstration picture as the figure4 and figure 5.

In the POV-ray scene, we simulate a fisheye lens to take pictures of the apple tree's crown while we are altering the apple tree parameters (Gilles Tran), shown as the figure. 6. The picture after segmentation is as figure 7.

The proportion of the apple tree in the image stands for the sunlight interception, and the increment of the apple tree in the diameter for the apple tree mass increase. We develop a simulate model which present the relationship between the sunlight interception and the apple structure.
<figure><img src="image_5.png" /><figcaption>Fig. 4. Apple tree with shadow</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 5. Perspective of Apple tree</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>Fig. 6. The crown of the tree in fisheye</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Fig. 7. The segmentation of the apple tree crown</figcaption></figure>

## 3 Test Results

In this test, two factors, the branch angle and the branch radius, was tested, the branch angle was tested at level 15, 30, 45, 60 and 90 degree, and the branch radius was at 0.7 cm, 1.7 cm, 2.7 cm. the test result is as the table 2.

The "Area/box" shows the ratio of the leaves in the whole area of the picture, and the sum means the total numbers of the pixel of the apple tree leaves.

The figure 8 shows the relationship between the interception and the branch angles, the horizontal axis shows the branch angles, and the vertical axis shows the numbers of the pixels the leaves occupied.
<table><caption>Table 2. The statics data of the segmented picture.</caption><thead><tr><td>No.</td><td>Branch angel</td><td>Branch radius</td><td>Area/box</td><td>sum</td><td>stdev</td></tr></thead><tbody><tr><td>1</td><td>15</td><td>0.7</td><td>0.93</td><td>142</td><td>0.16</td></tr><tr><td>2</td><td>15</td><td>1.7</td><td>0.94</td><td>143.04</td><td>0.15</td></tr><tr><td>3</td><td>15</td><td>2.7</td><td>0.91</td><td>123</td><td>0.18</td></tr><tr><td>4</td><td>30</td><td>0.7</td><td>0.91</td><td>544</td><td>0.19</td></tr><tr><td>5</td><td>30</td><td>1.7</td><td>0.91</td><td>501.46</td><td>0.2</td></tr><tr><td>6</td><td>30</td><td>2.7</td><td>0.9</td><td>456.06</td><td>0.2</td></tr><tr><td>7</td><td>45</td><td>0.7</td><td>0.9</td><td>941.05</td><td>0.21</td></tr><tr><td>8</td><td>45</td><td>1.7</td><td>0.88</td><td>823</td><td>0.22</td></tr><tr><td>9</td><td>45</td><td>2.7</td><td>0.86</td><td>754.38</td><td>0.23</td></tr><tr><td>10</td><td>60</td><td>0.7</td><td>0.9</td><td>1234.62</td><td>0.21</td></tr><tr><td>11</td><td>60</td><td>1.7</td><td>0.88</td><td>1056.71</td><td>0.22</td></tr><tr><td>12</td><td>60</td><td>2.7</td><td>0.85</td><td>846.27</td><td>0.23</td></tr><tr><td>13</td><td>90</td><td>0.7</td><td>0.9</td><td>1504</td><td>0.21</td></tr><tr><td>14</td><td>90</td><td>1.7</td><td>0.89</td><td>1327.17</td><td>0.22</td></tr><tr><td>15</td><td>90</td><td>2.7</td><td>0.89</td><td>1106.68</td><td>0.22</td></tr></tbody></table>

<figure><img src="image_9.png" /><figcaption>Fig. 8. The relationship between the branch angle and the light interception</figcaption></figure>

The formula of the angle and the light interception is a logarithmic line, and R is near 1. The relationship shows as the equation 1.

$$ \text{Light\_interception}=670.09*\ln(\text{angle})-1713.8 \quad (1) $$
## 4 Discuses

The branch angle is the most important factor (1995, C. Jourdan) which affects the apple tree light interception. The result shows that the relationship between the branch angle and the light interception is a logarithmic line.

The relationship between the branch radius and the light interception cannot be described incorrectly, because when the radius of the stem increases, it will cover a big block of the branches and leaves, as shown in figure 7. From table 2, there is an inverse ratio between the two factors. Obviously, it is contrary to the general knowledge. In future, we will find a more reasonable and fitness methods to solve this problem.

## 5 References

1. C. Godin, E. Costes, H. Sinoquet. A Method for Describing Plant Architecture which Integrates Topology and Geometry. Annals of Botany, 84:343–357, 1999.

2. C. Bassette, F. Bussie`re, 3-D modeling of the banana architecture for simulation of rainfall interception parameters. Agricultural and Forest Meteorology 129, 95–100, 2005.

3. C. Jourdan, H. Rey and Y. Guédon. Architectural analysis and modelling of the branching process of the young oil-palm root system. Plant and Soil 177: 63-72, 1995.

4. Daniel Barthelemy, Yves Caraglio. Plant Architecture: A Dynamic, Multilevel and Comprehensive Approach to Plant Form, Structure and Ontogeny. Annals of Botany 99: 375–407, 2007.

5. D. A. King, S. J. Davies, etc. Tree growth is related to light interception and wood density in two mixed dipterocarp forests of Malaysia. Functional Ecology, 2005, 19, 445–453.

6. D.A. Pouliot, D.J. King, F.W. Bell, D.G. Pitt. Automated tree crown detection and delineation in high-resolution digital camera imagery of coniferous forest regeneration. Remote Sensing of Environment 82 (2002) 322–334.

7. E. Costes, H. Sinoquet, etc. Exploring Within-tree Architectural Development of Two Apple Tree Cultivars over 6 Years. Annals of Botany 91: 91-104, 2003.

8. Gilles Tran. MakeTree v1.0. http://www.oyonale.com.

9. H. Sinoquet, S. Thanisawanyangkura, etc. Characterization of the light environment in canopies using 3D digitising and Image Processing. Annals of Botany 82: 203-212, 1988.

10. J. Phattaralerphong, H. Sinoquet. A method for 3D reconstruction of tree crown volume from photographs: assessment with 3D-digitized plants. Tree Physiology, 25, 1229–1242, 2005.

11. Loch B, Belward J, Hanan J. Application of surface fitting techniques for the representation of leaf surfaces [A]. In: Zerger A, Argent R M (eds). International Congress on Modelling and Simulation [C]. Melbourne: MODSIM Press, 2005: 1272–1278.
12.python development team. Python v2.6.5 document.(last updated Mar 19, 2010).
http://www.python.org/.

13.Rodrigo A. Gutie'rrez, Dennis E. Shasha, and Gloria M. Coruzzi. Systems Biology for the Virtual Plant. Plant Physiology, June 2005, Vol. 138, pp. 550-554.