摘 要

研究树木的自然生长是否与植物叶片的重叠最小部分，以获得最大的有效迎风面积。随着人们生活水平的不断提高，农副产品生产的质量要求也在不断提高。风的强度和吹风的时间是影响农副产品的重要条件之一。

首先查询春天阳光的直射纬度，并根据太阳高度角的计算公式计算白天1小时太阳高度角的具体值。发现早晨和下午的相应时刻的太阳仰角是相同的。首先，通过映射，通过太阳高度角分析一天中8小时的球冠的迎风视图。利用积分公式，得到了球冠迎风面积与太阳仰角之间的关系。然后，制作锥形冠的迎风示意图，发现锥形冠的迎风面积为0，因此球冠的迎风面积比锥形冠大8小时。将日期转换为日角，代入第二个问题，得到了球冠的迎风面积与太阳仰角之间的关系，即球冠超迎风面积的变化规律。结合前三个问题的结果，使树顶尽可能光滑，并完全收起以获得最完整的表冠。通过MATLAB软件，建立植物叶片的多目标优化模型，再进行求解，然后将其与稳定阶段树冠的测量高度和半径进行比较。最后，执行误差分析，误差小于5％。

关键词：树冠；叶片表面积估算；植物模型建立

Abstract

The aim of this study was to determine whether the minimum overlap of plant leaves was used to obtain the maximum effective illumination area for tree natural growth. With the continuous improvement of people's living standards, the production quality requirements of agricultural by-products are also improving. Among them, the intensity and time of solar illumination is one of the important conditions affecting agricultural by-products. The time and intensity of solar illumination are different in different time and places.

Firstly, the direct latitude of the autumn equinox sun is found, and according to the formula for calculating the sun's altitude angle, the specific value of the sun's altitude angle one hour apart during the day is obtained. It is found that the sun's altitude angle at the corresponding time in the morning and afternoon is the same. Firstly, the schematic diagram of the light receiving of the spherical canopy for more than 8 hours in a day is analyzed by drawing. The relationship between the light receiving area of the spherical canopy and the angle of the sun's height is obtained from the angle of the sun's height and the integral formula. Then the light-receiving schematic diagram of conical crown is made, and the light-receiving area of conical crown is zero. It is concluded that the light-receiving area of spherical crown is larger than that of conical crown for 8 hours. Converting the date to the sun angle, the relationship between the sunshine area of the spherical canopy and the solar altitude angle has been obtained by substituting the second problem, that is, the change rule of the sunshine area of the spherical canopy in one day. Combining the results of the first three questions, we can make the top of the tree as smooth and smooth as possible, and get the best crown. With the help of MATLAB software, the multi-objective optimization model of plant leaves is established and solved. Then, the height and radius of tree crown are compared with the measured height and radius of tree crown at the stable stage. Finally, the error analysis is carried out, and the error is less than 5%. The experiment proves that the model is reliable and accurate.

Key words: crown；estimation of blade surface area；establishment of plant model

目 录

1 引言 1

1.1 地面三维激光扫描技术 1

1.2树冠面积计算方法 3

1.3 研究进展 5

2 植物叶片有效迎风面积模型建立 6

2.1树的轮廓分析 6

2.2模型的建立 7

2.3改进模型的建立 9

2.4 讨论 10

3 树冠正对迎风面积估算 11

3.1问题分析 11

3.2模型假设 11

3.3符号说明 11

3.4模型建立与求解 12

3.4.1 计算太阳高度角 12

3.4.2计算球形树冠的迎风面积，并与圆锥形树冠的迎风面积做比较 13

3.4.3 圆锥形树冠的迎风面积 14

3.4.4球形树冠迎风面积的变化规律 15

3.5最优树冠设计 16

4 总结与展望 18

4.1 本文工作总结 18

致谢 19

参考文献 20

附录 程序 21

1 引言

1.1 地面3D激光扫描技术

地面3D激光扫描是一种新型的绘图技术。从全球定位系统技术研发出来至今，它是测绘科学界一个具有象征意义的转折点。地面3D扫描技术具有全自动和精度准确这两个明显的特点，业内专业人士又称之为“实景复制技术”。3D激光扫描是一种很基础的数据采集方法，它主要是基于物体的表面来进行数据的操作，通过获得大量离散点云数据，并以此来强调突出物体的真实三维形态。因为这种情况的存在，也可以将3D激光扫描技术称之为逆向工程。地面3D激光扫描技术不仅可以快速获取目标的三维点云坐标，而且无需高效接触。并在有效处理点云坐标数据之后，在极短的时间内重新建立目标的3D图像模型。地面3D激光扫描技术在现实生活中有着广泛的应用，例如某些需要测量数据的工程、农业资源以及森林资源的调查、应用结构的测量和满足地面3D激光扫描系统。地面3D激光扫描系统最为关键的一个组成部分有地面3D激光扫描仪、数据处理平台以及电源设备，这是一种将许多先进技术集成在一个共同环境下的空间信息及数据的采集技术，无论什么样的复杂环境或者空间，地面3D扫描技术都可以在极短的时间内精确有效的重新建立的3D模型，并输出各种绘图数据，如线，面，体和空间。同时，可以对收集的3D激光点云数据执行各种后处理分析应用，例如映射，测量，监测，虚拟现实等。收集的3D点云数据及3D建模结果，可以将它们转换成标准格式或者转换成其他软件可以读取并处理的文件格式。图1所展示的就是一个完整的地面3D 扫描系统，它主要的工作原理是通过非接触式的告诉激光来测量，以此来获得复杂地形及物体的几何数据，随后激光扫描软件会识别并提取所收集的离散点的云数据，然后，将图像数据转换成坐标数据，以获得所收集的对象的空间位置坐标。

图1 地面3D激光扫描仪系统