三维树干曲面的模拟与构建

Taper equation is an important approach to reflect the tree trunk form and therefore was widely applied in forest in the past few decades. However, two major drawbacks of this approach were found in practical application, which are （1）The modeling idea of the descriptive theory for the traditional trunk form is established based on the pole-timber mathematical model of the circular section generated by different trunk form curve arounding the axis of rotation. It cannot describe the actual tree trunk form accurately no matter how to change the trunk curve due to invariable cross sectional shape and the straight line for the trunk center axis. (1) the taper equation just descripe the average variation of the tree trunk forms in the whole stand or sample plot, but in fact, the trunk form of different tree may be great difference due to the variances of their state of self-growth, genetic features, site and habit conditions. Determination of tree trunk form is a key technology for forestry conversion, and the precision of it would affect the conversion results.Therefore, this project would focus on the following three scientific problems: (1) Give a set of field investigation technology system for 3D laser scanning and an approach to extract the parameters from the point-cloud data for tree trunk form study. (2) Three-dimensional tree trunk surface models would be constructed based on the approaches of traditional least square regression and nonlinear mixed-effects models and the module for individual tree trunk surface simulation also would be developed in the ForStat software. (3) Based on the above research results, the three-dimension tree trunk surface models would be developed firstly using Populus as an example.

削度方程是描述树干干形的一种重要方法，过去几十年中得到广泛应用。但实际应用时，发现这种方法存在2个主要缺陷：第一、传统树干形状描述理论的建模思想是以不同的干曲线绕坐标轴旋转形成圆截面的原条数学模型。但由于截面形状不变，树干中心轴是直线，不论怎样改变干曲线，都不可能准确地表达实际树干形状。第二、削度方程只能反映整个林分或样地树木干形的平均变化，但实际情形中，每棵树木因自身生长状况，遗传因素、所处立地和生境条件不同，树干形状可能有较大差异。然而树木干形的确定是林业造材的一项关键技术，其精度高低决定了造材的成败。为此，本项目重点解决三个问题：（1）给出一套针对树干干形研究的三维激光扫描外业调查技术体系以及多株林木点云数据的参数提取；（2）利用近代统计模型方法构建三维树干曲面模型，并在ForStat中创建单株树干曲面模拟模块；（3）基于以上研究成果，以杨树为例，首次实现三维单木树干曲面模型的构建。

传统上采用削度方程描述树干干形，实际应用时这种方法有如下缺陷：（1）其以干曲线绕坐标轴旋转形成圆截面为基础理论来构建数学模型，然而树干中心线不是直线，树干横断面也不是圆截面。因此无论如何构建削度方程，均无法准确反映树干干形的弯曲特征及树干横断面非圆的不规则特征。（2）削度方程反映的是整个林分或样地中所有树木干形的平均变化，然而每株树都因其自身的立地条件与遗传特征而使林分中每株树的树干形状各不相同，这导致林分水平上构建的削度方程无法准确反映单株树木的干形特征。由于单株树木干形的确定不仅是林业造材的一项关键技术，也是准确计算材积等林业重要数据的基础。基于此，本项目使用地面三维激光扫描仪（TLS）获取的树木点云为数据，以准确构建单木三维树干干形模型以及树干曲面模型为目的开展一系列研究工作，其主要内容包括：（1）单木定位与单木点云提取，包括从林分点云中定位每株样木的位置，通过移除树桩点云与削枝操作提取单木的树干点云等；（2）单木树干及曲面模型构建，包括构建树干三维干轴曲线与树干横断面轮廓曲线簇，构建树干Delaunay三角网表面模型，自动优选法估计树干削度方程等；（3）基于树干模型的单木参数提取及相关模型构建，包括树木冠幅提取，树干任意位置处横断面的准确定位，树干任意位置处直径的准确提取（凸包折线法，三次B样条曲线与三次Bezier曲线模拟围尺测量轨迹法)，横断面断面积的准确估算（横断面轮廓曲线所围面积是断面积)，树干干形参数计算（树干任意位置处曲率、挠率与倾角）以及非线性混合效应气候敏感的地上生物量模型，基于机载雷达数据和度量误差回归方法构建单木直径和地上生物量，相容性模型系统，考虑交互作用的非线性混合效应模型构建及参数估计方法等。通过上述工作的开展，项目组取得一系列具有原创性的研究成果，这不仅为准确描述树干干形与树干曲面模型提供有效的基础理论及构建方法，也为从TLS点云数据中精确提取树木相关参数提供技术支撑。