10. Crown Parameters
The crown attributes (Figure) can be evaluated if the tree position and tree height are computed. Crown height, crown base height, crown width, crown centroid, and crown position deviation are then computed automatically. These variables are recomputed automatically if the tree position is changed.
Figure: A - The description of the crown attributes: crown height (CH), crown base height (CBH), crown center (CC), crown total height (CTH), crown length (CL), crown width (CW). B – The example of calculated parameters and the deviation of the projection of the crown center (green) from the base of the trunk (blue). C – The concave planar projections and volume/surface of the crown as calculated according to the concave polyhedron. D – The convex planar projections and crown volume/surface calculated using a convex envelope. E – The example of the visual output of the 3D Forest when calculating the shared space of crowns (yellow) using 3D convex covers.
The crown cloud can be adjusted manually via Crowns → Set manual or automatically via Crowns → Set automatic. The dialog window gives an option to select the tree of interest. The manual mode then enables to remove the stem points. The automatic mode creates cross-sections of the tree along the z-axis with the height 0.5 m at first. The width of each section is computed by averaging the x and y-axis values of the respective section. The widths are successively compared from the lowest to the highest section. If three consecutive sections are wider more than 25 % than the last thin section, the last thin section is marked as a starting place for detailed search. The detailed search begins by setting a subset of points with a height of 10 cm at the beginning of the thin section. Using LSR the stem diameters at the start and the end of the subset of points are computed. These diameters enable to predict the center of the next diameter, located another 10 cm along the section. The diameter itself is then computed using only the points lying within the range of the doubled value of the preceding diameter. This is to avoid the influence of overhanging branches. Predicting the new diameter center and diameter evaluation continues until the difference between the last two diameters is less than 25%. This point is then considered as the base of the crown.
The crown volume by voxels is estimated via Crowns → Volume by voxels. The dialogue window enables to select the tree and to set voxel size in cm. The volume is shown in the project attribute table. Voxels are not visualized due to the computational demands.
The crown volume and surface area by cross-sections are computed via Crowns → Volume and surface by concave polyhedron. The dialogue window enables to select the tree of interest, set the section height, and set the threshold distance for section concave hull. In case that other than implicit values are set, the crown position and position deviation are recomputed with external points extracted by these new parameters. The crown position is calculated as an average coordinate from external points, i.e. the 2D concave hulls of horizontal cross-sections (slices) with the threshold distance 1 m and section height 1 m; see Concave Planar Projection. The external points can be visualized by the icon . Crown volume is then computed as the total amount of sections volume, where each section volume is computed by its planar projection area (created by concave hull) times section height. The surface area is computed by strip triangulation. The algorithm is reliable, although there are cases when intersecting triangles may occur. To show/hide resulting objects use icon . The triangulation algorithm connects vertices of concave hulls of adjacent sections by the shortest possible sum of edges.
The crown volume and surface area by 3D convex hull are accessible via Crowns → Compute 3D ConvexHull. The computation (3D Delaunay triangulation and mesh parameter algorithms) is done using the VTK libraries. The dialogue window allows selecting the tree of interest and offers the checkbox for computation using all crown points. The external points and points belonging to the lowest and highest sections are used by default. This provides a significant decrease in computational time with comparable results as if all crown points are used. To show/hide resulting shapes use icon .
The crown intersections evaluation is available via Crowns → Intersections. All existing crowns are tested for intersections. The existing intersection between two crowns is computed using VTK as Boolean AND in 3D space. The convex shapes are only possible for the evaluation thus to create the 3D objects volume and surface by 3D convex hull have to be computed first. The following variables of intersecting crowns are computed: horizontal angle (azimuth), vertical angle (from horizontal plane), and distance from crown position to intersection center of gravity, intersection volume, and surface area. These attributes are listed in the intersections table, called by icon . Intersecting parts can be shown/hidden by icon , the lines connecting crowns positions with intersection center of gravity, and angles are also visible.