Three-dimensional modelling of a crown shape developed by measuring the crowns of standing trees

Abstract

To date, simple function models, such as a sphere, a cone, or an ellipse, have been used for modeling a crown of a softwood or hardwood tree. This paper shows (1) how to generate a digital crown model (DCM) of a crown shape with three-dimensional coordinates from measured crown outlines with a simple instrument in the field, and discusses (2) the application of the DCM and the function model. The modeling procedure is: 1) Crown outlines are measured with vertical and horizontal angles from two or more measuring points around an object tree. 2) The data are converted to each x-y-z coordinate of which an origin is the measuring point. 3) The crown outlines are interpolated using a parametric spline function. Some knot data are generated from the measured outline data. 4) A DCM is developed by interpolating both horizontal and vertical outlines simultaneously to develop a three-dimensional crown shape model. Besides the DCM, a function model of one hardwood crown is developed, which approximates the hardwood crown as an ellipsoid of revolution. The section area and the surface area of the crown shape developed from each model are calculated to compare their shapes. The result shows it is too approximate to apply these function models for the analysis of a tree crown and other numerical analyses of a crown. The DCM may make a numerical analysis of crown shapes possible. This is considered with a relationship between tree crown shape and growth.