 This paper presents a new method for constructing quickly and automatically precision tree models from point clouds obtained by terrestrial laser scanning, which involves robustly reconstructing the surface and branching structure of the tree using a local approach that covers the point cloud with small sets corresponding to connected surface patches in the tree surface. The model is constructed step-by-step using neighbor relations and geometrical properties of these cover sets and can be validated using both measured and modeled terrestrial laser scanner data from real trees and detailed 3D models. The approach allows for easy extraction of various tree attributes from point clouds obtained through terrestrial or mobile laser scanning. This article was authored by Matthias Disney, Marcus Holopaynon, Miko Vasteranta, and others.