Improved OBB fitting method for elongated objects

We present a new method of calculating OBBs of the internal nodes in OBB-tree for elongated objects which are partially ordered. By establishing a new estimating function, we convert the problem of determining OBB´s orientation to constrained extrema problem which can be solved by Lagrange multiplier method. After solving the estimating function we get a local axis of the OBB. The remaining two directions are calculated using minimal-area bounding rectangle algorithm. Project all the vertices to the local axes respectively then the size and center of the OBB can be finally determined. A large amount of tests have revealed that the OBB-tree constructed by this method fits better than those constructed by the already existing methods. Now the method proposed by this paper has been adopted by actual project.