Accurate Volume Calculation Driven by Delaunay Triangulation for Coal Measurement

Abstract

Volume calculation from 3D point cloud is widely used in engineering and applications. The existing methods either have large errors or are time-consuming. This paper focuses on the coal measurement. Based on the triangular mesh generated from the point cloud, each triangle is projected downward to the base plane to form a voxel. We derive the calculation formula of voxel by an integral method, which is more efficient than the method of decomposing voxel into tetrahedrons and more accurate than slicing methods. Furthermore, this paper proposes a Delaunay triangulation-driven volume calculation (DTVC) method. DTVC does not preserve the Delaunay triangles but directly calculates the volume in the process of triangulation. It saves memory and running time. Experimental results show that DTVC has achieved a good balance between error and efficiency.