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.

中文翻译：

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Delaunay三角剖分驱动的精确体积计算，用于煤炭测量

3D点云的体积计算在工程和应用中被广泛使用。现有方法要么误差较大，要么很费时间。本文着重于煤的测量。基于从点云生成的三角形网格，每个三角形向下投影到基本平面以形成体素。我们通过积分方法推导了体素的计算公式，该公式比将体素分解为四面体的方法更有效，并且比切片方法更准确。此外，本文提出了Delaunay三角驱动体积计算（DTVC）方法。DTVC不会保留Delaunay三角形，而是直接在三角测量过程中计算体积。这样可以节省内存和运行时间。实验结果表明，DTVC在误差和效率之间取得了良好的平衡。