任意三角网格模型体积的快速精确计算方法

三角网格是使用最为广泛的网格模型。提出了一种仅根据三角网格模型的三角面片集合计算模型体积的方法。该方法通过指定投影平面，计算每个三角面片及其在投影平面上的投影所围成的凸五面体的带符号体积（必要时对三角面片进行细分），整个模型的体积为所有凸五面体带符号体积的代数和。所提出的三角网格模型体积计算方法能实现模型体积的快速准确计算。在大型水电工程施工模拟中施工单元的方量计算测试和不同规模的三角网格模型体积计算测试都证实了该方法的有效性。

Fast and accurate volume calculation method for arbitrary triangular meshes

Triangular meshes are widely used in many field.In this paper，a new volume calculation method for arbitrary triangular mesh is presented based on the triangles set of the mesh only.Give a projecting plane，sign volume of pentahedron for each triangle in mesh，which is constructed by the triangle and it projection in projecting plane，is computed.Volume of the mesh is algebraic sum of all pentahedrons’ signed volume.Triangles will be partition into several smaller triangles when necessary.Volume calculation method presented in this paper can computed volume of meshes rapidly and accurately.Applications of the method to compute volume for constructing moulding unit in simulating large water and hydropower project constructing，and test result of computing volume for triangular meshes with different number of triangles，it is proved the effectiveness of the volume calculation method presented in this paper.