In studies related to ground excavations, glaciers, human brains, or many other branches of science, a need to know often arises regarding the volume of an irregularly shaped object or region in 3D space. An approach using finite elements offers a closed form solution that can accommodate uneven spacing with scattered data points and arbitrary boundaries. Using numerical examples, results from the proposed method are presented and accuracy compared with known solutions.
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Birendranath Mukherji (2011) studied this question.
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