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In this paper we propose a new volumetric implicit surface data structure as an alternative representation to perform mesh processing algorithms. We introduce a new triangulation algorithm suitable for our voxel-based volumetric structure which is a vector field distance transform from an explicit mesh. This new representation is an extension of the implicit scalar field distance function of a mesh. We show our new vector field function is more accurate than the classic scalar field function by comparing both representations with an error metric evaluation. We adapt to this new vector representation mesh integration operation in the reconstruction process of 3D objects from scanned data which was previously performed on the implicit scalar field function. Results show that using this new vector field representation, our mesh integration and mesh triangulation algorithm designs outperform the previous processes based on the implicit scalar field function representation.