We propose a new data structure for the compact encoding of a Level-Of-Detail (LOD) model of a threedimensional scalar field based on unstructured tetrahedral meshes. Such data structure, called a Half-Edge Tree (HET), is built through the iterative application of a half-edge collapse, i.e. by contracting an edge to one of its endpoints. We also show that selective refined meshes extracted from an HET contain on average about 34% and up to 75% less tetrahedra than those extracted from an LOD model built through a general edge collapse.