In various visualization application contexts, shapes are often represented by triangular meshes, which are of extreme complexity and their storage, transmission, and rendering is a threat to the available graphics hardware. The displaced subdivision mesh is an alternative surface representation, which because of its regular connectivity and being amenable to multiresolution structure successfully tackles these problems. This surface representation defines a detailed mesh with a displacement map over a smooth domain surface. The construction of smooth domain surface is the challenging task in this representation. In this paper we introduce a new method to define smooth domain surface based on √3 subdivision. In our algorithm, we exploit a memory efficient and fast simplification method with simple heuristic that helps preserve the normal space of the original surface and linear sparse system to define optimized control mesh, so it is computationally more efficient and consumes less memory as compared to the original algorithm by Lee et al. and the resulting surface has more levels of detail due to the specific nature of √3 sub-division if a prescribed target complexity of the mesh must not be exceeded. To corroborate our approach, we present the conversion results using several models.