Automatic quadrilateral (quad) or hexahedral (hex) multiblock decomposition has been a topic of research for many years. The key challenges are to automatically determine where to place mesh singularities and how to generate a decomposition based on the mesh singularities to get the desired mesh orientation and distribution. In this work, a new idea of achieving these is proposed based on an auxiliary subdivision of the domain into smaller subdomains, followed by applying an equation, which calculates the net number of mesh singularities of a surface, to locate the quad mesh singularities. Under this idea, two different methods are presented based on the medial axis and the inward boundary offset. Both methods are conformal to the vertex classifications of the original domain, which guarantees a good mesh quality at the boundary. The mesh results are compared with a paving method and a cross-field method.