In high performance computing, block structured grids are favored due to their geometric adaptability while supporting computational performance optimizations connected with structured grid discretizations. However, many problems on geometrically complex domains are traditionally solved using fully unstructured (usually simplicial) meshes. We attempt to address this deficiency in the two-dimensional case by presenting a method which generates block structured grids with a prescribed number of blocks from an arbitrary triangular grid. Special attention was paid to mesh quality while simultaneously allowing for complex domains. Our method guarantees fulfillment of user-defined minimal element quality criteria—an essential feature for grid generators in simulations using finite element or finite volume methods. The performance of the proposed method is evaluated on grids constructed for regional ocean problems utilizing two-dimensional shallow water equations.