Acoustic cloaking is an intriguing phenomenon that has attracted lots of attention. The required inhomogeneous and anisotropic properties of acoustic cloaks derived with transformation acoustics make them difficult to realize. In this paper, a new mapping relation is presented. An acoustic cloak can be divided into any number of arbitrary triangular patterns, which are mapped from similar patterns in virtual space. Transformation from one triangular domain to another leads to homogeneous properties using transformation acoustics. The resulting cloak is composed of homogeneous triangular parts, each having just two alternating layers of material. The manner of division of the cloak affects the properties of each triangular part dramatically, which can be leveraged to vary the properties of each triangular part for more realistic material properties. Simulations of models based on this method show good cloaking performance at reducing the reflected and scattered waves due to the cloaked obstacle.

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