Abstract: Different from constructing the degenerate smooth surface patches in the field of classical geometric modeling, the paper constructs an interpolation operator based on the singular H regularity parameterization in the isogeometric analysis. First, the definition of H regularity is introduced based on singular parameterization. Then, the definition of D-patch and interpolation operator is discussed. Finally, the Gsmoothness of the interpolation surface is verified and numerical examples are given.