<p>The extruded continuum structure (ECS) is one of the most common types of structures in the engineering field and is created by deforming a parametric surface along a straight trajectory. However, in level set-based topology optimization, the level set function for ECS with irregular boundaries is typically defined by embedding the structure within an expanded design domain. The expansion of the design domain increases computational costs, which continue to escalate with the number of iterations. Additionally, the irregular ECS cannot generate initial designs for optimization as efficiently as box-like structures. To overcome these challenges, we propose a cubic-parameter-domain construction (CPDC) framework, implemented through a mapping-remeshing-extrusion procedure, that establishes a mapping between the ECS and a cubic parameter domain. Based on the mapping relationship, the definition and solution of the level set function can be equivalently performed within the cubic parameter domain, which features a regular boundary and a structured discrete form, facilitating seamless integration with the traditional level set-based optimization framework. The proposed framework preserves the advantages of the traditional level set method while improving the geometric adaptability and computational efficiency of ECS topology optimization, as demonstrated by the numerical examples.</p>