In the paper we present a new representation of curves, named parametric curves with implicit domain(PCID), which is a type of curves in parametric form defined on an implicit domain.The PCID provides a bridge between parametric curves and implicit curves because the conversion of parametric form or implicit form to PCID is very convenient and in low cost.We propose a framework model for mapping given points to the implicit domain homeomorphically.The resulting map is smooth and overlapping-free.This framework can be used for many applications such as volume data parametrization, compatible triangulation and warping.We also present experimental results and some examples to demonstrate the effectiveness of our proposed framework model.