In the blanking layout problem of special-shaped parts, the most difficult thing is to determine the position of special-shaped parts for high material utilization rate, and the complexity of the algorithm increases rapidly with the increase of the quantity and boundary complexity of special-shaped parts. The critical polygon algorithm is a basic geometric tool for calculating the position and overlap between special-shaped parts, and the performance of the critical polygon algorithm is closely related to the efficiency of the blanking algorithm. In this paper, an improved and more efficient algorithm to calculate no-fit polygon (NFP) is proposed and it is based on the trace line presented. The algorithm effectively combines the mobile collision algorithm and the trajectory algorithm, and gives full play to the respective advantages of the two algorithms, thus improving the speed of calculating no-fit polygon.