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Pipe assembly that connects over hundreds of various pipes to mechanical structures is a fundamental challenge to complex product developments. This paper presents a pipe routing algorithm for automatic generation of pipe assembly plans within a constrained space between inner and outer casings of an aeroengine. In this paper, pipes are first ordered in accordance with interference degrees and other engineering rules. Then, a projection-based routing heuristic is developed to find satisfactory collision-free pipe paths in 2D or 3D spaces. Further, the heuristic is modified, by replacing projections with geodesics, to meet requirements of routing pipes on surfaces. Numerical computations of a 119 pipe routing problem are performed to demonstrate the effectiveness and efficiency of the proposed pipe routing algorithm.