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In multistage manufacturing processes equipped with high-definition metrology (HDM), part surface quality characteristics can be observed to change or “morph” from stage to stage. Such part surface variation propagations are caused by the physical processes, part attributes, and the interaction between stages. Previous research on variation propagation modeling focuses on part dimensional quality using discrete key product characteristics or vectors which have limitations in analyzing complex surface variation patterns contained in the HDM data. This paper proposes a new concept of functional morphing to characterize the surface changes and applies it to process control in high-precision manufacturing. Unlike conventional morphing algorithms that focus on transformations between geometries only, functional morphing integrates process physical insights into the geometric mappings, thus characterizing the complex HDM data patterns in physically meaningful ways. Specifically, a functional free form deformation approach including forward and backward mappings is developed to extract mapping functions between manufacturing stages to enable surface variation propagation analysis. The forward mapping function allows for accurate interstage adjustment that introduces shape deformation upstream to compensate for the end-of-line errors. The backward mapping function can predict surfaces at intermediate stages based on end-of-line measurements, leading to a cost-effective interstage process monitoring scheme. The interstage monitoring can also ensure the repeatability of a process controlled by the interstage compensation algorithm. The developed monitoring and adjustment methods are demonstrated via a case study of a two-stage machining process. Other potential applications of functional morphing such as process tolerance design are also discussed.