Machining is a fundamental manufacturing capability critical to the production of end-user goods and systems, as well as the tooling and equipment used in virtually every industrial process. Machine tool programming to support these processes is critical for both production and cost estimation. However, currently available automated process planning methods constrain the tool to follow geometrically simple paths to minimize computational requirements, limit the tool velocity and/or tool orientation during a simple path to constant values, also to save computational burden, and/or process one geometrical feature at a time without attempting to optimize the entire process. This award supports fundamental research to provide knowledge needed for development of a novel computer-aided process planning and control architecture for integrated complex tool path generation and optimization. The resulting new mathematical algorithms will drive effective real-time control and optimization of manufacturing processes and enable substantial increases in machine productivity. These capabilities will have potential for broad-ranging impact on the domestic economy, which uses machining in the vast majority of products, due to its flexibility, speed, cost, and accuracy advantages relative to other processes. The research integrates several complementary technical domains, including advanced manufacturing, geometric computing, and high performance parallel computing. Conventional computer-aided manufacturing approaches for toolpath optimization are inherently post-hoc methods that are not well integrated for supporting simultaneous generation and optimization of the process plan. This research will investigate generic optimization and control architectures for automated toolpath optimization, which require global solutions to highly non-linear, constrained optimization problems in high-dimensional search spaces of tool motions with time-varying positions and orientations. To address this challenge, the research approach will utilize a bi-directional optimization scheme that consists of: (l) a top-down, multi-level decomposition of the problem into fundamental model motions (e.g., curved blocks, peel layers, tool swipes) and (2) a bottom-up optimization of these fundamental geometric model motions. The latter schema element will fully support the option of selecting cutting tools to maximize material removal rate and/or surface finish and will build upon theoretical formulations and efficient computing implementations of volume preserving offsetting, steady motion interpolation, and ball morphing surface interpolation. The resulting fundamental motion models and associated fast, parallel computing algorithms will provide for rapid analysis of swept regions, collision avoidance and computing material removal rates that are critical for facilitating rapid toolpath optimization.