High-end subtractive fabrication machining technology with high efficiency and high surface quality occupies a growing proportion in complex workpiece manufacturing. The whole frame includes computer aided design (CAD), computer aided manufacturing (CAM) and computer numerical control (CNC) processes. Among them, tool path generation is a fundamental element, as it bridges the geometry designed in CAD and the machining process controlled in CAM. Therefore, the quality of the tool path intrinsically influences the machining accuracy and efficiency of the machined surface. The construction of a tool path in free form surface machining can be based on plenty of quality objectives, such as less machining error and shorter path length, which would directly impact the performance and costs in the entire product lifecycle from design to recycling. However, the current tool path planning processes omit the global geometric construction, and these methods would lose some essential geometric information (such as sharp features) during machining. Therefore, we implement a global tool path planning method with effective preservation of sharp features, which consists of optimal surface segmentation for CNC and tool path planning using Connected Fermat Spirals (CFS). We take G-nurbs spline surface as input, and give a fast and robust optimal surface segmentation method by establishing a weighted graph and searching the minimum spanning tree of the graph for extraordinary points. The method is easy to implement and can control the number of segmented patches while preserving the sharp features of the workpiece. Then, we build the connected weighted graph between each surface patch, obtain its corresponding minimum spanning tree, and construct the global CFS tool path that parallel to sharp features. The entire path contains only one start point and one end point, which means that we do not need to frequently lift and switch the cutter, thus improving the machining efficiency.