Section I Basics Part Surfaces: Geometry Elements of Differential Geometry of Surfaces On the Difference between Classical Differential Geometry and Engineering Geometry of Surfaces On the Classification of Surfaces Principal Kinematics of Part Surface Generation Kinematics of Sculptured Part Surface Generation Generating Motions of the Cutting Tool Motions of Orientation of the Cutting Tool Relative Motions Causing Sliding of a Surface over Itself Possible Kinematic Schemes of Part Surface Generation Kinematics of Part Surface Machining Processes Axodes and Pitch Surfaces in Generation of Part Surface Examples of Implementation of the Principal Kinematic Schemes of Part Surface Generation Applied Coordinate Systems and Linear Transformations Applied Coordinate Systems Coordinate System Transformation Useful Equations Chains of Consequent Linear Transformations and a Closed Loop of Consequent Coordinate Systems Transformations Impact of the Coordinate Systems Transformations on Fundamental Forms of the Surface Section II Fundamentals Geometry of Contact between a Sculptured Part Surface and Generating Surface of the Form-Cutting Tool Local Relative Orientation of a Part Surface and of the Cutting Tool The First-Order Analysis: Common Tangent Plane The Second-Order Analysis: Second Fundamental Form The Second-Order Analysis: Planar Characteristic Images Degree of Conformity of Two Smooth Regular Surfaces in the First Order of Tangency Plücker Conoid: More Characteristic Curves Feasible Types of Contact of a Part Surface P and Generating Surface T of the Cutting Tool Profiling of Form-Cutting Tools of Optimal Design for Machining a Given Part Surface Profiling of the Form-Cutting Tools for Sculptured Surface Machining Generation of Enveloping Surfaces Profiling of the Form-Cutting Tools for Machining Parts on Conventional Machine Tools Characteristic Line E of the Surface P and Generating Surface T of the Cutting Tool Selection of the Form-Cutting Tools of Rational Design Form-Cutting Tools Having Continuously Changeable Generating Surface T Incorrect Problems in Profiling the Form-Cutting Tools Principal Types of Problems in Profiling Form-Cutting Tools The Geometry of the Active Part of a Cutting Tool Transformation of the Body Bounded by the Generating Surface T into the Cutting Tool Geometry of the Active Part of Cutting Tools in the Tool-in-Hand System Geometry of the Active Part of Cutting Tools in the Tool-in-Use System On the Capabilities of the Analysis of Geometry of the Active Part of Cutting Tools Conditions of Proper Part Surface Generation Optimal Workpiece Orientation on the Worktable of a Multiaxis Numerical Control (NC) Machine Necessary and Sufficient Conditions of Proper Part Surface Generation Global Verification of Satisfaction of the Conditions of Proper Part Surface Generation Accuracy of Surface Generation Two Principal Types of Deviations of the Machined Part Surface from the Nominal Part Surface Local Approximation of the Contacting Part Surface P and the Generating Surface T of the Form-Cutting Tool Calculation of the Elementary Surface Deviations Total Displacement of the Cutting Tool with Respect to the Part Surface Effective Reduction of the Elementary Surface Deviations Principle of Superposition of the Elementary Surface Deviations Section III Application Selection of the Criterion of Optimization Criteria of the Efficiency of Part Surface Machining Productivity of Part Surface Machining Interpretation of the Part Surface Generation Output as a Function of Conformity Synthesis of the Part Surface Machining Operations Synthesis of the Most Favorable Part Surface Generation Process: The Local Analysis Synthesis of the Most Favorable Part Surface Generation Process: The Regional Analysis Synthesis of the Most Favorable Part Surface Generation Process: The Global Analysis Rational Reparameterization of the Part Surface Possibility of the DG/K-based CAD/CAM System for Optimal Sculptured Part Surface Machining Major Blocks of the DG/K-based CAD/CAM System Examples of Implementation of the DG/K-Based Method of Part Surface Generation Machining of Sculptured Part Surfaces on a Multiaxis Numerical Control (NC) Machine Machining of Surfaces of Revolution Finishing of Involute Gears Conclusion References Appendices Index.