Envelopes and Swept Volumes

Books:

• Cohn-Vossen, H., Geometry and The Imagination, Chelsea Publishing, 1983.
• Struik, D. J., Lectures in Classical Differential Geometry, Dover Publication, 1965.

• Al-Daccak, M., and Angeles, J., The Calculation of the Volumetric Properties of Sweep Generated Solids Via Line Integration, ASME Journal of Mechanical Design, Vol. 115, 1993, pp. 110-117.
• Barr, A. H., Superquadrics and Angle-Preserving Transformations, IEEE Computer Graphics and Applications, Vol. 1, No. 1, 1981, pp. 11-23.
• Bloomenthal, M., and Riesenfeld R., Approximation of Sweep Surfaces by Tensor Product NURBS, SPIE Curves and Surfaces in Computer Vision and Graphics II, Vol. 1610, 1991, pp. 132-144.
• Blacmore, D., Leu, M. C., and Wang, L. P., The Sweep-Envelope Differential Equation Algorithm and its Application to NC Machining Verification, Computer Aided Design, Vol. 29, No. 9, 1997, pp. 629-637.
• Blackmore, D., Leu, M. C., and Qin, D., Improved Flow Approach for Swept Volumes, Proceedings of the Japan-USA Symposium on Flexible Automation, 1994, pp. 1191-1198.
• Blackmore, D., Leu, M. C., and Shih, F., Analysis and Modeling of Deformed Swept Volumes, Computer Aided Design, Vol. 26, 1994, pp. 315-326.
• Blackmore, D., Leu, M. C., and Wang, K. K., Applications of Flows and Envelopes to NC Machining, Annals of the CIRP, Vol. 41, No. 1, 1992, pp. 493-496.
• Blackmore, D., and Leu, M. C., Analysis of Swept Volume Via Lie Groups and Differential Equations, The International Journal of Robotics Research, Vol. 11, No. 6, 1992, pp. 516-537.
• Blackmore, D., Leu, M. C., and Wang, W., Classification and Analysis of Robot Swept Volumes, ASME Japan/USA Symposium on Flexible Automation, Vol. 1, 1992, pp. 69-75.
• Boussac, S., and Crosnier, A., Swept Volumes Generated from Deformable Objects Application to NC Verification, Proceedings of the IEEE International Conference on Robotics and Automation, 1996, pp. 1813-1818.
• Brechner, E., General Tool Offset Curves and Surfaces, ASME Design Automation Conference, DE-Vol. 23, Part 1, 1990, pp. 273-282.
• Coquillart, S., A Control Point Based Sweeping Technique, IEEE Computer Graphics and Applications, Vol. 7, No. 11, 1987, pp. 36-45.
• Elber, G., and Cohen, E., Error Bounded Variable Distance Offset Operator for Free Form Curves and Surfaces, International Journal of Computational Geometry and Applications, Vol. 1, No. 1, 1991, pp. 67-78.
• Fischer, A., and Wang, K. K., A Method for Extracting and Thickening a Mid-Surface of a 3D Thin Object Represented in NURBS, ASME Journal of Manufacturing Science and Engineering, Vol. 119B, 1997, pp. 706-712.
• Flaquer, J., Garate, G., and Pragada, M., Envelopes of Moving Quadric Surfaces, Computer Aided Geometric Design, Vol. 9, 1992, pp. 299-312.
• Frey, D. D., Otto, K. N., and Pflager, W., Swept Envelopes of Cutting Tools in Integrated Machine and Workpiece Error Budgeting, Annals of the CIRP, Vol. 46, No. 1, 1997, pp. 475-480.
• Ge, Q. J., Kinematics Driven Geometric Modeling: A Framework for Simultaneous NC Tool Path Generation and Sculptured Surface Design, Proceedings of the IEEE International Conference on Robotics and Automation, 1996, pp. 1819-1824.
• Guggenheimer, H., Computing Frames Along a Trajectory, Computer Aided Geometric Design, Vol. 6, 1989, pp. 77-78.
• Hu, Z-J., Ling, Z-K., Generating Swept Volumes With Instantaneous Screw Axes, Proceedings of the ASME Mechanism Synthesis and Analysis Conference, DE-Vol. 70., 1994, pp. 7-14.
• Klock, F., Two Moving Coordinate Frames for Sweeping along a 3D Trajectory, Computer Aided Geometric Design, Vol. 3, 1986, pp. 217-229.
• Gelston, S. M., and Dutta, D., Boundary Surface Recovery from Skeleton Curves and Surfaces, Computer Aided Geometric Design, Vol. 12, No. 1, pp. 27-51.
• Leu, M. C., Wang, L., Blackmore, D., A Verification Program for 5-Axis NC Machining with General APT Tools, Annals of the CIRP, Vol. 46, No. 1, 1997, pp. 419-424.
• Leu, M. C., Park, S. H., and Wang, K. K., Geometric Representation of Translational Swept Volume and its Applications, ASME Journal of Engineering for Industry, Vol. 108, 1986, pp. 113-119.
• Martin, R. R., and Stephenson, P., Sweeping of Three-Dimensional Objects, Computer Aided Design, Vol. 22, 1990, pp. 223-234.
• Oancea, N., and Oancea, V. G., Geometrical Modeling of Surface Generation Through Wrapping, ASME Journal of Manufacturing Sciences and Engineering, Vol. 119B, 1997, pp. 829-834.
• Parida, L., and Mudur, S., Computational Methods for Evaluating Swept Object Boundaries, Visual Computer, Vol. 10, 1994, pp. 266-276.
• Sambandan, K., and Wang, K. K., Five-Axis Swept Volumes for Graphic NC Simulation and Verification, Proceedings of the ASME Design Automation Conference, DE-Vol. 19-1, 1989, pp. 143-150.
• Takeuchi, Y., and Idemura, T., Five-Axis Control Machining and Grinding Based on Solid Model, Annals of the CIRP, Vol. 40, No. 1, 1990, pp. 455-459.
• Wang, W. P., and Wang, K. K., Geometric Modeling for Swept Volume of Moving Solids, IEEE Computer Graphics and Applications, Vol. 6, No. 12, 1986, pp. 8-17.