Abstract
This paper presents a practical technique for approximating the boundary surface of the volume swept out by three-dimensional objects using the depth-buffer. Objects may change their geometries and orientations while sweeping. The sweep volume is approximated as a union of volume elements, which are just rendered inside appropriate viewing frusta of virtual cameras and mapped into screen viewports with depth-buffer. From the depth of each pixel in the screen space of each rendering, the corresponding point in the original world space can be computed. Appropriately connecting these points yields polygonal faces forming polygonal surface patches approximately covering some portion of the sweep volume. Each view frustum adds one or more surface patches in this way, and these presumably overlapped polygonal surface patches approximately enclose the whole sweep volume. These patches may further be processed to yield non-overlapped polygonal surfaces as an approximation to the boundary of the original 3D sweep volume.
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References
K. Abdel-Malek, and H. J. Yeh, “Geometric Representation of the Swept Volume Using Jacobian Rank-Deficiency Conditions”, Computer-Aided Design, 29(6):457–468, 1997.
J. Ahn, M.-S. Kim, and S.-B. Lim, “Approximate General Sweep Boundary of a 2D Curved Object”, CVGIP: Graphical Models and Image Processing, 55(2):98–128, March 1993.
J. Ahn, “Fast Generation of Ellipsoids,” Graphics Gems V, pp. 179–190, AP Professional, Boston, 1995.
D. Blackmore, M. C. Leu, and F. Shin, “Analysis and Modeling of Deformed Swept Volumes”, Computer-Aided Design, 26(4):315–326, 1994.
D. Blackmore, M. C. Leu, and L. P. Wang, “The Sweep-Envelope Differential Equation Algorithm and Its Application to NCMachining Verification”, Computer-Aided Design, 29(9):629–637, 1997.
J. D. Foley, A. van Dam, S. Feiner, and J. Hughes, Computer Graphics: Principles and Practice, 2ed, Addison-Wesley, Reading, MA, 1990.
M. Ganter, “Dynamic Collision Detection Using Kinematics and Solid Modelling Techniques”, Ph.D Thesis, Dept. of Mechanical Engineering, Univ. of Wisconsin-Madison, August 1985.
H. Hoppe, T. DeRose, T. DuChamp, J. McDonald, and W. Stuetzle, “Surface Reconstruction from Unorganized Points”, Proceedings of SIGGRAPH 1992, 26(2):71–78, July 1992.
K. C. Hui, “Solid Sweeping in image space-application in NC simulation”, The Visual Computer, 10:306–316, 1994.
J. Kieffer, and F. L. Litvin, “Swept Volume Determination and Interference Detection for Moving 3-D Solids”, ASME Journal of Mechanical Design, 113:456–463, 1990.
J. Korein, “A Geometric Investigation of Reach”, An ACM Distinguished Dissertation 1984, The MIT Press, Cambridge, Massachusetts, 1985.
R. R. Martin, and P. C. Stephenson, “Sweeping of three-dimensional objects”, Computer-Aided Design, 22(4):223–234, May 1990.
K. Sambandan, “Geometry Generated by Sweeps of Polygons and Polyhedra”, Ph.D. Thesis, Cornell Univ., August 1990.
D. Shreiner, OpenGL ARB, and D. Schreiner, OpenGL Reference Manual, 3ed: The Official Reference Document to OpenGL, Version 1.2, Addison-Wesley, Reading, MA, 1999.
W. Stuerzlinger, “Imaging all Visible Surfaces”, Proceedings of Graphics Interface, pp. 115–122, 1999.
W. P. Wang, and K. K. Wang, “Geometric Modeling for Swept Volume of Moving Solids”, IEEE Computer Graphics and Applications, 6(6):8–17, 1986.
J. D. Weld, and M. C. Leu, “Geometric Representation of Swept Volumes with Application to Polyhedral Objects”, The International Journal of Robotics Research, 9(5):105–117, October 1990.
J. van Wijk, “Ray Tracing Objects Defined by Sweeping a Sphere”, Proceedings of Eurographics’ 84 Conference, Amsterdam, pp. 73–82, 1984.
M. Woo, J. Neider, T. David, D. Shriner, T. Davis, OpenGL ARB, and D. Shreiner, OpenGL 1.2 Programming Guide, 3ed: The Official Guide to Learning OpenGL, Version 1.2, Addison-Wesley, Reading, MA, 1999.
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© 2003 Springer-Verlag Berlin Heidelberg
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Ahn, J., Hong, S.J. (2003). Approximating 3D General Sweep Boundary Using Depth-Buffer. In: Kumar, V., Gavrilova, M.L., Tan, C.J.K., L’Ecuyer, P. (eds) Computational Science and Its Applications — ICCSA 2003. ICCSA 2003. Lecture Notes in Computer Science, vol 2669. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44842-X_52
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DOI: https://doi.org/10.1007/3-540-44842-X_52
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