Research Papers

A Graphics Processor Unit-Accelerated Freeform Surface Offsetting Method for High-Resolution Subtractive Three-Dimensional Printing (Machining)

[+] Author and Article Information
Mohammad M. Hossain

College of Computing,
Georgia Institute of Technology,
Atlanta, GA 30332-0765

Chandra Nath

School of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332-0405
e-mail: nathc2@asme.org

Thomas M. Tucker

Tucker Innovations, Inc,
Charlotte, NC 28173

Richard W. Vuduc

School of Computational Science
and Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332-0765

Thomas R. Kurfess

School of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332-0405

1Present address: Applied Machine Learning lab at Facebook, Inc. Menlo Park, CA.

2Present address: Hitachi America, Ltd. Research & Development Division, Farmington Hills, MI 48335.

3Corresponding author.

Manuscript received June 13, 2017; final manuscript received November 15, 2017; published online February 13, 2018. Assoc. Editor: Zhijian J. Pei.

J. Manuf. Sci. Eng 140(4), 041012 (Feb 13, 2018) (11 pages) Paper No: MANU-17-1371; doi: 10.1115/1.4038599 History: Received June 13, 2017; Revised November 15, 2017

Machining is one of the major manufacturing methods having very wide applications in industries. Unlike layer-by-layer additive three-dimensional (3D) printing technology, the lack of an easy and intuitive programmability in conventional toolpath planning approach in machining leads to significantly higher manufacturing cost for direct computer numerical control (CNC)-based prototyping (i.e., subtractive 3D printing). In standard computer-aided manufacturing (CAM) packages, general use of B-rep (boundary representation) and non-uniform rational basis spline (NURBS)-based representations of the computer-aided design (CAD) interfaces make core computations of tool trajectories generation process, such as surface offsetting, difficult. In this work, the problem of efficient generation of freeform surface offsets is addressed with a novel volumetric (voxel) representation. It presents an image filter-based offsetting algorithm, which leverages the parallel computing engines on modern graphics processor unit (GPU). The compact voxel data representation and the proposed computational acceleration on GPU together are capable to process voxel offsetting at four-fold higher resolution in interactive CAM application. Additionally, in order to further accelerate the offset computation, the problem of offsetting with a large distance is decomposed into successive offsetting using smaller distances. The performance trade-offs between accuracy and computation time of the offset algorithms are thoroughly analyzed. The developed GPU implementation of the offsetting algorithm is found to be robust in computation, and demonstrates a 50-fold speedup on single graphics card (NVIDIA GTX780Ti) relative to prior best-performing algorithms developed for multicores central processing units (CPU). The proposed offsetting approach has been validated for a variety of complex parts produced on different multi-axis CNC machine tools including turning, milling, and compound turning-milling.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.


Hossain, M. M. , 2016, “ Voxel-Based Offsetting at High Resolution With Tunable Speed and Precision Using Hybrid Dynamic Trees,” Ph.D. thesis, Georgia Institute of Technology, Atlanta, GA. https://smartech.gatech.edu/handle/1853/56305
Hossain, M. M. , Nath, C. , Tucker, T. M. , Kurfess, T. R. , and Vuduc, R. W. , 2016, “ A Graphical Approach for Freeform Surface Offsetting With GPU Acceleration for Subtractive 3D Printing,” ASME Paper No. MSEC2016-8525.
Piegl, L. A. , and Tiller, W. , 1999, “ Computing Offsets of NURBS Curves and Surfaces,” Comput.-Aided Des., 31(2), pp. 147–156. [CrossRef]
Maekawa, T. , 1999, “ An Overview of Offset Curves and Surfaces,” Comput.-Aided Des., 31(3), pp. 165–173.
Herholz, P. , Matusik, W. , and Alexa, M. , 2015, “ Approximating Free-Form Geometry With Height Fields for Manufacturing,” Comput. Graph. Forum, 34(2), pp. 239–251. [CrossRef]
Soille, P. , 2004, Morphological Image Analysis: Principles and Applications, Springer, New York. [CrossRef]
Rossignac, J. R. , and Requicha, A. A. G. , 1986, “ Offsetting Operations in Solid Modelling,” Comput. Aided Geom. Des., 3(2), pp. 129–148. [CrossRef]
Sud, A. , Govindaraju, N. , Gayle, R. , and Manocha, D. , 2006, “ Interactive 3D Distance Field Computation Using Linear Factorization,” Symposium on Interactive 3D Graphics and Games (I3D '06), Redwood City, CA, Mar. 14–17, pp. 117–124. http://gamma.cs.unc.edu/GVD/LINFAC/
Pavic, D. , and Kobbelt, L. , 2008, “ High-Resolution Volumetric Computation of Offset Surfaces With Feature Preservation,” Comput. Graph. Forum, 27(2), pp. 165–174. [CrossRef]
Liu, S. , and Wang, C. C. L. , 2011, “ Fast Intersection-Free Offset Surface Generation From Freeform Models With Triangular Meshes,” IEEE Trans. Autom. Sci. Eng., 8(2), pp. 347–360. [CrossRef]
Chen, Y. , and Wang, C. C. L. , 2011, “ Uniform Offsetting of Polygonal Model Based on Layered Depth-Normal Images,” Comput.-Aided Des., 43(1), pp. 31–46. [CrossRef]
Wang, C. C. L. , and Manocha, D. , 2013, “ GPU-Based Offset Surface Computation Using Point Samples,” Comput.-Aided Des., 45(2), pp. 321–330. [CrossRef]
Varadhan, G. , and Manocha, D. , 2006, “ Accurate Minkowski Sum Approximation of Polyhedral Models,” Graphical Models, 68(4), pp. 343–355. [CrossRef]
Yin, K. , Liu, Y. , and Wu, E. , 2011, “ Fast Computing Adaptively Sampled Distance Field on GPU,” Pacific Graphics Short Papers, The Eurographics Association, Lyon, France.
Li, W. , and Mcmains, S. , 2011, “ Voxelized Minkowski Sum Computation on the GPU with Robust Culling,” Comput.-Aided Des., 43(10), pp. 1270–1283. [CrossRef]
Meagher, D. , 1980, “ Octree Encoding: A New Technique for the Representation, Manipulation and Display of Arbitrary 3-D Objects by Computer,” Rensselaer Polytechnic Institute, New York, Report No. IPL-TR-80-111.
Laine, S. , and Karras, T. , 2010, “ Efficient Sparse Voxel Octrees,” ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games (I3D '10), Washington, DC, Feb. 19–21, pp. 55–63. http://research.nvidia.com/publication/efficient-sparse-voxel-octrees
Hou, Q. , Sun, X. , Zhou, K. , Lauterbach, C. , and Manocha, D. , 2011, “ Memory-Scalable GPU Spatial Hierarchy Construction,” IEEE Trans. Visualization Comput. Graphics, 17(4), pp. 466–474. [CrossRef]
Crassin, C. , Neyret, F. , Lefebvre, S. , and Eisemann, E. , 2009, “ GigaVoxels: Ray-Guided Streaming for Efficient and Detailed Voxel Rendering,” Symposium on Interactive 3D Graphics and Games (I3D '09), Boston, MA, Feb. 27–Mar. 1, pp. 15–22. http://maverick.inria.fr/Publications/2009/CNLE09/
Hossain, M. M. , Tucker, T. M. , Kurfess, T. R. , and Vuduc, R. W. , 2016, “ Hybrid Dynamic Trees for Extreme-Resolution 3D Sparse Data Modeling,” International Parallel and Distributed Processing Symposium (IPDPS '16), Chicago, IL, May 23–27, pp. 1–10.
Hossain, M. M. , Tucker, T. M. , Kurfess, T. R. , and Vuduc, R. W. , 2015, “ A GPU-Parallel Construction of Volumetric Tree,” Fifth Workshop on Irregular Applications: Architectures and Algorithms (IA3 '15), Austin, TX, Nov. 15, pp. 1–10. https://dl.acm.org/citation.cfm?id=2833191
Gonzalez, R. C. , and Woods, R. E. , 2001, Digital Image Processing, Prentice Hall, Upper Saddle River, NJ.
Gurbuz, A. Z. , and Zeid, I. , 1995, “ Offsetting Operations Via Closed Ball Approximation,” Comput.-Aided Des., 27(11), pp. 805–810. [CrossRef]
Zhuang, X. , and Haralick, R. M. , 1986, “ Morphological Structuring Element Decomposition,” Comput. Vision, Graph. Image Process., 35(3), pp. 370 –382. [CrossRef]


Grahic Jump Location
Fig. 1

Application of surface offsetting in CNC machining: (a) target part, (b) part shown inside stock, (c) shrunk stock, (d) expanded part, (e) contact volume, and (f) stock after toolpass

Grahic Jump Location
Fig. 2

Illustration of a quadtree: (a) A quadtree representation of a triangle and (b) resulting quadtree

Grahic Jump Location
Fig. 3

Illustration of a tiled grid structure: (a) two-Level (tiled) grid and (b) tiled grid in a sample 2D cross section of a 3D solid

Grahic Jump Location
Fig. 4

HDT representation and illustration: (a) layout of an HDT and (b) HDT in a sample 2D cross section

Grahic Jump Location
Fig. 5

Processing of the HDT leaf grid in CUDA: (a) CUDA framework (courtesy of NVIDIA) and (b) leaf grid layout in a CUDA threadblock

Grahic Jump Location
Fig. 6

Offsetting illustration: (a) A 2D ring template (or structuring element), (b) cross section of input HDT swept with ring template, and (c) cross section of dilated HDT overlaid with the original HDT

Grahic Jump Location
Fig. 7

Dilations of candle holder: (a) 10 voxels, (b) 20 voxels, and (c) 40 voxels

Grahic Jump Location
Fig. 8

Erosions of candle holder: (a) 10 voxels, (b) 20 voxels, and (c) 40 voxels

Grahic Jump Location
Fig. 9

Offsetting error analysis: (a) normalized average error and (b) normalized maximal error

Grahic Jump Location
Fig. 10

Successive offsetting performance

Grahic Jump Location
Fig. 11

Successive offsetting error analysis: (a) normalized average error and (b) normalized maximal error

Grahic Jump Location
Fig. 12

Surface dilation of a Buddha model (polygonal mesh comprising 1.1 million triangles): (a) original and (b) dilated

Grahic Jump Location
Fig. 17

Propeller (multi-axis turning and milling): (a) propeller CAD model and (b) machined propeller

Grahic Jump Location
Fig. 16

Ball joint (multi-axis turning and milling): (a) balljoint CAD model and (b) machined balljoint

Grahic Jump Location
Fig. 15

Swirled prism (three axis milling): (a) prism CAD model and (b) machined prism

Grahic Jump Location
Fig. 14

Pawn with two-axis turning: (a) pawn CAD model and (b) machined pawn

Grahic Jump Location
Fig. 13

Wiggle CAD model to part: (a) target voxel model, (b) toolpaths superimposed, (c) contact volume, and (d) machined part



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In