This paper introduces a new method that uses slice geometry to compute the global visibility map (GVM). Global visibility mapping is a fundamentally important process that extracts geometric information about an object, which can be used to solve hard problems, for example, setup and process planning in computer numerical control (CNC) machining. In this work, we present a method for creating the GVM from slice data of polyhedron models, and then show how it can help determine around which axis of rotation a part can be machined. There have been various methods of calculating the GVM to date, tracing back to the well-known seminal methods that use Gaussian mapping. Compared to the considerable amount of work in this field, the proposed method has an advantage of starting from feature-free models like stereolithography (STL) files and has adjustable resolution. Moreover, since it is built upon slicing the model, the method is embarrassingly parallelizable in nature, thus suitable for high-performance computing. Using the GVM obtained by this method, we generate an axis of rotation map to facilitate the setup planning for four-axis CNC milling machines as one implementation example.

References

References
1.
Kweon
,
S.
, and
Medeiros
,
D. J.
,
1998
, “
Part Orientations for CMM Inspection Using Dimensioned Visibility Maps
,”
Comput. Aided Des.
,
30
(
9
), pp.
741
749
.
2.
Wang
,
N.
, and
Tang
,
K.
,
2007
, “
Automatic Generation of Gouge-Free and Angular-Velocity-Compliant Five-Axis Toolpath
,”
Comput. Aided Des.
,
39
(
10
), pp.
841
852
.
3.
Balasubramaniam
,
M.
,
Sarma
,
S. E.
, and
Marciniak
,
K.
,
2003
, “
Collision-Free Finishing Toolpaths From Visibility Data
,”
Comput. Aided Des.
,
35
(
4
), pp.
359
374
.
4.
Suh
,
S.-H.
, and
Lee
,
J.-J.
,
1998
, “
Five-Axis Part Machining With Three-Axis CNC Machine and Indexing Table
,”
ASME J. Manuf. Sci. Eng.
,
120
(
1
), pp.
120
128
.
5.
Morishige
,
K.
,
Takeuchi
,
Y.
, and
Kase
,
K.
,
1999
, “
Tool Path Generation Using C-Space for 5-Axis Control Machining
,”
ASME J. Manuf. Sci. Eng.
,
121
(
1
), pp.
144
149
.
6.
Elber
,
G.
, and
Zussman
,
E.
,
1998
, “
Cone Visibility Decomposition of Freeform Surface
,”
Comput. Aided Des.
,
30
(
4
), pp.
315
320
.
7.
Fu
,
M. W.
,
2008
, “
The Application of Surface Demoldability and Moldability to Side-Core Design in Die and Mold CAD
,”
Comput. Aided Des.
,
40
(
5
), pp.
567
575
.
8.
Chen
,
L.-L.
,
Chou
,
S.-Y.
, and
Woo
,
T. C.
,
1995
, “
Partial Visibility for Selecting a Parting Direction in Mold and Die Design
,”
J. Manuf. Syst.
,
14
(
5
), pp.
319
330
.
9.
Priyadarshi
,
A. K.
, and
Gupta
,
S. K.
,
2004
, “
Geometric Algorithms for Automated Design of Multi-Piece Permanent Molds
,”
Comput. Aided Des.
,
36
(
3
), pp.
241
260
.
10.
Bittner
,
J.
, and
Wonka
,
P.
,
2003
, “
Visibility in Computer Graphics
,”
Environ. Plann. B
,
30
(
5
), pp.
729
755
.
11.
Zach
,
C.
, and
Karner
,
K.
,
2003
, “
Progressive Compression of Visibility Data for View-Dependent Multiresolution Meshes
,”
11th International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision
, Plzen, Czech Republic, Feb. 3–7, Vol.
11
, pp.
546
553
.
12.
Lu
,
Y.
,
Ding
,
Y.
, and
Zhu
,
L.
,
2016
, “
Smooth Tool Path Optimization for Flank Milling Based on the Gradient-Based Differential Evolution Method
,”
ASME J. Manuf. Sci. Eng.
,
138
(
8
), p.
081009
.
13.
Xu
,
K.
, and
Tang
,
K.
,
2016
, “
Optimal Workpiece Setup for Time-Efficient and Energy-Saving Five-Axis Machining of Freeform Surfaces
,”
ASME J. Manuf. Sci. Eng.
,
139
(
5
), p.
051003
.
14.
Song
,
X.
,
Pan
,
Y.
, and
Chen
,
Y.
,
2015
, “
Development of a Low-Cost Parallel Kinematic Machine for Multidirectional Additive Manufacturing
,”
ASME J. Manuf. Sci. Eng.
,
137
(
2
), p.
021005
.
15.
Chen
,
L. L.
, and
Woo
,
T. C.
,
1992
, “
Computational Geometry on the Sphere With Application to Automated Machining
,”
ASME J. Mech. Des.
,
114
(
2
), pp.
288
295
.
16.
Tang
,
K.
,
Woo
,
T.
, and
Gan
,
J.
,
1992
, “
Maximum Intersection of Spherical Polygons and Workpiece Orientation for 4- and 5-Axis Machining
,”
ASME J. Mech. Des.
,
114
(
3
), pp.
477
485
.
17.
Chen
,
L. L.
,
Chou
,
S. Y.
, and
Woo
,
T. C.
,
1993
, “
Separating and Intersecting Spherical Polygons—Computing Machinability on Three-, Four-, and Five-Axis Numerically Controlled Machines
,”
ACM Trans. Graphic
,
12
(
4
), pp.
305
326
.
18.
Chen
,
L.-L.
,
Chou
,
S.-Y.
, and
Woo
,
T. C.
,
1993
, “
Parting Directions for Mould and Die Design
,”
Comput. Aided Des.
,
25
(
12
), pp.
762
768
.
19.
Suh
,
S. H.
, and
Kang
,
J. K.
,
1995
, “
Process Planning for Multi-Axis Nc Machining of Free Surfaces
,”
Int. J. Prod. Res.
,
33
(
10
), pp.
2723
2738
.
20.
Li
,
Y.
, and
Frank
,
M. C.
,
2007
, “
Computing Non-Visibility of Convex Polygonal Facets on the Surface of a Polyhedral CAD Model
,”
Comput. Aided Des.
,
39
(
9
), pp.
732
744
.
21.
Tarbox
,
G. H.
, and
Gottschlich
,
S. N.
,
1995
, “
Planning for Complete Sensor Coverage in Inspection
,”
Comput. Vision Image Understanding
,
61
(
1
), pp.
84
111
.
22.
Spitz
,
S. N.
, and
Requicha
,
A. A. G.
,
2000
, “
Accessibility Analysis Using Computer Graphics Hardware
,”
IEEE Trans. Visualization Comput. Graphics
,
6
(
3
), pp.
208
219
.
23.
Frank
,
M. C.
,
Wysk
,
R. A.
, and
Joshi
,
S. B.
,
2006
, “
Determining Setup Orientations From the Visibility of Slice Geometry for Rapid Computer Numerically Controlled Machining
,”
ASME J. Manuf. Sci. Eng.
,
128
(
1
), pp.
228
238
.
24.
Stewart,
A. J.
,
1999
, “
Computing Visibility From Folded Surfaces
,”
Comput. Graphics
,
23
(
5
), pp.
693
702
.
25.
Hou
,
Z.
,
Li
,
X.
,
Huang
,
Y.
, and
Ho
,
S. T.
,
2013
, “
Physics of Elliptical Reflectors at Large Reflection and Divergence Angles—I: Their Design for Nano-Photonic Integrated Circuits and Application to Low-Loss Low-Crosstalk Waveguide Crossing
,”
Opt. Commun.
,
287
, pp.
96
105
.
26.
Suthunyatanakit
,
K.
,
Bohez
,
E. L. J.
, and
Annanon
,
K.
,
2009
, “
A New Global Accessibility Algorithm for a Polyhedral Model With Convex Polygonal Facets
,”
Comput. Aided Des.
,
41
(
12
), pp.
1020
1033
.
27.
Dhaliwal
,
S.
,
Gupta
,
S. K.
,
Huang
,
J.
, and
Priyadarshi
,
A.
,
2003
, “
Algorithms for Computing Global Accessibility Cones
,”
ASME J. Comput. Inf. Sci. Eng.
,
3
(
3
), pp.
200
209
.
28.
Liu
,
M.
, and
Ramani
,
K.
,
2007
, “
Computing an Exact Spherical Visibility Map for Meshed Polyhedra
,”
ACM Symposium on Solid and Physical Modeling
(
SPM
),
Beijing, China
, June 4–6, pp.
367
372
.
29.
Liu
,
M.
,
Liu
,
Y. S.
, and
Ramani
,
K.
,
2009
, “
Computing Global Visibility Maps for Regions on the Boundaries of Polyhedra Using Minkowski Sums
,”
Comput. Aided Des.
,
41
(
9
), pp.
668
680
.
30.
Joshi
,
A. M.
,
2015
, “
Computer Aided Process Planning for Multi-Axis CNC Machining Using Feature Free Polygonal CAD Models
,”
Ph.D. dissertation
, Iowa State University, Ames, IA.
31.
Li
,
Y.
, and
Frank
,
M. C.
,
2012
, “
Computing Axes of Rotation for Setup Planning Using Visibility of Polyhedral Computer-Aided Design Models
,”
ASME J. Manuf. Sci. Eng.
,
134
(
4
), p.
041005
.
32.
Rajab
,
S. M.
,
2016
, “
Reverse Engineer Blade
,” GrabCAD, Cambridge, MA, accessed Dec. 30, 2016, https://grabcad.com/library/reverse-engineer-blade-1
33.
Čapo
,
B.
,
2016
, “
Tea Pot
,” GrabCAD, Cambridge, MA, accessed Dec. 30, 2016, https://grabcad.com/library/tea-pot-11
34.
Boose
,
C.
,
2015
, “
Smooth Fluted Pitcher
,” GrabCAD, Cambridge, MA, accessed Dec. 30, 2016, https://grabcad.com/library/smooth-fluted-pitcher-1
35.
Pundir
,
N.
,
2016
, “
Fortune Cookie
,” GrabCAD, Cambridge, MA, accessed Dec. 30, 2016, https://grabcad.com/library/fortune-cookie-1
36.
Li
,
Y.
, and
Frank
,
M. C.
,
2006
, “
Machinability Analysis for 3-Axis Flat End Milling
,”
ASME J. Manuf. Sci. Eng.
,
128
(
2
), pp.
454
464
.
37.
Siraskar
,
N.
,
Paul
,
R.
, and
Anand
,
S.
,
2015
, “
Adaptive Slicing in Additive Manufacturing Process Using a Modified Boundary Octree Data Structure
,”
ASME J. Manuf. Sci. Eng.
,
137
(
1
), p.
011007
.
You do not currently have access to this content.