This paper presents an enhanced marching cubes algorithm to construct an iso-boundary for in-process geometric modeling for material removal processes. The author first analyzes the tool motion and the geometric properties in material removal processes. The result shows that the in-process geometry is the complement of the tool swept volume from the raw material. The in-process geometry can be determined by continuously updating itself from the swept volume of the tool. This study uses a three-dimensional G-buffer to update the intersection information between the tool swept volume and the in-process geometry. Rather than traditionally searching for all intersection points ranging in a cube, the developed algorithm uses certain specific intersection points that are selected based on the removal geometry properties to construct the iso-boundary. It avoids the unfavorable ambiguities and holes on constructed boundaries. In addition, the developed algorithm is able to handle multiple intersection points in a cubical edge. This study also discusses material removal volume and tool collision issues. The computer implementation shows that the developed method is superior to the traditional ones in material removal applications.

1.
Chiou
,
C. J.
, and
Lee
,
Y. S.
, 2002, “
A Machining Potential Field Approach to Tool Path Generation for Multi-Axis Sculptured Surface Machining
,”
Comput.-Aided Des.
0010-4485,
34
, pp.
357
371
.
2.
Simeon
,
T.
,
Leroy
,
S.
, and
Laumond
,
J.
, 2002, “
Path Coordination for Multiple Mobile Robots: A Resolution-Complete Algorithm
,”
IEEE Trans. Rob. Autom.
1042-296X,
18
(
1
), pp.
42
49
.
3.
Dachille
,
I.
,
Qin
,
H.
, and
Kaufman
,
A.
, 2001, “
A Novel Haptic-Based Interface and Sculpting System for Physics-Based Geometric Design
,”
Comput.-Aided Des.
0010-4485,
33
, pp.
403
420
.
4.
Hook
,
V.
, 1986,
“Real-time Shaded NC Milling Display
,”
SIGGRAPH ’86, Computer Graphics Proceedings
, pp.
57
66
.
5.
Jerard
,
B.
,
Drysdale
,
R.
,
Hauck
,
K.
,
Schaudt
,
B.
, and
Magewick
,
J.
, 1989, “
Methods for Detecting Errors in Sculptured Surface Machining
,”
IEEE Comput. Graphics Appl.
0272-1716,
9
(
1
), pp.
26
39
.
6.
Xavier
,
P.
, 1997, “
Fast Swept-Volume Distance for Robust Collision Detection
,”
Proceedings of IEEE International Conference on Robotics and Automation
, pp.
1162
1169
.
7.
Basdogan
,
C.
, and
Srinivasan
,
M.
, 2001, “
Haptic Rendering in Virtual Environments
,”
Handbook of Virtual Environments
,
K. M.
Stanney
, ed.,
Lowrenece Erlbaum Associates
,
Mahwah, NJ
, pp.
117
134
.
8.
Zhu
,
W.
, and
Lee
,
Y. S.
, 2004, “
Five-Axis Pencil-Cut Planning and Virtual Prototyping with 5-Degree-Of-Freedom Haptic Interface
,”
Comput.-Aided Des.
0010-4485,
36
(
13
), pp.
1295
1307
.
9.
Kim
,
K. I.
,
Chon
,
Y. J.
, and
Kim
,
K.
, 1996, “
Simulation and Verification of CNC Tool Path for Sculptured Surfaces
,”
Trans. NAMRI/SME
1047-3025,
24
, pp.
69
74
.
10.
Waurzyniak
,
P.
, 2001, “
Simulations Speed Production
,”
Manuf. Eng.
0361-0853,
126
(
4
), pp.
36
46
.
11.
Wang
,
W. P.
, and
Wang
,
K. K.
, 1986, “
Geometric Modeling for Swept Volume of Moving Solids
,”
IEEE Comput. Graphics Appl.
0272-1716,
6
(
12
), pp.
8
17
.
12.
Fussell
,
B.
,
Jerard
,
R.
, and
Hemmet
,
J.
, 2003,
“Modeling of Cutting Geometry and Forces for 5-Axis Sculptured Surface Machining
,”
Comput.-Aided Des.
0010-4485,
35
(
4
), pp.
333
346
.
13.
Benouamer
,
M.
, and
Michelucci
,
D.
, 1997, “
Bridging the Gap Between CSG and Brep Via a Triple Ray Representation
,”
ACM Symposium on Solid Modeling and Applications ’97
,
Atlanta
, pp.
68
79
.
14.
Sutton
,
P.
, and
Hansen
,
C.
, 2000, “
Accelerated Isosurface Extraction in Time-Varying Fields
,”
IEEE Trans. Vis. Comput. Graph.
1077-2626,
6
(
2
), pp.
98
107
.
15.
Huang
,
J.
,
Yagel
,
R.
,
Filippov
,
V.
, and
Kurzion
,
Y.
, 1998, “
An Accurate Method for Voxelizing Polygon Meshes
,”
ACM Symposium on Volume Visualization
, pp.
119
126
.
16.
Peng
,
X.
,
Zhang
,
W.
,
Asam
,
S.
, and
Leu
,
M.
, “
Surface Reconstruction from Dexel Data for Virtual Sculpturing
,”
Proceedings of IMECE04
, Anaheim, CA, ASME, New York.
17.
Zhu
,
W.
, and
Lee
,
Y-S.
, 2005, “
A Visibility Sphere Marching Algorithm of Constructing Polyhedral Models for Haptic Sculpting and Product Prototyping
,”
Rob. Comput.-Integr. Manufact.
0736-5845,
21
(
1
), pp.
19
36
.
18.
Kobbelt
,
L.
,
Botsch
,
M.
,
Schwanecke
,
U.
, and
Seidel
,
H.
, 2001, “
Feature Sensitive Surface Extraction from Volume Data
,”
SIGGRAPH ’01, Computer Graphics Proceedings
, pp.
57
66
.
19.
Lorensen
,
W.
, and
Cline
,
H.
, 1987, “
Marching Cubes: A High Resolution 3D Surface Construction Algorithm
,” Siggraph ’87 Conf. Proc.
ACM Computer Graphics
,
21
(
4
), pp.
163
170
.
20.
Chernyaev
,
E.
, 1995, “
Marching Cubes 33: Construction of Topologically Correct Isosurfaces
,” Technical Report CERN CN 95-17, CERN.
21.
Montaniz
,
C.
,
Scateni
,
R.
, and
Scopignoy
,
R.
, 1994, “
Discretized Marching Cubes
,”
Proceedings of Visualization ’94
,
IEEE Computer Society Press
,
New York
, pp.
281
287
.
22.
Nielson
,
G.
, and
Hamann
,
B.
, 1992, “
The Asymptotic Decider: Resolving the Ambiguity in Marching Cubes
,”
Proc. IEEE Visualization ’92
, pp.
83
91
.
23.
Montani
,
C.
,
Scateni
,
R.
, and
Scopigno
,
R.
, 1994, “
A Modified Look-Up Table for Implicit Disambiguation of Marching Cubes
,”
Piping Eng.
0385-9894,
10
, pp.
353
355
.
24.
Natarajan
,
B. K.
, 1994, “
On Generating Topologically Consistent Iso-Surfaces from Uniform Samples
,”
Piping Eng.
0385-9894,
11
(
1
), pp.
52
62
.
25.
Allamandri
,
F.
,
Cignoni
,
P.
,
Montani
,
C.
, and
Scopigno
,
R.
, 1998, “
Adaptively Adjusting Marching Cubes Output to Fit a Trilinear Reconstruction Filter
,”
Visualization in Scientific Computing ’98
, Proceedings of the Eurographics, pp.
25
34
.
26.
Bloomenthal
,
J.
, 1994, “
An Implicit Surface Polygonizer
,”
Graphics Gems IV
,
Academic Press
,
New York
, pp.
324
349
.
27.
Cignoni
,
P.
,
Marino
,
P.
,
Montani
,
C.
,
Puppo
,
E.
, and
Scopigno
,
R.
, 1997, “
Speeding Up Isosurface Extraction Using Interval Tree
,”
IEEE Trans. Vis. Comput. Graph.
1077-2626,
3
(
2
), pp.
158
169
.
28.
Kral
,
I. H.
, 1986,
Numerical Control Programming in APT
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
29.
Mahvash
,
M.
,
Hayward
,
V.
, and
Lloyd
,
J.
, 2002, “
Haptic Rendering of Tool Contact
,”
Proceedings of Eurohaptics
, pp.
110
115
.
30.
Craig
,
J.
, 1989,
Introduction to Robotics: Mechanics and Control
, 2nd ed.,
Addison-Wesley
,
Reading, MA
.
31.
Sacks
,
E.
, 2003, “
Path Planning for Planar Articulated Robots Using Configuration Spaces and Compliant Motion
,”
IEEE Trans. Rob. Autom.
1042-296X,
19
(
3
), pp.
381
390
.
32.
Frey
,
D. D.
,
Otto
,
K. N.
, and
Pflager
,
W.
, 1997, “
Swept Envelopes of Cutting Tools in Integrated Machine and Workpiece Error Budgeting
,”
CIRP Ann.
0007-8506,
46
(
1
), pp.
475
480
.
33.
Blackmore
,
D.
,
Leu
,
M. C.
, and
Wang
,
L. P.
, 1997, “
The Swept-Envelope Differential Equation Algorithm and Its Application to NC Machining Verification
,”
Comput.-Aided Des.
0010-4485,
29
(
9
), pp.
629
638
.
34.
Chiou
,
C. J.
, and
Lee
,
Y. S.
, 1999, “
A Shape-Generating Approach for Multi-Axis Machining G-Buffer Models
,”
Comput.-Aided Des.
0010-4485,
31
(
12
), pp.
761
776
.
35.
Blackmore
,
D.
, and
Leu
,
M. C.
, 1992, “
Analysis of Swept Volume via Lie Group and Differential Equations
,”
Int. J. Robot. Res.
0278-3649,
11
(
6
), pp.
516
537
.
36.
Ganter
,
M. A.
, and
Uicker
,
J. J.
, 1986, “
Dynamic Collision Detection Using Swept Solids
,”
ASME J. Mech., Transm., Autom. Des.
0738-0666
108
(
4
), pp.
549
555
.
You do not currently have access to this content.