Behandish,
M.
, and
Ilieş,
H. T.
, 2015, “
Haptic Assembly Using Skeletal Densities and Fourier Transforms,” ASME Paper No. DETC2015-47923.

Bullinger,
H. J.
,
Breining,
R.
, and
Bauer,
W.
, 1999, “
Virtual Prototyping-State of the Art in Product Design,” 26th International Conference on Computers and Industrial Engineering, pp. 103–107.

Wang,
G. G.
, 2002, “
Definition and Review of Virtual Prototyping,” ASME J. Comput. Inf. Sci. Eng.,
2(3), pp. 232–236.

[CrossRef]
Deviprasad,
T.
, and
Kesavadas,
T.
, 2003, “
Virtual Prototyping of Assembly Components Using Process Modeling,” J. Manuf. Syst.,
22(1), pp. 16–27.

[CrossRef]
Bordegoni,
M.
,
Colombo,
G.
, and
Formentini,
L.
, 2006, “
Haptic Technologies for the Conceptual and Validation Phases of Product Design,” Comput. Graphics,
30(3), pp. 377–390.

[CrossRef]
Seth,
A.
,
Su,
H. J.
, and
Vance,
J. M.
, 2006, “
SHARP: A System for Haptic Assembly and Realistic Prototyping,” ASME Paper No. DETC2006-99476.

Seth,
A.
,
Su,
H. J.
, and
Vance,
J. M.
, 2008, “
Development of a Dual-Handed Haptic Assembly System: SHARP,” ASME J. Comput. Inf. Sci. Eng.,
8(4), pp. 1–8.

[CrossRef]
Gomes de Sa,
A.
, and
Zachmann,
G.
, 1999, “
Virtual Reality as a Tool for Verification of Assembly and Maintenance Processes,” Comput. Graphics,
23(3), pp. 389–403.

[CrossRef]
Volkov,
S.
, and
Vance,
J. M.
, 2001, “
Effectiveness of Haptic Sensation for the Evaluation of Virtual Prototypes,” ASME J. Comput. Inf. Sci. Eng.,
1(2), pp. 123–128.

[CrossRef]
Seth,
A.
,
Vance,
J. M.
, and
Oliver,
J. H.
, 2011, “
Virtual Reality for Assembly Methods Prototyping: A Review,” Virtual Reality,
15(1), pp. 5–20.

[CrossRef]
Vance,
J. M.
, and
Dumont,
G.
, 2011, “
A Conceptual Framework to Support Natural Interaction for Virtual Assembly Tasks,” ASME Paper No. WINVR2011-5570.

Perret,
J.
,
Kneschke,
C.
,
Vance,
J. M.
, and
Dumont,
G.
, 2013, “
Interactive Assembly Simulation With Haptic Feedback,” Assem. Autom.,
33(3), pp. 214–220.

[CrossRef]
Behandish,
M.
, and
Ilieş,
H. T.
, 2014, “
Peg-in-Hole Revisited: A Generic Force Model for Haptic Assembly,” ASME Paper No. DETC2014-35290.

Behandish,
M.
, and
Ilieş,
H. T.
, 2015, “
Peg-in-Hole Revisited: A Generic Force Model for Haptic Assembly,” ASME J. Comput. Inf. Sci. Eng.,
15(4), p. 041004.

[CrossRef]
Lysenko,
M.
,
Nelaturi,
S.
, and
Shapiro,
V.
, 2010, “
Group Morphology With Convolution Algebras,” 14th ACM Symposium on Solid and Physical Modeling (SPM’2010), pp. 11–22.

Lysenko,
M.
, 2013, “
Fourier Collision Detection,” Int. J. Rob. Res.,
32(4), pp. 483–503.

[CrossRef]
Behandish,
M.
, and
Ilieş,
H. T.
, 2015, “
Analytic Methods for Geometric Modeling Via Spherical Decomposition,” Comput.-Aided Des.,
70, pp. 100–115.

[CrossRef]
Roerdink,
J. B. T. M.
, 2000, “
Group Morphology,” Pattern Recognit.,
33(6), pp. 877–895.

[CrossRef]
Nelaturi,
S.
, and
Shapiro,
V.
, 2011, “
Configuration Products and Quotients in Geometric Modeling,” Comput.-Aided Des.,
43(7), pp. 781–794.

[CrossRef]
Behandish,
M.
, and
Ilieş,
H. T.
, 2014, “
Shape Complementarity Analysis for Objects of Arbitrary Shape,” University of Connecticut, Technical Report No. CDL-TR-14-01.

Lozano-Perez,
T.
, 1983, “
Spatial Planning: A Configuration Space Approach,” IEEE Trans. Comput.,
C-32(2), pp. 108–120.

[CrossRef]
Kavraki,
L. E.
, 1995, “
Computation of Configuration-Space Obstacles Using the Fast Fourier Transform,” IEEE Trans. Rob. Autom.,
11(3), pp. 408–413.

[CrossRef]
Chan,
L. S. H.
, and
Choi,
K. S.
, 2009, “
Integrating PhysX and OpenHaptics: Efficient Force Feedback Generation Using Physics Engine and Haptic Devices,” Joint Conferences on Pervasive Computing (JCPC’2009), Institute of Electrical and Electronics Engineers (IEEE), pp. 853–858.

Sagardia,
M.
,
Stouraitis,
T.
, and
Silva,
J. L. E.
, 2014, “
A New Fast and Robust Collision Detection and Force Computation Algorithm Applied to the Physics Engine Bullet: Method, Integration, and Evaluation,” Conference and Exhibition of the European Association of Virtual and Augmented Reality (EuroVR’2014).

Renouf,
M.
,
Acary,
V.
, and
Dumont,
G.
, 2005, “
3D Frictional Contact and Impact Multibody Dynamics. A Comparison of Algorithms Suitable for Real-Time Applications,” ECCOMAS Thematic Conference on Multibody Dynamics.

Tching,
L.
, and
Dumont,
G.
, 2008, “
Haptic Simulations Based on Non-Smooth Dynamics for Rigid-Bodies,” 15th ACM Symposium on Virtual Reality Software and Technology (VRST’2008), Association for Computing Machinery (ACM), pp. 87–90.

Lin,
M.
, and
Gottschalk,
S.
, 1998, “
Collision Detection Between Geometric Models: A Survey,” IMA Conference on Mathematics of Surfaces, Vol.
1, pp. 37–56.

Jimenez,
P.
,
Thomas,
F.
, and
Torras
, 2001, “
3D Collision Detection: A Survey,” Comput. Graphics,
25(2), pp. 269–285.

[CrossRef]
Kockara,
S.
,
Halic,
T.
,
Iqbal,
K.
,
Bayrak,
C.
, and
Rowe,
R.
, 2007, “
Collision Detection: A Survey,” IEEE International Conference on Systems, Man and Cybernetics (ISIC’2007), Institute of Electrical and Electronics Engineers (IEEE), pp. 4046–4051.

Hasegawa,
S.
, and
Fujii,
N.
, 2003, “
Real-Time Rigid Body Simulation Based on Volumetric Penalty Method,” 11th Symposium on Haptic Interfaces for Virtual Environment and Teleoperator Systems, Institute of Electrical and Electronics Engineers (IEEE), pp. 326–332.

Hasegawa,
S.
, and
Sato,
M.
, 2004, “
Real-Time Rigid Body Simulation for Haptic Interactions Based on Contact Volume of Polygonal Objects,” Comput. Graphics Forum,
23(3), pp. 529–538.

[CrossRef]
Lötstedt,
P.
, 1984, “
Numerical Simulation of Time-Dependent Contact and Friction Problems in Rigid Body Mechanics,” SIAM J. Sci. Stat. Comput.,
5(2), pp. 370–393.

[CrossRef]
Stewart,
D. E.
, 2000, “
Rigid-Body Dynamics With Friction and Impact,” SIAM Rev.,
42(1), pp. 3–39.

[CrossRef]
Marcelino,
L.
,
Murray,
N.
, and
Fernando,
T.
, 2003, “
A Constraint Manager to Support Virtual Maintainability,” Comput. Graphics,
27(1), pp. 19–26.

[CrossRef]
Murray,
N.
, and
Fernando,
T.
, 2004, “
An Immersive Assembly and Maintenance Simulation Environment,” IEEE International Symposium on Distributed Simulation and Real-Time Applications (DS-RT’2004), Institute of Electrical and Electronics Engineers (IEEE), pp. 159–166.

Iacob,
R.
,
Mitrouchev,
P.
, and
Leon,
J. C.
, 2008, “
Contact Identification for Assembly-Disassembly Simulation With a Haptic Device,” Visual Comput.,
24(11), pp. 973–979.

[CrossRef]
Iacob,
R.
,
Mitrouchev,
P.
, and
Leon,
J. C.
, 2011, “
Assembly Simulation Incorporating Component Mobility Modelling Based on Functional Surfaces,” Int. J. Interact. Des. Manuf.,
5(2), pp. 119–132.

[CrossRef]
Boussuge,
F.
,
Léon,
J. C.
,
Hahmann,
S.
, and
Fine,
L.
, 2012, “
An Analysis of DMU Transformation Requirements for Structural Assembly Simulations,” 8th International Conference on Engineering Computational Technology.

Mirtich,
B.
, 1998, “
V-Clip: Fast and Robust Polyhedral Collision Detection,” ACM Trans. Graphics,
17(3), pp. 177–208.

[CrossRef]
Ehmann,
S. A.
, and
Lin,
M. C.
, 2000, “
Accelerated Proximity Queries Between Convex Polyhedra by Multi-Level Voronoi Marching,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS'2000), Vol.
3, Institute of Electrical and Electronics Engineers (IEEE).

Ehmann,
S. A.
, and
Lin,
M. C.
, 2001, “
Accurate and Fast Proximity Queries Between Polyhedra Using Convex Surface Decomposition,” Comput. Graphics Forum,
20(3), pp. 500–511.

[CrossRef]
Gregory,
A.
,
Lin,
M. C.
,
Gottschalk,
S.
, and
Taylor,
R.
, 1999, “
A Framework for Fast and Accurate Collision Detection for Haptic Interaction,” ACM SIGGRAPH 2005 Courses, Vol.
34, Association for Computing Machinery (ACM), pp. 38–45.

Gottschalk,
S.
,
Lin,
M. C.
, and
Manocha,
D.
, 1996, “
OBBTree: A Hierarchical Structure for Rapid Interference Detection,” 23rd Annual Conference on Computer Graphics and Interactive Techniques, pp. 171–180.

McNeely,
W. A.
,
Puterbaugh,
K. D.
, and
Troy,
J. J.
, 2005, “
Six Degree-of-Freedom Haptic Rendering Using Voxel Sampling,” ACM SIGGRAPH’2005 Courses, Vol.
42, Association for Computing Machinery (ACM).

McNeely,
W. A.
,
Puterbaugh,
K. D.
, and
Troy,
J. J.
, 2006, “
Voxel-Based 6-DOF Haptic Rendering Improvements,” Haptics-e,
3(7).

Barbič,
J.
, and
James,
D.
, 2007, “
Time-Critical Distributed Contact for 6-DOF Haptic Rendering of Adaptively Sampled Reduced Deformable Models,” ACM SIGGRAPH’2007/Eurographics Symposium on Computer Animation, Association for Computing Machinery (ACM), pp. 171–180.

Sagardia,
M.
,
Hulin,
T.
,
Preusche,
C.
, and
Hirzinger,
G.
, 2008, “
Improvements of the Voxmap-PointShell Algorithm-Fast Generation of Haptic Data-Structures,” 53rd Internationales Wissenschaftliches Kolloquium, Technische Universität Ilmenau.

Hubbard,
P. M.
, 1996, “
Approximating Polyhedra With Spheres for Time-Critical Collision Detection,” ACM Trans. Graphics,
15(3), pp. 179–210.

[CrossRef]
Bradshaw,
G.
, and
O'Sullivan,
C.
, 2004, “
Adaptive Medial-Axis Approximation for Sphere-Tree Construction,” ACM Trans. Graphics,
23(1), pp. 1–26.

[CrossRef]
Weller,
R.
, and
Zachmann,
G.
, 2009, “
Inner Sphere Trees for Proximity and Penetration Queries,” Robotics: Science and Systems Conference (RSS'2009), Vol.
2.

Weller,
R.
, and
Zachmann,
G.
, 2011, “
Inner Sphere Trees and Their Application to Collision Detection,” Virtual Realities,
G. Brunnett
,
S. Coquillart
, and
G. Welch
, eds.,
Springer,
Vienna, Austria, pp. 181–201.

Ruffaldi,
E.
,
Morris,
D.
,
Barbagli,
F.
,
Salisbury,
K.
, and
Bergamasco,
M.
, 2008, “
Voxel-Based Haptic Rendering Using Implicit Sphere Trees,” 16th International Symposium on Haptic Interfaces for Virtual Environment and Teleoperator Systems, Institute of Electrical and Electronics Engineers (IEEE), pp. 319–325.

Weller,
R.
, and
Zachmann,
G.
, 2009, “
A Unified Approach for Physically-Based Simulations and Haptic Rendering,” ACM SIGGRAPH’2009 Symposium on Video Games, Association for Computing Machinery (ACM), pp. 151–159.

Weller,
R.
, and
Zachmann,
G.
, 2009, “
Stable 6-DOF Haptic Rendering With Inner Sphere Trees,” ASME Paper No. DETC2009-87209.

Seth,
A.
,
Vance,
J. M.
, and
Oliver,
J. H.
, 2007, “
Combining Geometric Constraints With Physics Modeling for Virtual Assembly Using SHARP,” ASME Paper No. DETC2007-34681.

Seth,
A.
,
Vance,
J. M.
, and
Oliver,
J. H.
, 2010, “
Combining Dynamic Modeling With Geometric Constraint Management to Support Low Clearance Virtual Manual Assembly,” ASME J. Mech. Des.,
132(8), p. 081002.

[CrossRef]
Jayaram,
S.
,
Jayaram,
U.
,
Wang,
Y.
,
Tirumali,
H.
,
Lyons,
K.
, and
Hart,
P.
, 1999, “
VADE: A Virtual Assembly Design Environment,” J. Comput. Graphics Appl.,
19(6), pp. 44–50.

[CrossRef]
Wan,
H.
,
Gao,
S.
,
Peng,
Q.
,
Dai,
G.
, and
Zhang,
F.
, 2004, “
MIVAS: A Multi-Modal Immersive Virtual Assembly System,” ASME Paper No. DETC2004-57660.

Tching,
L.
,
Dumont,
G.
, and
Perret,
J.
, 2010, “
Interactive Simulation of CAD Models Assemblies Using Virtual Constraint Guidance,” Int. J. Interact. Des. Manuf.,
4(2), pp. 95–102.

[CrossRef]
Rosenberg,
L. B.
, 1993, “
Virtual Fixtures: Perceptual Tools for Telerobotic Manipulation,” IEEE Virtual Reality Annual International Symposium, Institute of Electrical and Electronics Engineers (IEEE), pp. 76–82.

Katznelson,
Y.
, 2004, An Introduction to Harmonic Analysis, 3rd ed.,
Cambridge University Press,
Cambridge, UK.

Cooley,
J. W.
, and
Tukey,
J.
, 1965, “
An Algorithm for the Machine Calculation of Complex Fourier Series,” Math. Comput.,
19(90), pp. 297–301.

[CrossRef]
Requicha,
A. G.
, 1980, “
Mathematical Models of Rigid Solid Objects,” Production Automation Project, Technical Memo. No. 28, University of Rochester.

Chazal,
F.
, and
Soufflet,
R.
, 2004, “
Stability and Finiteness Properties of Medial Axis and Skeleton,” J. Dyn. Control Syst.,
10(2), pp. 149–170.

[CrossRef]
Klein,
F.
, 2009, “
A New Approach to Point Membership Classification in B-Rep Solids,” Mathematics of Surfaces XIII,
Springer,
Berlin, Heidelberg, pp. 235–250.

Requicha,
A. G.
, 1980, “
Representations of Rigid Solid Objects,” Production Automation Project, Technical Memo. No. 29, University of Rochester.

Schöberl,
J.
, 1997, “
NETGEN: An Advancing Front 2D/3D-Mesh Generator Based on Abstract Rules,” Comput. Visualization Sci.,
1(1), pp. 41–52.

[CrossRef]
Hoff,
K. E., III
,
Culver,
T.
,
Keyser,
J.
,
Lin,
M.
, and
Manocha,
D.
, 1999, “
Fast Computation of Generalized Voronoi Diagrams Using Graphics Hardware,” 26th Annual Conference on Computer Graphics and Interactive Techniques, Association for Computing Machinery (ACM), pp. 277–286.

Shaeling,
B.
, 2014, The Boost C++ Libraries,
XML Press,
Laguna Hills, CA.

Frigo,
M.
, and
Johnson,
S. G.
, 2005, “
The Design and Implementation of FFTW3,” Proc. IEEE,
93(2), pp. 216–231.

[CrossRef]