Yassine,
A.
, and
Braha,
D.
, 2003, “
Complex Concurrent Engineering and the Design Structure Matrix Method,” Concurr. Eng.,
11(3), pp. 165–176.

[CrossRef]
Geis,
A.
,
Husung,
S.
,
Oberänder,
A.
, et al. ., 2015, “
Use of Vectorial Tolerances for Direct Representation and Analysis in CAD-Systems,” Procedia CIRP,
27, pp. 230–240.

[CrossRef]
Desrochers,
A.
, and
Clément,
A.
, 1994, “
A Dimensioning and Tolerancing Assistance Model for CAD/CAM Systems,” Int. J. Adv. Manuf. Technol.,
9(6), pp. 352–361.

[CrossRef]
Clément,
A.
,
Desrochers,
A.
, and
Riviere,
A.
, 1991, *Theory and Practice of 3-D Tolerancing for Assembly*, École de Technologie Supérieure.

Teissandier,
D.
,
Couetard,
Y.
, and
Delos,
V.
, 1999, “
Operations on Polytopes: Application to Tolerance Analysis,” Global Consistency of Tolerances,
Springer, Berlin, pp. 425–434.

Schleich,
B.
,
Anwer,
N.
,
Zhu,
Z.
, Qiao, L., Mathieu, L., and Wartzack, S., 2014, “
Comparative Study on Tolerance Analysis Approaches,” International Symposium on Robust Design (ISoRD'14), Copenhagen, Denmark, Aug., pp. 29–39.

https://hal.archives-ouvertes.fr/hal-01094270/document
Desrochers,
A.
, and
Rivière,
A.
, 1997, “
A Matrix Approach to the Representation of Tolerance Zones and Clearances,” Int. J. Adv. Manuf. Technol.,
13(9), pp. 630–636.

[CrossRef]
Charpentier,
F.
,
Ballu,
A.
, and
Pailhes,
J.
, 2011, “
A Scientific Point of View of a Simple Industrial Tolerancing Process,” Procedia Eng., **21**, p. 10.

Zou,
Z.
, and
Morse,
E. P.
, 2004, “
A Gap-Based Approach to Capture Fitting Conditions for Mechanical Assembly,” Comput-Aided Des.,
36(8), pp. 691–700.

[CrossRef]
Anselmetti,
B.
,
Mejbri,
H.
, and
Mawussi,
K.
, 2003, “
Coupling Experimental Design—Digital Simulation of Junctions for the Development of Complex Tolerance Chains,” Comput. Ind.,
50(3), pp. 277–292.

[CrossRef]
Shen,
Z.
,
Ameta,
G.
,
Shah,
J. J.
, and
Davidson,
J. K.
, 2005, “
A Comparative Study Of Tolerance Analysis Methods,” ASME J. Comput. Inf. Sci. Eng.,
5(3), p. 247.

[CrossRef]
Roy,
U.
, and
Li,
B.
, 1999, “
Representation and Interpretation of Geometric Tolerances for Polyhedral Objects—II: Size, Orientation and Position Tolerances,” Comput-Aided Des.,
31(4), pp. 273–285.

[CrossRef]
Arroyave-Tobón,
S.
,
Teissandier,
D.
, and
Delos,
V.
, 2017, “
Applying Screw Theory for Summing Sets of Constraints in Geometric Tolerancing,” Mech. Mach. Theory,
112, pp. 255–271.

[CrossRef]
Ballu,
A.
,
Mathieu,
L.
, and
Dantan,
J.-Y.
, 2015, “
Formal Language for GeoSpelling,” ASME J. Comput. Inf. Sci. Eng.,
15(2), p. 021009.

[CrossRef]
Mathieu,
L.
, and
Ballu,
A.
, 2003, “
GEOSPELLING: A Common Language for Specification and Verification to Express Method Uncertainty,” Eighth CIRP Seminar on Computer Aided Tolerancing, Charlotte, NC, pp. 28–29.

Zhang,
M.
,
Shi,
Z.
,
Mathieu,
L.
, Nabil, A., and Yang, J., 2015, “
Geometric Product Specification of Gears: The GeoSpelling Perspective,” Procedia CIRP,
27, pp. 90–96.

[CrossRef]
Ballu,
A.
, and
Mathieu,
L.
, 1996, “
Univocal Expression of Functional and Geometrical Tolerances for Design, Manufacturing and Inspection,” Computer-Aided Tolerancing,
F. Kimura
, ed.,
Springer,
Dordrecht, The Netherlands, pp. 31–46.

Anwer,
N.
,
Ballu,
A.
, and
Mathieu,
L.
, 2013, “
The Skin Model, a Comprehensive Geometric Model for Engineering Design,” CIRP Ann. Manuf. Technol.,
62(1), pp. 143–146.

[CrossRef]
Schleich,
B.
,
Anwer,
N.
,
Mathieu,
L.
, and
Wartzack,
S.
, 2014, “
Skin Model Shapes: A New Paradigm Shift for Geometric Variations Modelling in Mechanical Engineering,” Comput-Aided Des.,
50, pp. 1–15.

[CrossRef]
Zhang,
M.
,
Anwer,
N.
,
Stockinger,
A.
, Mathieu, L., and Wartzack, S., 2013, “
Discrete Shape Modeling for Skin Model Representation,” Proc. Inst. Mech. Eng. Part B,
227(5), pp. 672–680.

[CrossRef]
Anwer,
N.
,
Schleich,
B.
,
Mathieu,
L.
, and
Wartzack,
S.
, 2014, “
From Solid Modelling to Skin Model Shapes: Shifting Paradigms in Computer-Aided Tolerancing,” CIRP Ann. Manuf. Technol.,
63(1), pp. 137–140.

[CrossRef]
Schleich,
B.
,
Wartzack,
S.
,
Anwer,
N.
, and
Mathieu,
L.
, 2015, “
Skin Model Shapes: Offering New Potentials for Modelling Product Shape Variability,” ASME Paper No. DETC2015-46701.

Schleich,
B.
,
Anwer,
N.
,
Mathieu,
L.
, and
Wartzack,
S.
, 2016, “
Status and Prospects of Skin Model Shapes for Geometric Variations Management,” Procedia CIRP,
43, pp. 154–159.

[CrossRef]
Zhang,
Z.
,
Zhang,
Z.
,
Jin,
X.
, and
Zhang,
Q.
, 2018, “
A Novel Modelling Method of Geometric Errors for Precision Assembly,” Int. J. Adv. Manuf. Technol.,
94(1–4), pp. 1139–1160.

[CrossRef]
Lalehpour,
A.
, and
Barari,
A.
, 2017, “
Developing Skin Model in Coordinate Metrology Using a Finite Element Method,” Measurement,
109, pp. 149–159.

[CrossRef]
Lacroix,
C.
,
Mathieu,
L.
,
Thiébaut,
F.
, et al. 2015, “
Numerical Process Based on Measuring Data for Gap Prediction of an Assembly,” Procedia CIRP,
27, pp. 97–102.

[CrossRef]
Zhang,
X.
,
Zhang,
H.
,
He,
X.
, and
Xu,
M.
, 2015, “
Fast Evaluation of Minimum Zone Form Errors of Freeform NURBS Surfaces,” Procedia CIRP,
27, pp. 23–28.

[CrossRef]
Franciosa,
P.
,
Gerbino,
S.
, and
Patalano,
S.
, 2011, “
Simulation of Variational Compliant Assemblies With Shape Errors Based on Morphing Mesh Approach,” Int. J. Adv. Manuf. Technol.,
53(1–4), pp. 47–61.

[CrossRef]
Wagersten,
O.
,
Lindau,
B.
,
Lindkvist,
L.
, and
Söderberg,
R.
, 2014, “
Using Morphing Techniques in Early Variation Analysis,” ASME J. Comput. Inf. Sci. Eng.,
14(1), p. 011007.

[CrossRef]
Formosa,
F.
, and
Samper,
S.
, 2007, “
Modal Expression of Form Defects,” Models for Computer Aided Tolerancing in Design and Manufacturing,
Springer, Berlin, pp. 13–22.

Huang,
W.
, and
Ceglarek,
D.
, 2002, “
Mode-Based Decomposition of Part Form Error by Discrete-Cosine-Transform With Implementation to Assembly and Stamping System With Compliant Parts,” CIRP Ann. Manuf. Technol.,
51(1), pp. 21–26.

[CrossRef]
Wilma,
P.
, and
Giovanni,
M.
, 2015, “
Manufacturing Signature for Tolerance Analysis,” ASME J. Comput. Inf. Sci. Eng.,
15(2), p. 021005.

[CrossRef]
Armillotta,
A.
, 2016, “
Tolerance Analysis Considering Form Errors in Planar Datum Features,” Procedia CIRP,
43, pp. 64–69.

[CrossRef]
Bruyère,
J.
,
Dantan,
J.-Y.
,
Bigot,
R.
, and
Martin,
P.
, 2007, “
Statistical Tolerance Analysis of Bevel Gear by Tooth Contact Analysis and Monte Carlo Simulation,” Mech. Mach. Theory,
42(10), pp. 1326–1351.

[CrossRef]
Schleich,
B.
, and
Wartzack,
S.
, 2018, “
Novel Approaches for the Assembly Simulation of Rigid Skin Model Shapes in Tolerance Analysis,” Comput.-Aided Des., **101**, pp. 1–11.

Dantan,
J.-Y.
,
Huang,
Z.
,
Goka,
E.
, Lazhar, H., Alain, E., Nicolas, B., and Mickael, R., 2017, “
Geometrical Variations Management for Additive Manufactured Product,” CIRP Ann. Manuf. Technol., **66**(1), pp. 161–164.

Zhu,
Z.
,
Anwer,
N.
, and
Mathieu,
L.
, 2017, “
Deviation Modeling and Shape Transformation in Design for Additive Manufacturing,” Procedia CIRP,
60, pp. 211–216.

[CrossRef]
Bastani,
K.
,
Barazandeh,
B.
, and
Kong,
Z. J.
, 2017, “
Fault Diagnosis in Multistation Assembly Systems Using Spatially Correlated Bayesian Learning Algorithm,” ASME J. Manuf. Sci. Eng.,
140(3), p. 031003.

[CrossRef]
Zhao,
Z.
,
Li,
B.
,
Zhang,
G.
, Hechun, Y., Wenbo, W., Xin, H., Xiaoshuai, H., Xupeng, C., and Bo, Y., 2017, “
Study on the Evaluation of Cylinder's Global Sizes,” Precis. Eng., **49**, pp. 189–199.

Mailhe,
J.
,
Linares,
J. M.
,
Sprauel,
J. M.
, and
Bourdet,
P.
, 2008, “
Geometrical Checking by Virtual Gauge, Including Measurement Uncertainties,” CIRP Ann. Manuf. Technol.,
57(1), pp. 513–516.

[CrossRef]
Wang,
M.
,
Xi,
L.
, and
Du,
S.
, 2014, “
3D Surface Form Error Evaluation Using High Definition Metrology,” Precis. Eng.,
38(1), pp. 230–236.

[CrossRef]
Groeger,
S.
,
Segel,
F.
,
Uhlmann,
E.
, and
Rosskamp,
S.
, 2018, “
Definition of Edges in Correlation to Abrasive Flow Machining as a Finishing Process,” Surf. Topogr. Metrol. Prop.,

**6**(3), p. 034001.

https://orcid.org/0000-0002-7010-0993
Xingyu,
Y.
, and
Alex,
B.
, 2016, “
Toward an Automatic Generation of Part Models With Form Error,” Procedia CIRP,
43, pp. 23–28.

[CrossRef]
Movahhedy,
M.
,
Gadala,
M. S.
, and
Altintas,
Y.
, 2000, “
Simulation of the Orthogonal Metal Cutting Process Using an Arbitrary Lagrangian–Eulerian Finite-Element Method,” J. Mater. Process Technol.,
103(2), pp. 267–275.

[CrossRef]
Söderberg,
R.
,
Wärmefjord,
K.
,
Carlson,
J. S.
, and
Lindkvist,
L.
, 2017, “
Toward a Digital Twin for Real-Time Geometry Assurance in Individualized Production,” CIRP Ann.,
66(1), pp. 137–140.

[CrossRef]
Sattarpanah Karganroudi,
S.
,
Cuillière,
J.-C.
,
François,
V.
, and
Tahan,
S.-A.
, 2018, ‘
What-If’ Scenarios Towards Virtual Assembly-State Mounting for Non-Rigid Parts Inspection Using Permissible Loads,” Int. J. Adv. Manuf. Technol., **97**(1–4), pp. 353–373.

Forslund,
A.
,
Lorin,
S.
,
Lindkvist,
L.
, Wärmefjord, K., and Söderberg, R., 2017, “
Minimizing Weld Variation Effects Using Permutation Genetic Algorithms and Virtual Locator Trimming,” ASME Paper No. IMECE2017-71310

Li,
B.
,
Cao,
Y.
,
Ye,
X.
, Guan, J., and Yang, J., 2017, “
Multi-Scale Prediction of the Geometrical Deviations of the Surface Finished by Five-Axis Ball-End Milling,” Proc. Inst. Mech. Eng. Part B,
231(10), pp. 1685–1702.

[CrossRef]
Bo,
L.
,
Yanlong,
C.
,
Wenhua,
C.
, and
Jun,
P.
, 2017, “
Geometry Simulation and Evaluation of the Surface Topography in Five-Axis Ball-End Milling,” Int. J. Adv. Manuf. Technol.,
93(5–8), pp. 1651–1667.

[CrossRef]
Altintas,
Y.
,
Kersting,
P.
,
Biermann,
D.
, Budak, E., Denkena, B., and Lazoglu, I., 2014, “
Virtual Process Systems for Part Machining Operations,” CIRP Ann. Manuf. Technol.,
63(2), pp. 585–605.

[CrossRef]
Spence,
A. D.
,
Abrari,
F.
, and
Elbestawi,
M. A.
, 2000, “
Integrated Solid Modeller Based Solutions for Machining,” Comput-Aided Des.,
32(8–9), pp. 553–568.

[CrossRef]
Soori,
M.
,
Arezoo,
B.
, and
Habibi,
M.
, 2014, “
Virtual Machining Considering Dimensional, Geometrical and Tool Deflection Errors in Three-Axis CNC Milling Machines,” J. Manuf. Syst.,
33(4), pp. 498–507.

[CrossRef]
Lin,
Y.
, and
Shen,
Y.-L.
, 2004, “
Enhanced Virtual Machining for Sculptured Surfaces by Integrating Machine Tool Error Models Into NC Machining Simulation,” Int. J. Mach. Tools Manuf.,
44(1), pp. 79–86.

[CrossRef]
Zhang,
M.
,
Anwer,
N.
,
Mathieu,
L.
, and
Zhao,
H.
, 2011, “
A Discrete Geometry Framework for Geometrical Product Specifications,” 21st CIRP Design Conference, pp. 142–148.

Das,
A.
,
Franciosa,
P.
,
Williams,
D.
, and
Ceglarek,
D.
, 2016, “
Physics-Driven Shape Variation Modelling at Early Design Stage,” Procedia CIRP,
41, pp. 1072–1077.

[CrossRef]
Franciosa,
P.
, and
Gerbino,
S.
, 2009, “
Handling Tessellated Free Shape Objects With a Morphing Mesh Procedure in Comsol Multiphysics^{®},” COMSOL Conference, pp. 14–16.

Kingslake,
R.
, and
Shannon,
R. R.
, 1992, “
Basic Wavefront Aberration Theory for Optical Metrology,” Applied Optics and Optical Engineering, Vol.
11,
Academic Press,
New York.

Cao,
Y.
,
Li,
B.
,
Ye,
X.
, Jiayan, G., and Jiangxin, Y., 2015, “
Geometrical Simulation of Multiscale Toleranced Surface With Consideration of the Tolerancing Principle,” ASME J. Comput. Inf. Sci. Eng.,
15(2), p. 021006.

[CrossRef]
Ganti,
S.
, and
Bhushan,
B.
, 1995, “
Generalized Fractal Analysis and Its Applications to Engineering Surfaces,” Wear,
180(1–2), pp. 17–34.

[CrossRef]
Hasegawa,
M.
,
Liu,
J.
,
Okuda,
K.
, and
Nunobiki,
M.
, 1996, “
Calculation of the Fractal Dimensions of Machined Surface Profiles,” Wear,
192(1–2), pp. 40–45.

[CrossRef]
Nguyen,
H. T.
,
Wang,
H.
, and
Hu,
S. J.
, 2014, “
Modeling Cutter Tilt and Cutter-Spindle Stiffness for Machine Condition Monitoring in Face Milling Using High-Definition Surface Metrology,” Int. J. Adv. Manuf. Technol.,
70(5–8), pp. 1323–1335.

[CrossRef]
Mollon,
G.
, and
Zhao,
J.
, 2014, “
3D Generation of Realistic Granular Samples Based on Random Fields Theory and Fourier Shape Descriptors,” Comput. Methods Appl. Mech. Eng.,
279, pp. 46–65.

[CrossRef]
Schleich,
B.
, and
Wartzack,
S.
, 2015, “
Tolerance Analysis of Rotating Mechanism Based on Skin Model Shapes in Discrete Geometry,” Procedia CIRP,
27, pp. 10–15.

[CrossRef]
Schleich,
B.
, and
Wartzack,
S.
, 2015, “
Evaluation of Geometric Tolerances and Generation of Variational Part Representatives for Tolerance Analysis,” Int. J. Adv. Manuf. Technol.,
79(5–8), pp. 959–983.

[CrossRef]
Pacella,
M.
, and
Colosimo,
B. M.
, 2013, “
Different Formulations of Principal Component Analysis for 3D Profiles and Surfaces Modeling,” Procedia CIRP,
12, pp. 474–479.

[CrossRef]
Aguirre,
M. R.
,
Linguraru,
M. G.
,
Marias,
K.
, Ayache, N., Nolte, L.-p., and Ballester, M. A. G., 2007, “
Statistical Shape Analysis Via Principal Factor Analysis,” Fourth IEEE International Symposium on Biomedical Imaging: From Nano to Macro, Arlington, VA, Apr. 12–15, pp. 1216–1219.

Schwarz,
C.
,
Ackert,
P.
, and
Mauermann,
R.
, 2018, “
Principal Component Analysis and Singular Value Decomposition Used for a Numerical Sensitivity Analysis of a Complex Drawn Part,” Int. J. Adv. Manuf. Technol.,
94(5–8), pp. 2255–2265.

[CrossRef]
Raffin,
R.
,
Neveu,
M.
, and
Jaar,
F.
, 2000, “
Curvilinear Displacement of Free-Form-Based Deformation,” Vis. Comput.,
16(1), pp. 38–46.

[CrossRef]
Staten,
M. L.
,
Owen,
S. J.
,
Shontz,
S. M.
, Salinger, A. G., and Coffey, T. S., 2011, “
A Comparison of Mesh Morphing Methods for 3D Shape Optimization,” 20th International Meshing Roundtable, pp. 293–311.

Luo,
C.
,
Franciosa,
P.
,
Ceglarek,
D.
, et al. 2018, “
A Novel Geometric Tolerance Modeling Inspired by Parametric Space Envelope,” IEEE Trans. Autom. Sci. Eng., **15**(3), pp. 1–13.

Pierce,
R. S.
, and
Rosen,
D.
, 2008, “
A Method for Integrating Form Errors Into Geometric Tolerance Analysis,” ASME J. Mech. Des.,
130(1), p. 011002.

[CrossRef]
Pierce,
R. S.
, and
Rosen,
D.
, 2007, “
Simulation of Mating Between Nonanalytic Surfaces Using a Mathematical Programing Formulation,” ASME J. Comput. Inf. Sci. Eng.,
7(4), p. 314.

[CrossRef]
Kiridena,
V. S. B.
, and
Ferreira,
P. M.
, 1994, “
Kinematic Modeling of Quasistatic Errors of Three-Axis Machining Centers,” Int. J. Mach. Tools. Manuf.,
34(1), pp. 85–100.

[CrossRef]
Uddin,
M. S.
,
Ibaraki,
S.
,
Matsubara,
A.
, and
Matsushita,
T.
, 2009, “
Prediction and Compensation of Machining Geometric Errors of Five-Axis Machining Centers With Kinematic Errors,” Precis. Eng.,
33(2), pp. 194–201.

[CrossRef]
Bolle,
R. M.
, and
Vemuri,
B. C.
, 1991, “
On Three-Dimensional Surface Reconstruction Methods,” IEEE Trans. Pattern Anal. Mach. Intell.,
13(1), pp. 1–13.

[CrossRef]
Li,
Z.-L.
,
Tuysuz,
O.
,
Zhu,
L.-M.
, and
Altintas,
Y.
, 2018, “
Surface Form Error Prediction in Five-Axis Flank Milling of Thin-Walled Parts,” Int. J. Mach. Tools Manuf.,
128, pp. 21–32.

[CrossRef]
Wei,
Z. C.
,
Wang,
M. J.
,
Cai,
Y. J.
, Zhu, J. N., and Wang, L., 2013, “
Form Error Estimation in Ball-End Milling of Sculptured Surface With Z-Level Contouring Tool Path,” Int. J. Adv. Manuf. Technol.,
65(1–4), pp. 363–369.

[CrossRef]
Corrado,
A.
,
Polini,
W.
,
Moroni,
G.
, and
Petrò,
S.
, 2016, “
3D Tolerance Analysis With Manufacturing Signature and Operating Conditions,” Procedia CIRP,
43, pp. 130–135.

[CrossRef]
Corrado,
A.
,
Polini,
W.
, and
Moroni,
G.
, 2017, “
Manufacturing Signature and Operating Conditions in a Variational Model for Tolerance Analysis of Rigid Assemblies,” Res. Eng. Des., **28**, p. 529.

Corrado,
A.
,
Polini,
W.
,
Moroni,
G.
, and
Petrò,
S.
, 2018, “
A Variational Model for 3D Tolerance Analysis With Manufacturing Signature and Operating Conditions,” Assem. Autom.,
38(1), pp. 10–19.

[CrossRef]
Corrado,
A.
, and
Polini,
W.
, 2017, “
Manufacturing Signature in Jacobian and Torsor Models for Tolerance Analysis of Rigid Parts,” Robot. Comput.-Integr. Manuf.,
46, pp. 15–24.

[CrossRef]
Homri,
L.
,
Goka,
E.
,
Levasseur,
G.
, and
Dantan,
J.-Y.
, 2017, “
Tolerance Analysis – Form Defects Modeling and Simulation by Modal Decomposition and Optimization,” Comput-Aided Des.,
91, pp. 46–59.

[CrossRef]
Qiao,
L.
,
Wu,
J.
,
Zhu,
Z.
, and
Cui,
Y.
, 2016, “
Approach to the Deviation Representation of Non-Ideal Cylindrical Surfaces Based on the Curvilinear Coordinate System,” Procedia CIRP,
43, pp. 17–22.

[CrossRef]
Song,
S.
,
Wang,
A.
,
Huang,
Q.
, and
Tsung,
F.
, 2014, “
Shape Deviation Modeling for Fused Deposition Modeling Processes,” International Conference on Automation Science and Engineering (CASE), Taipei, Taiwan, Aug. 18–22, pp. 758–763.

Huang,
Q.
,
Nouri,
H.
,
Xu,
K.
, et al. ., 2014, “
Predictive Modeling of Geometric Deviations of 3D Printed Products-A Unified Modeling Approach for Cylindrical and Polygon Shapes,” IEEE International Conference on Automation Science and Engineering (CASE), Taipei, Taiwan, Aug. 18–22, pp. 25–30.

Sabbaghi,
A.
, and
Huang,
Q.
, 2016, “
Predictive Model Building Across Different Process Conditions and Shapes in 3D Printing,” IEEE International Conference on Automation Science and Engineering (CASE), Fort Worth, TX, Aug. 21–25, pp. 774–779.

Zernike,
F.
, 1942, “
Phase Contrast, a New Method for the Microscopic Observation of Transparent Objects,” Physica,
9(7), pp. 686–698.

[CrossRef]
Yao,
J.
,
Anderson,
A.
, and
Rolland,
J. P.
, 2018, “
Point-Cloud Noncontact Metrology of Freeform Optical Surfaces,” Opt Express,
26(8), p. 10242.

[CrossRef] [PubMed]
Schindlbeck,
C.
,
Pape,
C.
, and
Reithmeier,
E.
, 2018, “
Predictor-Corrector Framework for the Sequential Assembly of Optical Systems Based on Wavefront Sensing,” Opt. Express,
26(8), p. 10669.

[CrossRef] [PubMed]
Lê,
H. N.
, 2013, “
Influence des défauts de forme sur le comportement des liaisons: étude expérimentale et théorique,” thesis, Université Sciences et Technologies-Bordeaux I, Bordeaux, France.

Huang,
W.
, and
Kong,
Z.
, 2008, “
Simulation and Integration of Geometric and Rigid Body Kinematics Errors for Assembly Variation Analysis,” J. Manuf. Syst.,
27(1), pp. 36–44.

[CrossRef]
Huang,
W.
,
Liu,
J.
,
Chalivendra,
V.
, et al. ., 2014, “
Statistical Modal Analysis for Variation Characterization and Application in Manufacturing Quality Control,” IIE Trans,
46(5), pp. 497–511.

[CrossRef]
Jbira,
I.
,
Tlija,
M.
,
Louhichi,
B.
, and
Tahan,
A.
, 2017, “
CAD/Tolerancing Integration: Mechanical Assembly With Form Defects,” Adv. Eng. Softw., **114**, pp. 312–324.

Goka,
E.
,
Homri,
L.
,
Beaurepaire,
P.
, and
Dantan,
J.-Y.
, 2017, “
Geometrical Variation Simulation for Assembly With Form Defects,” ASME Paper No. IMECE2017-70118.

Wu,
J.
,
Qiao,
L.
,
Zhu,
Z.
, and
Anwer,
N.
, 2017, “
A Novel Representation Method of Non-Ideal Surface Morphologies and Its Application in Shaft-Hole Sealing Simulation Analysis,” Proc. Inst. Mech. Eng. Part B (epub).

Weersink,
R. A.
,
Chaudhary,
S.
,
Mayo,
K.
, He, J., and Wilson, B. C., 2017, “
Shape-Based Reconstruction for Transrectal Diffuse Optical Tomography Monitoring of Photothermal Focal Therapy of Prostate Cancer: Simulation Studies,” J. Biomed. Opt.,
22(4), p. 045004.

[CrossRef]
Cheung,
C. F.
,
Liu,
M.
,
Leach,
R.
, Feng, X., and Zhao, C., 2018, “
Hierarchical-Information-Based Characterization of Multiscale Structured Surfaces,” CIRP Ann., **67**(1), pp. 539–542.

Bondy,
J. A.
, and
Murty,
U. S. R.
, 1976, Graph Theory With Applications,
American Elsevier Pub,
Co., New York.

Chung,
F. R.
, 1997, Spectral Graph Theory,
American Mathematical Society, Providence, RI.

Ohtake,
Y.
,
Belyaev,
A.
, and
Bogaevski,
I.
, 2001, “
Mesh Regularization and Adaptive Smoothing,” Comput-Aided Des.,
33(11), pp. 789–800.

[CrossRef]
Vallet,
B.
, and
Lévy,
B.
, 2008, “
Spectral Geometry Processing With Manifold Harmonics,” Computer Graphics Forum,
Wiley, Hoboken, NJ, pp. 251–260.

Wang,
H.
,
Lu,
T.
,
Au,
O. K.-C.
, and
Tai,
C.-L.
, 2014, “
Spectral 3D Mesh Segmentation With a Novel Single Segmentation Field,” Graph Models,
76(5), pp. 440–456.

[CrossRef]
Liu,
R.
, and
Zhang,
H.
, 2007, “
Mesh Segmentation Via Spectral Embedding and Contour Analysis,” Computer Graphics Forum,
Wiley, Hoboken, NJ, pp. 385–394.

Zhang,
H.
,
Van Kaick,
O.
, and
Dyer,
R.
, 2010, “
Spectral Mesh Processing-COMPUTER GRAPHICS Forum,” Comput. Graph Forum,
29(6), pp. 1865–1894.

[CrossRef]
Lay,
D. C.
,
Lay,
S. R.
, and
McDonald,
J.
, 2016, Linear Algebra and Its Applications, Fifth Edition,
Pearson,
Boston, MA.

Ballu,
A.
,
Gomes,
R.
,
Mimoso,
P.
, Cristovao, C., and Correia, N., 2017, “
Comparison of Mode Decomposition Methods Tested on Simulated Surfaces,” Advances on Mechanics, Design Engineering and Manufacturing,
Springer, Berlin, pp. 1053–1062.

Ledoux,
Y.
,
Samper,
S.
, and
Grandjean,
J.
, 2016, “
Integrating Form Defects of Mechanical Joints Into the Tolerance Studies,” Advances in Mathematics and Computer Science and Their Applications,
WSEAS Press,
Venice, Italy.

Goic,
G. L.
,
Favrelière,
H.
,
Samper,
S.
, and
Formosa,
F.
, 2011, “
Multi Scale Modal Decomposition of Primary Form, Waviness and Roughness of Surfaces,” Scanning,
33(5), pp. 332–341.

[CrossRef] [PubMed]
Goïc,
G. L.
,
Bigerelle,
M.
,
Samper,
S.
, Favrelière, H., and Pillet, M., 2016, “
Multiscale Roughness Analysis of Engineering Surfaces: A Comparison of Methods for the Investigation of Functional Correlations,” Mech. Syst. Signal Process,
66–67, pp. 437–457.

[CrossRef]
Brient,
A.
,
Laniel,
R.
,
Miroir,
M.
, Le Goic, G., and Sangleboeuf, J. C., 2015, “Multiscale Topography Analysis of Waterjet Pocketing of Silica Glass Surfaces,” 15th International Conference on Metrology and Properties of Engineering Surfaces, Charlotte, NC, Mar.

Guo,
J.
,
Li,
B.
,
Liu,
Z.
, et al. ., 2016, “
Integration of Geometric Variation and Part Deformation Into Variation Propagation of 3-D Assemblies,” Int. J. Prod. Res.,
54(19), pp. 5708–5721.

[CrossRef]
Grandjean,
J.
,
Ledoux,
Y.
,
Samper,
S.
, and
Favrelière,
H.
, 2013, “
Form Errors Impact in a Rotating Plane Surface Assembly,” Procedia CIRP,
10, pp. 178–185.

[CrossRef]
Grandjean,
J.
,
Ledoux,
Y.
, and
Samper,
S.
, 2013, “
On the Role of Form Defects in Assemblies Subject to Local Deformations and Mechanical Loads,” Int. J. Adv. Manuf. Technol.,
65(9–12), pp. 1769–1778.

[CrossRef]
Zeng,
P.
, 2007, Fundamentals of Finite Element Analysis,
Tsinghua University Press,
Beijing, China.

Adler,
R. J.
, and
Taylor,
J. E.
, 2007, Random Fields and Geometry,
Springer Science + Business Media,
New York.

Li,
C.
, and
Der Kiureghian,
A.
, 1993, “
Optimal Discretization of Random Fields,” J. Eng. Mech.,
119(6), pp. 1136–1154.

[CrossRef]
Sudret,
B.
, and
Der Kiureghian,
A.
, 2000, “Stochastic Finite Element Methods and Reliability: A State-of-the-Art Report,”
University of California Berkeley,
Berkeley, CA, Report No. UCB/SEMM-2000/08.

Henke,
R. P.
,
Summerhays,
K. D.
,
Baldwin,
J. M.
, et al. 1999, “
Methods for Evaluation of Systematic Geometric Deviations in Machined Parts and Their Relationships to Process Variables,” Precis. Eng.,
23(4), pp. 273–292.

[CrossRef]
Ballu,
A.
,
Mathieu,
L.
, and
Dantan,
J.-Y.
, 2003, “
Global View of Geometrical Specifications,” Geometric Product Specification and Verification: Integration of Functionality,
Springer, Dordrecht, The Netherlands, pp. 13–24.

ISO, 2011, “
Geometric Product Specification-General Concepts—Part 1: Model for Geometrical Specification and Verification,” International Organization for Standardization, Geneva, Switzerland, Standard No. 17450-1.

Kurokawa,
S.
, and
Ariura,
Y.
, 2005, “
Evaluation of Shot Peened Surfaces Using Characterization Technique of Three-Dimensional Surface Topography,” J. Phys. Conf. Ser.,
13, pp. 9–12.

[CrossRef]
Samper,
S.
,
Adragna,
P.-A.
,
Favreliere,
H.
, and
Pillet,
M.
, 2009, “
Modeling of 2D and 3D Assemblies Taking Into account Form Errors of Plane Surfaces,” ASME J. Comput. Inf. Sci. Eng.,
9(4), p. 041005.

[CrossRef]ISO, 2012, “
Geometrical Product Specifications (GPS)—Surface Texture: Areal—Part 2: Terms, Definitions and Surface Texture Parameters,” International Organization for Standardization, Geneva, Switzerland, Standard No. 25178-2.

Chen,
X.
,
Raja,
J.
, and
Simanapalli,
S.
, 1995, “
Multi-Scale Analysis of Engineering Surfaces,” Int. J. Mach. Tools Manuf., **35**(2), pp. 231–238.