M. Rodgers and K. Thompson, Benefits of Freeform Mirror Surfaces in Optical Design, Proc. ASPE Winter Top, pp.73-78, 2004.

R. Henselmans, The NANOMEFOS non-contact measurement machine for freeform optics, Precision Engineering, vol.35, issue.4, 2009.
DOI : 10.1016/j.precisioneng.2011.04.004

Y. Li and P. Gu, Free-form surface inspection techniques state of the art review, Computer-Aided Design, vol.36, issue.13, pp.1395-1417, 2004.
DOI : 10.1016/j.cad.2004.02.009

E. Savio and L. Dechiffre, An artefact for traceable freeform measurements on coordinate measuring machines, Precision Engineering, vol.26, issue.1, pp.58-68, 2002.
DOI : 10.1016/S0141-6359(01)00098-8

E. Savio, L. De-chiffre, and R. Schmitt, Metrology of freeform shaped parts, CIRP Annals - Manufacturing Technology, vol.56, issue.2, pp.810-835, 2007.
DOI : 10.1016/j.cirp.2007.10.008

M. L. Culpepper, M. V. Kartik, and C. Dibiasio, Design of integrated eccentric mechanisms and exact constraint fixtures for micron-level repeatability and accuracy, Precision Engineering, vol.29, issue.1, pp.65-80, 2005.
DOI : 10.1016/j.precisioneng.2004.05.007

L. Zhu, J. Barhak, V. Srivatsan, and R. Katz, Efficient registration for precision inspection of free-form surfaces, The International Journal of Advanced Manufacturing Technology, vol.18, issue.5, pp.5-6, 2006.
DOI : 10.1007/s00170-005-0370-9

E. M. Bispo and R. B. Fisher, Free-form Surface Matching for Surface Inspection, Proc. 6th IMA Conf. Math. Surfaces, pp.119-136, 1994.

G. Sharp, S. W. Lee, and D. K. Wehe, ICP registration using invariant features, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.24, issue.1, pp.90-102, 2002.
DOI : 10.1109/34.982886

C. F. Cheung, L. Kong, and M. Ren, Measurement and characterization of ultra-precision freeform surfaces using an intrinsic surface feature-based method, Measurement Science and Technology, vol.21, issue.11, p.115109, 2010.
DOI : 10.1088/0957-0233/21/11/115109

H. Nouira, J. Salgado, N. El-hayek, S. Ducourtieux, A. Delvallée et al., Setup of a high-precision profilometer and comparison of tactile and optical, Meas. Sci. Technol, vol.25, 2014.

E. Catmull and J. Clark, Recursively generated B-spline surfaces on arbitrary topological meshes, Computer-Aided Design, vol.10, issue.6, pp.350-355, 1978.
DOI : 10.1016/0010-4485(78)90110-0

M. Eck and H. Hoppe, Automatic reconstruction of B-spline surfaces of arbitrary topological type, Proceedings of the 23rd annual conference on Computer graphics and interactive techniques , SIGGRAPH '96, pp.325-334, 1996.
DOI : 10.1145/237170.237271

Y. Lai, L. Kobbelt, and S. Hu, An incremental approach to feature aligned quad dominant remeshing, Proceedings of the 2008 ACM symposium on Solid and physical modeling , SPM '08, pp.137-145, 2008.
DOI : 10.1145/1364901.1364921

C. Loop and S. Schaefer, Approximating Catmull-Clark subdivision surfaces with bicubic patches, ACM Transactions on Graphics, vol.27, issue.1, 2008.
DOI : 10.1145/1330511.1330519

J. Peters, Patching Catmull-Clark meshes, Proceedings of the 27th annual conference on Computer graphics and interactive techniques , SIGGRAPH '00, pp.255-258, 2000.
DOI : 10.1145/344779.344908

J. Stam, Exact evaluation of Catmull-Clark subdivision surfaces at arbitrary parameter values, Proceedings of the 25th annual conference on Computer graphics and interactive techniques , SIGGRAPH '98, pp.395-404, 1998.
DOI : 10.1145/280814.280945

L. Zhang, R. Zhou, J. Zhu, and X. Wu, Piecewise B-spline Surfaces Fitting to Arbitrary Triangle Meshes, CIRP Annals - Manufacturing Technology, vol.51, issue.1, pp.131-134, 2002.
DOI : 10.1016/S0007-8506(07)61483-8

X. Zhang, H. Zhang, X. He, M. Xu, and X. Jiang, Chebyshev fitting of complex surfaces for precision metrology, Measurement, vol.46, issue.9, pp.3720-3724, 2013.
DOI : 10.1016/j.measurement.2013.04.017

X. Zhang, X. Jiang, and P. Scott, A minimax fitting algorithm for ultra-precision aspheric surfaces, Journal of Physics: Conference Series, vol.311, p.12031, 2011.
DOI : 10.1088/1742-6596/311/1/012031

A. Küng, A. Nicolet, and F. Meli, Virtual CMM method applied to aspherical lens parameters calibration, Proc. 13th Int. Conf. Eur. Soc. Precising Eng, pp.83-86, 2013.

P. Alliez, D. Cohen-steiner, Y. Tong, and M. Desbrun, Voronoi-based Variational Reconstruction of Unoriented Point Sets, Eurographics Symp, pp.39-48, 2007.

Q. Merigot, M. Ovsjanikov, and L. J. Guibas, Voronoi-Based Curvature and Feature Estimation from Point Clouds, IEEE Transactions on Visualization and Computer Graphics, vol.17, issue.6, pp.1-14, 2010.
DOI : 10.1109/TVCG.2010.261

URL : https://hal.archives-ouvertes.fr/inria-00406575

N. J. Mitra, A. Nguyen, and L. Guibas, ESTIMATING SURFACE NORMALS IN NOISY POINT CLOUD DATA, International Journal of Computational Geometry & Applications, vol.14, issue.04n05, pp.261-276, 2004.
DOI : 10.1142/S0218195904001470

D. Ouyang and H. Feng, On the normal vector estimation for point cloud data from smooth surfaces, Computer-Aided Design, vol.37, issue.10, pp.1071-1079, 2005.
DOI : 10.1016/j.cad.2004.11.005

S. Liu and C. C. Wang, Orienting unorganized points for surface reconstruction, Computers & Graphics, vol.34, issue.3, pp.209-218, 2010.
DOI : 10.1016/j.cag.2010.03.003

I. Arbizu and C. Perez, Surface roughness prediction by factorial design of experiments in turning processes, J. Mater. Process. Technol, pp.143-144, 2003.

H. Hansen, K. Carneiro, H. Haitjema, L. Dechiffre, D. Micro et al., Dimensional Micro and Nano Metrology, CIRP Annals - Manufacturing Technology, vol.55, issue.2, pp.721-743, 2006.
DOI : 10.1016/j.cirp.2006.10.005

X. Jiang and D. Whitehouse, Technological shifts in surface metrology, CIRP Ann. - Manuf, Technol, vol.61, issue.2, pp.815-836, 2012.

A. Weckenmann, P. Kraemer, and J. Hoffmann, Manufacturing metrology ? State of the art and prospects, 9th Int. Symp. Meas. Qual. Control, 2007.

T. Arnold, G. Böhm, R. Fechner, J. Meister, A. Nickel et al., Ultra-precision surface finishing by ion beam and plasma jet techniques???status and outlook, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, vol.616, issue.2-3, pp.2-3, 2010.
DOI : 10.1016/j.nima.2009.11.013

Y. Shi, D. Zheng, L. Hu, Y. Wang, and L. Wang, NC polishing of aspheric surfaces under control of constant pressure using a magnetorheological torque servo, The International Journal of Advanced Manufacturing Technology, vol.11, issue.1, pp.1061-1073, 2012.
DOI : 10.1007/s00170-011-3445-9

P. R. Dumas, J. Fleig, G. W. Forbes, D. Golini, W. I. Kordonski et al., Flexible Polishing and metrology solutions for free-form optics, ASPE Proceedings, 2004.

I. Fortmeier, M. Stavridis, A. Wiegmann, M. Schulz, G. B. Baer et al., Results of a Sensitivity Analysis for the Tilted-Wave Interferometer, Work. Adv. Opt. Imaging Metrol, pp.701-706, 2014.
DOI : 10.1007/978-3-642-36359-7_129

X. Jiang, P. Scott, D. Whitehouse, and L. Blunt, Paradigm shifts in surface metrology. Part II. The current shift, Proc. R. Soc. A Math, pp.2071-2099, 2007.
DOI : 10.1098/rspa.2007.1873

A. Weckenmann, G. Peggs, and J. Hoffmann, Probing systems for dimensional micro- and nano-metrology, Measurement Science and Technology, vol.17, issue.3, pp.504-509, 2006.
DOI : 10.1088/0957-0233/17/3/S08

A. Küng, F. Meli, and R. Thalmann, Ultraprecision micro-CMM using a low force 3D touch probe, Measurement Science and Technology, vol.18, issue.2, pp.319-327, 2007.
DOI : 10.1088/0957-0233/18/2/S01

A. Vissière, H. Nouira, M. Damak, O. Gibaru, and J. David, A newly conceived cylinder measuring machine and methods that eliminate the spindle errors, Measurement Science and Technology, vol.23, issue.9, p.94015, 2012.
DOI : 10.1088/0957-0233/23/9/094015

M. Vermeulen, High-Precision 3D-Coordinate Measuring Machine: Design and Prototype-Development, 1999.
DOI : 10.1016/s0007-8506(07)62871-6

URL : http://repository.tue.nl/605134

A. Weckenmann, T. Estler, G. N. Peggs, and D. Mcmurtry, Probing Systems in Dimensional Metrology, CIRP Annals - Manufacturing Technology, vol.53, issue.2, pp.657-684, 2004.
DOI : 10.1016/S0007-8506(07)60034-1

J. Chen and C. Ling, Improving the machine accuracy through machine tool metrology and error correction, The International Journal of Advanced Manufacturing Technology, vol.11, issue.3, pp.198-205, 1996.
DOI : 10.1007/BF01351325

M. Conroy and J. Armstrong, A comparison of surface metrology techniques, Conf. Ser. 13 pp, pp.458-465, 2005.

G. Bönsch and E. Potulski, Measurement of the refractive index of air and comparison with modified Edlén's formulae, Metrologia, p.133, 1998.

I. Malinovsky, A. Titov, J. A. Dutra, H. Belaïdi, R. Dos-santos-franca et al., Toward subnanometer uncertainty in interferometric length measurements of short gauge blocks, Applied Optics, vol.38, issue.1, pp.101-112, 1999.
DOI : 10.1364/AO.38.000101

P. J. Scott and X. Jiang, Freeform surface characterisation: theory and practice, Conf. Ser. 483 pp. 012005, 2014.
DOI : 10.1088/1742-6596/483/1/012005

M. Mccarthy, S. Brown, A. Evenden, and A. Robinson, NPL freeform artefact for verification of non-contact measuring systems, Three-Dimensional Imaging, Interaction, and Measurement, pp.78640-78640, 2011.
DOI : 10.1117/12.876705

W. Khaled, S. Reichling, O. Bruhns, H. Boese, M. Baumann et al., A New Haptic Sensor Actuator System for Virtual Reality Applications in Medicine, Image Comput. Comput. Interv, pp.132-140, 2003.
DOI : 10.1007/978-3-540-39899-8_17

P. Payeur, C. Pasca, A. M. Cretu, and E. M. Petriu, Intelligent Haptic Sensor System for Robotic Manipulation, IEEE Transactions on Instrumentation and Measurement, vol.54, issue.4, pp.1583-1592, 2005.
DOI : 10.1109/TIM.2005.851422

J. Chaves-jacob, J. M. Linarès, and J. M. Sprauel, Increasing of surface quality in friction free-form surfaces of knee prosthesis, CIRP Annals - Manufacturing Technology, vol.60, issue.1, pp.531-534, 2011.
DOI : 10.1016/j.cirp.2011.03.059

URL : https://hal.archives-ouvertes.fr/hal-01437103

S. Marcos, S. Barbero, and I. Jiménez-alfaro, Optical quality and depth-of-field of eyes implanted with spherical and aspheric intraocular lenses, J. Refract. Surg, vol.21, issue.3, pp.223-258, 2005.

N. E. Claytor, D. M. Combs, O. M. Lechuga, J. J. Mader, and J. Udayasankaran, An overview of freeform optics production, Proc. ASPE Winter Top. Meet, 2004.

F. Z. Fang, X. D. Zhang, A. Weckenmann, G. X. Zhang, and C. Evans, Manufacturing and measurement of freeform optics, CIRP Annals - Manufacturing Technology, vol.62, issue.2, pp.823-846, 2013.
DOI : 10.1016/j.cirp.2013.05.003

E. Robert, What is the relevance of asphericity in today's ophthalmic practice ?, Philipp. J. Ophthalmol, vol.36, issue.1, pp.5-6, 2011.

J. E. Makem, H. Ou, and C. G. Armstrong, A virtual inspection framework for precision manufacturing of aerofoil components, Computer-Aided Design, vol.44, issue.9, pp.858-874, 2012.
DOI : 10.1016/j.cad.2012.04.002

R. Schuhmann, Aspheres in Optical Design ? Changes and Limits, 2007.

G. W. Forbes, Shape specification for axially symmetric optical surfaces, Optics Express, vol.15, issue.8, pp.5218-5244, 2007.
DOI : 10.1364/OE.15.005218

G. W. Forbes, C. P. Brophy, . Asphere, and . Asphere, how shall we describe thee?, Opt. Syst. Des, vol.7100, issue.1, pp.710002-710002, 2008.

G. W. Forbes, Effective Characterization of the Nominal Shape of Aspheric Optics, Opt. Des. Eng, 2010.

G. W. Forbes, Characterizing the shape of freeform optics, Optics Express, vol.20, issue.3, pp.2483-99, 2012.
DOI : 10.1364/OE.20.002483

R. J. Campbell and P. J. Flynn, A Survey Of Free-Form Object Representation and Recognition Techniques, Computer Vision and Image Understanding, vol.81, issue.2, pp.166-210, 2001.
DOI : 10.1006/cviu.2000.0889

P. Besl, The Free-Form Surface Matching Problem, Mach. Vis. Three-Dimensional Scenes, pp.25-40, 1990.
DOI : 10.1016/B978-0-12-266722-0.50006-3

K. Garrard, T. Bruegge, J. Hoffman, T. Dow, and A. Sohn, Design tools for freeform optics, Current Developments in Lens Design and Optical Engineering VI, 2005.
DOI : 10.1117/12.617680

A. Lasemi, D. Xue, and P. Gu, Recent development in CNC machining of freeform surfaces: A state-of-the-art review, Computer-Aided Design, vol.42, issue.7, pp.641-654, 2010.
DOI : 10.1016/j.cad.2010.04.002

M. Petitcuenot, L. Pierre, and B. Anselmetti, ISO Specifications of Complex Surfaces: Application on Aerodynamic Profiles, 13th CIRP Conf. Comput. Aided Toler, 2014.
DOI : 10.1016/j.procir.2015.04.037

URL : https://hal.archives-ouvertes.fr/hal-01094158

H. Kim, E. Kim, and B. Song, Diamond turning of large off-axis aspheric mirrors using a fast tool servo with on-machine measurement, Journal of Materials Processing Technology, vol.146, issue.3, pp.349-355, 2004.
DOI : 10.1016/j.jmatprotec.2003.11.028

G. Wanders, Advanced techniques in freeform manufacturing, 2006.

E. Brinksmeier, D. Grimme, and W. Preuss, Generation of Freeform Surfaces by Diamond Machining, Proc. 17th Annu. Meet. ASPE, pp.542-545, 2002.

E. Brinksmeier and L. Autschbach, Ball-end Milling of Free-form Surfaces for Optical Mold Inserts, Proc. ASPE Annu. Meet, pp.4-7, 2004.

M. Weiser, Ion beam figuring for lithography optics, Nucl. Instruments Methods Phys, Res. Sect. B Beam Interact. with Mater. Atoms, vol.267, pp.8-9, 2009.

D. Walker, D. Brooks, R. Freeman, A. King, G. Mccavana et al., <title>First aspheric form and texture results from a production machine embodying the precession process</title>, Optical Manufacturing and Testing IV, pp.267-276, 2001.
DOI : 10.1117/12.453652

C. Brecher, S. Lange, M. Merz, F. Niehaus, C. Wenzel et al., NURBS Based Ultra-Precision Free-Form Machining, CIRP Annals - Manufacturing Technology, vol.55, issue.1, pp.547-550, 2006.
DOI : 10.1016/S0007-8506(07)60479-X

P. F. Bariani, S. Bruschi, and T. Negro, Integrating physical and numerical simulation techniques to design the hot forging process of stainless steel turbine blades, International Journal of Machine Tools and Manufacture, vol.44, issue.9, pp.945-951, 2004.
DOI : 10.1016/j.ijmachtools.2004.01.020

N. S. Qu and Z. Y. Xu, Improving machining accuracy of electrochemical machining blade by optimization of cathode feeding directions, The International Journal of Advanced Manufacturing Technology, vol.62, issue.3, pp.5-8, 2013.
DOI : 10.1007/s00170-013-4943-8

H. Nouira, R. Bergmans, A. Küng, H. Piree, R. Henselmans et al., Spaan, Ultra-high precision CMMs as well as tactile and optical single scanning probes evaluation in dimensional metrology, Int. J. Metrol. Qual. Eng, pp.1-13, 2014.

E. Abbe, Messapparte für physiker, Zeits Fürinstrumenten-Kd. 10 pp, pp.446-448, 1890.

R. Leach, Book: Optical measurement of surface topography, 2011.

D. Whitehouse, Book: Surfaces and their measurement, 2004.

G. B. Baer, J. Schindler, C. Pruss, and W. Osten, Comparison of alignment errors in asphere metrology between an interferometric null-test measurement and a non-null measurement with the tilted-wave-interferometer, Optifab 2013, pp.88840-88840, 2013.
DOI : 10.1117/12.2028756

T. H. Yoon, J. Ye, J. L. Hall, and J. Chartier, Absolute frequency measurement of the iodine-stabilized He-Ne laser at 633??nm, Applied Physics B, vol.72, issue.2, pp.221-226, 2001.
DOI : 10.1007/s003400000473

I. Misumi, S. Gonda, T. Kurosawa, and K. Takamasu, Uncertainty in pitch measurements of one-dimensional grating standards using a nanometrological atomic force microscope, Measurement Science and Technology, vol.14, issue.4, pp.463-471, 2003.
DOI : 10.1088/0957-0233/14/4/309

I. Widdershoven, R. L. Donker, H. , and M. Spaan, Realization and calibration of the "Isara 400" ultra-precision CMM, Conf. Ser. 311 pp. 012002, 2011.
DOI : 10.1088/1742-6596/311/1/012002

L. Cacace, Development of a nanometer accuracy non-contact probe for NANOMEFOS, 2006.

A. Vissière, H. Nouira, M. Damak, O. Gibaru, and J. David, Concept and architecture of a new apparatus for cylindrical form measurement with a nanometric level of accuracy, Measurement Science and Technology, vol.23, issue.9, p.2012
DOI : 10.1088/0957-0233/23/9/094014

J. B. Bryan and D. L. Carter, Design of a new error-corrected co-ordinate measuring machine, Precision Engineering, vol.1, issue.3, pp.125-128, 1979.
DOI : 10.1016/0141-6359(79)90036-9

A. Vissière, Mesure de cylindricité de très haute exactitude: Développement d'une nouvelle machine de référence, Arts et Métiers ParisTech, 2013.

G. Baer, C. Pruss, J. Schindler, and W. Osten, The Tilted Wave Interferometer (TWI): A quick and flexible approach to measure aspheric and freeform surfaces, 2013.

G. Baer, J. Schindler, C. Pruss, and W. Osten, Measurement of Aspheres and Free-Form Surfaces with the Tilted-Wave-Interferometer, pp.87-95, 2014.
DOI : 10.1007/978-3-642-36359-7_10

G. B. Baer, C. Pruss, and W. Osten, Correction of misalignment introduced aberration in non-null test measurements of free-form surfaces, Journal of the European Optical Society: Rapid Publications, vol.8, pp.1-5, 2013.
DOI : 10.2971/jeos.2013.13074

V. Zelený and V. Stejskal, The most recent ways of CMM calibration, in: XVI IMEKO World Congr, pp.2-7, 2000.

R. Thalmann, A New High Precision Length Measuring Machine, in: 8th Int, Congr. Metrol, pp.1-4, 1997.

D. Flack, Measurement Good Practice Guide No. 40-43, 2001.

D. Vaissiere, Métrologie tridimensionnelle des états de surface par microscopie confocale à champ étendu, 2003.

J. Charron, Book: Mesures sans contact, Méthodes optiques (partie 1), CETIM, 1999.

H. Nouira, N. El-hayek, X. Yuan, and N. Anwer, Characterization of the main error sources of chromatic confocal probes for dimensional measurement, Measurement Science and Technology, vol.25, issue.4, 2014.
DOI : 10.1088/0957-0233/25/4/044011

H. Nouira, N. El-hayek, X. Yuan, N. Anwer, and J. Salgado, Metrological characterization of optical confocal sensors measurements (20 and 350 travel ranges), Journal of Physics: Conference Series, vol.483, issue.1, p.12015, 2014.
DOI : 10.1088/1742-6596/483/1/012015

W. Black and W. Carr, Application of a Differential Interferometer to the Measurement of Heat Transfer Coefficients, Review of Scientific Instruments, vol.42, issue.3, pp.337-340, 1971.
DOI : 10.1063/1.1685088

N. El-hayek, H. Nouira, N. Anwer, O. Gibaru, and M. Damak, Comparison of tactile and chromatic confocal measurements of aspherical lenses for form metrology, Int. J. Precis. Engineeing Manuf, vol.15, issue.5, pp.821-829, 2014.

N. El-hayek, N. Anwer, H. Nouira, O. Gibaru, M. Damak et al., 3D Measurement and Characterization of Ultra-precision Aspheric Surfaces, 13th CIRP Conf. Comput. Aided Toler, 2014.
DOI : 10.1016/j.procir.2015.04.041

J. M. Sprauel, J. M. Linarès, J. Bachmann, and P. Bourdet, Uncertainties in CMM Measurements, Control of ISO Specifications, CIRP Annals - Manufacturing Technology, vol.52, issue.1, pp.423-426, 2003.
DOI : 10.1016/S0007-8506(07)60616-7

URL : https://hal.archives-ouvertes.fr/hal-01408960

C. M. Shakarji and V. Srinivasan, Theory and Algorithms for Weighted Total Least-Squares Fitting of Lines, Planes, and Parallel Planes to Support Tolerancing Standards, Journal of Computing and Information Science in Engineering, vol.13, issue.3, p.31008, 2013.
DOI : 10.1115/1.4024854

G. Lukacs, R. R. Martin, and A. D. Marshall, Faithful least-squares fitting of spheres, cylinders, cones and tori for reliable segmentation, Proc. 5th Eur. Conf. Comput. Vis, pp.671-686, 1998.
DOI : 10.1007/BFb0055697

C. F. Cheung, H. Li, L. Kong, W. Lee, and S. To, Measuring ultra-precision freeform surfaces using a robust form characterization method, Measurement Science and Technology, vol.17, issue.3, pp.488-494, 2006.
DOI : 10.1088/0957-0233/17/3/S05

H. Aceves-campos, Profile Identification of Aspheric Lenses, Applied Optics, vol.37, issue.34, pp.8149-8150, 1998.
DOI : 10.1364/AO.37.008149

Z. Chen, Z. Guo, Q. Mi, Z. Yang, and R. Bai, Research of fitting algorithm for coefficients of rotational symmetry aspheric lens, 4th International Symposium on Advanced Optical Manufacturing and Testing Technologies: Optical Test and Measurement Technology and Equipment, 2009.
DOI : 10.1117/12.833085

W. Sun, J. W. Mcbride, and M. Hill, A new approach to characterising aspheric surfaces, Precision Engineering, vol.34, issue.1, pp.171-179, 2010.
DOI : 10.1016/j.precisioneng.2009.05.005

Z. Zhang, Parameter estimation techniques: a tutorial with application to conic fitting, Image and Vision Computing, vol.15, issue.1, pp.59-76, 1997.
DOI : 10.1016/S0262-8856(96)01112-2

URL : https://hal.archives-ouvertes.fr/inria-00074015

H. Park, A solution for NURBS modelling in aspheric lens manufacture, The International Journal of Advanced Manufacturing Technology, vol.23, issue.1-2, pp.1-10, 2004.
DOI : 10.1007/s00170-002-1518-5

N. El-hayek, H. Nouira, N. Anwer, M. Damak, and O. Gibaru, A new method for aspherical surface fitting with large-volume datasets, Precision Engineering, vol.38, issue.4, pp.935-947, 2014.
DOI : 10.1016/j.precisioneng.2014.06.004

URL : https://hal.archives-ouvertes.fr/hal-01069743

C. M. Shakarji, Least-squares fitting algorithms of the NIST algorithm testing system, Journal of Research of the National Institute of Standards and Technology, vol.103, issue.6, p.633, 1998.
DOI : 10.6028/jres.103.043

K. Pulli, Multiview registration for large data sets, Second International Conference on 3-D Digital Imaging and Modeling (Cat. No.PR00062), pp.160-168, 1999.
DOI : 10.1109/IM.1999.805346

S. Ahn, Book: Least Squares Orthogonal Distance Fitting of Curves and Surfaces in Space, 2004.

V. Srinivasan, Computational Metrology for the Design and Manufacture of Product Geometry: A Classification and Synthesis, Journal of Computing and Information Science in Engineering, vol.7, issue.1, pp.3-9, 2007.
DOI : 10.1115/1.2424246

S. Rusinkiewicz and M. Levoy, Efficient variants of the ICP algorithm, Proceedings Third International Conference on 3-D Digital Imaging and Modeling, pp.145-152, 2001.
DOI : 10.1109/IM.2001.924423

F. Pomerleau, F. Colas, R. Siegwart, and S. Magnenat, Comparing ICP variants on real-world data sets, Autonomous Robots, vol.25, issue.3, pp.133-148, 2013.
DOI : 10.1007/s10514-013-9327-2

URL : https://hal.archives-ouvertes.fr/hal-01143458

P. Besl and N. Mckay, A method for registration of 3-D shapes, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.14, issue.2, pp.239-256, 1992.
DOI : 10.1109/34.121791

K. Borgwardt, Book: The Simplex Method -Algorithms and Combinatorics, 1987.

P. Lancaster, Error analysis for the Newton-Raphson method, Numerische Mathematik, vol.9, issue.1, pp.55-68, 1966.
DOI : 10.1007/BF02165230

E. Süli and D. Mayers, Book: An Introduction to Numerical Analysis, 2003.

M. K. Transtrum and J. P. Sethna, Improvements to the Levenberg-Marquardt algorithm for nonlinear least-squares minimization, arXiv Prepr, 2012.

J. Moré, The Levenberg-Marquardt algorithm: Implementation and theory, Numer. Anal. Lect. Notes Math, vol.11, pp.105-116, 1978.
DOI : 10.1137/0111030

X. Jiang, X. Zhang, and P. Scott, Template matching of freeform surfaces based on orthogonal distance fitting for precision metrology, Measurement Science and Technology, vol.21, issue.4, p.45101, 2010.
DOI : 10.1088/0957-0233/21/4/045101

P. Halmos, What Does the Spectral Theorem Say?, The American Mathematical Monthly, vol.70, issue.3, pp.241-247, 1963.
DOI : 10.2307/2313117

T. Speer, M. Kuppe, and J. Hoschek, Global reparametrization for curve approximation, Computer Aided Geometric Design, vol.15, issue.9, pp.869-877, 1998.
DOI : 10.1016/S0167-8396(98)00024-7

T. Cormen, C. Leiserson, R. Rivest, and C. Stein, Book: Introduction to Algorithms, 2009.

M. Greenspan and M. Yurick, Approximate K-D tree search for efficient ICP, Fourth International Conference on 3-D Digital Imaging and Modeling, 2003. 3DIM 2003. Proceedings., pp.442-448, 2003.
DOI : 10.1109/IM.2003.1240280

A. Nuchter, K. Lingemann, and J. Hertzberg, Cached k-d tree search for ICP algorithms, Sixth International Conference on 3-D Digital Imaging and Modeling (3DIM 2007), pp.419-426, 2007.
DOI : 10.1109/3DIM.2007.15

M. Walker, L. Shao, and R. Volz, Estimating 3-D location parameters using dual number quaternions, CVGIP: Image Understanding, vol.54, issue.3, pp.358-367, 1991.
DOI : 10.1016/1049-9660(91)90036-O

K. Arun, T. Huang, and S. Blostein, Least-Squares Fitting of Two 3-D Point Sets, Pattern Anal, Mach. Intell, vol.9, issue.5, pp.698-700, 1987.

A. Fitzgibborn, Robust registration of 2D and 3D point sets, Image and Vision Computing, vol.21, issue.13-14, pp.1145-1153, 2001.
DOI : 10.1016/j.imavis.2003.09.004

H. Liu, J. Yan, and D. Zhang, Three-dimensional surface registration: A neural network strategy, Neurocomputing, vol.70, issue.1-3, pp.597-602, 2006.
DOI : 10.1016/j.neucom.2006.04.004

S. Park and M. Subbarao, An accurate and fast point-to-plane registration technique, Pattern Recognition Letters, vol.24, issue.16, pp.2967-2976, 2003.
DOI : 10.1016/S0167-8655(03)00157-0

N. El-hayek, H. Nouira, N. Anwer, M. Damak, and O. Gibaru, Reconstruction of freeform surfaces for metrology, Journal of Physics: Conference Series, vol.483, issue.1, p.12003, 2014.
DOI : 10.1088/1742-6596/483/1/012003

URL : https://hal.archives-ouvertes.fr/hal-01069726

J. Nocedal and S. Wright, Book: Numerical optimization, 2006.

W. Zheng, P. Bo, Y. Liu, and W. Wang, Fast B-spline curve fitting by L-BFGS, Computer Aided Geometric Design, vol.29, issue.7, pp.448-462, 2012.
DOI : 10.1016/j.cagd.2012.03.004

L. Dong and J. , On the Limited Memory BFGS method for large scale Optimization, Math. Program, vol.45, pp.503-528, 1989.

Y. Lin, K. Damodharan, and C. M. Shakarji, Standardised Reference Data Sets Generation for Coordinate Measuring Machine (CMM) Software Assessment, The International Journal of Advanced Manufacturing Technology, vol.18, issue.11, pp.819-830, 2001.
DOI : 10.1007/s001700170007

E. Marsh, Book, Journal of Nutrition Education, vol.16, issue.1, 2010.
DOI : 10.1016/S0022-3182(84)80070-9

G. Davis, J. Roblee, and A. Hedges, Comparison of freeform manufacturing techniques in the production of monolithic lens arrays, Optical Manufacturing and Testing VIII, p.742605, 2009.
DOI : 10.1117/12.824451.3

N. El-hayek, N. Anwer, H. Nouira, M. Damak, and O. Gibaru, Characterization of Ultra-precise aspherical surfaces using Forbes equation, Proc. Jt. Conf. Mech, 2014.

W. Ma and J. Kruth, NURBS curve and surface fitting for reverse engineering, The International Journal of Advanced Manufacturing Technology, vol.21, issue.6, pp.918-927, 1998.
DOI : 10.1007/BF01179082

H. Hoppe, T. Derose, T. Duchamp, J. Mcdonald, and W. Stuetzle, Surface reconstruction from unorganized points, ACM SIGGRAPH Computer Graphics, vol.26, issue.2, pp.71-78, 1992.
DOI : 10.1145/142920.134011

H. Edelsbrunner, Surface Reconstruction by Wrapping Finite Sets in Space, Discrete Comput. Geom, vol.25, pp.379-404, 2003.
DOI : 10.1007/978-3-642-55566-4_17

N. Amenta, S. Choi, T. K. Dey, and N. Leekha, A simple algorithm for homeomorphic surface reconstruction, Proc. Sixt. Annu. Symp. Comput. Geom. -SCG '00, pp.213-222, 2000.

N. Amenta and M. Bern, The Crust and the ? -Skeleton : Combinatorial Curve Reconstruction, Graph. Model Image Process, pp.125-135, 1998.

F. Cazals and J. Giesen, Delaunay Triangulation Based Surface Reconstruction, 2004.
DOI : 10.1007/978-3-540-33259-6_6

URL : https://hal.archives-ouvertes.fr/inria-00070609

R. Chaine, A geometric convection approach of 3-D reconstruction, Eurographics Symp. Geom. Process., Eurographics Association, pp.218-229, 2003.
URL : https://hal.archives-ouvertes.fr/inria-00071898

T. K. Dey, J. Giesen, and J. Hudson, Delaunay based shape reconstruction from large data, Proceedings IEEE 2001 Symposium on Parallel and Large-Data Visualization and Graphics (Cat. No.01EX520), pp.19-146, 2001.
DOI : 10.1109/PVGS.2001.964399

H. Zhao, S. Osher, and R. Fedkiw, Fast Surface Reconstruction Using the Level Set Method, Proc. IEEE Work, pp.194-201, 2001.

G. Moore, The evolution of the concept of homeomorphism, Historia Mathematica, vol.34, issue.3, pp.333-343, 2007.
DOI : 10.1016/j.hm.2006.07.006

R. Dyer, H. Zhang, and M. Torsten, A survey of Delaunay structures for surface representation, 2009.

T. K. Dey and W. Zhao, Approximate medial axis as a Voronoi subcomplex, Computer-Aided Design, vol.36, issue.2, pp.195-202, 2004.
DOI : 10.1016/S0010-4485(03)00061-7

N. Amenta, M. Bern, and M. Kamvysselis, A new Voronoi-based surface reconstruction algorithm, Proceedings of the 25th annual conference on Computer graphics and interactive techniques , SIGGRAPH '98, pp.415-421, 1998.
DOI : 10.1145/280814.280947

T. K. Dey, Book: Curve and Surface Reconstruction: Algorithms with Mathematical Analysis, 2007.

L. Scharf, Computing the Hausdorff distance between sets of curves, 2003.

F. Razafindrazaka, Delaunay Triangulation Algorithm and Application to Terrain Generation, 2009.

H. Edelsbrunner, Triangulations and meshes in computational geometry, Acta Numer, pp.1-81, 2000.

H. Edelsbrunner and E. P. Mücke, Three-dimensional alpha shapes, ACM Transactions on Graphics, vol.13, issue.1, pp.43-72, 1994.
DOI : 10.1145/174462.156635

F. Hurtado, M. Noy, and J. Urrutia, Flipping Edges in Triangulations, Discrete & Computational Geometry, vol.22, issue.3, pp.333-346, 1999.
DOI : 10.1007/PL00009464

N. Salman, From 3D point clouds to feature preserving meshes, 2011.
URL : https://hal.archives-ouvertes.fr/tel-00536984

S. Funke and E. A. Ramos, Smooth-Surface Reconstruction in Near-Linear Time, SODA '02 Proc. Thirteen. Annu. ACM-SIAM Symp. Discret. Algorithms, pp.781-790, 2000.

D. Attali, J. Boissonnat, and A. Lieutier, Complexity of the delaunay triangulation of points on surfaces the smooth case, Proceedings of the nineteenth conference on Computational geometry , SCG '03, pp.201-210, 2003.
DOI : 10.1145/777792.777823

T. K. Dey, S. Funke, and E. A. Ramos, Surface Reconstruction in Almost Linear Time under Locally Uniform Sampling, EuroGraphics Work, pp.129-132, 2001.

D. Freedman, An incremental algorithm for reconstruction of surfaces of arbitrary codimension, Computational Geometry, vol.36, issue.2, pp.106-116, 2007.
DOI : 10.1016/j.comgeo.2006.05.004

J. Boissonnat, Geometric structures for three-dimensional shape representation, ACM Transactions on Graphics, vol.3, issue.4, pp.266-286, 1984.
DOI : 10.1145/357346.357349

F. Cazals, J. Giesen, M. Pauly, and A. Zomorodian, Conformal alpha shapes, Proceedings Eurographics/IEEE VGTC Symposium Point-Based Graphics, 2005., pp.55-61, 2005.
DOI : 10.1109/PBG.2005.194064

F. Bernardini, J. Mittleman, H. Rushmeier, C. Silva, and G. Taubin, The ball-pivoting algorithm for surface reconstruction, IEEE Transactions on Visualization and Computer Graphics, vol.5, issue.4, pp.349-359, 1999.
DOI : 10.1109/2945.817351

. Meshlab, available: http://meshlab.sourceforge.net, 2014.

N. Amenta and M. Bern, Surface Reconstruction by Voronoi Filtering, Discrete & Computational Geometry, vol.22, issue.4, pp.481-504, 1999.
DOI : 10.1007/PL00009475

N. Amenta, S. Choi, and R. Kolluri, The power crust, unions of balls, and the medial axis transform, Computational Geometry, vol.19, issue.2-3, pp.127-153, 2001.
DOI : 10.1016/S0925-7721(01)00017-7

T. K. Dey and S. Goswami, Tight cocone, Proceedings of the eighth ACM symposium on Solid modeling and applications , SM '03, pp.127-134, 2003.
DOI : 10.1145/781606.781627

T. K. Dey, R. Dyer, and L. Wang, Localized Cocone surface reconstruction, Computers & Graphics, vol.35, issue.3, pp.483-491, 2011.
DOI : 10.1016/j.cag.2011.03.014

T. K. Dey and S. Goswami, Provable surface reconstruction from noisy samples, Computational Geometry, vol.35, issue.1-2, pp.124-141, 2006.
DOI : 10.1016/j.comgeo.2005.10.006

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

D. Meagher and . Book, Octree Encoding: a New Technique for the Representation, Manipulation and Display of Arbitrary 3-D Objects by Computer, 1980.

J. Boissonnat and F. Cazals, Smooth surface reconstruction via natural neighbour interpolation of distance functions, Computational Geometry, vol.22, issue.1-3, pp.185-203, 2002.
DOI : 10.1016/S0925-7721(01)00048-7

URL : https://hal.archives-ouvertes.fr/inria-00072662

R. Sibson, A vector identity for the Dirichlet tesselation, Math. Proc. Cambridge Philos. Soc, pp.151-155, 1979.

R. Allègre, R. Chaine, and S. Akkouche, A flexible framework for surface reconstruction from large point sets, Computers & Graphics, vol.31, issue.2, pp.190-204, 2007.
DOI : 10.1016/j.cag.2006.11.013

E. A. Ramos and B. Sadri, Geometric and Topological Guarantees for the Wrap Reconstruction Algorithm, Proc. 18th Annu. ACM-SIAM Symp, pp.1086-1095, 2007.

J. Giesen and M. John, The flow complex: A data structure for geometric modeling, Computational Geometry, vol.39, issue.3, pp.178-190, 2008.
DOI : 10.1016/j.comgeo.2007.01.002

R. Edgeworth and R. G. Wilhelm, Adaptive sampling for coordinate metrology, Precision Engineering, vol.23, issue.3, pp.144-154, 1999.
DOI : 10.1016/S0141-6359(99)00004-5

S. M. Obeidat and S. Raman, An intelligent sampling method for inspecting free-form surfaces, The International Journal of Advanced Manufacturing Technology, vol.40, issue.11, pp.11-12, 2008.
DOI : 10.1007/s00170-008-1427-3

J. Wang, X. Jiang, and L. Blunt, Simulation of Adaptive Sampling in Profile Measurement for Structured Surfaces, Proc. Comput, pp.48-53, 2010.

A. Weckenmann, H. Eitzert, M. Garmer, and H. Webert, Functionality-oriented evaluation and sampling strategy in coordinate metrology, Precision Engineering, vol.17, issue.4, pp.244-252, 1995.
DOI : 10.1016/0141-6359(94)00020-Z

G. Lee, J. Mou, and Y. Shen, Sampling strategy design for dimensional measurement of geometric features using coordinate measuring machine, International Journal of Machine Tools and Manufacture, vol.37, issue.7, pp.917-934, 1997.
DOI : 10.1016/S0890-6955(96)00096-X

J. C. Carr, R. K. Beatson, J. B. Cherrie, T. J. Mitchell, W. R. Fright et al., Reconstruction and representation of 3D objects with radial basis functions, Proceedings of the 28th annual conference on Computer graphics and interactive techniques , SIGGRAPH '01, pp.67-76, 2001.
DOI : 10.1145/383259.383266

Y. Ohtake, A. Belyaev, M. Alexa, G. Turk, and H. Seidel, Multi-level partition of unity implicits, ACM Transactions on Graphics, vol.22, issue.3, pp.463-470, 2003.
DOI : 10.1145/882262.882293

M. Kazhdan, M. Bolitho, and H. Hoppe, Poisson Surface Reconstruction, Proc. Fourth Eurographics Symp. Geom. Process, 2006.

P. Mullen, F. De-goes, M. Desbrun, D. Cohen-steiner, and P. Alliez, Signing the Unsigned: Robust Surface Reconstruction from Raw Pointsets, Computer Graphics Forum, vol.2005, issue.5, pp.1733-1741, 2010.
DOI : 10.1111/j.1467-8659.2010.01782.x

URL : https://hal.archives-ouvertes.fr/inria-00502473

J. Bloomenthal and B. , Book: Introduction to Implicit Surfaces, 1997.

S. Liu and C. Wang, Quasi-interpolation for surface reconstruction from scattered data with radial basis function, Computer Aided Geometric Design, vol.29, issue.7, pp.435-447, 2012.
DOI : 10.1016/j.cagd.2012.03.011

G. Wyvill, C. Mcpheeters, and B. , Data structure for soft objects, pp.227-234, 1986.

P. Ning and J. Bloomenthal, An evaluation of implicit surface tilers, IEEE Computer Graphics and Applications, vol.13, issue.6, pp.33-41, 1993.
DOI : 10.1109/38.252552

D. Dobkin, S. Levy, W. Thurston, and A. Wilks, Contour tracing by piecewise linear approximations, ACM Transactions on Graphics, vol.9, issue.4, pp.389-423, 1990.
DOI : 10.1145/88560.88575

J. Sethian, A fast marching level set method for monotonically advancing fronts., Proc. Natl. Acad. Sci, pp.1591-1595, 1996.
DOI : 10.1073/pnas.93.4.1591

J. Sethian, Book: Fast marching methods and level set methods for propagating interfaces, 1999.

M. Kass, A. Witkin, and T. Demetri, Snakes: Active contour models, International Journal of Computer Vision, vol.5, issue.6035, pp.321-331, 1988.
DOI : 10.1007/BF00133570

H. Pottmann, S. Leopoldseder, and M. Hofer, Approximation with active B-spline curves and surfaces, 10th Pacific Conf, Comput. Graph. Appl. pp, pp.8-25, 2002.

J. Hoschek, F. Schneider, and F. Wassum, Optimal approximate conversion of spline surfaces, Computer Aided Geometric Design, vol.6, issue.4, pp.293-306, 1989.
DOI : 10.1016/0167-8396(89)90030-7

Y. Kineri, M. Wang, H. Lin, and T. Maekawa, -spline surface fitting by iterative geometric interpolation/approximation algorithms, Computer-Aided Design, vol.44, issue.7, pp.697-708, 2012.
DOI : 10.1016/j.cad.2012.02.011

W. Ma and J. Kruth, Parameterization of randomly measured points for least squares fitting of B-spline curves and surfaces, Computer-Aided Design, vol.27, issue.9, pp.663-675, 1995.
DOI : 10.1016/0010-4485(94)00018-9

H. Park, Choosing nodes and knots in closed B-spline curve interpolation to point data, Computer-Aided Design, vol.33, issue.13, pp.967-974, 2001.
DOI : 10.1016/S0010-4485(00)00133-0

W. Wang, H. Pottmann, and Y. Liu, Fitting B-Spline Curves to Point Clouds by Squared Distance Minimization, 2004.

P. Azariadis, Parameterization of clouds of unorganized points using dynamic base surfaces, Computer-Aided Design, vol.36, issue.7, pp.607-623, 2004.
DOI : 10.1016/S0010-4485(03)00138-6

H. D. Minh and A. B. Forbes, New Method for free-form surface fitting in precision metrology, in: XX IMEKO World Congr, Metrol. Green Growth

H. Yang, W. Wang, and J. Sun, Control point adjustment for B-spline curve approximation, Computer-Aided Design, vol.36, issue.7, pp.639-652, 2004.
DOI : 10.1016/S0010-4485(03)00140-4

E. Cohen, T. Lyche, and R. Riesenfeld, Discrete B-splines and subdivision techniques in computer-aided geometric design and computer graphics, Computer Graphics and Image Processing, vol.14, issue.2, pp.87-111, 1980.
DOI : 10.1016/0146-664X(80)90040-4

J. L. Bentley, Multidimensional binary search trees used for associative searching, Communications of the ACM, vol.18, issue.9, pp.509-517, 1975.
DOI : 10.1145/361002.361007

K. Koch, Uncertainty of NURBS surface fit by Monte Carlo simulations, Journal of Applied Geodesy, vol.3, issue.4, pp.239-247, 2009.
DOI : 10.1515/JAG.2009.024