N. Amenta, S. Choi, and R. K. Kolluri, The power crust, Proceedings of the sixth ACM symposium on Solid modeling and applications , SMA '01, pp.249-266, 2001.
DOI : 10.1145/376957.376986

L. Barthe, N. A. Dodgson, M. A. Sabin, B. Wyvill, and V. Gaildrat, Two-dimensional Potential Fields for Advanced Implicit Modeling Operators, Computer Graphics Forum, vol.19, issue.3, pp.23-33, 2003.
DOI : 10.1111/1467-8659.00530

B. G. Batchelor, HIERARCHICAL SHAPE DESCRIPTION BASED UPON CONVEX HULLS OF CONCAVITIES, Journal of Cybernetics, vol.4, issue.1-3, pp.205-210, 1980.
DOI : 10.1080/01969728008927632

P. Benko, G. Kos, T. Varady, L. Andor, and R. Martin, Constrained fitting in reverse engineering, Computer Aided Geometric Design, vol.19, issue.3, pp.173-205, 2002.
DOI : 10.1016/S0167-8396(01)00085-1

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.7.1307

P. Benko and T. Varady, Direct segmentation of smooth, multiple point regions, Geometric Modeling and Processing. Theory and Applications. GMP 2002. Proceedings, pp.169-178, 2002.
DOI : 10.1109/GMAP.2002.1027508

S. Bhashyam, K. H. Shin, and D. Dutta, An integrated CAD system for design of heterogeneous objects, Rapid Prototyping Journal, vol.6, issue.2, pp.119-135, 2000.
DOI : 10.1108/13552540010323547

A. Biswas and V. Shapiro, Approximate distance fields with non-vanishing gradients, Graphical Models, vol.66, issue.3, pp.133-159, 2004.
DOI : 10.1016/j.gmod.2004.01.003

A. Biswas, V. Shapiro, and I. Tsukanov, Heterogeneous material modeling with distance fields, Computer Aided Geometric Design, vol.21, issue.3, pp.215-242, 2004.
DOI : 10.1016/j.cagd.2003.08.002

J. Blinn, A Generalization of Algebraic Surface Drawing, ACM Transactions on Graphics, vol.1, issue.3, pp.235-256, 1982.
DOI : 10.1145/357306.357310

J. Bloomenthal, Polygonization of implicit surfaces, Computer Aided Geometric Design, vol.5, issue.4, pp.341-355, 1988.
DOI : 10.1016/0167-8396(88)90013-1

J. Bloomenthal, C. Bajaj, J. Blinn, M. Cani-gascuel, A. Rockwood et al., Introduction to implicit surfaces, 1997.

A. Bowyer, SvLis ? Introduction and User Manual, Information Geometers, 1995.

D. E. Breen and R. T. Whitaker, A level-set approach for the metamorphosis of solid models, IEEE Transactions on Visualization and Computer Graphics, vol.7, issue.2, pp.173-192, 2001.
DOI : 10.1109/2945.928169

P. Brunet and I. Navazo, Solid representation and operation using extended octrees, ACM Transactions on Graphics, vol.9, issue.2, pp.170-197, 1990.
DOI : 10.1145/78956.78959

S. F. Buchele and R. H. Crawford, Three-dimensional halfspace constructive solid geometry tree construction from implicit boundary representations, Computer-Aided Design, vol.36, issue.11, pp.1063-1073, 2004.
DOI : 10.1016/j.cad.2004.01.006

F. Cazals and M. Pouget, Estimating differential quantities using polynomial fitting of osculating jets, Computer Aided Geometric Design, vol.22, issue.2, pp.121-146, 2005.
DOI : 10.1016/j.cagd.2004.09.004

URL : https://hal.archives-ouvertes.fr/hal-00103047

K. Chen and X. Feng, Computer-aided design method for the components made of heterogeneous materials, Computer-Aided Design, vol.35, issue.5, pp.453-466, 2003.
DOI : 10.1016/S0010-4485(02)00069-6

L. Chevalier, F. Jaillet, and A. Baskurt, Segmentation and superquadric modeling of 3d objects, Proceedings of WSCG 2003, 2003.

D. Dobkin, L. Guibas, J. Hershberger, and J. Snoeynik, An efficient algorithm for finding the CSG representation of a simple polygon, ACM SIGGRAPH Computer Graphics, vol.22, issue.4, pp.31-40, 1988.
DOI : 10.1145/378456.378472

P. Fayolle, A. Pasko, E. Kartasheva, and N. Mirenkov, Shape recovery using functionally represented constructive models, Proceedings Shape Modeling Applications, 2004., pp.375-378, 2004.
DOI : 10.1109/SMI.2004.1314531

P. Fayolle, A. Pasko, and N. Mirenkov, Fitting of parameterized frep shape models, The Journal of Three Dimensional Images, vol.18, issue.1, pp.40-46, 2004.

P. Fayolle, A. Pasko, N. Mirenkov, C. Rosenberger, and C. Toinard, Constructive tree recovery using genetic algorithms, Procedings of the International Conference on Visualization, Imaging and Image Processing, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00461021

P. Fayolle, A. Pasko, B. Schmitt, and N. Mirenkov, Constructive Heterogeneous Object Modeling Using Signed Approximate Real Distance Functions, Journal of Computing and Information Science in Engineering, vol.6, issue.3, 2006.
DOI : 10.1115/1.2218366

P. Fayolle, C. Rosenberger, and C. Toinard, 3D shape reconstruction of template models using genetic algorithms, Proceedings of the 17th International Conference on Pattern Recognition, 2004. ICPR 2004., pp.269-272, 2004.
DOI : 10.1109/ICPR.2004.1334158

P. Fayolle, B. Schmitt, Y. Goto, and A. Pasko, Web-based Constructive Shape Modeling Using Real Distance Functions, IEICE Transactions on Information and Systems, vol.88, issue.5, pp.88-828, 2005.
DOI : 10.1093/ietisy/e88-d.5.828

J. D. Foley, A. Vand-dam, S. K. Feiner, and J. F. Hugues, Computer Graphics : Principles and Practices, 1995.

M. Freytag, V. Shapiro, and I. Tsukanov, Field modeling with sampled distances, Computer-Aided Design, vol.38, issue.2, pp.87-100, 2006.
DOI : 10.1016/j.cad.2005.06.004

S. F. Frisken, R. N. Perry, A. P. Rockwood, and T. R. Jones, Adaptively sampled distance fields, Proceedings of the 27th annual conference on Computer graphics and interactive techniques , SIGGRAPH '00, pp.249-254, 2000.
DOI : 10.1145/344779.344899

R. N. Goldman, Two Approaches to a Computer Model for Quadric Surfaces, IEEE Computer Graphics and Applications, vol.3, issue.6, pp.21-24, 1983.
DOI : 10.1109/MCG.1983.263208

J. Hart, Sphere tracing : A geometric method for the antialiased ray tracing of implicit surfaces. The Visual Computer, pp.527-545, 1996.

C. John and . Hart, Distance to an ellipsoid, Graphics Gems IV, pp.113-119, 1994.

K. Hoff, T. Culver, J. Keyser, M. Lin, and D. Manocha, Fast computation of generalized voronoi diagrams using graphics hardware, Proceedings of ACM SIGGRAPH, pp.277-286, 1999.

H. Hoppe, Surface reconstruction from unorganized points, 1994.

P. Hsu and C. Lee, The Scale Method for Blending Operations in Functionally-Based Constructive Geometry, Computer Graphics Forum, vol.44, issue.1, pp.143-158, 2003.
DOI : 10.1111/1467-8659.1530165

T. R. Jackson, Analysis of functionally graded material object representation methods, 2000.

M. Jones and M. Chen, A New Approach to the Construction of Surfaces from Contour Data, Computer Graphics Forum, vol.13, issue.3, pp.75-84, 1994.
DOI : 10.1111/1467-8659.1330075

E. Kartasheva, V. Adzhiev, A. Pasko, O. Fryazinov, and V. Gasilov, Surface and Volume Discretization of Functionally Based Heterogeneous Objects, Journal of Computing and Information Science in Engineering, vol.3, issue.4, pp.285-294, 2003.
DOI : 10.1115/1.1630817

V. Kumar, D. Burns, D. Dutta, and C. Hoffman, A framework for object modeling, Computer-Aided Design, vol.31, issue.9, pp.541-546, 1999.
DOI : 10.1016/S0010-4485(99)00051-2

V. Kumar and D. Dutta, An approach to modeling multi-material objects, Proceedings of the fourth ACM symposium on Solid modeling and applications , SMA '97, pp.336-345, 1997.
DOI : 10.1145/267734.267812

H. Liu, W. Cho, T. R. Jackson, N. M. Patrikalakis, and E. M. Sachs, Algorithms for design and interrogation of functionally gradient material objects, Proceedings of ASME 2000 IDETC/CIE 2000 ASME Design Automation Conference, 2000.

W. E. Lorensen and H. E. Cline, Marching cubes: A high resolution 3D surface construction algorithm, Proceedings of SIGGRAPH 87, pp.163-169, 1987.
DOI : 10.1145/37402.37422

D. Marshall, G. Lukacs, and R. Martin, Robust segmentation of primitives from range data in the presence of geometry degeneracy, IEEE Transactions on pattern analysis and machine intelligence, vol.23, issue.3, 2001.

S. Mauch, Efficient Algorithms for Solving Static Hamilton-Jacobi Equations, 2003.

J. Mccormack and A. Sherstyuk, Creating and Rendering Convolution Surfaces, Computer Graphics Forum, vol.17, issue.2, pp.113-120, 1998.
DOI : 10.1111/1467-8659.00232

B. Morse, T. Yoo, D. Chen, P. Rheingans, and K. Subramanian, Interpolating implicit surfaces from scattered surface data using compactly supported radial basis functions, Proceedings of Shape modeling international, pp.89-98, 2001.
DOI : 10.1109/sma.2001.923379

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.22.9607

S. Muraki, Volumetric shape description of range data using "blobby model, Proceedings of SIGGRAPH, pp.227-235, 1991.

G. Nielson, Volume Modelling, pp.29-48, 2000.
DOI : 10.1007/978-1-4471-0737-8_2

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

Y. Ohtake, A. Belyaev, and H. Seidel, Ridge-valley lines on meshes via implicit surface fitting, ACM Transactions on Graphics, vol.23, issue.3, pp.609-612, 2004.
DOI : 10.1145/1015706.1015768

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.61.3562

Y. Ohtake, A. Belyaev, and H. Seidel, An integrating approach to meshing scattered point data, Proceedings of the 2005 ACM symposium on Solid and physical modeling , SPM '05, pp.61-69, 2005.
DOI : 10.1145/1060244.1060252

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.72.1884

A. Pasko, V. Adzhiev, B. Schmitt, and C. Schlick, Constructive Hypervolume Modeling, Graphical Models, vol.63, issue.6, pp.413-442, 2001.
DOI : 10.1006/gmod.2001.0560

URL : https://hal.archives-ouvertes.fr/hal-00308016

A. Pasko, V. Adzhiev, A. Sourin, and V. Savchenko, Function representation in geometric modeling : concept, implementation and applications. The Visual Computer, pp.429-446, 1995.
DOI : 10.1007/bf02464333

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.51.9043

A. Pasko, V. Pilyugin, and V. Pokrovskiy, Geometric modeling in the analysis of trivariate functions, Computers & Graphics, vol.12, issue.3-4, pp.457-465, 1988.
DOI : 10.1016/0097-8493(88)90070-2

A. Pasko and V. Savchenko, Blending operations for the functionally based constructive geometry, set-theoretic Solid Modeling : Techniques and Applications , CSG 94 Conference Proceedings, pp.151-161, 1994.

X. Qian and D. Dutta, Physics based b-spline heterogeneous object modeling, DETC and Computers and Information in Engineering Conference. ASME, 2001.

A. Requicha, Representations for Rigid Solids: Theory, Methods, and Systems, ACM Computing Surveys, vol.12, issue.4, pp.437-464, 1980.
DOI : 10.1145/356827.356833

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.83.4337

A. A. Requicha and H. B. Voelcker, Constructive solid geometry, 1977.

A. Ricci, A constructive geometry for computer graphics, The Computer Journal, vol.16, issue.2, pp.157-160, 1973.
DOI : 10.1093/comjnl/16.2.157

URL : http://comjnl.oxfordjournals.org/cgi/content/short/16/2/157

C. Roessl, F. Zeilfelder, G. Nurnberger, and H. Seidel, Spline approximation of general volumetric data, In Proceedings of ACM Solid Modeling. ACM Solid Modeling, 2004.

V. Rvachev, On the analytical description of some geometric objects, pp.765-767, 1963.

V. Rvachev, Methods of Logic Algebra in Mathematical Physics, Naukova Dumka, 1974.

V. Rvachev, Theory of R-functions and Some Applications, Naukova Dumka, 1982.

V. L. Rvachev, L. V. Kurpa, N. G. Sklepus, and L. A. Uchishvili, Method of rfunctions in problems on bending and vibrations of plates of complex shape, 1973.

M. Sabin, The use of potential surfaces for numerical geometry, British Aircraft Corporation, 1968.

V. Savchenko, A. Pasko, O. Okunev, and T. Kunii, Function Representation of Solids Reconstructed from Scattered Surface Points and Contours, Computer Graphics Forum, vol.14, issue.4, pp.181-188, 1995.
DOI : 10.1111/1467-8659.1440181

J. Sethian, Level-Set Methods and Fast Marching Methods, 1999.

V. Shapiro, Theory of r-functions and applications : A primer, 1988.

V. Shapiro, Real functions for representation of rigid solids, Computer Aided Geometric Design, vol.11, issue.2, 1994.
DOI : 10.1016/0167-8396(94)90030-2

V. Shapiro, A CONVEX DEFICIENCY TREE ALGORITHM FOR CURVED POLYGONS, International Journal of Computational Geometry & Applications, vol.11, issue.02, pp.215-238, 2001.
DOI : 10.1142/S0218195901000468

V. Shapiro, Handbook of Computer Aided Geometric Design, chapter Solid Modeling, 2002.

V. Shapiro and D. L. Vossler, Separation for boundary to CSG conversion, ACM Transactions on Graphics, vol.12, issue.1, pp.35-55, 1993.
DOI : 10.1145/169728.169723

S. Silva, P. Fayolle, J. Vincent, G. Pauron, C. Rosenberger et al., Evolutionary computation approaches for shaped modelling and fitting, Proceedings of EPIA, 2005.
DOI : 10.1007/11595014_15

Y. K. Siu and S. T. Tan, Modeling the material grading and structures of heterogeneous objects for layered manufacturing, Computer-Aided Design, vol.34, issue.10, pp.705-716, 2002.
DOI : 10.1016/S0010-4485(01)00200-7

A. Sud, A. Otaduy, and D. Manocha, DiFi: Fast 3D Distance Field Computation Using Graphics Hardware, Proceedings of Eurographics, pp.557-566, 2004.
DOI : 10.1109/TPAMI.2003.1177156

W. Thibault and B. Naylor, Set operations on polyhedra using binary space partitioning trees, ACM SIGGRAPH Computer Graphics, vol.21, issue.4, pp.153-162, 1987.
DOI : 10.1145/37402.37421

S. B. Tor and A. E. Middleditch, Convex Decomposition of Simple Polygons, ACM Transactions on Graphics, vol.3, issue.4, pp.244-265, 1984.
DOI : 10.1145/357346.357348

Y. R. Tsai, Rapid and Accurate Computation of the Distance Function Using Grids, Journal of Computational Physics, vol.178, issue.1, pp.175-195, 2002.
DOI : 10.1006/jcph.2002.7028

G. Turk and J. Obrien, Shape transformation using variational implicit functions, Proceedings of SIGGRAPH, pp.335-342, 1999.

M. Vanco, A direct approach for the segmentation of unorganized points and recognition of simple algebraic surfaces, 2003.

T. Varady, R. R. Martin, and J. Cox, Reverse engineering of geometric models???an introduction, Computer-Aided Design, vol.29, issue.4, pp.255-268, 1997.
DOI : 10.1016/S0010-4485(96)00054-1

K. Watanabe and A. G. Belyaev, Detection of Salient Curvature Features on Polygonal Surfaces, Computer Graphics Forum, vol.20, issue.3, 2001.
DOI : 10.1111/1467-8659.00531

J. R. Woodwark and A. L. Wallis, Graphical input to a Boolean solid modeller, Proc. CAD'82, pp.681-688, 1982.
DOI : 10.1016/0010-4485(82)90246-9

H. Zhao, A fast sweeping method for Eikonal equations, Mathematics of Computation, vol.74, issue.250, 2004.
DOI : 10.1090/S0025-5718-04-01678-3

Y. Zhou, A. Kaufman, and A. Toga, 3d skeleton and centerline generation based on an approximate minimum distance field. The Visual Computer References [1], Wyvill, and G. Wyvill, Introduction to implicit surfaces, pp.303-314, 1997.

A. Pasko, V. Adzhiev, A. Sourin, and V. Savchenko, Function representation in geometric modeling: concepts, implementation and applications, The Visual Computer, vol.2, issue.8, pp.429-446, 1995.
DOI : 10.1007/BF02464333

R. Goldman, Two Approaches to a Computer Model for Quadric Surfaces, IEEE Computer Graphics and Applications, vol.3, issue.6, pp.21-24, 1983.
DOI : 10.1109/MCG.1983.263208

J. Rossignac and A. Requicha, Constant-radius blending in solid modeling, Computers in Mechanical Engineering, vol.3, issue.1, pp.65-73, 1984.

B. Payne and A. Toga, Distance field manipulation of surface models, IEEE Computer Graphics and Applications, vol.12, issue.1, pp.65-71, 1992.
DOI : 10.1109/38.135885

M. Jones and M. Chen, A New Approach to the Construction of Surfaces from Contour Data, Computer Graphics Forum, vol.13, issue.3, pp.75-84, 1994.
DOI : 10.1111/1467-8659.1330075

J. Hart, Sphere tracing: a geometric method for the antialiased ray tracing of implicit surfaces, The Visual Computer, vol.12, issue.10, pp.527-545, 1996.
DOI : 10.1007/s003710050084

Y. Zhou, A. Kaufman, and A. Toga, Three-dimensional skeleton and centerline generation based on an approximate minimum distance field, The Visual Computer, vol.14, issue.7, pp.303-314, 1998.
DOI : 10.1007/s003710050142

A. Biswas, V. Shapiro, and I. Tsukanov, Heterogeneous material modeling with distance fields, Computer Aided Geometric Design, vol.21, issue.3, pp.215-242, 2004.
DOI : 10.1016/j.cagd.2003.08.002

R. Cartwright, V. Adzhiev, A. Pasko, Y. Goto, and T. Kunii, Web-Based Shape Modeling with Hyperfun, IEEE Computer Graphics and Applications, vol.25, issue.2
DOI : 10.1109/MCG.2005.49

A. Adzhiev, R. Cartwright, E. Faussett, A. Ossipov, A. Pasko et al., Hyperfun project: a framework for collaborative multidimensional f-rep modeling, Proceeding Implicit Surfaces '99, Eurographics/ACM Workshop, pp.59-69, 1999.

W. Regli, Internet-enabled computer aided design, IEEE Internet Computing, vol.1, issue.1, pp.39-50, 1997.
DOI : 10.1109/4236.585171

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.469.4505

R. Oxman and A. Shabo, The Web as a visual design medium, 1999 IEEE International Conference on Information Visualization (Cat. No. PR00210), pp.266-271, 1999.
DOI : 10.1109/IV.1999.781569

B. Wyvill and A. Guy, The blob tree, implicit modeling and vrml, Proceedings Iternational conference from the desktop to the webtop: virtual environments on the internet, WWW and networks, pp.193-206, 1997.

R. Gimis and D. Nadeau, Creating vrml extensions to support scientific visualisation, Proceeding 1995 Symposium on Virtual Reality Modeling Language, pp.13-20, 1995.

H. Grahn, T. Volk, and H. J. Wolters, NURBS in VRML, Proceedings of the fifth symposium on Virtual reality modeling language (Web3D-VRML) , VRML '00, pp.35-43, 2000.
DOI : 10.1145/330160.330173

L. F. Min, A. Sourin, and K. Levinski, Function-based 3d web visualization, Proceedings of International Symposium Cyber Worlds: Theory and practice, pp.428-435, 2002.

A. Ricci, A constructive geometry for computer graphics, The Computer Journal, vol.16, issue.2, pp.157-160, 1973.
DOI : 10.1093/comjnl/16.2.157

URL : http://comjnl.oxfordjournals.org/cgi/content/short/16/2/157

M. Sabin, The use of potential surfaces for numerical geometry, British Aircraft Corporation, 1968.

V. Rvachev, On the analytical description of some geometric objects, pp.765-767, 1963.

V. Rvachev, Methods of Logic Algebra in Mathematical Physics, 1974.

V. Rvachev, Theory of R-functions and Some Applications, 1982.

A. Biswas and V. Shapiro, Approximate distance fields with non-vanishing gradients, Graphical Models, vol.66, issue.3, pp.133-159, 2004.
DOI : 10.1016/j.gmod.2004.01.003

L. Barthe, N. A. Dodgson, M. A. Sabin, B. Wyvill, and V. Gaildrat, Two-dimensional Potential Fields for Advanced Implicit Modeling Operators, Computer Graphics Forum, vol.19, issue.3, pp.23-33, 2003.
DOI : 10.1111/1467-8659.00530

J. C. Hart, Distance to an Ellipsoid, pp.113-119, 1994.
DOI : 10.1016/B978-0-12-336156-1.50019-7

R. Cartwright, Geometric aspects of empiricla modelling: issues in design and implementation, 1998.

A. Pasko, V. Pilyugin, and V. Pokrovskiy, Geometric modeling in the analysis of trivariate functions, Computers & Graphics, vol.12, issue.3-4, pp.457-465, 1988.
DOI : 10.1016/0097-8493(88)90070-2

W. Lorensen and H. Cline, Marching cubes: A high resolution 3D surface construction algorithm, Proceedings of SIGGRAPH 87, pp.163-169, 1987.
DOI : 10.1145/37402.37422

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.132.3930

V. Kumar and D. Dutta, An approach to modeling multimaterial objects, Fourth Symposium on Solid Modeling and Applications, pp.336-345, 1997.
DOI : 10.1145/267734.267812

A. Ricci, A constructive geometry for computer graphics, The Computer Journal, vol.16, issue.2, pp.157-160, 1973.
DOI : 10.1093/comjnl/16.2.157

URL : http://comjnl.oxfordjournals.org/cgi/content/short/16/2/157

M. Sabin, V. Kumar, and D. Dutta, The Use of Potential Surfaces for Numerical Geometry An Approach to Modeling Multi-Material Objects, Fourth Symposium on Solid Modeling and Applications, pp.336-345, 1968.

V. Kumar, D. Burns, D. Dutta, H. C. Bhashyam, S. Shin et al., A framework for object modeling, Computer-Aided Design, vol.31, issue.9, pp.541-546, 1999.
DOI : 10.1016/S0010-4485(99)00051-2

K. Chen, X. Feng, A. Biswas, V. Shapiro, and I. Tsukanov, Computer-Aided Design Method for the Components Made of Heterogeneous Materials Heterogeneous Material Modeling with Distance Fields, Computer-Aided Design Computer Aided Geometric Design, vol.35, issue.213, pp.453-466, 2003.

A. Requicha, Representations for Rigid Solids: Theory, Methods, and Systems, ACM Computing Surveys, vol.12, issue.4, pp.437-464, 1980.
DOI : 10.1145/356827.356833

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.83.4337

G. Nielson, Volume Modelling, pp.29-48, 2000.
DOI : 10.1007/978-1-4471-0737-8_2

A. Pasko, V. Adzhiev, B. Schmitt, and C. Schlick, Constructive Hypervolume Modeling, Graphical Models, vol.63, issue.6, pp.413-442, 2001.
DOI : 10.1006/gmod.2001.0560

URL : https://hal.archives-ouvertes.fr/hal-00308016

A. Pasko, V. Adzhiev, A. Sourin, and V. Savchenko, Function representation in geometric modeling: concepts, implementation and applications, The Visual Computer, vol.2, issue.8, pp.429-446, 1995.
DOI : 10.1007/BF02464333

V. Rvachev, On the Analytical Description of some Geometric Objects, Ukranian Academy of Sciences, vol.153, issue.4, pp.765-767, 1963.

X. Qian and D. Dutta, Physics Based B-Spline Heterogeneous Object Modeling, ASME Design Engineering Technical Conference, 2001.

T. R. Jackson, Analysis of Functionally Graded Material Object Representation Methods, 2000.

Y. K. Siu and S. T. Tan, Modeling the material grading and structures of heterogeneous objects for layered manufacturing, Computer-Aided Design, vol.34, issue.10, pp.705-716, 2002.
DOI : 10.1016/S0010-4485(01)00200-7

H. Liu, W. Cho, T. R. Jackson, N. M. Patrikalakis, and E. M. Sachs, Algorithms for Design and Interrogation of Functionally Gradient Material Objects, Proceedings of ASME 2000 IDETC/CIE 2000 ASME Design Automation Conference, 2000.

S. Frisken, R. Perry, A. Rockwood, and T. Jones, Adaptively sampled distance fields, Proceedings of the 27th annual conference on Computer graphics and interactive techniques , SIGGRAPH '00, pp.249-254, 2000.
DOI : 10.1145/344779.344899

D. Cohen-or, D. Levin, A. Solomovic, Y. Zhou, A. Kaufman et al., Sphere Tracing: A Geometric Method for the Antialiased Ray Tracing of Implicit Surfaces The Visual Computer 3d Skeleton and Centerline Generation Based on an Approximate Minimum Distance Field Two Approaches to a Computer Model for Quadric Surfaces Hybrid Distance Field Computation A Fast Sweeping Method for Eikonal Equations Rapid and Accurate Computation of the Distance Function Using Grids Spline Approximation of General Volumetric Data Level-Set Methods and Fast Marching Methods Implicit Surface Reconstruction and Deformation Using the Level-Set Method " , In the 1st IEEE workshop on variational and level-set methods in computer vision Multi-Level Partition of Unity Implicits A Level-Set Based Variational Method for Design and Optimization of Heterogeneous Objects Computer Aided Design, special issue on " Heterogeneous Object Models and their Applications Approximate Distance Fields with Non-Vanishing Gradients Three-Dimensional Halfspace Constructive Solid Geometry Tree Construction from Implicit Boundary Representations Separation for Boundary to Csg Conversion Two-Dimensional Potential Fields for Advanced Implicit Modeling Operators Distance to an Ellipsoid Constructive Representation of Heterogeneous Objects A Two-Dimensional Interpolation Function for Irregularly Spaced Data Transfinite Interpolation Over Implicitly Defined Sets Surface and Volume Discretization of Functionally Based Heterogeneous Objects, New Approach to the Construction of Surfaces from Contour Data Proceedings of the eighth ACM symposium on Solid modeling and applications proceeding of the 23 National Conference., and Gasilov, pp.116-141, 1968.

. P. References, G. Benko, T. Kos, L. Varady, R. Andor et al., Constrained fitting in reverse engineering, Computer Aided Geometric Design, vol.19, pp.173-205, 2002.

D. [. Dennis, R. E. Gay, and . Welsch, An Adaptive Nonlinear Least-Squares Algorithm, ACM Transactions on Mathematical Software, vol.7, issue.3, pp.348-368, 1981.
DOI : 10.1145/355958.355965

]. R. Fis02 and . Fisher, Applying knowledge to reverse engineering problems, Proceedings of Geometric Modeling and Processing, pp.149-155, 2002.

G. [. Goffe, J. Ferrier, and . Rogers, Global optimization of statistical functions with simulated annealing, Journal of Econometrics, vol.60, issue.1-2, pp.65-99, 1994.
DOI : 10.1016/0304-4076(94)90038-8

]. B. Haj88 and . Hajek, Cooling schedules for optimal annealing, Mathematics of Operations Research, vol.13, pp.311-329, 1988.

C. [. Kirkpatrick, M. Gelatt, and . Vecchi, Optimization by simulated annealing, Science, vol.220, pp.4598-671, 1983.

]. J. Mor78 and . Moré, The levenberg-marquardt algorithm implementation and theory, Lecture notes in mathematics No630 Numerical analysis, pp.105-116, 1978.

Y. Ohtake, A. Belyaev, M. Alexa, G. Turk, H. Seidel et al., Multi-level partition of unity implicits, Proceedings of SIG- GRAPH A hybrid marquardt simulated annealing method for solving the groundwater inverse problem, Calibration and reliability in groundwater modeling, number 265, pp.157-163, 2000.

P. Benko, G. Kos, T. Varady, L. Andor, and R. Martin, Constrained fitting in reverse engineering, Computer Aided Geometric Design, vol.19, issue.3, pp.173-205, 2002.
DOI : 10.1016/S0167-8396(01)00085-1

J. Dennis, D. Gay, and R. Welsch, An Adaptive Nonlinear Least-Squares Algorithm, ACM Transactions on Mathematical Software, vol.7, issue.3, pp.348-368, 1981.
DOI : 10.1145/355958.355965

R. Fisher, Applying knowledge to reverse engineering problems, Proceedings of Geometric Modeling and Processing, pp.149-155, 2002.
DOI : 10.1016/s0010-4485(03)00158-1

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.109.1311

P. Frey and H. Borouchaki, Geometric surface mesh optimization . Computing and visualization in science, pp.113-121, 1998.
DOI : 10.1007/s007910050011

J. Hart, Sphere tracing: A geometric method for the antialiased ray tracing of implicit surfaces. The Visual Computer, pp.527-545, 1996.

E. Kartasheva, V. Adzhiev, A. Pasko, O. Fryazinov, and V. Gasilov, Discretization of functionally based heterogeneous objects, Proceedings of the eighth ACM symposium on Solid modeling and applications , SM '03, pp.145-156, 2003.
DOI : 10.1145/781606.781630

S. Kirkpatrick, C. Gelatt, and M. Vecchi, Optimization by Simulated Annealing, Science, vol.220, issue.4598, pp.671-680, 1983.
DOI : 10.1126/science.220.4598.671

L. Kobbelt, M. Botsch, U. Schwanecke, and H. Seidel, Feature sensitive surface extraction from volume data, Proceedings of the 28th annual conference on Computer graphics and interactive techniques , SIGGRAPH '01, pp.57-66, 2001.
DOI : 10.1145/383259.383265

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller, Equation of State Calculations by Fast Computing Machines, The Journal of Chemical Physics, vol.21, issue.6, pp.1087-1092, 1953.
DOI : 10.1063/1.1699114

J. Moré, The Levenberg-Marquardt algorithm: Implementation and theory, Lecture notes in mathematics No630 Numerical analysis, pp.105-116, 1978.
DOI : 10.1137/0111030

A. Pasko, V. Adzhiev, A. Sourin, and V. Savchenko, Function representation in geometric modeling: concepts, implementation and applications, The Visual Computer, vol.2, issue.8, pp.429-446, 1995.
DOI : 10.1007/BF02464333

G. Pasko, A. Pasko, C. Vilbrandt, and T. Ikedo, Virtual Shikki and Sazaedo: shape modeling in digital preservation of Japanese lacquer ware and temples, Proceedings Spring Conference on Computer Graphics, pp.147-154, 2001.
DOI : 10.1109/SCCG.2001.945349

H. Seo, N. Magnenat-thalmann, G. Kos, T. Varady, L. Andor et al., An example based approach to human body manipulation Constrained fitting in reverse engineering, Graphical Models Computer Aided Geometric Design, vol.66, issue.19, pp.1-23173, 2002.

J. E. Dennis, D. M. Gay, and R. E. Welsch, An Adaptive Nonlinear Least-Squares Algorithm, ACM Transactions on Mathematical Software, vol.7, issue.3, pp.348-368, 1981.
DOI : 10.1145/355958.355965

P. Fayolle, A. Pasko, E. Kartasheva, and N. Mirenkov, Shape recovery using functionally represented constructive models, Proceedings Shape Modeling Applications, 2004., 2004.
DOI : 10.1109/SMI.2004.1314531

R. Fisher, Applying knowledge to reverse engineering problems, Proceedings of Geometric Modeling and Processing, pp.149-155, 2002.

J. H. Holland, Adaptation in Natural and Artificial Systems, 1975.

C. Houck, J. Joines, and M. Kay, A genetic algorithm for function optimization: A matlab implementation, 1995.

S. Kirkpatrick, C. Gelatt, and M. Vecchi, Optimization by Simulated Annealing, Science, vol.220, issue.4598, pp.671-680, 1983.
DOI : 10.1126/science.220.4598.671

Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs, 1996.

J. Moré, The Levenberg-Marquardt algorithm: Implementation and theory, Lecture notes in mathematics No630 Numerical analysis, pp.105-116, 1978.
DOI : 10.1137/0111030

Y. Ohtake, A. Belyaev, and H. Seidel, A multi-scale approach to 3d scattered data interpolation with compacly supported radial basis functions, Proceedings of Shape Modelling, 2003.

A. Pasko, V. Adzhiev, A. Sourin, and V. Savchenko, Function representation in geometric modeling: concepts, implementation and applications. The visual Computer, pp.429-446, 1995.

J. Smith, Three Applications of Optimization in Computer Graphics, 2003.

]. A. Requicha and H. B. Voelcker, Constructive solid geometry, 1977.

V. L. Rvachev, Geometric applications of logic algebra, 1967.

V. Shapiro, Theory of r-functions and applications: A primer, 1991.

A. Pasko, V. Adzhiev, A. Sourin, and V. Savchenko, Function representation in geometric modeling: Concepts , implementation and applications, The Visual Computer, pp.429-446, 1995.

T. Varady, R. R. Martin, and J. Cox, Reverse engineering of geometric models???an introduction, Computer-Aided Design, vol.29, issue.4, pp.255-268, 1997.
DOI : 10.1016/S0010-4485(96)00054-1

P. Benko and T. Varady, Direct segmentation of smooth, multiple point regions, Geometric Modeling and Processing. Theory and Applications. GMP 2002. Proceedings, pp.169-178, 2002.
DOI : 10.1109/GMAP.2002.1027508

V. Shapiro and D. L. Vossler, Construction and optimization of CSG representations, Computer-Aided Design, vol.23, issue.11, pp.4-20, 1991.
DOI : 10.1016/0010-4485(91)90095-E

V. Shapiro and D. L. Vossler, Efficient CSG Representations of Two-Dimensional Solids, Journal of Mechanical Design, vol.113, issue.3, pp.292-305, 1991.
DOI : 10.1115/1.2912782

V. Shapiro and D. L. Vossler, Separation for boundary to CSG conversion, ACM Transactions on Graphics, vol.12, issue.1, pp.35-55, 1993.
DOI : 10.1145/169728.169723

S. Buchele and R. Crawford, Three-dimensional halfspace constructive solid geometry tree construction from implicit boundary representations, Computer-Aided Design, vol.36, issue.11, pp.1063-1073, 2004.
DOI : 10.1016/j.cad.2004.01.006

V. L. Rvachev, L. V. Kurpa, N. G. Sklepus, and L. A. Uchishvili, Method of r-functions in problems on bending and vibrations of plates of complex shape, 1973.

D. P. Peterson, Boundary to constructive solid geometry mappings: A focus on 2D issues, Computer-Aided Design, vol.18, issue.1, pp.3-14, 1986.
DOI : 10.1016/S0010-4485(86)80003-3

V. Shapiro, A CONVEX DEFICIENCY TREE ALGORITHM FOR CURVED POLYGONS, International Journal of Computational Geometry & Applications, vol.11, issue.02, pp.215-238, 2001.
DOI : 10.1142/S0218195901000468

A. Pasko and V. Savchenko, Blending operations for the functionally based constructive geometry, Proc. of CSG 94 Set-theoretic Solid Modeling: Techniques and Applications, pp.151-161, 1994.

V. Savchenko and A. Pasko, Transformation of functionally defined shapes by extended space mappings, The Visual Computer, pp.257-270, 1998.

H. Hoppe, Surface reconstruction from unorganized points, 1995.
DOI : 10.1145/133994.134011

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.153.4735

D. Goldberg, Genetic Algorithms in search, optimization and machine learning, 1989.

W. Banzhaf, P. Nordin, R. E. Keller, and F. D. Francone, Genetic Programming -An Introduction, 1998.

P. Benko, G. Kos, T. Varady, L. Andor, and R. Martin, Constrained fitting in reverse engineering, Computer Aided Geometric Design, vol.19, issue.3, pp.173-205, 2002.
DOI : 10.1016/S0167-8396(01)00085-1

F. Costantini and C. Toinard, Collaboration and Virtual Early Prototyping Using the Distributed Building Site Metaphor, ): Multimedia Networking: Technology, Management and Applications, pp.290-332, 2002.
DOI : 10.4018/978-1-930708-14-3.ch014

URL : https://hal.archives-ouvertes.fr/hal-01124679

P. Fayolle, C. Rosenberger, and C. Toinard, Shape Recovery and Functional Modeling Using Genetic Algorithms, Proceedings of IEEE LAVAL VIRTUAL, pp.227-232, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00461170

P. Fayolle, A. Pasko, E. Kartasheva, and N. Mirenkov, Shape recovery using functionally represented constructive models, Proceedings Shape Modeling Applications, 2004., 2004.
DOI : 10.1109/SMI.2004.1314531

R. Fisher, Applying Knowledge to Reverse Engineering Problems, Proceedings of Geometric Modeling and Processing, pp.149-155, 2002.

D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning, 1989.

J. H. Holland, Adaptation in Natural and Artificial Systems. The University of, 1975.

C. Houck, J. Joines, and M. Kay, A Genetic Algorithm for Function Optimization: A Matlab Implementation, 1995.

J. R. Koza, Genetic programming as a means for programming computers by natural selection, Statistics and Computing, vol.4, issue.2, 1992.
DOI : 10.1007/BF00175355

S. Luke and L. Panait, Lexicographic Parsimony Pressure, Proceedings of GECCO-2002, pp.829-836, 2002.

Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs, 1996.

Z. Michalewicz and D. B. Fogel, How to Solve It: Modern Heuristics, 2004.
DOI : 10.1007/978-3-662-04131-4

D. J. Montana, Strongly Typed Genetic Programming, Evolutionary Computation, vol.3, issue.2, 1994.
DOI : 10.1115/1.3662552

A. Pasko, V. Adzhiev, A. Sourin, and V. Savchenko, Function representation in geometric modeling: concepts, implementation and applications, The Visual Computer, vol.2, issue.8, pp.429-446, 1995.
DOI : 10.1007/BF02464333

C. Robertson, R. Fisher, N. Werghi, and A. Ashbrook, An Evolutionary Approach to Fitting Constrained Degenerate Second Order Surfaces, EvoWorkshops, pp.1-16, 1999.
DOI : 10.1007/10704703_1

H. Seo and N. Magnenat-thalmann, An example-based approach to human body manipulation, Graphical Models, vol.66, issue.1, pp.1-23, 2004.
DOI : 10.1016/j.gmod.2003.07.004

S. Silva, GPLAB ? A Genetic Programming Toolbox for MATLAB, 2005.

S. Silva and E. Costa, Dynamic Limits for Bloat Control -Variations on Size and Depth, Proceedings of GECCO- 2004, pp.666-677, 2004.

W. Banzhaf, P. Nordin, R. E. Keller, and F. D. Francone, Genetic Programming -An Introduction, 1998.

P. Benko, G. Kos, T. Varady, L. Andor, and R. Martin, Constrained fitting in reverse engineering, Computer Aided Geometric Design, vol.19, issue.3, pp.173-205, 2002.
DOI : 10.1016/S0167-8396(01)00085-1

F. Costantini and C. Toinard, Collaboration and Virtual Early Prototyping Using the Distributed Building Site Metaphor, ): Multimedia Networking: Technology, Management and Applications, pp.290-332, 2002.
DOI : 10.4018/978-1-930708-14-3.ch014

URL : https://hal.archives-ouvertes.fr/hal-01124679

P. Fayolle, C. Rosenberger, and C. Toinard, Shape Recovery and Functional Modeling Using Genetic Algorithms, Proceedings of IEEE LAVAL VIRTUAL, pp.227-232, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00461170

P. Fayolle, A. Pasko, E. Kartasheva, and N. Mirenkov, Shape recovery using functionally represented constructive models, Proceedings Shape Modeling Applications, 2004., 2004.
DOI : 10.1109/SMI.2004.1314531

R. Fisher, Applying Knowledge to Reverse Engineering Problems, Proceedings of Geometric Modeling and Processing, pp.149-155, 2002.

D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning, 1989.

J. H. Holland, Adaptation in Natural and Artificial Systems. The University of, 1975.

C. Houck, J. Joines, and M. Kay, A Genetic Algorithm for Function Optimization: A Matlab Implementation, 1995.

J. R. Koza, Genetic programming as a means for programming computers by natural selection, Statistics and Computing, vol.4, issue.2, 1992.
DOI : 10.1007/BF00175355

S. Luke and L. Panait, Lexicographic Parsimony Pressure, Proceedings of GECCO-2002, pp.829-836, 2002.

Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs, 1996.
DOI : 10.1007/978-3-662-02830-8

Z. Michalewicz and D. B. Fogel, How to Solve It: Modern Heuristics, 2004.
DOI : 10.1007/978-3-662-04131-4

D. J. Montana, Strongly Typed Genetic Programming, Evolutionary Computation, vol.3, issue.2, 1994.
DOI : 10.1115/1.3662552

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.38.4986

A. Pasko, V. Adzhiev, A. Sourin, and V. Savchenko, Function representation in geometric modeling: concepts, implementation and applications, The Visual Computer, vol.2, issue.8, pp.429-446, 1995.
DOI : 10.1007/BF02464333

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.51.9043

C. Robertson, R. Fisher, N. Werghi, and A. Ashbrook, An Evolutionary Approach to Fitting Constrained Degenerate Second Order Surfaces, EvoWorkshops, pp.1-16, 1999.
DOI : 10.1007/10704703_1

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.157.4942

H. Seo and N. Magnenat-thalmann, An example-based approach to human body manipulation, Graphical Models, vol.66, issue.1, pp.1-23, 2004.
DOI : 10.1016/j.gmod.2003.07.004

S. Silva, GPLAB ? A Genetic Programming Toolbox for MATLAB, 2005.

S. Silva and E. Costa, Dynamic Limits for Bloat Control -Variations on Size and Depth, Proceedings of GECCO- 2004, pp.666-677, 2004.