Advertisement

Towards a better integration of modelers and black box constraint solvers within the product design process

  • Jean-Philippe Pernot
  • Dominique Michelucci
  • Marc Daniel
  • Sebti FoufouEmail author
Article

Abstract

This paper presents a new way of interaction between modelers and solvers to support the Product Development Process (PDP). The proposed approach extends the functionalities and the power of the solvers by taking into account procedural constraints. A procedural constraint requires calling a procedure or a function of the modeler. This procedure performs a series of actions and geometric computations in a certain order. The modeler calls the solver for solving a main problem, the solver calls the modeler’s procedures, and similarly procedures of the modeler can call the solver for solving sub-problems. The features, specificities, advantages and drawbacks of the proposed approach are presented and discussed. Several examples are also provided to illustrate this approach.

Keywords

Geometric modeling Constraints Procedural constraints Solver Modeler 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Fiores II 2000–03, Character preservation and modelling in aesthetic and engineering design. GROWTH Project GRD-CT-2000-0003. http://www.fiores.com
  2. 2.
    Aim@Shape: Engineering Design Methods: Strategies Design Product. Advanced and Innovative Models and Tools for the Development of Semantic-Based Systems for Handling, Acquiring, and Processing Knowledge Embedded in Multi-Dimensional Digital Objects. European Network of Excellence Key Action: 2.3.1.7. Semantic-based Knowledge Systems, VI Framework (2004)Google Scholar
  3. 3.
    Ait-Aoudia, S., Foufou, S.: A 2d geometric constraint solver using a graph reduction method. Adv. Eng. Softw. 41, 1187–1194 (2010)CrossRefzbMATHGoogle Scholar
  4. 4.
    Ait-Aoudia, S., Jegou, R., Michelucci, D.: Reduction of constraint systems. arXiv:1405.6131. (Third COMPUGRAPHICS 1993, pp. 331–340) (2014)
  5. 5.
    Bierlaire, M.: Optimization: Principles and Algorithms. EPFL Press, Lausanne (2015)zbMATHGoogle Scholar
  6. 6.
    Blender.org: Blender for Open source 3D Creation. https://www.blender.org/
  7. 7.
    Bonnans, J.F., Gilbert, J.C., Lemaréchal, C., Sagastizábal, C.A.: Numerical optimization: theoretical and practical aspects. Springer Science & Business Media (2006)Google Scholar
  8. 8.
    Bouchard, C., Aoussat, A., Duchamp, R.: Role of sketching in conceptual design of car styling. Journal of Design Research 5(1), 116–148 (2006)CrossRefGoogle Scholar
  9. 9.
    Büskens, C., Wassel, D.: The ESA NLP Solver WORHP. In: Fasano, G., Pint’er, J.D. (eds.) Modeling and Optimization in Space Engineering, vol. 73, pp 85–110. Springer, New York (2013)Google Scholar
  10. 10.
    Byrd, R.H., Lu, P., Nocedal, J., Zhu, C.: A limited memory algorithm for bound constrained optimization. SIAM J. Sci. Comput. 16, 1190–1208 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Camba, J.D., Contero, M., Company, P.: Parametric cad modeling: an analysis of strategies for design reusability. Comput. Aided Des. 74, 18–31 (2016)CrossRefGoogle Scholar
  12. 12.
    Cheutet, V., Daniel, M., Hahmann, S., La Gréca, R., Léon, J. C., Maculet, R., Ménégaux, D., Sauvage, B.: Constraint modeling for curves and surfaces in CAGD: a survey. Int. J. Shape Model. 13(2), 159–199 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Contero, M., Company, P., Vila, C., Aleixos, N.: Product data quality and collaborative engineering. IEEE Comput. Graph. Appl. 22, 32–42 (2002)CrossRefGoogle Scholar
  14. 14.
    Cross, N.: Engineering Design Methods: Strategies for Design Product, 3rd edn. Wiley, Chichester (2000)Google Scholar
  15. 15.
    Danglade, F., Pernot, J.P., Véron, P.: On the use of machine learning to defeature CAD models for simulation. Comput.-Aided Des. Applic. 11(3), 358–368 (2014)CrossRefGoogle Scholar
  16. 16.
    Decriteau, D., Pernot, J.P., Daniel, M.: Towards declarative CAD modeler built on top of a CAD modeler. In: Proceedings of CAD’15, Computer Aided Design and Applications, pp. 107–112 (2015)Google Scholar
  17. 17.
    Dufourd, J.F., Mathis, P., Schreck, P.: Formal resolution of geometrical constraint systems by assembling. In: Proceedings of the Fourth ACM Symposium on Solid Modeling and Applications, pp. 271–284. ACM (1997)Google Scholar
  18. 18.
    Dufourd, J.F., Mathis, P., Schreck, P.: Geometric construction by assembling solved subfigures. Artif. Intell. 99(1), 73–119 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Elber, G., Kim, M.S.: Geometric constraint solver using multivariate rational spline functions. In: Proceedings of the Sixth ACM Symposium on Solid Modeling and Applications, pp 1–10. ACM, New York (2001)Google Scholar
  20. 20.
    Essert-Villard, C., Schreck, P., Dufourd, J.F.: Sketch-based pruning of a solution space within a formal geometric constraint solver. Artif. Intell. 124(1), 139–159 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Eva Catalano, C., Falcidieno, B., Giannini, F., Monti, M.: A survey of computer-aided modeling tools for aesthetic design. J. Comput. Inf. Sci. Eng. 2, 11–20 (2002)CrossRefGoogle Scholar
  22. 22.
    Falcidieno, B., Giannini, F., Léon, J.-C., Pernot, J.-P.: Processing free form objects within a Product Development Process framework. In: Michopoulos, J.G., Paredis, C.J.J., Rosen, D.W., Vance, J.M. (eds.) Advances in Computers and Information in Engineering Research, vol. 1, pp. 317–344. ASME-Press (2014)Google Scholar
  23. 23.
    Fischer, I.: Dual-Number Methods in Kinematics, Statics and Dynamics. Routledge, Evanston (2017)CrossRefGoogle Scholar
  24. 24.
    Foufou, S., Michelucci, D.: Bernstein basis and its application in solving geometric constraint systems. Journal of Reliable Computing 17, 192–208 (2012)MathSciNetzbMATHGoogle Scholar
  25. 25.
    Foufou, S., Michelucci, D.: Interrogating witnesses for geometric constraint solving. Inf. Comput. 216, 24–38 (2012). Special Issue: 8th Conference on Real Numbers and ComputersMathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    FreeCAD: FreeCAD: An open-source parametric 3D CAD modeler. https://www.freecadweb.org/
  27. 27.
    FreeSHIP: FreeSHIP: Surface Modeling. https://sourceforge.net/projects/freeship/
  28. 28.
    Fünfzig, C., Michelucci, D., Foufou, S.: Nonlinear systems solver in floating-point arithmetic using lp reduction. In: 2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling, SPM’09, pp 123–134. ACM, New York (2009)Google Scholar
  29. 29.
    Ge, J.X., Chou, S.C., Gao, X.S.: Geometric constraint satisfaction using optimization methods. Comput.-Aided Des. 31(14), 867–879 (1999)CrossRefzbMATHGoogle Scholar
  30. 30.
    GeoGebra.org: GeoGebra: Dynamic Mathematics for Learning and Teaching. https://www.geogebra.org/
  31. 31.
    Giannini, F., Montani, E., Monti, M., Pernot, J.P.: Semantic evaluation and deformation of curves based on aesthetic criteria. Comput.-Aided Des. Applic. 8 (3), 449–464 (2011)CrossRefGoogle Scholar
  32. 32.
    Gouaty, G., Fang, L., Michelucci, D., Daniel, M., Pernot, J.P., Raffin, R., Lanquetin, S., Neveu, M.: Variational geometric modeling with black box constraints and DAGs. Comput. Aided Des. 75, 1–12 (2016)CrossRefGoogle Scholar
  33. 33.
    Hendrickson, B.: Conditions for unique graph realizations. SIAM J. Comput. 21 (1), 65–84 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    Hoffmann, C.M.: Geometric and Solid Modeling: an Introduction. Morgan Kaufman, San Mateo (1989)Google Scholar
  35. 35.
    Hoffmann, C.M., Joan-Arinyo, R.: Symbolic constraints in constructive geometric constraint solving. J. Symb. Comput. 23(2-3), 287–299 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    Hoffmann, C.M., Lomonosov, A., Sitharam, M.: Geometric constraint decomposition. In: Geometric Constraint Solving and Applications, pp. 170–195. Springer (1998)Google Scholar
  37. 37.
    Hu, H., Kleiner, M., Pernot, J.P.: Over-constraints detection and resolution in geometric equation systems. Comput. Aided Des. 90, 84–94 (2017)CrossRefGoogle Scholar
  38. 38.
    Jaulin, L., Kieffer, M., Didrit, O., Walter, É.: Interval Analysis. Springer, London (2001)CrossRefzbMATHGoogle Scholar
  39. 39.
    Jermann, C., Trombettoni, G., Neveu, B., Mathis, P.: Decomposition of geometric constraint systems: a survey. Int. J. Comput. Geom. Appl. 16(05n06), 379–414 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  40. 40.
    Joan-Arinyo, R., Soto-Riera, A.: Combining constructive and equational geometric constraint-solving techniques. ACM Trans. Graph. (TOG) 18(1), 35–55 (1999)CrossRefGoogle Scholar
  41. 41.
    Khorramizadeh, M.: An application of the Dulmage-Mendelsohn decomposition to sparse null space bases of full row rank matrices. In: International Mathematical Forum, vol. 52, pp 2549–2554 (2012)Google Scholar
  42. 42.
    Kondo, K.: Algebraic method for manipulation of dimensional relationships in geometric models. Comput. Aided Des. 24(3), 141–147 (1992)CrossRefzbMATHGoogle Scholar
  43. 43.
    Kubicki, A., Michelucci, D., Foufou, S.: Witness computation for solving geometric constraint systems. In: Science and Information Conference (SAI), 2014, pp. 759–770. IEEE (2014)Google Scholar
  44. 44.
    Lesage, D., Léon, J. C., Sebah, P., Rivière, A.: A proposal of structure for a variational modeler based on functional specifications. In: Gogu, G., Coutellier, D., Chedmail, P., Ray, P. (eds.) Recent Advances in Integrated Design and Manufacturing in Mechanical Engineering, pp. 73–84. Springer (2003)Google Scholar
  45. 45.
    Li, Z., Giannini, F., Pernot, J.P., Véron, P., Falcidieno, B.: Re-using heterogeneous data for the conceptual design of shapes in virtual environments. Virtual Reality 21(3), 127–144. Springer (2017)Google Scholar
  46. 46.
    Linke, T., Wassel, D., Büskens, C.: Recent advances in the solution of large nonlinear optimisation. In: Rodrigues, H., Herskovits, J., Soares, C.M., Guedes, J.M. (eds.) Engineering Optimization IV, pp 141–146. Taylor & Francis, New York (2014)Google Scholar
  47. 47.
    Lovász, L., Plummer, M.D.: Matching Theory. American Mathematical Society Providence, USA. ISBN13 9780821847596 (2009)Google Scholar
  48. 48.
    Michelucci, D., Foufou, S.: Interrogating witnesses for geometric constraint solving. In: 2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling, pp. 343–348. ACM (2009)Google Scholar
  49. 49.
    Moinet, M., Mandil, G., Serre, P.: Defining tools to address over-constrained geometric problems in computer aided design. Comput. Aided Des. 48, 42–52 (2014)CrossRefGoogle Scholar
  50. 50.
    Mourrain, B., Pavone, J.P.: Subdivision methods for solving polynomial equations. J. Symb. Comput. 44(3), 292–306 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  51. 51.
    Owen, J.C.: Algebraic solution for geometry from dimensional constraints. In: Proceedings of the First ACM Symposium on Solid modeling Foundations and CAD/CAM Applications, pp. 397–407. ACM (1991)Google Scholar
  52. 52.
    Pernot, J.P., Falcidieno, B., Giannini, F., Léon, J. C.: A hybrid models deformation tool for free-form shapes manipulation. In: 34Th Design Automation Conference (ASME DETC08-DAC 49524), pp. 647-657. ASME, New-York (2008)Google Scholar
  53. 53.
    Pernot, J.P., Falcidieno, B., Giannini, F., Léon, J. C.: Incorporating free-form features in aesthetic and engineering product design: state-of-the-art report. Comput. Ind. 59(6), 626–637 (2008)CrossRefGoogle Scholar
  54. 54.
    Rameau, J.F., Serré, P.: Computing mobility condition using Groebner basis. Mech. Mach. Theory 91, 21–38 (2015)CrossRefGoogle Scholar
  55. 55.
    Rao, R.: Jaya: a simple and new optimization algorithm for solving constrained and unconstrained optimization problems. Int. J. Ind. Eng. Comput. 7(1), 19–34 (2016)Google Scholar
  56. 56.
    Saad, Y.: Iterative methods for sparse linear systems. SIAM, Philadelphia (2003)CrossRefzbMATHGoogle Scholar
  57. 57.
    Schreck, P., Mathis, P.: Geometrical constraint system decomposition: a multi-group approach. Int. J. Comput. Geom. Appl. 16(05n06), 431–442 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  58. 58.
    Schreck, P., Schramm, É.: Using invariance under the similarity group to solve geometric constraint systems. Comput. Aided Des. 38(5), 475–484 (2006)CrossRefzbMATHGoogle Scholar
  59. 59.
    Serrano, D.: Automatic dimensioning in design for manufacturing. In: Proceedings of the First ACM Symposium on Solid Modeling Foundations and CAD/CAM Applications, SMA ’91, pp 379–386. ACM, New York (1991)Google Scholar
  60. 60.
    Solomon, C., Gibson, S.J., Maylin, M.I.S: A new computational methodology for the construction of forensic, facial composites. In: Proceedings of the 3rd IWCF, Netherlands, 2009. Lecture Notes in Computer Science, vol. 5718, pp. 67–77. Springer (2009)Google Scholar
  61. 61.
    Sommese, A.J., Wampler, C.W. II: The Numerical Solution of Systems of Polynomials Arising in Engineering and Science. World Scientific, Singapore (2005)CrossRefzbMATHGoogle Scholar
  62. 62.
    Stiteler, M.: Construction History and Parametrics: Improving Affordability through Intelligent CAD Data Exchange. Chaps program final report, Advance Technology Institute (2004)Google Scholar
  63. 63.
    Thierry, S.E., Schreck, P., Michelucci, D., Fünfzig, C., Génevaux, J. D.: Extensions of the witness method to characterize under-, over-and well-constrained geometric constraint systems. Comput. Aided Des. 43(10), 1234–1249 (2011)CrossRefGoogle Scholar
  64. 64.
    Tovey, M.: Intuitive and objective processes in automotive design. Des. Stud. 13 (1), 23–41 (1992)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Arts et MétiersLISPEN EA 7515, HeSamAix-en-ProvenceFrance
  2. 2.LE2I, CNRS UMR 5158University of Burgundy Franche-ComtéDijonFrance
  3. 3.LIS Laboratory, UMR CNRS 7020Aix-Marseille UniversityMarseilleFrance
  4. 4.Computer ScienceNew York UniversityAbu DhabiUnited Arab Emirates

Personalised recommendations