1. i MAGIS is a joint project of CNRS - INPG - INRIA - UJF iMAGIS-GRAVIR / IMAG Painting folds using expansion textures Jean Combaz Fabrice Neyret http://www-imagis.imag.fr/Membres/Jean.Combaz/

2. iMAGIS-GRAVIR / IMAG Motivations More realistic images More details More complexity Drape and folds –Cloth material –Elastic surface + constraints folds

3. iMAGIS-GRAVIR / IMAG Motivations 2 solutions: –Physical simulation –Shape modeling But: –We just want a plausible shape, not a physical one –Physical parameters, initial conditions ? –Fastidious task in a geometric modeler

4. iMAGIS-GRAVIR / IMAG Motivations Goal: –Add details on a surface –High level of control –Close to sculpture

5. iMAGIS-GRAVIR / IMAG Plan Motivations Previous work –Specifying the detailled shapes –Representing the detailled shapes Expansion textures –From the user’s point of view –From the programmer’s point of view Results Conclusion

6. iMAGIS-GRAVIR / IMAG Previous work: specifying the detailled shapes Interactive tools Details editor detailsuser [Hanrahan90] Direct painting[Sederberg86][Coquillart90] FFDModeler Alias wavefrontMaya Artisan™

7. iMAGIS-GRAVIR / IMAG Previous work: specifying the detailled shapes Procedural tools Details generator detailsuser [Perlin85][Fleischer95] ([Ebert94], [Fournier80], [Perlin89]) ([Badler90], [Wong97]) Generic generators Specialized generators [Prusinkiewicz93]

8. iMAGIS-GRAVIR / IMAG Previous work: specifying the detailled shapes Simulation tools Physical solver detailsuser Cloth material Biological patterns [Breen94][Baraff98] [Fowler92][Turk91] [Terzopoulos88][Witkin91]

9. iMAGIS-GRAVIR / IMAG Plan Motivations Previous work –Specifying the detailled shapes –Representing the detailled shapes Expansion textures –From the user’s point of view –From the programmer’s point of view Results Conclusion

10. iMAGIS-GRAVIR / IMAG 3D surface encoding Polygonal meshes Voxels Surfels Displacement mapping Bump maps Previous work: representing the detailled shapes [Guskov99] ([Wang00]) ([Blinn78])

11. iMAGIS-GRAVIR / IMAG Texels, hypertextures Transitions Previous work: representing the detailled shapes [Neyret98][Perlin89][Kajiya89] ([Becker93], [Max86]) [Cohen98]

12. iMAGIS-GRAVIR / IMAG Plan Motivations Previous work –Specifying the detailled shapes –Representing the detailled shapes Expansion textures –From the user’s point of view –From the programmer’s point of view Results Conclusion

13. iMAGIS-GRAVIR / IMAG Geometry: Triangular mesh Expansion textures: user’s point of view

14. iMAGIS-GRAVIR / IMAG Geometry: Triangular mesh Expansion texture Offline painting Interactive painting Procedural generation Expansion textures: user’s point of view

15. iMAGIS-GRAVIR / IMAG Geometry: Triangular mesh Expansion texture –Location Expansion textures: user’s point of view

16. iMAGIS-GRAVIR / IMAG Geometry: Triangular mesh Expansion texture –Location –Orientation Expansion textures: user’s point of view

17. iMAGIS-GRAVIR / IMAG Geometry: Triangular mesh Expansion texture –Location –Orientation –Magnitude of expansion x 1.5 Expansion textures: user’s point of view

18. iMAGIS-GRAVIR / IMAG Geometry: Triangular mesh Expansion texture –Location –Orientation –Magnitude of expansion –Style information Desired wavelength Expansion textures: user’s point of view

19. iMAGIS-GRAVIR / IMAG Geometry: Triangular mesh Expansion texture –Location –Orientation –Magnitude of expansion –Style information Desired wavelength Regularity Expansion textures: user’s point of view

20. iMAGIS-GRAVIR / IMAG Geometry: Triangular mesh Expansion texture –Location –Orientation –Magnitude of expansion –Style information Desired wavelength Regularity –Constraints, attachments Expansion textures: user’s point of view

21. iMAGIS-GRAVIR / IMAG Example: Interactive painting of folds Expansion textures: user’s point of view

22. iMAGIS-GRAVIR / IMAG Example: Interactive painting of folds Expansion textures: user’s point of view

23. iMAGIS-GRAVIR / IMAG Example: Interactive painting of folds Expansion textures: user’s point of view

24. iMAGIS-GRAVIR / IMAG Example: Interactive painting of folds Expansion textures: user’s point of view

25. iMAGIS-GRAVIR / IMAG Example: Interactive painting of folds Expansion textures: user’s point of view

26. iMAGIS-GRAVIR / IMAG Example: Interactive painting of folds Expansion textures: user’s point of view

27. iMAGIS-GRAVIR / IMAG Plan Motivations Previous work –Specifying the detailled shapes –Representing the detailled shapes Expansion textures –From the user’s point of view –From the programmer’s point of view Results Conclusion

28. iMAGIS-GRAVIR / IMAG Expansion textures: programmer’s point of view Algorithm

29. iMAGIS-GRAVIR / IMAG Expansion textures: programmer’s point of view Algorithm –Reference state Triangular mesh Rest length l 0 Rest curvature  0

30. iMAGIS-GRAVIR / IMAG Expansion textures: programmer’s point of view Algorithm –Reference state Triangular mesh l 0,  0 –Expansion (or contraction)

31. iMAGIS-GRAVIR / IMAG Expansion textures: programmer’s point of view Algorithm –Reference state Triangular mesh l 0,  0 –Expansion (or contraction) →Update rest lengths

32. iMAGIS-GRAVIR / IMAG Expansion textures: programmer’s point of view Algorithm –Reference state Triangular mesh l 0,  0 –Expansion (or contraction) →Update rest lengths –Mesh optimization According to the new rest lengths

33. iMAGIS-GRAVIR / IMAG Expansion textures: programmer’s point of view Algorithm –Reference state Triangular mesh l 0,  0 –Expansion (or contraction) →Update rest lengths –Mesh optimization –Solver →Displacements to decrease the stress

34. iMAGIS-GRAVIR / IMAG Expansion textures: programmer’s point of view Texture Expansion Physical model Solver

35. iMAGIS-GRAVIR / IMAG Expansion textures: programmer’s point of view Texture Expansion An expansion tensor field 2x2 symetric matrix τ 2D vector u new length u t τ u Isotropic expansion Expansion Anisotropic unidirectional expansion Anisotropic expansion

36. iMAGIS-GRAVIR / IMAG Expansion textures: programmer’s point of view Pysical model 3 kinds of forces : Tangential response F T F T = F E - (F E. N) N F E is a elastic force (Green-Lagrange F.E.)

37. iMAGIS-GRAVIR / IMAG Displacements dP = .F = .(F T + F N + F  ) Expansion textures: programmer’s point of view

38. iMAGIS-GRAVIR / IMAG Expansion textures: programmer’s point of view Displacements dP = .F = .(F T + F N + F  ) F T : tangential response F T = F E - (F E. N) N F E is a elastic force N

39. iMAGIS-GRAVIR / IMAG Expansion textures: programmer’s point of view Displacements dP = .F = .(F T + F N + F  ) F T : tangential response F N : normal response F N = (k p f(  -  0) + k pi ) C a N to create folds N

40. iMAGIS-GRAVIR / IMAG Expansion textures: programmer’s point of view Displacements dP = .F = .(F T +F N +F  ) F T : tangential response F N : normal response F  : curvature control F  = - k  (  -  0 ) N to smooth folds NN

41. iMAGIS-GRAVIR / IMAG Plan Motivations Previous work –Specifying the detailled shapes –Representing the detailled shapes Expansion textures –From the user’s point of view –From the programmer’s point of view Results Conclusion

42. iMAGIS-GRAVIR / IMAG Results: Regular folds Initial shape:square Expansion rate:1.5 (anisotropic) Constraint:left and right border attached Real plastic cover

43. iMAGIS-GRAVIR / IMAG Results: Non uniform expansion Initial shape:square Expansion rate:1.0 1.5 (anisotropic) Constraint:all borders are attached

44. iMAGIS-GRAVIR / IMAG Results: Coat folded in a ring area Initial shape:square Expansion rate:1.5 (anisotropic) Constraint:all borders are attached

45. iMAGIS-GRAVIR / IMAG Results: scrunchy Initial shape:torus Expansion rate:2.5 (anisotropic) Constraint:a small torus inside the shape

46. iMAGIS-GRAVIR / IMAG Results: scrunchy Initial shape:torus Expansion rate:2.5 (anisotropic) Constraint:a small torus inside the shape

47. iMAGIS-GRAVIR / IMAG Results: circumvolution shapes isotropic expansion

48. iMAGIS-GRAVIR / IMAG Results: circumvolution shapes isotropic expansion

49. iMAGIS-GRAVIR / IMAG Conclusion Expansion textures: a new paradigm High level of control Add thin details Close to a physical simulation solver Close to sculpture and painting from the user point of view

50. iMAGIS-GRAVIR / IMAG Future work To be improved –Solver (computation time) –Folds shape control Bump mapping Morphogenesis (huge expansion) –Self-intersections –Generation of procedural expansion textures

51. iMAGIS-GRAVIR / IMAG Questions ?