Geometric Modeling of Fractal Forms for CAD. Christian Gentil

Geometric Modeling of Fractal Forms for CAD

4Figure 4.1. Example of the user interface of “MODITERE”, the iterative modeler d...Figure 4.2. Example of orientation constraints of edges for the definition of th...Figure 4.3. Example of configuration of edge orientation for the attractor of Fi...Figure 4.4. Issues in the orientation of edges. On the left, the connection for ...Figure 4.5. Definition and application of the permutation operator. On the left,...Figure 4.6. Construction of a connection between two edges of opposite orientati...Figure 4.7. The three curves have a single internal dimension, and vertices of d...Figure 4.8. The definition of the connections for volume cells can prove complex...Figure 4.9. Illustration of the definitions of face permutations: on the left, a...Figure 4.10. Examples of construction of the topological tensor product. For a c...Figure 4.11. Example of cellular decomposition of a tensor product of two curves...Figure 4.12. Automaton of the curve aFigure 4.13. Quotient graph of curve aFigure 4.14. Automaton of a surface automatically generated from the automatons ...Figure 4.15. Quotient graph of a surface induced by adjacency relations combinin...Figure 4.16. Quotient graph obtained from adjacency relations on incidence opera...Figure 4.17. Automaton of a volume structure obtained by tensor product of three...Figure 4.18. Example of an automatically generated tree, whose leaves will perfe...Figure 4.19. First stages of subdividing a tree bordered by a curveFigure 4.20. The types of subdivisions of the tree depend on the types of edge s...Figure 4.21. Automaton representing a tree structure whose set of leaves is divi...Figure 4.22. Double trees bordered by quadrangular surfacesFigure 4.23. Example of surface obtained by the tensor product of a NURBS curve ...Figure 4.24. Automaton representing the construction of a connection structure b...Figure 4.25. Connection subdivision process. The red, green and blue mesh, respe...Figure 4.26. Connections built between different pairs of surfaces: a Doo–Sabin ...Figure 4.27. Example of a lacunar surface, co-imagined by architects (IBOIS-EPFL...Figure 4.28. Example of the definition of a 2D lacunar structure by tiling the p...Figure 4.29. Example of construction of the Menger sponge. In red, the cube is d...Figure 4.30. Lacunar structures obtained by removing the central part of a regul...Figure 4.31. Menger–Excoffier sponge with walls of the same thickness between ea...Figure 4.32. The Menger–Excoffier sponge is built from two subdivision systems o...Figure 4.33. For the Menger–Excoffier sponge, the two 3D subdivision systems are...Figure 4.34. “Triangle”-type cells have been added to the structure of Figure 4....Figure 4.35. Design of a lacunar structure from two types of cell: a tetrahedron...Figure 4.36. Two copies of the 3D lacunar topological structure obtained from th...Figure 4.37. Prototypes designed by assembly of tetrahedral structures shown in ...Figure 4.38. Illustration of the topological subdivision of the lacunar face. Fo...Figure 4.39. Lacunar face at iteration levels 3 (on the left) and 4 (in the cent...Figure 4.40. Illustration of the cellular decomposition and the subdivision proc...Figure 4.41. Example of the design of a lacunar structure, built from a truncate...Figure 4.42. Example of filling using porous volumes. On the left, the geometry ...Figure 4.43. Examples of the design of lacunar structures through the assembly o...Figure 4.44. Assembly according to the structure of a diamond. On the left, an e...Figure 4.45. Examples of rough surfaces. For a color version of this figure, see...Figure 4.46. Example of a variant of the Von Koch curve filling up almost an ent...Figure 4.47. Example of a rough, or even chaotic, surface, designed on the princ...Figure 4.48. Both surfaces are designed from the same topological structure as s...Figure 4.49. Example of a self-supporting hull, built by wood panel assembly (IB...Figure 4.50. On top, prototype of the thermal exchanger manufactured in aluminum...Figure 4.51. Construction of the display primitive linking two levels of the exc...Figure 4.52. Internal structure of the switch. For a color version of this figur...