1. intro
   1. Bark is the result of tree growth: The wood dividing tissue (the phellogen)
   2. physical simulation of bark is not reasonable
   3. the outside layers (i.e. the visible bark) are older than the inside ones
   4. rely on crack simulation
   5. based on two complementary evolving structures
      1. circular strips of bark
      2. axial cracks
2. Previous Work
   1. Work on textures
      1. Only classical mapped textures (color, bump, displacement) have been used to handle bark
      2. Texture resynthesis on the surface
         1. Turk pro-poses
            1. able to reproduce the non–locality and the conservative property
            2. cannot easily handle a progressive change in the parameters
            3. does not provide control to the artist
            4. does not allow an interactive tuning of the parameters
      3. The image quilting approach
         1. Efros and Freeman
            1. brings some user control and can handle transitions
            2. adapting it to three dimensions (and possibly to resynthesis) is not trivial.
            3. its method of transition handling does not permit it to manage a continuous variations of parameters
   2. Work on bark
      1. Two kinds of work
         1. static dressing using textures
            1. main issue: surface parameterization
            2. Bloomenthal
            3. Maritaud et al.
            4. Hart and Baker
            5. In industry
            6. direct painting on the surface
            7. blending of multiple maps
         2. simulation
            1. Federl and Prusinkiewicz
            2. Hirota et al.
   3. Work on cracks
      1. Terzopoulos et al.
      2. Norton et al.
      3. Smith et al.
      4. Muller et al.
      5. O’Brien and Hodgins
      6. Neff et al.
   4. The physics of fractures
      1. A break occurs in a material when the internal constraints exceed a strength threshold.
      2. The molecular link is then broken and a crack starts.
      3. Two kind of fracture
         1. The fragile fracture
         2. The ductile fracture
            1. difficult and not in the scope of this paper
      4. The Inglis approach
      5. The Griffith approach
3. Base Representation
   1. our approach
      1. characterizing the phenomenological properties of bark
      2. simulating a simpler material having the same visual characteristics
   2. Case Study and Hypothesis
      1. case study
         1. the original epidermis is conserved;
         2. large, similar–looking fractures result from tree growth;
         3. the bark layer is affected by tree growth, but has no retroactive effect on it;
         4. the growth is strongly oriented (radially), as are the fractures (longitudinally);
         5. the material is elastic in the short term, and plastic at long term;
         6. fractures influence each other
         7. small strips appear between close fractures
         8. fractures are torn–open wounds whose edges can have various appearances
         9. several scales of fractures can exist.
      2. hypothesis
         1. we consider longitudinal slices of bark that are orthogonally crossed by fractures
         2. we suppose that the epidermal portions in this slice are quasi–rigid
         3. we assume an elastic mode of material fracture
         4. we simulate a quasi-static state
      3. aspects of our fracture simulator
         1. aspects
   3. Our Bark Model
      1. Three phenomena
         1. the appearance of new cracks in the bark;
         2. the propagation of cracks;
         3. the opening of existing fractures.
      2. Model of Material
         1. the bark
            1. a set of strips parallel to the growing direction
         2. a strip
            1. original epidermal elements
            2. quasi–rigid
            3. fracture elements
            4. soft
         3. Bark stiffness
            1. material stiffness
            2. R=Kl_0
            3. element stiffness
            4. K_1=\frac{l_{0}K}{l_1}
            5. K_2=\frac{l_{0}K}{l_2}
         4. Fracture stiffness
            1. linked to the quality of the connection to the substrate and to the shape of the fracture
            2. We assume the bark’s evolution is quasi–static, so the strip has to be at equilibrium
            3. Fracture opening and propagation algorithm
      3. Fracture creation
         1. is based on upon the relative lengthening of elements
      4. Fracture location
         1. a weakness map
         2. jittering
         3. recursive fractures
      5. Fracture propagation
         1. based on the Inglis observations
         2. Propagation criterion
         3. Propagation direction
      6. Fracture opening
   4. Dressing the Model with Details
      1. The epidermal texture must not contain large scale fractures, since our model will generate it
      2. The final step
         1. first need to
            1. reconstruct smooth fracture silhouettes from the discreet data;
            2. produce a mesh which embeds these silhouettes;
            3. map the user textures onto the epidermal and fracture regions of the mesh;
            4. optionally, determine and store the relief information.
         2. geometry
         3. texture
4. Results for flat bark
5. Extended Model: Mappable Bark
   1. take new constraints into account
      1. cyclic strips;
      2. attachment of the bark to the substrate;
      3. strips of varying width and length;
      4. branchings.
   2. Handling the Attachment to the Substrate
   3. Mapping Fractures on a Tree
      1. assume
         1. the tree geometry is provided by the user
         2. the curvilinear parameterization is available for the trunk and each branch.
      2. the evolution of the parameterization
         1. The growing of the tree is handled by the application.
         2. The tree shape is given at various time steps.
         3. The user is not interested in the animation of the growing tree.
   4. Adapting the Fracture Simulation
      1. Two aspects of the fracture simulation are affected
         1. the mechanical properties in distorted strips
         2. the propagation of fractures through strips, in particular at branchings.
      2. Adapting the strips material
         1. K=\frac{Rw}{l_{0}}
         2. w: width of the strip
      3. Adapting the propagation of fracture through strips
   5. Mappable Dressing
      1. Fracture shape construction
         1. bark mesh
         2. bark texture