1. Abstract
   1. process
      1. input
         1. 2D hand-drawn object
      2. construct a 2.5D model
         1. 2.5D model of the input object
      3. generate the Voronoi textures on the 2.5D object model
      4. cracking gaps on the Voronoi textures are widened progressively
2. 1. Introduction
   1. challenges
      1. Currently physically based approaches for animating crack fractures require 3D models
      2. have to introduce 3D information such as thickness to broken shapes
      3. object shadows
3. 2. Related work
   1. Physical approaches
   2. Procedural methods
      1. Voronoi-based methods
         1. Worley [23]
         2. Raghavachary [24]
         3. Mould [25]
      2. other ways
         1. Wyvill et al.
         2. Martinet et al. [27]
4. 3. Surface and volume approximation
   1. front half (FH)
   2. back half(BH)
   3. hard task: thickness
   4. stored in two layers
5. 4. Voronoi textures
   1. algorithms for constructing the Voronoi diagram[28]
      1. using graphics hardware [29]
      2. Lischinski [30]
   2. basic model for crack fractures
      1. Voronoi diagram on two layers of FH and BH
      2. Voronoi diagram (solid) and Delaunay triangulation (dot)
   3. involves
      1. seeding the interior of contours
      2. the resulting point set
      3. constructing the Voronoi network.
6. 5. Modeling cracking
   1. simulation of crack advancing
      1. several Voronoi vertices are chosen by the user
      2. Each activating seed nucleates a cracking line
      3. the cracking line zigging along its corresponding edge
      4. When a cracking line reaches an inactivated vertex, this vertex became a new activating seed
   2. gap widening
      1. the older, the wider
7. 6. Modeling fracturing
   1. add thickness
      1. divide objects into two categories
         1. solid objects
            1. thicker
         2. vacant inside
   2. collision of fragments arises during falling
      1. elastic collision
      2. inelastic collision
      3. simulated by use of the Physx library [31]
   3. set up a virtual 3D ground plane interactively on the background picture
   4. set some mechanical characteristics required by Physx
      1. density of the object
      2. the gravity
      3. the restitution parameter
      4. friction parameter
8. 7. Treatment of shadows
   1. in two phases
      1. 1. remain
      2. 2. fracturing phase
         1. the traditional shadow map algorithm