Splitting TechniqueWe introduce a splitting technique to represent both abstract andnatural patterns, similar in spirit to the work by Federl [2003], butnot based on physics. We randomly place an irregular trail in theregion first. We propose two controls for the splitting. One sugges-tion is that if the curve exceeds the length threshold, it emits a fewnew particles evenly at ∆l length (see Figure 13). The new particlesare spawned on alternating sides of the parent curve. Their direc-tion is rotated from the tangent direction of the parent curve withthe same or similar angles. Each particle travels for an interval,until a sufficient length of the curve is attained. Another sugges-tion is that, after having the first curve, the process repeats for aknown number of stages, each time emitting a fixed number (n) of particles along the previous curve and only stopping when the max-imum number of stages is reached. The random irregular curve (ascurve type II) is generated by randomly choosing the sign of thecharge q while f (t) returns a random value uniformly taken fromthe interval [0.00001, 0.1]. This curve type is used in Figure 6 (a),(b), (e) and (f) as well.
Figure 14 demonstrates the splitting results under the length con-trol. Sparse versions (larger ∆l) are shown on the left side, whiledense tessellations (smaller ∆l) are shown on the right side. Fig-ure 15 demonstrates the splitting results under stage control (n =7). This process introduces a lot of irregularities and randomnessinto the final effects. Sometimes the even spatial distribution is lost(e.g., Figure 14 (e)) and big empty areas appear. Even then, be-cause each child curve has similar starting angles along its parentcurve, and the same angle occurs frequently in this region, humanscan easily detect the similarities and group them into a texture. Wequickly discriminate each group of tiles based on the angles. Visually, the length control provides better spatial control but the stagecontrol might be suitable for some branching phenomena.We can use this process for creating shapes reminiscent of cracks orleaves. As Federl mentioned, cracking in dried mud is commonlyseen splitting at 90 degree [Federl 2003]. Figure 14 (a) (b) andFigure 15 (a) resemble this cracking phenomenon, while Figures 14(f) and 15 (c) are more like leaves. Figure 1 (b) shows a simplecombination by putting our cracks on top of a painting generatedby the image parsing method [Zeng et al. 2009]. It nicely simulatesthe craquelure seen in many old oil paintings. Figure 1 (a) showsanother example by introducing the colors from the artist’s work inFigure 2 (a) to present an abstraction for tree leaves.
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