The Visual Computer

, Volume 25, Issue 5–7, pp 519–527 | Cite as

Fluid-based hatching for tone mapping in line illustrations

  • Afonso Paiva
  • Emilio Vital Brazil
  • Fabiano Petronetto
  • Mario Costa Sousa
Original Article


This paper presents a novel meshless, physically-based framework for line art rendering of surfaces with complex geometry and arbitrary topology. We apply an inviscid fluid flow simulation using Smoothed Particles Hydrodynamics to compute the global velocity and cross fields over the surface model. These fields guide the automatic placement of strokes while extracting the geometric and topological coherence of the model. Target tones are matched by tonal value maps allowing different hatching and cross-hatching effects. We demonstrate the simplicity and effectiveness of our method with sample renderings obtained for a variety of models.


Non-photorealistic rendering Pen and ink hatching Direction fields Smoothed particles hydrodynamics Computational fluid dynamics 


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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Afonso Paiva
    • 1
  • Emilio Vital Brazil
    • 2
  • Fabiano Petronetto
    • 3
  • Mario Costa Sousa
    • 4
  1. 1.ICMC (Institute of Mathematics and Computer Science)USPSão CarlosBrazil
  2. 2.IMPA (Institute of Pure and Applied Mathematics)Rio de JaneiroBrazil
  3. 3.Department of MathematicsPUC-RioRio de JaneiroBrazil
  4. 4.Department of Computer ScienceUniversity of CalgaryCalgaryCanada

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