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Environmentally Affected Tree Growth using L-Systems and Voxels

This study explores the hypothesis that computer-simulated plant development impacted by environmental factors can be effectively achieved using L-systems within a 3D voxel environment. The methodology involves generating L-systems to simulate tree growth behaviors, such as phototropism and collision avoidance. Results indicate success in modeling realistic growth patterns influenced by luminosity and competition. The discussion covers the implications and potential improvements for future work, including more advanced stochastic algorithms and enhanced phototropic responses.

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Environmentally Affected Tree Growth using L-Systems and Voxels

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  1. Andrew Leeuwenberg Environmentally Affected Tree Growth using L-Systems and Voxels

  2. Content • Hypothesis & Aim • Methodology summary • Result • Discussion and Future work • Conclusion

  3. Aim

  4. Hypothesis H1 is that computer simulated plant development that is affected by their environment can be achieved by generating L-systems in a 3D voxel environment

  5. Null Hypothesis H0is that computer simulated plant development that is affected by their environment cannot be achieved by generating L-systemsin a 3D voxel environment.

  6. Collision avoidance

  7. Phototropism

  8. Competition

  9. Methodologysummary

  10. Grow L-System

  11. Grow L-system F…

  12. Grow L-System F[+…

  13. Grow L-system F[+F…

  14. Grow L-System F[+F][-F…

  15. Grow L-System F[+F[+F][-F]][-F[+F][-F]]…

  16. Collision avoidance

  17. Collision avoidance

  18. Luminosity

  19. Luminosity • E = 4/7 ≈ 0.57

  20. Luminosity • Adjust • Growth rate • Growth direction • Leaf growth • Leaf surface area

  21. Original development FF[+F[+X][-X]FX[-F[+X][-X]FX] FFF[+X][-X]FX

  22. New development FF[+F[+X][-X]FX[-F[+X][-X]FX] FFF[+X][-X]FX

  23. Multiple trees

  24. Multiple trees

  25. Result

  26. Collision avoidance

  27. Collision avoidance

  28. Phototropism

  29. Competition

  30. Discussionand Future Work

  31. Stem structure

  32. Stem structure • Bracketed OL-system implemented • Limited: • Not stochastic • Self-similar • More advanced Partial L-systems • Stochastic • Reduced self-similarity • Re-writing separate from growth • Method still valid

  33. Phototropism(Rotations)

  34. Current implementation • Calculate average luminosity (Ē) • North - South • East – West • Rotate towards greatest luminosity ĒN

  35. Euler rotation problem X: 90° w.s. X: 90° l.s.

  36. Euler rotation problem X, Y, Z ?

  37. Quaternions • Slerp

  38. Luminosity direction • Improve phototropism

  39. Luminosity direction

  40. Luminosity direction

  41. Luminosity direction

  42. Real-time

  43. Separating the processes

  44. Maya.cmds Generate tree 01 Generate tree 02 Return results Generate L-string Voxelize collision geometry Generate tree 03 Generate tree 04

  45. Maya.node Generate L-string Generate tree 01 Generate L-string Generate tree 02 Voxelize collision geometry Update results Generate tree 03 Generate L-string Generate tree 04 Generate L-string

  46. Maya.node Generate L-string Generate tree 01 Generate L-string Generate tree 02 Voxelize collision geometry Update results Generate tree 03 Generate L-string Generate tree 04 Generate L-string

  47. Maya.node Generate L-string Generate tree 01 Generate L-string Generate tree 02 Voxelize collision geometry Update results Generate tree 03 Generate L-string Generate tree 04 Generate L-string

  48. Competition Generate L-string Generate tree 01 Generate L-string Generate tree 02 Growth manager Update results Voxelize collision geometry Generate tree 03 Generate L-string Generate tree 04 Generate L-string

  49. Factors affecting speed Axiom length Successor length L-string length L-string interpretation Generations Growth time

  50. Factors affecting speed Number of samples Voxel Size Topology Luminosity Voxilizing geometry

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