# Algorithm

## Starting Point

`TRACE_PARTICLE(start_x, start_y, start_vx, start_vy, T, alpha) x = start_x y = start_y vx = start_vx vy = start_vy t = 0 dt = 1 points = array() while t <   Add new point [x, y] to points  q = (T - t)^(-alpha)  x = x + vx * dt  y = y + vy * dt  ax =  -vy * q  ay = vx * q  vx = vx + ax * dt  vy = vy + ay * dt end return pointsend`

# Results

## Summary

• Initial stem width (in pixels)
• Initial curl direction (left or right)
• Number of curve levels
• Parameters of the curve at each level (Length/Curvature/Number of branches)
• Clip-art element type
• Ornament region points
• Control points for the base step of the ornament

# Conclusions and Future Work

## Possible Extensions

• To produce the magnetic curves I used the same charge function as suggested in the paper. Other functions could be experimented with to produce more interesting types of curves. Xu touches upon this subject and notes that triangular waves are a good choice for experimentation.
• One of the main problems with the magnetic curves algorithm is its ability to produce attractive space-filling curves. In this article I address this issue by requiring user input. It would be great to do it automatically. One possible way to address this issue is to make the charge function repeat with some period and make the main charged particle bounce off the edges of the ornament region. The magnetic field strength B can be increased along the region boundaries to achieve this effect. Moreover, the parameters of the charge function can be updated at runtime to facilitate space filling.
• Some of the historical example of floral ornament that I had seen allowed an intersection between stems by arranging them into plait-work. This would be an interesting idea to experiment with.

# Bibliography

1. Wong M. T., Zongker D. E., Salesin D. H.: Computer-generated floral ornament. In Proceedings of SIGGRAPH ’98 (1998), ACM Press, pp. 423–434.
2. “Frame” The Grove Encyclopedia of Decorative Arts. Ed. Gordon Campbell. © Oxford University Press 2006. The Grove Encyclopedia of Decorative Arts: (e-reference edition). Oxford University Press. [Accessed April 15th, 2010]
3. Introduction to Luke-Arts, Northwestern Church of Christ, Dec. 2008. [Online] http://www.nwcofc.com/bible-studies/ [Accessed April 15th, 2010]
4. Illuminated Manuscript Leaf on Vellum, Bloomsbury Auctions, Apr. 2008. [Online] http://ny.bloomsburyauctions.com/detail/NY008/20.0 [Accessed April 15th, 2010]
5. Lewis F. Day. Nature in Ornament. B.T. Batsford, London, 1898.
6. Judaica Collection, Yale University Library, Oct 2008. [Online] http://www2.library.yale.edu/judaica/newacquisitions2006.html [Accessed April 15th, 2008]
7. Sheet of wallpaper, late 17th century. Museum no. E.1003–1976, Victoria and Albert Museum. [Online] http://www.vam.ac.uk/images/image/22261-popup.html [Accessed April 15th, 2010]
8. Floral wallpaper, about 1850–75. Museum no. E.800–1969, Victoria and Albert Museum. [Online] http://www.vam.ac.uk/images/image/22252-popup.html [Accessed April 15th, 2010]
9. W Red, Black and Taupe Large Scale Modern Floral Wallpaper, Home Depot Catalog, Catalog #100632840, 2010.
10. Floral Ornament Vector Pack, Ideal Hut, Oct. 2009. [Online] http://www.idealhut.com/freebies/freebie-release-5-floral-ornaments-vector-pack/ [Accessed April 15th, 2010]
11. Xu L., Mould D.: Magnetic Curves: Curvature-Controlled Aeshetic Curves Using Magnetic Fields. In Computational Aesthetics in Graphics, Visualization, and Imaging (2009). pp. 1- 8.
12. Catmull, Edwin and Rom, Raphael, A class of local interpolating splines, in R.E. Barnhill and R.F. Riesenfed (eds.) Computer Aided Geometric Design, Academic Press, New York, 1974, 317–326.

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## More from Anton L.

Eng Manager @Snapchat. Android hacker, and a product design geek. Previously: cofounder of @UmanoApp (acquired by @Dropbox), @Google, @Pixar, @Kik.

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## Anton L.

Eng Manager @Snapchat. Android hacker, and a product design geek. Previously: cofounder of @UmanoApp (acquired by @Dropbox), @Google, @Pixar, @Kik.