Trajectory Extension¶
This extension can be used to predefine trajectories that are based on mathematical functions and geometrical primitives.
The renderer can evaluate those functions at runtime according to its own update rate.
Consequently, the accuracy of the trajectory is preserved according to the quality/granularity of the renderer.
This approach can be compared to differences between vector graphics (e.g., .eps
) and raster graphics (e.g., .bmp
).
Suggested Functions¶
Taxonomy of trajectories suggest five different kinds
Style | Curve Type |
Constant | Point |
Periodic | Lines, Curves, Lissajous Figures, Bresenham’s Algorithm |
Quasi-Periodic | Invariant Tori, Spirals, Spirographs, Turtle Graphics |
Chaotic | Strange Attractors, Webs and Wreaths, Mazes, Space Filling Curves, L-Systems |
Stochastic | Random Walks, Noise, Jitter |
Periodic Curves¶
Closed Curves | Open Curves | |
Broken | Unbroken | |
Bicorn | Swastika Curve | Lituus Curve |
Lemniscate | Devil’s Curve | Witch of Agnesi |
Scarabaeus | Plateau Curve | |
Rose Curve | Cissoid of Diocles | |
Butterfly Curve | ||
Cornoid | ||
Gear Curve | ||
Lissajous Curve and in 3D | ||
Superellipse | ||
Limaçon Curve | ||
Hypotrochoid | ||
Epitrochoid, Epicycloid | ||
Hypocycloid | ||
Circular Motion |
Quasi-Periodic¶
- Poinsot's Spirals
- Logarithmic Spiral
- Archimedean Spiral
- Concho-Spiral
- Hyperbolic Spiral
- Fermat’s Spiral
- Conical Spiral
Chaotic¶
Stochastic Trajectories¶
- Random Walk (i.e., brownian motion)
Sources¶
- James, S. G. (2005). Developing a flexible and expressive realtime polyphonic wave terrain synthesis instrument based on a visual and multidimensional methodology. Master’s thesis, Edith Cowan University, Perth, Australia. [pdf]
- Nara Hahn, Keunwoo Choi, Hyunjoo Chung, and Koeng-Mo Sung (2010). Trajectory Sampling for Computationally Efficient Reproduction of Moving Sound Sources, 128th AES Convention, Preprint 8080.
- Fernando Lopez-Lezcano: A dynamic spatial locator ugen for CLM, SMC 2008 [pdf]
- Garry Kendall. Composing from a geometric model:” five-leaf rose”. Computer Music Journal, 5(4):66–73, 1981.
- National Curve bank: http://curvebank.calstatela.edu/home/home.htm