A SuperCollider Quark to encapsulate a set of points which represent a spherical design, allowing for searching, basic transformations and visualization of the design.
Let X be a finite subset of S(n−1). Spherical codes and spherical designs are nothing but finite subsets of S(n−1). Roughly speaking, the code theoretical viewpoint is to try to find X, whose points are scattered on S(n−1) as far as possible, i.e. the minimum distance dmin of X is as large as possible for a given size of X. ... On the other hand, the design theoretical viewpoint is to try to find X which globally approximates the sphere S(n−1) very well. 1
This library does not strictly enforce the definition of a spherical design, in
fact it is simply a collection of points (Cartesian objects) which
you can set arbitrarily. The expectation however is that you'll be importing
designs that are provided, such as those t-designs available through
the subclass TDesign, or assigning your own points to be
regarded as a spherical design.
Once your design is initialized, you can perform basic manipulations such as rotation, mirroring, and sorting/selection of points in the design. :crystal_ball:
Install via SuperCollider's command line:
Quarks.install("https://github.com/ambisonictoolkit/SphericalDesign")
This will also install the PointView Quark, which is used to visualize the design.
Known issues are logged at GitHub.
The method of formulating a triangulation of points, found in -calcTriplets
and its associated methods were copied, with some modification, from Scott
Wilson's port (VBAPSpeakerArray) of Ville Pukki's VBAP library in PureData.
See extSphericalDesign.sc.
The T-Designs found here are from the work of Hardin and Sloane. 2 These and other designs can be downloaded directly from their site: http://neilsloane.com/sphdesigns/. If you use any of these designs, please acknowledge this source.
The development of the Spherical Design Library for SuperCollider3 is supported by The University of Washington's Center for Digital Arts and Experimental Media (DXARTS).
Copyright the ATK Community, Joseph Anderson, and Michael McCrea, 2018.
- Michael McCrea (@mtmccrea)
- Joseph Anderson (@joslloand)
- Daniel Peterson (@dmartinp)
[1] Bannai, E., Bannai, E. A survey on spherical designs and algebraic combinatorics on spheres. European Journal of Combinatorics, Volume 30, Issue 6, August 2009, Pages 1392-1425.
[2] R. H. Hardin and N. J. A. Sloane, McLaren's Improved Snub Cube and Other New Spherical Designs in Three Dimensions. Discrete and Computational Geometry, 15 (1996), pp. 429-441.