Topological Exploration and Analysis of Simplicial Complexes Using Audio Signals

In this project we explore a new technique for traversing simplicial complexes (i.e., triangulations or meshes) and producing sounds from the output of this traversal. The traversal algorithm was invented in order to extract temporal information from static geometric structures; this information is used as input to an additive sound synthesis algorithm. A systematic traversal of complexes and associating data to parameters of sound synthesis has many possible applications including the topological analysis of objects of dimension 4 or higher, topological exploration of large data sets, and music composition. In the first phase of our work, which we presented at the VROOM exhibit at SIGGRAPH '94, we invented the traversal algorithm and mapped the output of that traversal in a straightforward way to parameters of an additive synthesis algorithm.

Click on the icon to listen to an example of sounds produced in this first phase. (Note to SGI users: reset the audio output rate to 22 kHz after playing this 8 kHz file.) It sounds as if it were composed, and yet it's produced purely from the geometric structure of the data, algorithms, and output from VSS (VSS is the sound server being developed by the Audio Development Group, NCSA).

In the next phase of our work, which will be presented at the GII Testbed at Supercomputing '95 in San Diego, we will extend this work in a number of ways. Users will be given the opportunity to explore large data sets in real-time by selecting starting points for exploration, indicating regions of interest, and changing features of the object under study. To achieve this performance, we must implement the traversal code on a parallel platform. In addition, we will extend the mapping to the sound synthesis algorithms with additional parameters, changing timescales, localization, and multi-layer controls.


Ulrike Axen
Department of Computer Science and Audio Development Group, NCSA
University of Illinois

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