An Algorithm for Automatic Geometry Simplification for Room Acoustical Simulation Based on Regression Planes

The numerical simulation of room acoustics is based – besides other properties – on the geometry of the evaluated room. During the planning phase of a building, these geometry data are usually available as a closed polyhedron stored in a computer readable CAD file format, that was prepared for other purposes as, e.g., visualisation. These geometry data must be processed to extract a reasonable small number of acoustically appropriate polygons to reduce calculation times for the simulation of room acoustics. The size of the appropriate polygons is closely related to the sound wave length.

This paper presents an algorithm to reduce the number of polygons by iteratively replacing a group of polygons by a bigger polygon. This polygon is defined by a regression plane minimizing the squared distances of the points in the polygons of the group. The group of polygons is a growing set containing polygons with vertices within a layer of limited thickness around the intermediate regression plane. This thickness can be adopted to the examined wavelength.

Besides the presentation of the basic algorithm with examples, some hints for the practical application in room acoustics are discussed together with the possibility to use intermediate results from the calculation of the regression planes to estimate the additional scattering coefficients that are necessary to model the original roughness of the simplified surface.