Controlling the Geometry System

One of the biggest advances that Pachyderm offers is the option to choose how room geometry is represented - NURBS or Mesh. You designate this in the Pachyderm Options:

1. Type Options into the command prompt.

2. Click 'Pachyderm_Acoustic' in the list of 'Document Properties' pages.

3. In the upper left corner of the 'Pachyderm Acoustic' options page, a radio button control called 'Geometry System' can be used to designate the geometry system.

A few things to note are the following:

- Multi-Resolution Meshes is diabled. This is because it is an idea which has as yet not been realized, but may become available sometime in the future.

- Clicking the NURBS geometry system disables the 'Processing' control and switches the program to single processing. This is because at this time, the Pachyderm relies on the NURBS tracing routines provided by NcNeel with the Rhinoceros program. These routines do not support multi-processing, and so NURBS tracing in Pachyderm must be done on a single processor. A multi-processing NURBS tracer is slated for future development, unless McNeel one day provides one with Rhino.

 

Making the Geometry System Call

Each geometry system has advantages over the other. The Mesh based system is accurate in most conditions, and it is fast and efficient. Where large and dominant curved surfaces are present in a room, it may falter in accuracy. This is where the NURBS based geometry systems is useful.

One such case pf this is the curved over-stage reflector, which can be found in many rooms all around the world. To demonstrate this, a simple model has been constructed, and has been presented below:

Using Pachyderm's Mapping Interface, designating the floor-like plane below as the mapping surface, many rays were cast, both with the Mesh geometry system, and the NURBS geometry system. The results are shown below:

It is apparent from these results that the selection of geometry system makes a great difference. This is because the mesh system will represent the curve as individual flat faces. While they seem to approximate the curve with reasonable precision, at each edge between polygons, a shadow will be cast by the raytracer.. This is what leads to the banding shown in the mesh case.

One may also observe that the reflections seem lower in strength in the case of the NURBS geometry system. This is because in a reflection from a curved surface, energy is dispersed in such a way that a wavefront rapidly increases in area, which lowers reflection strength from what would be expected from a flat surface. Ray-tracing on NURBS surfaces can approximate this difference in wavefront propagation more accurately than ray-tracing on a mesh representation of a curve.

It is important to remember, when using this tool, that a wavefront may reflect from a curved surface of a given radius differently at one frequency than at another. Frequency dependent curved surface reflection is as yet still poorly understood, though, and so this is one of the best tools available for quickly finding the reflection attenuation of a curved surface.

For this reason, it is important to understand that the results of a NURBS-based simulation for rooms with curved surfaces will be more accurate at high frequencies than at low frequencies. Since this is generally true for mesh based simulations as well, this should not alter anyone's expectations of the simulation significantly.