## Acoustic Reflection Form Finding

In the post, Acoustic Reflection Patterns, we described an approach to reflecting a set of rays off of surfaces to see how the pattern of rays diffusive.  We’ve also explored how to find the form of a panel based on where you want these rays to reflect.

There are three main parameters used in both approaches: the source point, the diffusive surface, and the target points (or intersection of the rays with the sampling surface).  In the previous approach, the source point and diffusive surfaces were known and the simulation found the target points.  In this case, the source point and the target points are known, then the diffusive shaping or reflection planes are found.

To find the reflection plane, first a line is drawn from the source point to the center of each of the cells that a reflection plane is created within.  This is the initial ray.  Next a line is drawn from each target point to only one of the reflection planes so there must be at least one reflection plane for each target point.  Now there are two lines, the bisector of which represents the normal angle of our reflection plane. Below is a video showing a few variations on how this approach can play out.  One interesting piece to this is that changing which cell a target point is paired with will visually alter the diffusive surface, but the reflection pattern will stay the same.

This example only takes into account the first reflections off of the surface, but it would be possible to calculate and aim higher degree bounces, but with each additional reflection there is added complexity to calculating the solution.  The source point is also driving the process because the orientation of the reflection planes would change as the source point is moved.  More source points could be accommodated by adding more facets to each grid cell.  There is one other parameter that we’re failing to address here which is the wavelength for a given frequency of sound.  The lower the frequency, the larger the wavelength of the sound wave so in some cases the wavelength could end up being too large to acoustically “see” the reflection surface.  These are all things that we’re hoping to study as we take this research forward.