This project was a research project at the Acoustic Lab at Waseda University in Tokyo. It extended on the research of Kataoka et. al. about Real-time Measurement and Display System of 3D Sound Intensity Map using Optical See-Through Head Mounted Display.

By using the collected data I developed a pseudo algorithm, that localized a sound source and visualized the recorded sound in circular waves.

Unity Editor 2018.4.36f1 HoloToolkit 2017.4.3.0

HoloLens 1

For the following approach I assume that the recorded sound is coming from a single source, and that each recorded data point is measuring the same sound from a different position. Each recorded data point is classified as a Particle and has two relevant properties: direction and sound intensity.

struct Particle {
	position: Vector3
	intensity: Vector3
}

position is the particle's world position relative to a given reference point. The direction of the property intensity defines the direction in which the recorded sound travelled, whereas the vector's length is determined by the sound intensity.

Function 
Data: particles: List<Particles>,
	with particles[i].position: Vector3
	and particles[i].intensity: Vector3
Result: center: Vector3
	centerCandidates : List <Vector3>
	for i ← 0 to particles.length by 1 do
		for j ← 0 to particles.length by 1 do
			if i != j then
				centerCandidate ← SkewDistanceCenter(
					particles[i].position + particles[i].intensity,
					particles[j].position + particles[j].intensity
				)
		 		centerCandidates.Add(centersCandidate)
			end
		end
	end
 	return AveragePosition(centerCandidates)

For each pair of two distinct particles I calculate the closest point between their direction vectors, which is the center between these two vectors. For a number of n particles I then get n^2 center candidates. By calculating the avarage position of these n^2 positions, I determine a hypothetical sound source, named center.

The intensity vector is then updated by using the following steps:

1. Determine its new direction = particle.position - center
2. Calculating the angle α between direction and particle.intensity
3. Adjust the new intensity level particle.intensity = ((180−α)/180) * particle.intensity

By adjusting the particles' intensity to the new center, it is considered that sound could be scattered, reflected, or refracted.

I assume that the sound propagates spherically. Therefore, we represent the sound propagation as a sphere with center as its center and with its vertices displaced depending on the adjusted particles. The bigger the angle between a particle's intensity and its closest sphere vertex, the smaller its impact on the vertex displacement. The result is a deformed sphere that represents the sound propagation.

The deformed sphere's vertices are passed to the shader SineFragmentDisplacement.shader that generates a 2D plane. This plane then renders an intersection of the sphere and illustrates the sound propagation as wave impulses.