Geometric Audio 4: Taxi-Cab Distance Bounds on Integer Lattice Maps

Recall from the introductory post, the taxi-cab distance metric on the integer lattice map relates the max-order of image-sources to the lattice volume or the total number of image-sources contained within a radius “ball”. This quantity is useful for determining the total costs of processing individual image-sources in cases where can be known or estimated beforehand… Read More Geometric Audio 4: Taxi-Cab Distance Bounds on Integer Lattice Maps

Geometric Audio 2: Gauss Circle Problem for Integer Sized Room Models

In the previous post on image-sources for room modeling, we made the observations that There exist a unique path from each image-source coordinate that can be back-traced to a receiver The distance and direction between image-source coordinate and listener are equal sum total of the back-traced ray lengths and the final leg of the back-traced… Read More Geometric Audio 2: Gauss Circle Problem for Integer Sized Room Models

Geometric Audio 1: Image-Source Room Models

A common audio technique for adding depth to a mix is to throw in echos or early reflections following the direct sound-source arrival to a listener. To model such reflections, many reverberation algorithms treat a sound-source and listener as a point emitter and receiver within an imaginary room or box. The reasoning follows that such a configuration… Read More Geometric Audio 1: Image-Source Room Models