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 3: Gauss Circle Problem for Integer Sized Room Models (part 2)

Recall in the previous post our derivation of the Gauss circle recurrence relation generalized to arbitrary dimensions, scaling, offset, and weights: where the cost of computing for for max-distance requires flops. In practice, the summation should be transposed so that is incremented within the inner loop as to take advantage of vectorization/SIMD memory access patterns. A second approach for… Read More Geometric Audio 3: Gauss Circle Problem for Integer Sized Room Models (part 2)

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