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