Comparison of 2D and 3D multichannel audio rendering methods for hearing research applications using technical and perceptual measures

Open Access

Table 2

Angular errors $E_{r_{v}, 2 D}$ ${E}_{{\mathbf{r}}_v,2D}$ , $E_{r_{v}, 3 D}$ ${E}_{{\mathbf{r}}_v,3D}$ , $E_{r_{E}, 2 D}$ ${E}_{{\mathbf{r}}_E,2D}$ and $E_{r_{E}, 3 D}$ ${E}_{{\mathbf{r}}_E,3D}$ for the tested rendering methods, averaged across 360 points on a ring (2D) or 2432 points on a sphere (3D), respectively. The standard deviations are given in parentheses.

Label	N	$E_{r_{v}, 2 D}$ ${E}_{{\mathbf{r}}_v,2D}$	$E_{r_{v}, 3 D}$ ${E}_{{\mathbf{r}}_v,3D}$	$E_{r_{E}, 2 D}$ ${E}_{{\mathbf{r}}_E,2D}$	$E_{r_{E}, 3 D}$ ${E}_{{\mathbf{r}}_E,3D}$
minimal	1	90.0 (52.0)	90.0 (39.1)	90.0 (52.0)	90.0 (39.1)
hoa2d	16	0.0 (0.0)	32.6 (21.6)	0.0 (0.0)	32.6 (21.6)
hoa2d_basic	16	0.0 (0.0)	32.6 (21.6)	0.0 (0.0)	32.6 (21.6)
hoa29_pinv	29	0.7 (0.4)	3.0 (3.4)	0.7 (0.2)	6.1 (6.8)
hoa29_allrad	29	0.2 (0.1)	0.6 (0.4)	1.7 (0.9)	4.7 (3.4)
nsp45	45	5.6 (3.3)	15.0 (8.6)	5.6 (3.3)	15.0 (8.6)
hoa45_allrad	45	0.5 (0.2)	0.7 (0.5)	3.0 (1.2)	4.8 (3.4)
vbap45	45	0.0 (0.0)	0.0 (0.0)	2.2 (1.0)	5.7 (3.5)

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