supdeq_haversine

% SUpDEq - Spatial Upsampling by Directional Equalization

 function d = supdeq_haversine(AzEl1, AzEl2, radius) 

 This function calculates the great circle distance between two points on
 a sphere by applying the inverse haversine function 

 Output:
 d                     - Great circle distance d between two points on the sphere

 Input:
 AzEl1 / AzEl2         - Spatial sampling point (e.g., [0,90]), where the first 
                       value is the azimuth and the second the elevation (both in degree).
                       Azimuth in degree (0=front, 90=left, 180=back, 270=right)
                       (0 points to positive x-axis, 90 to positive y-axis)
                       Elevations in degree (0=North Pole, 90=front, 180=South Pole)
                       (0 points to positive z-axis, 180 to negative z-axis)
 radius                - Head/Sphere radius in m
                       Default: 0.0875 m

 Dependencies: -

 (C) 2020 by JMA, Johannes M. Arend
             TH Köln - University of Applied Sciences
             Institute of Communications Engineering
             Department of Acoustics and Audio Signal Processing

0001 %% SUpDEq - Spatial Upsampling by Directional Equalization
0002 %
0003 % function d = supdeq_haversine(AzEl1, AzEl2, radius)
0004 %
0005 % This function calculates the great circle distance between two points on
0006 % a sphere by applying the inverse haversine function
0007 %
0008 % Output:
0009 % d                     - Great circle distance d between two points on the sphere
0010 %
0011 % Input:
0012 % AzEl1 / AzEl2         - Spatial sampling point (e.g., [0,90]), where the first
0013 %                       value is the azimuth and the second the elevation (both in degree).
0014 %                       Azimuth in degree (0=front, 90=left, 180=back, 270=right)
0015 %                       (0 points to positive x-axis, 90 to positive y-axis)
0016 %                       Elevations in degree (0=North Pole, 90=front, 180=South Pole)
0017 %                       (0 points to positive z-axis, 180 to negative z-axis)
0018 % radius                - Head/Sphere radius in m
0019 %                       Default: 0.0875 m
0020 %
0021 % Dependencies: -
0022 %
0023 % (C) 2020 by JMA, Johannes M. Arend
0024 %             TH Köln - University of Applied Sciences
0025 %             Institute of Communications Engineering
0026 %             Department of Acoustics and Audio Signal Processing
0027 
0028 function d = supdeq_haversine(AzEl1, AzEl2, radius) 
0029 
0030 if nargin < 3 || isempty(radius)
0031     radius = 0.0875;
0032 end
0033 
0034 %% Transform sampling points to radiant in matlab coordinates system
0035 
0036 AzEl1 = AzEl1*pi/180;
0037 AzEl1(:,2) = pi/2 - AzEl1(:,2);
0038 
0039 AzEl2 = AzEl2*pi/180;
0040 AzEl2(:,2) = pi/2 - AzEl2(:,2);
0041 
0042 %% Apply formula
0043 
0044 %Get distance between angular values
0045 dAz = AzEl2(:,1) - AzEl1(:,1);
0046 dEl = AzEl2(:,2) - AzEl1(:,2);
0047 
0048 %Get great circular distance
0049 d = 2 * radius * asin( sqrt( sin(dAz/2).^2 + cos(AzEl1(:,1)) .* cos(AzEl2(:,1)) .* sin(dEl/2).^2));
0050 
0051 end
0052