Home > SPlaC v1_0 > Ellipsoids > EllOblateGeomFact.m

EllOblateGeomFact

PURPOSE ^

Returns geometrical factors associated with a given oblate spheroid (for which a=b>c)

SYNOPSIS ^

function stEllGeom = EllOblateGeomFact(a,c,sOption)

DESCRIPTION ^

 Returns geometrical factors associated with a given oblate spheroid (for which a=b>c)
 The relevant formulae are given in Sec. G.2.

 Parameters:
 - a,c: scalars or row vectors [1 x G]
          semi-axis length along x (same as y), and z
 - sOptions: string (optional)
           if 'L', only L_1, L_3 are returned
           if 'x', or 'z', only properties related to corresponding
           axis are computed
           if 'All' (default), then all properties are returned
 Returns:
 - stEllGeom: structure with fields, all of size [1 x G]
 stEllGeom.a, c for future reference
 stEllGeom.S: surface area (in squared units of a, b, and c)
 stEllGeom.type: ='Oblate' (type of ellipsoid)
 stEllGeom.L1, L3: Geometrical factors (see Sec. G.1.5)
 stEllGeom.exix2ave: <|e_xi . e_x|^2>
 stEllGeom.exiz2ave: <|e_xi . e_z|^2>
 stEllGeom.exix4ave: <|e_xi . e_x|^4>
 stEllGeom.exiz4ave: <|e_xi . e_z|^4>
 stEllGeom.exix2y2ave: <|e_xi . e_x|^2 |e_xi . e_y|^2>
 stEllGeom.exix2z2ave: <|e_xi . e_x|^2 |e_xi . e_z|^2>

 This file is part of the SPlaC v1.0 package (copyright 2008)
 Check the README file for further information

EXAMPLE OF OUTPUT ^

Example figure output

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 if nargin<4, sOption='All'; end
0002 
0003 bxaxis=true; bzaxis=true;
0004 if strcmpi(sOption,'x'), bzaxis=false; end
0005 if strcmpi(sOption,'z'), bxaxis=false; end
0006 
0007 stEllGeom.a=a;
0008 stEllGeom.c=c;
0009 stEllGeom.type='Oblate'; % for reference
0010 
0011 stEllGeom.h=a./c; % aspect ratio
0012 eo=sqrt(1-(c./a).^2); % eccentricity (Eq. G.44, note that the sqrt is missing in the book)
0013 stEllGeom.e=eo; 
0014 
0015 fo=(1-eo.^2)./(2*eo) .* log( (1+eo)./(1-eo)); % Eq. G.46
0016 
0017 % surface area
0018 stEllGeom.S=2*pi*a.^2 .* (1+fo); % Eq. G.47
0019 
0020 % geometrical factors
0021 L1=0.5./(eo.^2).* ( sqrt(1-eo.^2)./eo .* asin(eo) - (1-eo.^2)); % Eq. G.45
0022 
0023 if (bxaxis)
0024     stEllGeom.L1=L1;
0025 end
0026 if (bzaxis)
0027     stEllGeom.L3=1-2*L1; % Eq. G.45
0028 end
0029 
0030 if ~strcmpi(sOption,'L') % compute other geometrical averages
0031 
0032     exiz2ave=1./eo.^2 .*(1-fo)./(1+fo); % Eq. G.48
0033     exiz4ave=1./eo.^4 .*(3-2*eo.^2-3*fo)./(1+fo); % Eq. G.50
0034     if (bxaxis)
0035         stEllGeom.exix2ave=0.5*(1-exiz2ave); % Eq. G.49
0036         stEllGeom.exix4ave=3/8*(1-2*exiz2ave+exiz4ave); % Eq. G.51
0037         % alternative direct calculation
0038         % stEllGeom.exix4ave=3/8*(1-eo.^2)./eo.^4.*(3-eo.^2-(3+eo.^2).*fo)./(1+fo); % Eq. G.51
0039     end
0040     if (bzaxis)
0041         stEllGeom.exiz2ave=exiz2ave;
0042         stEllGeom.exiz4ave=exiz4ave;
0043     end
0044     if strcmpi(sOption,'All')
0045         stEllGeom.exix2y2ave= (1-2*exiz2ave+exiz4ave ...
0046                 -2*stEllGeom.exix4ave)/2;
0047         stEllGeom.exix2z2ave=(1-2*stEllGeom.exix2ave-stEllGeom.exiz4ave)/2;
0048     end
0049 end
0050 
0051 
0052 
0053

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