% VDV - Calculate volume function and its derivative:
%  [V,DV] = VDV(THETA)
% THETA must be in radians. Function is correctly vectorized.
% Reads global variables V_D, R, R1

% Philip D Loewen, 2010-02-24; 2011-03-15

function [V,dV] = vdv(theta)

global global_V_D global_r global_R1

% Make local copies to make formulas more readable.
V_D= global_V_D; 
r  = global_r;   
R1 = global_R1;

% Compute the square root just once, for efficiency:
radical = (R1^2 - sin(theta).^2).^(0.5);

V = V_D/(r-1) + 0.5 * V_D * (1 + R1 - cos(theta) - radical);

dV = 0.5 * V_D * sin(theta) .* (1 + cos(theta)./radical);