%Determines the optimal angle to fire a projectile given a specified force.
%
%m = mass of the projectile/ball
%g = gravity
%R = resistance force
%Fi_init = input force magnitude (force is always an impulse)
%theta_min, theta_max = interval of angles between which the optimal angle
%will be searched for
%t = time for simulation. If specified as integer, dictates running time of
%simulation. If specified as array, dictates time points to evaluate model
%during simulation
%TOL = if abs(midp-theta_min) < TOL, stop searching for a root, where midp
%is the midpoint b/w theta_min & theta_max
%interm_plots = boolean indicating whether to plot intermediate plots
%
%remark: returns negative answer if no soln found
function [theta_opt] = launched_ball_opt_angle(m, g, R, target_x, target_y, Fi_init, t, TOL, theta_min, theta_max, interm_plots)
%set values of global vars
global soln_x soln_y;

%determine the needed theta to hit the target
theta_opt = bisection(@(theta) sim_launched_ball_err(m, g, R, target_x, target_y, Fi_init, theta, t, interm_plots), theta_min, theta_max, TOL, 1000);

if abs(theta_opt-theta_max) < TOL || abs(theta_opt-theta_min) < TOL %|| abs(x_soln_coord-target_x) > abs(target_x*0.1)
    %fprintf('\nNo solution found')
    axis([0 target_x+50 target_y-100 max(soln_y)+50]);
    theta_opt = NaN;
else
    hold on
    plot(soln_x, soln_y, 'k','LineWidth', 3); axis([0 target_x+10 0 max(soln_y)+10]); %axis([0 target_x+10 target_y-50 max(soln_y)+10]);
end

%plot target
plot(target_x,target_y, '*r');

end

function [err] = sim_launched_ball_err(m, g, R, target_x, target_y, Fi_init, theta, t, interm_plots)
global soln_x soln_y;

[err,soln_x,soln_y] = sim_launched_ball(m, g, R, target_x, target_y, Fi_init, theta, t);

%make itermediate plots
if (interm_plots)
    hold on
    plot(soln_x, soln_y)
end

return
end