% SETUP - NEED ALL OF THESE
clc;
clear;
close all;
hold on;
echo off;

% LOAD DATA (FROM FILE, PROBLEM SET, ETC.)
xcurve = [0,1,2,3,4];
ycurve = [0,2.6,3.5,3.9,4];
spline_method = @spline; % can be @spline, @interp1, @pchip

% HERE ARE THE START AND STOP CONDITIONS
xstart = 3.9;
xend = 0.1;
efficiency = 1;

% CHOOSE A PLOT RANGE
xrange = [0,4];

% CREATE FUNCTIONS FOR OPERATING LINE AND DATA CURVE
myline = @(x)x;
curve_function = @(x)spline_method(xcurve,ycurve,x);
inverse_curve_function = @(y)fzero(@(x)curve_function(x)-y,xrange);

% PLOT
fplot(myline,xrange);
fplot(curve_function,xrange);

% INITIALIZE X, Y, AND NUMBER OF STEPS
current_x = xstart;
current_y = myline(xstart);
numsteps = 0;

while current_x > xend
    % CHOOSE NEW COORDINATES
    new_x = inverse_curve_function(current_x);
    new_x = (current_x - new_x)*(1-efficiency) + new_x;
    new_y = myline(new_x);
    
    % DRAW STAIRCASE STEP
    plot([current_x,new_x],[current_y,current_y]);
    plot([new_x,new_x],[current_y,new_y]);
    
    % UPDATE THE CURRENT X, Y, AND NUMBER OF STEPS
    current_x = new_x;
    current_y = new_y;
    numsteps = numsteps + 1;
end

disp(sprintf('Number of steps: %d',numsteps))