exp_240910_defence.m

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%% Videos for the Defence
% This script generates animations for the defence presentation.
% WARNING: This script contains a lot of repetition and is not very efficient.
 
clear; close all; clc;
 
rng(11); % For reproducibility
 
%% generate noise
 
% Time specifications:
Fs = 200;
t_end = 30;
t = 0:1/Fs:t_end-1/Fs;
 
% animation specifications
width = 1920;
height = 800;
folder = "C:\Users\moss\OneDrive - ZHAW\MT\Presentations\Defence";
samples_visible = 400;
margin = 0.05;
zhaw_blue = [0, 100, 166] / 255;
zhaw_orange = [213, 78, 18] / 255;
zhaw_green = [0, 105, 53] / 255;
skip = 4;
 
%% noise (acceleration)
true_acc = zeros(size(t));
std_noise = sqrt(5.3e-3 * sqrt(Fs)); % std of noise
noise = std_noise * randn(size(t));
bias = 0.1;
 
%% noise Animation
F = struct('cdata', cell(1, length(t)), 'colormap', cell(1, length(t)));
fig = figure("Position", [0, 0, width, height], "Visible", "on", "Color", "black");
plt = plot(t(1), noise(1), "Color", zhaw_blue, "LineWidth", 4);
xlabel("Time [s]");
ylabel("Acceleration [m/s^2]");
grid on;
 
% set font style
set(findall(fig, 'Type', 'axes'), ...
    'FontName', 'CMU Bright', ...
    'FontSize', 20, ...
    'FontWeight', 'bold', ...
    'GridColor', 'white', ...
    'GridLineWidth', 1, ...
    'Color', 'black', ...
    'XColor', 'white', ...
    'YColor', 'white');
 
% set axis limits
ylim(get_axis_limits(margin, noise));
 
F(1) = getframe(gcf);
 
for i = skip+1:skip:length(t)
    
    % update plot
    set(plt, "XData", t(1:i), "YData", noise(1:i));
    x_start = max(1, i - samples_visible);
    x_end = min(i + margin * samples_visible, length(t));
    xlim([t(x_start), t(x_end)]);
    
    % save frame
    F(i) = getframe(gcf);
    
end
 
% remove empty frames
F = F(1:skip:end);
 
% export animation
v = VideoWriter(folder + "\01_noise_animation.mp4", "MPEG-4");
v.Quality = 75;
v.FrameRate = 25;
open(v);
writeVideo(v, F);
close(v);
 
%%  mean noise animation
evolving_mean = cumsum(noise) ./ (1:length(noise));
 
% Animation
F = struct('cdata', cell(1, length(t)), 'colormap', cell(1, length(t)));
fig = figure("Position", [0, 0, width, height], "Visible", "off", "Color", "black");
plt(1) = semilogx(t(1), evolving_mean(1), "Color", zhaw_blue, "LineWidth", 4);
hold on
plt(2) = semilogx(t(1), 0, "Color", zhaw_orange, "LineWidth", 4);
xlabel("Time [s]");
ylabel("Acceleration [m/s^2]");
grid on;
 
% set font style
set(findall(fig, 'Type', 'axes'), ...
    'FontName', 'CMU Bright', ...
    'FontSize', 20, ...
    'FontWeight', 'bold', ...
    'GridColor', 'white', ...
    'GridLineWidth', 1, ...
    'Color', 'black', ...
    'XColor', 'white', ...
    'YColor', 'white');
 
% set axis limits
ylim(get_axis_limits(margin, evolving_mean));
 
F(1) = getframe(gcf);
 
for i = skip+1:skip:length(t)
    
    % update plot
    set(plt(1), "XData", t(1:i), "YData", evolving_mean(1:i));
    set(plt(2), "XData", t(1:i), "YData", zeros(i, 1));
    x_start = 1; % max(1, i - samples_visible);
    x_end = min(i + margin * samples_visible, length(t));
    xlim([t(x_start), t(x_end)]);
    
    % save frame
    F(i) = getframe(gcf);
    
end
 
% remove empty frames
F = F(1:skip:end);
 
% export animation
v = VideoWriter(folder + "\02_mean_noise_animation.mp4", "MPEG-4");
v.Quality = 75;
v.FrameRate = 25;
open(v);
writeVideo(v, F);
close(v);
 
%% double integral noise
% first integration (velocity)
vel = cumsum(noise) / Fs;
pos = cumsum(vel) / Fs;
 
% Animation
F = struct('cdata', cell(1, length(t)), 'colormap', cell(1, length(t)));
 
fig = figure("Position", [0, 0, width, height], "Visible", "off", "Color", "black");
plt(1) = plot(t(1), pos(1), "Color", zhaw_blue, "LineWidth", 4);
xlabel("Time [s]");
ylabel("Displacement [m]");
grid on;
 
% set font style
set(findall(fig, 'Type', 'axes'), ...
    'FontName', 'CMU Bright', ...
    'FontSize', 20, ...
    'FontWeight', 'bold', ...
    'GridColor', 'white', ...
    'GridLineWidth', 1, ...
    'Color', 'black', ...
    'XColor', 'white', ...
    'YColor', 'white');
 
% set axis limits
ylim(get_axis_limits(margin, pos(1)));
 
% save first frame
F(1) = getframe(gcf);
 
for i = skip+1:skip:length(t)
    
    % update plot
    set(plt(1), "XData", t(1:i), "YData", pos(1:i));
    x_start = max(1, i - samples_visible);
    x_end = min(i + margin * samples_visible, length(t));
    xlim([t(x_start), t(x_end)]);
    ylim(get_axis_limits(margin, pos(1:i)));
    
    % save frame
    F(i) = getframe(gcf);
    
end
 
% remove empty frames
F = F(1:skip:end);
 
% export animation
v = VideoWriter(folder + "\03_double_integral_noise_animation.mp4", "MPEG-4");
v.Quality = 75;
v.FrameRate = 25;
open(v);
writeVideo(v, F);
close(v);
 
%% double integral noise with additional bias
vel = cumsum(noise + bias) / Fs;
pos = cumsum(vel) / Fs;
 
% Animation
F = struct('cdata', cell(1, length(t)), 'colormap', cell(1, length(t)));
 
fig = figure("Position", [0, 0, width, height], "Visible", "off", "Color", "black");
plt(1) = plot(t(1), pos(1), "Color", zhaw_blue, "LineWidth", 4);
xlabel("Time [s]");
ylabel("Displacement [m]");
grid on;
 
% set font style
set(findall(fig, 'Type', 'axes'), ...
    'FontName', 'CMU Bright', ...
    'FontSize', 20, ...
    'FontWeight', 'bold', ...
    'GridColor', 'white', ...
    'GridLineWidth', 1, ...
    'Color', 'black', ...
    'XColor', 'white', ...
    'YColor', 'white');
 
% set axis limits
ylim(get_axis_limits(margin, pos(1)));
 
% save first frame
F(1) = getframe(gcf);
 
for i = skip+1:skip:length(t)
    
    % update plot
    set(plt(1), "XData", t(1:i), "YData", pos(1:i));
    x_start = max(1, i - samples_visible);
    x_end = min(i + margin * samples_visible, length(t));
    xlim([t(x_start), t(x_end)]);
    ylim(get_axis_limits(margin, pos(1:i)));
    
    % save frame
    F(i) = getframe(gcf);
    
end
 
% remove empty frames
F = F(1:skip:end);
 
% export animation
v = VideoWriter(folder + "\04_double_integral_noise_bias_animation.mp4", "MPEG-4");
v.Quality = 75;
v.FrameRate = 25;
open(v);
writeVideo(v, F);
close(v);
 
%% noisy movement
% generate movement (accelerate (0.5s), constant speed (0.5s), decelerate (0.5s), constant speed (0.5s), ...)
acc_mov = zeros(1, 2*Fs);
acc_mov(1:0.5*Fs) = 1;
acc_mov(Fs+1:1.5*Fs) = -1;
acc_mov = repmat(acc_mov, 1, ceil(t_end / 2));
acc_mov = acc_mov(1:size(t, 2));
acc_mov_noise = acc_mov + noise;
acc_mov_noise_bias = acc_mov + noise + bias;
 
% double integral
vel_mov = cumsum(acc_mov) / Fs;
vel_mov_noise = cumsum(acc_mov_noise) / Fs;
vel_mov_noise_bias = cumsum(acc_mov_noise_bias) / Fs;
pos_mov = cumsum(vel_mov) / Fs;
pos_mov_noise = cumsum(vel_mov_noise) / Fs;
pos_mov_noise_bias = cumsum(vel_mov_noise_bias) / Fs;
 
%% create a static plot with acc, vel, pos)
fig = figure("Position", [0, 0, 1000, 1100], "Visible", "off", "Color", "black");
splt(1) = subplot(3, 1, 1);
plot(t, acc_mov, "Color", zhaw_blue, "LineWidth", 4);
ylabel("Acceleration [m/s^2]");
xlim([0, 5])
grid on;
splt(2) = subplot(3, 1, 2);
plot(t, vel_mov, "Color", zhaw_blue, "LineWidth", 4);
ylabel("Velocity [m/s]");
xlim([0, 5])
grid on;
splt(3) = subplot(3, 1, 3);
plot(t, pos_mov, "Color", zhaw_blue, "LineWidth", 4);
ylabel("Displacement [m]");
xlim([0, 5])
xlabel("Time [s]");
grid on;
 
% set font style
set(splt, ...
    'FontName', 'CMU Bright', ...
    'FontSize', 20, ...
    'FontWeight', 'bold', ...
    'GridColor', 'white', ...
    'GridLineWidth', 1, ...
    'Color', 'black', ...
    'XColor', 'white', ...
    'YColor', 'white');
 
exportgraphics(fig, folder + "\00_static_plot.pdf", "ContentType", "vector");
 
%% animate acceleration
F = struct('cdata', cell(1, length(t)), 'colormap', cell(1, length(t)));
fig = figure("Position", [0, 0, width, height], "Visible", "off", "Color", "black");
plt(1) = plot(t(1), acc_mov_noise_bias(1), "Color", zhaw_blue, "LineWidth", 4);
hold on
plt(2) = plot(t(1), acc_mov(1), "Color", zhaw_orange, "LineWidth", 4);
xlabel("Time [s]");
ylabel("Acceleration [m/s^2]");
grid on;
 
% set font style
set(findall(fig, 'Type', 'axes'), ...
    'FontName', 'CMU Bright', ...
    'FontSize', 20, ...
    'FontWeight', 'bold', ...
    'GridColor', 'white', ...
    'GridLineWidth', 1, ...
    'Color', 'black', ...
    'XColor', 'white', ...
    'YColor', 'white');
 
% set axis limits
ylim(get_axis_limits(margin, acc_mov_noise_bias(1), acc_mov(1)));
 
% save first frame
F(1) = getframe(gcf);
 
for i = skip+1:skip:length(t)
    
    % update plot
    set(plt(1), "XData", t(1:i), "YData", acc_mov_noise_bias(1:i));
    set(plt(2), "XData", t(1:i), "YData", acc_mov(1:i));
    x_start = max(1, i - samples_visible);
    x_end = min(i + margin * samples_visible, length(t));
    xlim([t(x_start), t(x_end)]);
    ylim(get_axis_limits(margin, acc_mov_noise_bias(1:i), acc_mov(1:i)));
    
    % save frame
    F(i) = getframe(gcf);
    
end
 
% remove empty frames
F = F(1:skip:end);
 
% export animation
v = VideoWriter(folder + "\05_acceleration_animation.mp4", "MPEG-4");
v.Quality = 75;
v.FrameRate = 25;
open(v);
writeVideo(v, F);
close(v);
 
%% animate position
F = struct('cdata', cell(1, length(t)), 'colormap', cell(1, length(t)));
fig = figure("Position", [0, 0, width, height], "Visible", "off", "Color", "black");
plt(1) = plot(t(1), pos_mov_noise_bias(1), "Color", zhaw_blue, "LineWidth", 4);
hold on
plt(2) = plot(t(1), pos_mov(1), "Color", zhaw_orange, "LineWidth", 4);
xlabel("Time [s]");
ylabel("Displacement [m]");
grid on;
 
% set font style
set(findall(fig, 'Type', 'axes'), ...
    'FontName', 'CMU Bright', ...
    'FontSize', 20, ...
    'FontWeight', 'bold', ...
    'GridColor', 'white', ...
    'GridLineWidth', 1, ...
    'Color', 'black', ...
    'XColor', 'white', ...
    'YColor', 'white');
 
% set axis limits
ylim(get_axis_limits(margin, pos_mov_noise_bias(1), pos_mov(1)));
 
% save first frame
F(1) = getframe(gcf);
 
for i = skip+1:skip:length(t)
    
    % update plot
    set(plt(1), "XData", t(1:i), "YData", pos_mov_noise_bias(1:i));
    set(plt(2), "XData", t(1:i), "YData", pos_mov(1:i));
    x_start = max(1, i - samples_visible);
    x_end = min(i + margin * samples_visible, length(t));
    xlim([t(x_start), t(x_end)]);
    ylim(get_axis_limits(margin, pos_mov_noise_bias(1:i), pos_mov(1:i)));
    
    % save frame
    F(i) = getframe(gcf);
    
end
 
% remove empty frames
F = F(1:skip:end);
 
% export animation
v = VideoWriter(folder + "\06_position_animation.mp4", "MPEG-4");
v.Quality = 75;
v.FrameRate = 25;
open(v);
writeVideo(v, F);
close(v);
 
%% animate position with zero velocity updates
 
% find zero velocity
zero_vel = 351:400:length(t);
 
% change velocity vector and position vector
vel_uncorrected = vel_mov_noise_bias;
last_t = 0;
for i = 1:length(zero_vel)
    
    % velocity
    this_vel = vel_mov_noise_bias(zero_vel(i));
    vel_mov_noise_bias(zero_vel(i):end) = vel_mov_noise_bias(zero_vel(i):end) - this_vel;
    
    % velocity (w/o bias)
    this_vel2 = vel_mov_noise(zero_vel(i));
    vel_mov_noise(zero_vel(i):end) = vel_mov_noise(zero_vel(i):end) - this_vel2;
    
    % position
    t_between = t(zero_vel(i)) - last_t;
    last_t = t(zero_vel(i));
    
    p_diff = (this_vel * t_between) / 2;
    pos_mov_noise_bias(zero_vel(i):end) = pos_mov_noise_bias(zero_vel(i):end) - p_diff;
    
    p_diff = repmat(this_vel / Fs, size(pos_mov_noise_bias(zero_vel(i):end)));
    p_diff = cumsum(p_diff);
    pos_mov_noise_bias(zero_vel(i):end) = pos_mov_noise_bias(zero_vel(i):end) - p_diff;
end
 
%% Animation of Velocity with zero velocity updates
F = struct('cdata', cell(1, length(t)), 'colormap', cell(1, length(t)));
fig = figure("Position", [0, 0, width, height], "Visible", "off", "Color", "black");
plt(1) = plot(t(1), vel_mov_noise_bias(1), "Color", zhaw_blue, "LineWidth", 4);
hold on
plt(2) = plot(t(1), vel_mov(1), "Color", zhaw_orange, "LineWidth", 4);
plt(3) = plot(t(1), vel_uncorrected(1), "Color", "red", "LineWidth", 4);
xlabel("Time [s]");
ylabel("Velocity [m/s]");
grid on;
 
% set font style
set(findall(fig, 'Type', 'axes'), ...
    'FontName', 'CMU Bright', ...
    'FontSize', 20, ...
    'FontWeight', 'bold', ...
    'GridColor', 'white', ...
    'GridLineWidth', 1, ...
    'Color', 'black', ...
    'XColor', 'white', ...
    'YColor', 'white');
 
% set axis limits
ylim(get_axis_limits(margin, vel_mov_noise_bias(1), vel_mov(1), vel_uncorrected(1)));
 
F(1) = getframe(gcf);
 
for i = skip+1:skip:length(t)
    
    % update plot
    set(plt(1), "XData", t(1:i), "YData", vel_mov_noise_bias(1:i));
    set(plt(2), "XData", t(1:i), "YData", vel_mov(1:i));
    set(plt(3), "XData", t(1:i), "YData", vel_uncorrected(1:i));
    x_start = max(1, i - samples_visible);
    x_end = min(i + margin * samples_visible, length(t));
    xlim([t(x_start), t(x_end)]);
    ylim(get_axis_limits(margin, vel_mov_noise_bias(1:i), vel_mov(1:i), vel_uncorrected(1:i)));
    
    % save frame
    F(i) = getframe(gcf);
    
end
 
% remove empty frames
F = F(1:skip:end);
 
% export animation
v = VideoWriter(folder + "\07_velocity_zero_velocity_animation.mp4", "MPEG-4");
v.Quality = 75;
v.FrameRate = 25;
open(v);
writeVideo(v, F);
close(v);
 
%% Animation of Position with zero velocity updates
F = struct('cdata', cell(1, length(t)), 'colormap', cell(1, length(t)));
fig = figure("Position", [0, 0, width, height], "Visible", "off", "Color", "black");
plt(1) = plot(t(1), pos_mov_noise_bias(1), "Color", zhaw_blue, "LineWidth", 4);
hold on
plt(2) = plot(t(1), pos_mov(1), "Color", zhaw_orange, "LineWidth", 4);
xlabel("Time [s]");
ylabel("Displacement [m]");
grid on;
 
% set font style
set(findall(fig, 'Type', 'axes'), ...
    'FontName', 'CMU Bright', ...
    'FontSize', 20, ...
    'FontWeight', 'bold', ...
    'GridColor', 'white', ...
    'GridLineWidth', 1, ...
    'Color', 'black', ...
    'XColor', 'white', ...
    'YColor', 'white');
 
% set axis limits
ylim(get_axis_limits(margin, pos_mov_noise_bias(1), pos_mov(1)));
 
% save first frame
F(1) = getframe(gcf);
 
for i = skip+1:skip:length(t)
    
    % update plot
    set(plt(1), "XData", t(1:i), "YData", pos_mov_noise_bias(1:i));
    set(plt(2), "XData", t(1:i), "YData", pos_mov(1:i));
    x_start = 1; % max(1, i - samples_visible);
    x_end = min(i + margin * samples_visible, length(t));
    xlim([t(x_start), t(x_end)]);
    ylim(get_axis_limits(margin, pos_mov_noise_bias(1:i), pos_mov(1:i)));
    
    % save frame
    F(i) = getframe(gcf);
    
end
 
% remove empty frames
F = F(1:skip:end);
 
% export animation
v = VideoWriter(folder + "\08_position_zero_velocity_animation.mp4", "MPEG-4");
v.Quality = 75;
v.FrameRate = 25;
open(v);
writeVideo(v, F);
close(v);
 
%% Animation of Position with zero velocity updates and smoothing
 
% smooth position
pos_mov_noise_bias_smooth = pos_mov_noise;
 
% Animation
F = struct('cdata', cell(1, length(t)), 'colormap', cell(1, length(t)));
fig = figure("Position", [0, 0, width, height], "Visible", "off", "Color", "black");
plt(1) = plot(t(1), pos_mov_noise_bias_smooth(1), "Color", zhaw_blue, "LineWidth", 4);
hold on
plt(2) = plot(t(1), pos_mov(1), "Color", zhaw_orange, "LineWidth", 4);
xlabel("Time [s]");
ylabel("Displacement [m]");
grid on;
 
% set font style
set(findall(fig, 'Type', 'axes'), ...
    'FontName', 'CMU Bright', ...
    'FontSize', 20, ...
    'FontWeight', 'bold', ...
    'GridColor', 'white', ...
    'GridLineWidth', 1, ...
    'Color', 'black', ...
    'XColor', 'white', ...
    'YColor', 'white');
 
% set axis limits
ylim(get_axis_limits(margin, pos_mov_noise_bias_smooth(1), pos_mov(1)));
 
F(1) = getframe(gcf);
 
for i = skip+1:skip:length(t)
    
    % update plot
    set(plt(1), "XData", t(1:i), "YData", pos_mov_noise_bias_smooth(1:i));
    set(plt(2), "XData", t(1:i), "YData", pos_mov(1:i));
    x_start = 1;
    x_end = min(i + margin * samples_visible, length(t));
    xlim([t(x_start), t(x_end)]);
    ylim(get_axis_limits(margin, pos_mov_noise_bias_smooth(1:i), pos_mov(1:i)));
    
    % save frame
    F(i) = getframe(gcf);
    
end
 
% remove empty frames
F = F(1:skip:end);
 
% export animation
v = VideoWriter(folder + "\09_position_zero_velocity_smooth_animation.mp4", "MPEG-4");
v.Quality = 75;
v.FrameRate = 25;
open(v);
writeVideo(v, F);
close(v);
 
 
%% noisy movement 2
 
noise2 = std_noise * randn(size(t));
bias2 = -0.15;
 
% generate movement (constant speed (0.5s), accelerate (0.5s), constant speed (0.5s), decelerate (0.5s), ...)
acc_mov2 = zeros(1, 2*Fs);
acc_mov2(1:0.5*Fs) = -1;
acc_mov2(Fs+1:1.5*Fs) = 1;
acc_mov2 = repmat(acc_mov2, 1, ceil(t_end / 2));
acc_mov2 = acc_mov2(1:size(t, 2));
acc_mov_noise2 = acc_mov2 + noise2;
acc_mov_noise_bias2 = acc_mov2 + noise2 + bias2;
 
% double integral
vel_mov2 = cumsum(acc_mov2) / Fs + 0.5;
vel_mov_noise2 = cumsum(acc_mov_noise2) / Fs + 0.5;
vel_mov_noise_bias2 = cumsum(acc_mov_noise_bias2) / Fs + 0.5;
pos_mov2 = cumsum(vel_mov2) / Fs + 0.125;
pos_mov_noise2 = cumsum(vel_mov_noise2) / Fs + 0.125;
pos_mov_noise_bias2 = cumsum(vel_mov_noise_bias2) / Fs + 0.125;
 
%% Animation of both positions with zero velocity updates and smoothing
F = struct('cdata', cell(1, length(t)), 'colormap', cell(1, length(t)));
fig = figure("Position", [0, 0, width, height], "Visible", "off", "Color", "black");
plt(1) = plot(t(1), pos_mov_noise_bias_smooth(1), "Color", zhaw_blue, "LineWidth", 4);
hold on
plt(2) = plot(t(1), pos_mov_noise2(1), "Color", zhaw_green, "LineWidth", 4);
plt(3) = plot(t(1), pos_mov(1), "Color", zhaw_orange, "LineWidth", 2);
plt(4) = plot(t(1), pos_mov2(1), "Color", "yellow", "LineWidth", 2);
xlabel("Time [s]");
ylabel("Displacement [m]");
grid on;
 
% set font style
set(findall(fig, 'Type', 'axes'), ...
    'FontName', 'CMU Bright', ...
    'FontSize', 20, ...
    'FontWeight', 'bold', ...
    'GridColor', 'white', ...
    'GridLineWidth', 1, ...
    'Color', 'black', ...
    'XColor', 'white', ...
    'YColor', 'white');
 
% set axis limits
ylim(get_axis_limits(margin, pos_mov_noise_bias_smooth(1), pos_mov_noise2(1), pos_mov(1), pos_mov2(1)));
 
F(1) = getframe(gcf);
 
for i = skip+1:skip:length(t)
    
    % update plot
    set(plt(1), "XData", t(1:i), "YData", pos_mov_noise_bias_smooth(1:i));
    set(plt(2), "XData", t(1:i), "YData", pos_mov_noise2(1:i));
    set(plt(3), "XData", t(1:i), "YData", pos_mov(1:i));
    set(plt(4), "XData", t(1:i), "YData", pos_mov2(1:i));
    x_start = 1;
    x_end = min(i + margin * samples_visible, length(t));
    xlim([t(x_start), t(x_end)]);
    ylim(get_axis_limits(margin, pos_mov_noise_bias_smooth(1:i), pos_mov_noise2(1:i), pos_mov(1:i), pos_mov2(1:i)));
    
    % save frame
    F(i) = getframe(gcf);
    
end
 
% remove empty frames
F = F(1:skip:end);
 
% export animation
v = VideoWriter(folder + "\10_position_zero_velocity_smooth_animation_2.mp4", "MPEG-4");
v.Quality = 75;
v.FrameRate = 25;
open(v);
writeVideo(v, F);
close(v);
 
%% animation of both positions with same end position
 
% correct end position
pos_1_final = pos_mov;
pos_2_final = pos_mov2;
% Animation
F = struct('cdata', cell(1, length(t)), 'colormap', cell(1, length(t)));
fig = figure("Position", [0, 0, width, height], "Visible", "off", "Color", "black");
plt(1) = plot(t(1), pos_1_final(1), "Color", zhaw_blue, "LineWidth", 4);
hold on
plt(2) = plot(t(1), pos_2_final(1), "Color", zhaw_green, "LineWidth", 4);
xlabel("Time [s]");
ylabel("Displacement [m]");
grid on;
 
% set font style
set(findall(fig, 'Type', 'axes'), ...
    'FontName', 'CMU Bright', ...
    'FontSize', 20, ...
    'FontWeight', 'bold', ...
    'GridColor', 'white', ...
    'GridLineWidth', 1, ...
    'Color', 'black', ...
    'XColor', 'white', ...
    'YColor', 'white');
 
% set axis limits
ylim(get_axis_limits(margin, pos_1_final(1), pos_2_final(1)));
 
F(1) = getframe(gcf);
 
for i = skip+1:skip:length(t)
    
    % update plot
    set(plt(1), "XData", t(1:i), "YData", pos_1_final(1:i));
    set(plt(2), "XData", t(1:i), "YData", pos_2_final(1:i));
    x_start = 1;
    x_end = min(i + margin * samples_visible, length(t));
    xlim([t(x_start), t(x_end)]);
    ylim(get_axis_limits(margin, pos_1_final(1:i), pos_2_final(1:i)));
    
    % save frame
    F(i) = getframe(gcf);
    
end
 
% remove empty frames
F = F(1:skip:end);
 
% export animation
v = VideoWriter(folder + "\11_position_final_animation.mp4", "MPEG-4");
v.Quality = 75;
v.FrameRate = 25;
open(v);
writeVideo(v, F);
close(v);
 
function limits = get_axis_limits(margin, data)
 
arguments
    margin (1, 1) double = 0.05
end
 
arguments (Repeating)
    data (:, 1) double
end
 
low = inf;
high = -inf;
 
for i = 1:length(data)
    low = min(low, min(data{i}));
    high = max(high, max(data{i}));
end
 
low = low - margin * abs(low);
high = high + margin * abs(high);
 
if low >= high
    low = low - margin;
    high = high + margin;
end
 
limits = [low, high];
 
end