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jmgoldba
Last activity 2024 年 6 月 21 日

Add Tools->Basic Fitting->...Weighted least squares

An option for 10th degree polynomials but no weighted linear least squares. Seriously? Jesse

https://blogs.mathworks.com/community/2015/02/26/lets-code-make-a-cody-video/

Ned Gulley
Last activity 2024 年 6 月 13 日

Make a video: "How I Solved It"

Twitch built an entire business around letting you watch over someone's shoulder while they play video games. I feel like we should be able to make at least a few videos where we get to watch over someone's shoulder while they solve Cody problems. I would pay good money for a front-row seat to watch some of my favorite solvers at work. Like, I want to know, did Alfonso Nieto-Castonon just sit down and bang out some of those answers, or did he have to think about it for a while? What was he thinking about while he solved it? What resources was he drawing on? There's nothing like watching a master craftsman at work.

I can imagine a whole category of Cody videos called "How I Solved It". I tried making one of these myself a while back, but as far as I could tell, nobody else made one.

Here's the direct link to the video: https://www.youtube.com/watch?v=hoSmO1XklAQ

I hereby challenge you to make a "How I Solved It" video and post it here. If you make one, I'll make another one.

Ned Gulley
Last activity 2024 年 6 月 25 日

What's your opinion of the Ans Hack?

The Ans Hack is a dubious way to shave a few points off your solution score. Instead of a standard answer like this

function y = times_two(x)
  y = 2*x;
end

you would do this

function ans = times_two(x)
  2*x;
end

The ans variable is automatically created when there is no left-hand side to an evaluated expression. But it makes for an ugly function. I don't think anyone actually defends it as a good practice. The question I would ask is: is it so offensive that it should be specifically disallowed by the rules? Or is it just one of many little hacks that you see in Cody, inelegant but tolerable in the context of the surrounding game?

Incidentally, I wrote about the Ans Hack long ago on the Community Blog. Dealing with user-unfriendly code is also one of the reasons we created the Head-to-Head voting feature. Some techniques are good for your score, and some are good for your code readability. You get to decide with you care about.

Books

Athanasios Paraskevopoulos
Last activity 2024 年 6 月 9 日

Discovering an Excellent Resource on Ordinary Differential Equations

While searching the internet for some books on ordinary differential equations, I came across a link that I believe is very useful for all math students and not only. If you are interested in ODEs, it's worth taking the time to study it.

A First Look at Ordinary Differential Equations by Timothy S. Judson is an excellent resource for anyone looking to understand ODEs better. Here's a brief overview of the main topics covered:

Introduction to ODEs: Basic concepts, definitions, and initial differential equations.
Methods of Solution:

Separable equations
First-order linear equations
Exact equations
Transcendental functions

Applications of ODEs: Practical examples and applications in various scientific fields.
Systems of ODEs: Analysis and solutions of systems of differential equations.
Series and Numerical Methods: Use of series and numerical methods for solving ODEs.

This book provides a clear and comprehensive introduction to ODEs, making it suitable for students and new researchers in mathematics. If you're interested, you can explore the book in more detail here: A First Look at Ordinary Differential Equations.

goc3
Last activity 2024 年 6 月 7 日

Trick: Easy Digit Manipulation

There are a host of problems on Cody that require manipulation of the digits of a number. Examples include summing the digits of a number, separating the number into its powers, and adding very large numbers together.

If you haven't come across this trick yet, you might want to write it down (or save it electronically):

digits = num2str(4207) - '0'

That code results in the following:

digits =
     4     2     0     7

Now, summing the digits of the number is easy:

sum(digits)
ans =
    13

Chen Lin
Last activity 2024 年 10 月 1 日

Welcome to the Cody Discussion Channel! Please Read Before Posting

Hello and a warm welcome to everyone! We're excited to have you in the Cody Discussion Channel. To ensure the best possible experience for everyone, it's important to understand the types of content that are most suitable for this channel.

Content that belongs in the Cody Discussion Channel:

Tips & tricks: Discuss strategies for solving Cody problems that you've found effective.
Ideas or suggestions for improvement: Have thoughts on how to make Cody better? We'd love to hear them.
Issues: Encountering difficulties or bugs with Cody? Let us know so we can address them.
Requests for guidance: Stuck on a Cody problem? Ask for advice or hints, but make sure to show your efforts in attempting to solve the problem first.
General discussions: Anything else related to Cody that doesn't fit into the above categories.

Content that does not belong in the Cody Discussion Channel:

Comments on specific Cody problems: Examples include unclear problem descriptions or incorrect testing suites.
Comments on specific Cody solutions: For example, you find a solution creative or helpful.

Please direct such comments to the Comments section on the problem or solution page itself.

We hope the Cody discussion channel becomes a vibrant space for sharing expertise, learning new skills, and connecting with others.

Books

Oge Marques
Last activity 2024 年 10 月 29 日

New book announcement: "Image Processing Recipes in MATLAB"

📚 New Book Announcement: "Image Processing Recipes in MATLAB" 📚

I am delighted to share the release of my latest book, "Image Processing Recipes in MATLAB," co-authored by my dear friend and colleague Gustavo Benvenutti Borba.

This 'cookbook' contains 30 practical recipes for image processing, ranging from foundational techniques to recently published algorithms. It serves as a concise and readable reference for quickly and efficiently deploying image processing pipelines in MATLAB.

Gustavo and I are immensely grateful to the MathWorks Book Program for their support. We also want to thank Randi Slack and her fantastic team at CRC Press for their patience, expertise, and professionalism throughout the process.

___________

lazymatlab
Last activity 2024 年 5 月 18 日

Helped a high school student for a physics problem with this.

A high school student called for help with this physics problem:

Car A moves with constant velocity v.
Car B starts to move when Car A passes through the point P.
Car B undergoes...
uniform acc. motion from P to Q.
uniform velocity motion from Q to R.
uniform acc. motion from R to S.
Car A and B pass through the point R simultaneously.
Car A and B arrive at the point S simultaneously.

Q1. When car A passes the point Q, which is moving faster?

Q2. Solve the time duration for car B to move from P to Q using L and v.

Q3. Magnitude of acc. of car B from P to Q, and from R to S: which is bigger?

Well, it can be solved with a series of tedious equations. But... how about this?

Code below:

%% get images and prepare stuffs
figure(WindowStyle="docked"), 
ax1 = subplot(2,1,1);
hold on, box on
ax1.XTick = [];
ax1.YTick = [];
A = plot(0, 1, 'ro', MarkerSize=10, MarkerFaceColor='r');
B = plot(0, 0, 'bo', MarkerSize=10, MarkerFaceColor='b');
[carA, ~, alphaA] = imread('https://cdn.pixabay.com/photo/2013/07/12/11/58/car-145008_960_720.png');
[carB, ~, alphaB] = imread('https://cdn.pixabay.com/photo/2014/04/03/10/54/car-311712_960_720.png');
carA = imrotate(imresize(carA, 0.1), -90);
carB = imrotate(imresize(carB, 0.1), 180);
alphaA = imrotate(imresize(alphaA, 0.1), -90);
alphaB = imrotate(imresize(alphaB, 0.1), 180);
carA = imagesc(carA, AlphaData=alphaA, XData=[-0.1, 0.1], YData=[0.9, 1.1]);
carB = imagesc(carB, AlphaData=alphaB, XData=[-0.1, 0.1], YData=[-0.1, 0.1]);
txtA = text(0, 0.85, 'A', FontSize=12);
txtB = text(0, 0.17, 'B', FontSize=12);
yline(1, 'r--')
yline(0, 'b--')
xline(1, 'k--')
xline(2, 'k--')
text(1, -0.2, 'Q', FontSize=20, HorizontalAlignment='center')
text(2, -0.2, 'R', FontSize=20, HorizontalAlignment='center')
% legend('A', 'B') % this make the animation slow. why?
xlim([0, 3])
ylim([-.3, 1.3])
%% axes2: plots velocity graph
ax2 = subplot(2,1,2);
box on, hold on
xlabel('t'), ylabel('v')
vA = plot(0, 1, 'r.-');
vB = plot(0, 0, 'b.-');
xline(1, 'k--')
xline(2, 'k--')
xlim([0, 3])
ylim([-.3, 1.8])
p1 = patch([0, 0, 0, 0], [0, 1, 1, 0], [248, 209, 188]/255, ...
    EdgeColor = 'none', ...
    FaceAlpha = 0.3);
%% solution
v = 1; % car A moves with constant speed.
L = 1; % distances of P-Q, Q-R, R-S
% acc. of car B for three intervals
a(1) = 9*v^2/8/L;
a(2) = 0;
a(3) = -1;
t_BatQ = sqrt(2*L/a(1)); % time when car B arrives at Q
v_B2 = a(1) * t_BatQ; % speed of car B between Q-R
%% patches for velocity graph
p2 = patch([t_BatQ, t_BatQ, t_BatQ, t_BatQ], [1, 1, v_B2, v_B2], ...
    [248, 209, 188]/255, ...
    EdgeColor = 'none', ...
    FaceAlpha = 0.3);
p3 = patch([2, 2, 2, 2], [1, v_B2, v_B2, 1], [194, 234, 179]/255, ...
    EdgeColor = 'none', ...
    FaceAlpha = 0.3);
%% animation
tt = linspace(0, 3, 2000);
for t = tt
    A.XData = v * t;
    vA.XData = [vA.XData, t];
    vA.YData = [vA.YData, 1];
    if t < t_BatQ
        B.XData = 1/2 * a(1) * t^2;
        vB.XData = [vB.XData, t];
        vB.YData = [vB.YData, a(1) * t];
        p1.XData = [0, t, t, 0];
        p1.YData = [0, vB.YData(end), 1, 1];
    elseif t >= t_BatQ && t < 2
        B.XData = L + (t - t_BatQ) * v_B2;
        vB.XData = [vB.XData, t];
        vB.YData = [vB.YData, v_B2];
        p2.XData = [t_BatQ, t, t, t_BatQ];
        p2.YData = [1, 1, vB.YData(end), vB.YData(end)];
    else
        B.XData = 2*L + v_B2 * (t - 2) + 1/2 * a(3) * (t-2)^2;
        vB.XData = [vB.XData, t];
        vB.YData = [vB.YData, v_B2 + a(3) * (t - 2)];
        p3.XData = [2, t, t, 2];
        p3.YData = [1, 1, vB.YData(end), v_B2];
    end
    txtA.Position(1) = A.XData(end);
    txtB.Position(1) = B.XData(end);
    carA.XData = A.XData(end) + [-.1, .1];
    carB.XData = B.XData(end) + [-.1, .1];
    drawnow
end

Chen Lin
Last activity 2024 年 7 月 3 日

Northern Lights

Northern lights captured from this weekend at MathWorks campus ✨

Did you get a chance to see lights and take some photos?

Gregory Vernon
Last activity 2024 年 5 月 6 日

Support "hidden blocks" in Livescripts

Updating some of my educational Livescripts to 2024a, really love the new "define a function anywhere" feature, and have a "new" idea for improving Livescripts -- support "hidden" code blocks similar to the Jupyter Notebooks functionality.

For example, I often create "complicated" plots with a bunch of ancillary items and I don't want this code exposed to the reader by default, as it might confuse the reader. For example, consider a Livescript that might read like this:

-----

Noting the similar structure of these two mappings, let's now write a function that simply maps from some domain to some other domain using change of variable.

function x = ChangeOfVariable( x, from_domain, to_domain )
x = x - from_domain(1);
x = x * ( ( to_domain(2) - to_domain(1) ) / ( from_domain(2) - from_domain(1) ) );
x = x + to_domain(1);
end

Let's see this function in action

% HIDE CELL
clear
close all

from_domain = [-1, 1];
to_domain = [2, 7];
from_values = [-1, -0.5, 0, 0.5, 1];
to_values = ChangeOfVariable( from_values, from_domain, to_domain )

to_values = 1×5

2.0000 3.2500 4.5000 5.7500 7.0000

We can plot the values of from_values and to_values, showing how they're connected to each other:

% HIDE CELL
figure
hold on
for n = 1 : 5
    plot( [from_values(n) to_values(n)], [1 0], Color="k", LineWidth=1 )
end
ax = gca;
ax.YTick = [];
ax.XLim = [ min( [from_domain, to_domain] ) - 1,  max( [from_domain, to_domain] ) + 1 ];
ax.YLim = [-0.5, 1.5];
ax.XGrid = "on";
scatter( from_values, ones( 5, 1 ), Marker="s", MarkerFaceColor="flat", MarkerEdgeColor="k", SizeData=120, LineWidth=1, SeriesIndex=1 )
text( mean( from_domain ), 1.25, "$\xi$", Interpreter="latex", HorizontalAlignment="center", VerticalAlignment="middle" )
scatter( to_values, zeros( 5, 1 ), Marker="o", MarkerFaceColor="flat", MarkerEdgeColor="k", SizeData=120, LineWidth=1, SeriesIndex=2 )
text( mean( to_domain ), -0.25, "$x$", Interpreter="latex", HorizontalAlignment="center", VerticalAlignment="middle" )
scaled_arrow( ax, [mean( [from_domain(1), to_domain(1) ] ) - 1, 0.5], ( 1 - 0 ) / ( from_domain(1) - to_domain(1) ), 1 )
scaled_arrow( ax, [mean( [from_domain(end), to_domain(end)] ) + 1, 0.5], ( 1 - 0 ) / ( from_domain(end) - to_domain(end) ), -1 )
text( mean( [from_domain(1), to_domain(1) ] ) - 1.5, 0.5, "$x(\xi)$", Interpreter="latex", HorizontalAlignment="center", VerticalAlignment="middle" )
text( mean( [from_domain(end), to_domain(end)] ) + 1.5, 0.5, "$\xi(x)$", Interpreter="latex", HorizontalAlignment="center", VerticalAlignment="middle" )

-----

Where scaled_arrow is some utility function I've defined elsewhere... See how a majority of the code is simply "drivel" to create the plot, clear and close? I'd like to be able to hide those cells so that it would look more like this:

-----

Noting the similar structure of these two mappings, let's now write a function that simply maps from some domain to some other domain using change of variable.

function x = ChangeOfVariable( x, from_domain, to_domain )
x = x - from_domain(1);
x = x * ( ( to_domain(2) - to_domain(1) ) / ( from_domain(2) - from_domain(1) ) );
x = x + to_domain(1);
end

Let's see this function in action

▶ Show code cell

from_domain = [-1, 1];
to_domain = [2, 7];
from_values = [-1, -0.5, 0, 0.5, 1];
to_values = ChangeOfVariable( from_values, from_domain, to_domain )

to_values = 1×5

2.0000 3.2500 4.5000 5.7500 7.0000

We can plot the values of from_values and to_values, showing how they're connected to each other:

▶ Show code cell

-----

Thoughts?

Emma Farnan
Last activity 2024 年 5 月 6 日

Include information about the "Margin" toggles in Preferences

I recently had issues with code folding seeming to disappear and it turns out that I had unknowingly disabled the "show code folding margin" option by accident. Despite using MATLAB for several years, I had no idea this was an option, especially since there seemed to be no references to it in the code folding part of the "Preferences" menu.

It would be great if in the future, there was a warning that told you about this when you try enable/disable folding in the Preferences.

I am using 2023b by the way.

Jérôme
Last activity 2024 年 4 月 29 日

Highlighting structure fields in MATLAB editor

In the MATLAB editor, when clicking on a variable name, all the other instances of the variable name will be highlighted.

But this does not work for structure fields, which is a pity. Such feature would be quite often useful for me.

I show an illustration below, and compare it with Visual Studio Code that does it. ;-)

I am using MATLAB R2023a, sorry if it has been added to newer versions, but I didn't see it in the release notes.

Athanasios Paraskevopoulos
Last activity 2024 年 7 月 27 日

Seeking Contributors for Upcoming Book on Matrix Algebra with MATLAB for Undergraduate Students

Hello MathWorks Community,

I am excited to announce that I am currently working on a book project centered around Matrix Algebra, specifically designed for MATLAB users. This book aims to cater to undergraduate students in engineering, where Matrix Algebra serves as a foundational element.

Matrix Algebra is not only pivotal in understanding complex engineering concepts but also in applying these principles effectively in various technological solutions. MATLAB, renowned for its powerful computational capabilities, is an excellent tool to explore and implement these concepts, making it a perfect companion for this book.

As I embark on this journey to create a resource that bridges theoretical matrix algebra with practical MATLAB applications, I am looking for one or two knowledgeable individuals who have a firm grasp of both subjects. If you have experience in teaching or applying matrix algebra in engineering contexts and are familiar with MATLAB, your contribution could be invaluable.

Collaborators will help in shaping the content to ensure it is educational, engaging, and technically robust, making complex concepts accessible and applicable for students.

If you are interested in contributing to this project or know someone who might be, please reach out to discuss how we can work together to make this book a valuable resource for engineering students.

Thank you and looking forward to your participation!

Chen Lin
Last activity 2024 年 4 月 12 日

Spring is on the way!

What's the weather like in your place?

http://www-pord.ucsd.edu/matlab/

David
Last activity 2024 年 4 月 2 日

Ghost page

I feel like no one at UC San Diego knows this page, let alone this server, is still live. For the younger generation, this is what the whole internet used to look like :)

ghost pages

Gregory Vernon
Last activity 2024 年 4 月 2 日

Support for CData & CFunction in plot functions

In short: support varying color in at least the plot, plot3, fplot, and fplot3 functions.

This has been a thing that's come up quite a few times, and includes questions/requests by users, workarounds by the community, and workarounds presented by MathWorks -- examples of each below. It's a feature that exists in Python's Matplotlib library and Sympy. Anyways, given that there are myriads of workarounds, it appears to be one of the most common requests for Matlab plots (Matlab's plotting is, IMO, one of the best features of the product), the request precedes the 21st century, and competitive tools provide the functionality, it would seem to me that this might be the next great feature for Matlab plotting.

I'm curious to get the rest of the community's thoughts... what's everyone else think about this?

---

User questions/requests

User-provided workarounds

MathWorks-provided workarounds

https://www.mathworks.com/videos/coloring-a-line-based-on-height-gradient-or-some-other-value-in-matlab-97128.html
https://www.mathworks.com/videos/making-a-multi-color-line-in-matlab-97127.html
https://www.mathworks.com/matlabcentral/fileexchange/95663-color-trajectory-plot (contributed by a MathWorks staff member)
And perhaps more?

Athanasios Paraskevopoulos
Last activity 2024 年 3 月 25 日

MATLAB EduHub: A Collaborative Platform for Sharing Educational Resources

I would like to propose the creation of MATLAB EduHub, a dedicated channel within the MathWorks community where educators, students, and professionals can share and access a wealth of educational material that utilizes MATLAB. This platform would act as a central repository for articles, teaching notes, and interactive learning modules that integrate MATLAB into the teaching and learning of various scientific fields.

Key Features:

1. Resource Sharing: Users will be able to upload and share their own educational materials, such as articles, tutorials, code snippets, and datasets.

2. Categorization and Search: Materials can be categorized for easy searching by subject area, difficulty level, and MATLAB version..

3. Community Engagement: Features for comments, ratings, and discussions to encourage community interaction.

4. Support for Educators: Special sections for educators to share teaching materials and track engagement.

Benefits:

- Enhanced Educational Experience: The platform will enrich the learning experience through access to quality materials.

- Collaboration and Networking: It will promote collaboration and networking within the MATLAB community.

- Accessibility of Resources: It will make educational materials available to a wider audience.

By establishing MATLAB EduHub, I propose a space where knowledge and experience can be freely shared, enhancing the educational process and the MATLAB community as a whole.

eduhub

Emma Farnan
Last activity 2024 年 7 月 19 日

Set colormap limits when creating m colors

Several of the colormaps are great for a 256 color surface plot, but aren't well optimized for extracting m colors for plotting several independent lines. The issue is that many colormaps have start/end colors that are too similar or are suboptimal colors for lines. There are certainly many workarounds for this, but it would be a great quality of life to adjust that directly when calling this.

Example:

x = linspace(0,2*pi,101)'; 
y = [1:6].*cos(x); 
figure; plot(x,y,'LineWidth',2); grid on; axis tight;

And now if I wanted to color these lines, I could use something like turbo(6) or gray(6) and then apply it using colororder.

colororder(turbo(6))

But my issue is that the ends of the colormap are too similar. For other colormaps, you may get lines that are too light to be visible against the white background. There are plenty of workarounds, with my preference being to create extra colors and truncate that before using colororder.

cmap = turbo(8); cmap = cmap(2:end-1,:); % Truncate the end colors
figure; plot(x,y,'LineWidth',2); grid on; axis tight;
colororder(cmap)

I think it would be really awesome to add some name-argument input pair to these colormaps that can specify the range you want so this could even be done inside the colororder calling if desired. An example of my proposed solution would look something like this:

cmap = turbo(6,'Range',[0.1 0.8]); % Proposed idea to add functionality

Where in this scenario, the resulting colormap would be 6 equally spaced colors that range from 10% to 80% of the total color range. This would be especially nice because you could more quickly modify the range of colors, or you could set the limits regardless of whether you need to plot 3, 6, or 20 lines.

lazymatlab
Last activity 2024 年 2 月 20 日

행렬식은 면적이다? Determinant is area?

2 x 2 행렬의 행렬식은

행렬의 두 row 벡터로 정의되는 평행사변형의 면적입니다.
물론 두 column 벡터로 정의되는 평행사변형의 면적이기도 합니다.
좀 더 정확히는 signed area입니다. 면적이 음수가 될 수도 있다는 뜻이죠.
행렬의 두 행(또는 두 열)을 맞바꾸면 행렬식의 부호도 바뀌고 면적의 부호도 바뀌어야합니다.

일반적으로 n x n 행렬의 행렬식은

각 row 벡터(또는 각 column 벡터)로 정의되는 N차원 공간의 평행면체(?)의 signed area입니다.
제대로 이해하려면 대수학의 개념을 많이 가지고 와야 하는데 자세한 설명은 생략합니다.(=저도 모른다는 뜻)
더 자세히 알고 싶으시면 수학하는 만화의 '넓이 이야기' 편을 추천합니다.
수학적인 정의를 알고 싶으시면 위키피디아를 보시면 됩니다.
이렇게 생겼습니다. 좀 무섭습니다.

아래 코드는...

2 x 2 행렬에 대해서 이것을 수식 없이 그림만으로 증명하는 과정입니다.
gif 생성에는 ScreenToGif를 사용했습니다. (gif 만들기엔 이게 킹왕짱인듯)

Determinant of 2 x 2 matrix is...

An area of a parallelogram defined by two row vectors.
Of course, same one defined by two column vectors.
Precisely, a signed area, which means area can be negative.
If two rows (or columns) are swapped, both the sign of determinant and area change.

More generally, determinant of n x n matrix is...

Signed area of parallelepiped defined by rows (or columns) of the matrix in n-dim space.
For a full understanding, a lot of concepts from abstract algebra should be brought, which I will not write here. (Cuz I don't know them.)
For a mathematical definition of determinant, visit wikipedia.
A little scary, isn't it?

The code below is...

A process to prove the equality of the determinant of 2 x 2 matrix and the area of parallelogram.
ScreenToGif is used to generate gif animation (which is, to me, the easiest way to make gif).

% 두 점 (a, b), (c, d)의 좌표
a = 4;
b = 1;
c = 1;
d = 3;
% patch 색 pre-define
lightgreen = [144, 238, 144]/255;
lightblue = [169, 190, 228]/255;
lightorange = [247, 195, 160]/255;
% animation params.
anim_Nsteps = 30;
% create window
figure('WindowStyle','docked')
ax = axes;
ax.XAxisLocation = 'origin';
ax.YAxisLocation = 'origin';
ax.XTick = [];
ax.YTick = [];
hold on
ax.XLim = [-.4, a+c+1];
ax.YLim = [-.4, b+d+1];
% create ad-bc patch
area = patch([0, a, a+c, c], [0, b, b+d, d], lightgreen);
p_ab = plot(a, b, 'ko', 'MarkerFaceColor', 'k');
p_cd = plot(c, d, 'ko', 'MarkerFaceColor', 'k');
p_ab.UserData = text(a+0.1, b, '(a, b)', 'FontSize',16);
p_cd.UserData = text(c+0.1, d-0.2, '(c, d)', 'FontSize',16);
area.UserData = text((a+c)/2-0.5, (b+d)/2, 'ad-bc', 'FontSize', 18);
pause
%% Is this really ad-bc?
area.UserData.String = 'ad-bc...?';
pause
%% fade out ad-bc
fadeinout(area, 0)
area.UserData.Visible = 'off';
pause
%% fade in ad block
rect_ad = patch([0, a, a, 0], [0, 0, d, d], lightblue, 'EdgeAlpha', 0, 'FaceAlpha', 0);
uistack(rect_ad, 'bottom');
fadeinout(rect_ad, 1, t_pause=0.003)
draw_gridline(rect_ad, ["23", "34"])
rect_ad.UserData = text(mean(rect_ad.XData), mean(rect_ad.YData), 'ad', 'FontSize', 20, 'HorizontalAlignment', 'center');
pause
%% fade-in bc block
rect_bc = patch([0, c, c, 0], [0, 0, b, b], lightorange, 'EdgeAlpha', 0, 'FaceAlpha', 0);
fadeinout(rect_bc, 1, t_pause=0.0035)
draw_gridline(rect_bc, ["23", "34"])
rect_bc.UserData = text(b/2, c/2, 'bc', 'FontSize', 20, 'HorizontalAlignment', 'center');
pause
%% slide ad block
patch_slide(rect_ad, ...
    [0, 0, 0, 0], [0, b, b, 0], t_pause=0.004)
draw_gridline(rect_ad, ["12", "34"])
pause
%% slide ad block
patch_slide(rect_ad, ...
    [0, 0, d/(d/c-b/a), d/(d/c-b/a)],...
    [0, 0, b/a*d/(d/c-b/a), b/a*d/(d/c-b/a)], t_pause=0.004)
draw_gridline(rect_ad, ["14", "23"])
pause
%% slide bc block
uistack(p_cd, 'top')
patch_slide(rect_bc, ...
    [0, 0, 0, 0], [d, d, d, d], t_pause=0.004)
draw_gridline(rect_bc, "34")
pause
%% slide bc block
patch_slide(rect_bc, ...
    [0, 0, a, a], [0, 0, 0, 0], t_pause=0.004)
draw_gridline(rect_bc, "23")
pause
%% slide bc block
patch_slide(rect_bc, ...
    [d/(d/c-b/a), 0, 0, d/(d/c-b/a)], ...
    [b/a*d/(d/c-b/a), 0, 0, b/a*d/(d/c-b/a)], t_pause=0.004)
pause
%% finalize: fade out ad, bc, and fade in ad-bc
rect_ad.UserData.Visible = 'off';
rect_bc.UserData.Visible = 'off';
fadeinout([rect_ad, rect_bc, area], [0, 0, 1])
area.UserData.String = 'ad-bc';
area.UserData.Visible = 'on';
%% functions
function fadeinout(objs, inout, options)
arguments
    objs
    inout % 1이면 fade-in, 0이면 fade-out
    options.anim_Nsteps = 30
    options.t_pause = 0.003
end
for alpha = linspace(0, 1, options.anim_Nsteps)
    for i = 1:length(objs)
        switch objs(i).Type
            case 'patch'
                objs(i).FaceAlpha = (inout(i)==1)*alpha + (inout(i)==0)*(1-alpha);
                objs(i).EdgeAlpha = (inout(i)==1)*alpha + (inout(i)==0)*(1-alpha);
            case 'constantline'
                objs(i).Alpha = (inout(i)==1)*alpha + (inout(i)==0)*(1-alpha);
        end                
        pause(options.t_pause)
    end
end
end
function patch_slide(obj, x_dist, y_dist, options)
arguments
    obj
    x_dist
    y_dist
    options.anim_Nsteps = 30
    options.t_pause = 0.003
end
dx = x_dist/options.anim_Nsteps;
dy = y_dist/options.anim_Nsteps;
for i=1:options.anim_Nsteps
    obj.XData = obj.XData + dx(:);
    obj.YData = obj.YData + dy(:);
    obj.UserData.Position(1) = mean(obj.XData);
    obj.UserData.Position(2) = mean(obj.YData);
    pause(options.t_pause)
end
end
function draw_gridline(patch, where)
ax = patch.Parent;
for i=1:length(where)
    v1 = str2double(where{i}(1));
    v2 = str2double(where{i}(2));
    x1 = patch.XData(v1);
    x2 = patch.XData(v2);
    y1 = patch.YData(v1);
    y2 = patch.YData(v2);
    if x1==x2
        xline(x1, 'k--')
    else
        fplot(@(x) (y2-y1)/(x2-x1)*(x-x1)+y1, [ax.XLim(1), ax.XLim(2)], 'k--')
    end
end
end