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Let us consider how to draw a Happy Sheep. A Happy Sheep was introduced in the MATLAB Mini Hack contest: Happy Sheep!
In this contest there was the strict limitation on the code length. So the code of the Happy Sheep is very compact and is only 280 characters long. We will analyze the process of drawing the Happy Sheep in MATLAB step by step. The explanations of the even more compact version of the code of the same sheep are given below.
So, how to draw a sheep? It is very easy. We could notice that usually a sheep is covered by crimped wool. Therefore, a sheep could be painted using several geometrical curves of similar types. Of course, then it will be an abstract model of the real sheep. Let us select two mathematical curves, which are the most appropriate for our goal. They are an ellipse for smooth parts of the sheep and an ellipse combined with a rose for woolen parts of the sheep.
Let us recall the mathematical formulas of these curves. A parametric representation of the standard ellipse is the following:
Also we will use the following parametric representation of the rose (rhodonea) curve:
This curve was named by the mathematician Guido Grandi.
Let us combine them in one curve and add possible shifts:
Now if we would like to create an ellipse, we will set 
and 
. If we would like to create a rose, we will set 
and 
. If we would like to shift our curve, we will set 
and 
to the required values. Of course, we could set all non-zero parameters to combine both chosen curves and use the shifts.
and . If we would like to create a rose, we will set and . If we would like to shift our curve, we will set and to the required values. Of course, we could set all non-zero parameters to combine both chosen curves and use the shifts.Let us describe how to create these curves using the MATLAB code. To make the code more compact, it is possible to program both formulas for the combined curve in one line using the anonymous function. We could make the code more compact using the function handles for sine and cosine functions. Then the MATLAB code for an example of the ellipse curve will be the following.
% Handles
s=@sin;
c=@cos;
% Ellipse + Polar Rose
F=@(t,a,f) a(1)*f(t)+s(a(2)*t).*f(t)+a(3);
% Angles
t=0:.1:7;
% Parameters
E = [5 7;0 0;0 0];
% Painting
figure;
plot(F(t,E(:,1),c),F(t,E(:,2),s),'LineWidth',10);
axis equal
The parameter t varies from 0 to 7, which is the nearest integer greater than 
, with the step 0.1. The result of this code is the following ellipse curve with 
and 
.
, with the step 0.1. The result of this code is the following ellipse curve with and .
This ellipse is described by the following parametric equations:
The MATLAB code for an example of the rose curve will be the following.
% Handles
s=@sin;
c=@cos;
% Ellipse + Polar Rose
F=@(t,a,f) a(1)*f(t)+s(a(2)*t).*f(t)+a(3);
% Angles
t=0:.1:7;
% Parameters
R = [0 0;4 4;0 0];
% Painting
figure;
plot(F(t,R(:,1),c),F(t,R(:,2),s),'LineWidth',10);
axis equal
The result of this code is the following rose curve with 
and 
.
and .
This rose is described by the following parametric equations:
Obviously, now we are ready to draw main parts of our sheep! As we reproduce an abstract model of the sheep, let us select the following main parts for the representation: head, eyes, hoofs, body, crown, and tail. We will use ellipses for the first three parts in this list and ellipses combined with roses for the last three ones.
First let us describe drawing of each part independently.
The following MATLAB code will be used to do this.
% Handles
s=@sin;
c=@cos;
% Ellipse + Polar Rose
F=@(t,a,f) a(1)*f(t)+s(a(2)*t).*f(t)+a(3);
% Angles
t=0:.1:7;
% Parameters
Head = 1;
Eyes = 2:3;
Hoofs = 4:7;
Body = 8;
Crown = 9;
Tail = 10;
G=-13;
P=[5 7 repmat([.1 .5],1,6) 6 4 14 9 3 3;zeros(1,14) 8 8 12 12 4 4;...
-15 2 G 3 -17 3 -3 G 0 G 9 G 12 G -15 12 4 3 20 7];
% Painting
figure;
hold;
for i=Head
plot(F(t,P(:,2*i-1),c),F(t,P(:,2*i),s),'LineWidth',10);
end
axis([-25 25 -15 20]);
figure;
hold;
for i=Eyes
plot(F(t,P(:,2*i-1),c),F(t,P(:,2*i),s),'LineWidth',10);
end
axis([-25 25 -15 20]);
figure;
hold;
for i=Hoofs
plot(F(t,P(:,2*i-1),c),F(t,P(:,2*i),s),'LineWidth',10);
end
axis([-25 25 -15 20]);
figure;
hold;
for i=Body
plot(F(t,P(:,2*i-1),c),F(t,P(:,2*i),s),'LineWidth',10);
end
axis([-25 25 -15 20]);
figure;
hold;
for i=Crown
plot(F(t,P(:,2*i-1),c),F(t,P(:,2*i),s),'LineWidth',10);
end
axis([-25 25 -15 20]);
figure;
hold;
for i=Tail
plot(F(t,P(:,2*i-1),c),F(t,P(:,2*i),s),'LineWidth',10);
end
axis([-25 25 -15 20]);
The parameters 
, 
, 
, 
, 
, and 
are written in the different submatrices of the matrix P. The code generates the following curves to illustrate the different parts of our sheep.
, , , , , and are written in the different submatrices of the matrix P. The code generates the following curves to illustrate the different parts of our sheep.The following ellipse describes the head of the sheep.
The following submatrix of the matrix P represents its parameters.
The parametric equations of the head are the following:
The following ellipses describe the eyes of the sheep.
The following submatrices of the matrix P represent their parameters.
The parametric equations of the left and right eyes correspondingly are the following:
The following ellipses describe the hoofs of the sheep.
The following submatrices of the matrix P represent their parameters.
The parametric equations of the right front, left front, right hind, and left hind hoofs correspondingly are the following:
The following ellipse combined with the rose describes the crown of the sheep.
The following submatrix of the matrix P represents its parameters.
The parametric equations of the crown are the following:
The following ellipse combined with the rose describes the body of the sheep.
The following submatrix of the matrix P represents its parameters.
The parametric equations of the body are the following:
The following ellipse combined with the rose describes the tail of the sheep.
The following submatrix of the matrix P represents its parameters.
The parametric equations of the tail are the following:
Now all the parts of our sheep should be put together! It is very easy because all the parts are described by the same equations with different parameters.
The following code helps us to accomplish this goal and ultimately draw a Happy Sheep in MATLAB!
% Happy Sheep!
% By Victoria A. Sablina
% Handles
s=@sin;
c=@cos;
% Ellipse + Rose
F=@(t,a,f) a(1)*f(t)+s(a(2)*t).*f(t)+a(3);
% Angles
t=0:.1:7;
% Parameters
% Head (1:2)
% Eyes (3:6)
% Hoofs (7:14)
% Crown (15:16)
% Body (17:18)
% Tail (19:20)
G=-13;
P=[5 7 repmat([.1 .5],1,6) 6 4 14 9 3 3;zeros(1,14) 8 8 12 12 4 4;...
-15 2 G 3 -17 3 -3 G 0 G 9 G 12 G -15 12 4 3 20 7];
% Painting
hold;
for i=1:10
plot(F(t,P(:,2*i-1),c),F(t,P(:,2*i),s),'LineWidth',10);
end
This code is even more compact than the original code from the contest. It is only 253 instead of 280 characters long and generates the same Happy Sheep!
Our sheep is happy, because of becoming famous in the MATLAB community, a star!
Congratulations! Now you know how to draw a Happy Sheep in MATLAB!
Thank you for reading!
The File Exchange team is thrilled to introduce a more streamlined approach to working with GitHub and File Exchange - the MATLAB and Simulink Integration for GitHub!
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Starting April 16, 2024, your File Exchange submissions will no longer update automatically unless you take the following steps:
2. Follow the prompts on the page to install MATLAB and Simulink Integration for GitHub.
3. Complete the necessary steps in GitHub.
4. Return to the My File Exchange page and verify the installation.
If you prefer your File Exchange submission not to update automatically from GitHub, no action is required. Users will still be able to find and download your submissions. However, to release a new version of your code, you must either install the GitHub App or disconnect from GitHub and manually upload new versions of your code.
Should you have any questions or encounter issues with the App, please feel free to comment on this post!
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eye(3) - diag(ones(1,3))
11%
0 ./ ones(3)
9%
cos(repmat(pi/2, [3,3]))
16%
zeros(3)
20%
A(3, 3) = 0
32%
mtimes([1;1;0], [0,0,0])
12%
3009 票
MATLAB O/X Quiz
Answer BEFORE Googling!
- An infinite loop can be made using "for".
- "A == A" is always true.
- "round(2.5)" is 3.
- "round(-0.5)" is 0.
MATLAB Support Package for Quantum Computing lets you build, simulate, and run quantum algorithms.
Check out the Cheat Sheet here!
I think that MATLAB's Flipbook Mini Hack had quite some inspiring entries. My work largely deals with digital elevation models (DEMs). Hence I really liked the random renderings of landscapes, in particular this one written by Tim which inspired me to adopt the code and apply to the example data that comes with my software TopoToolbox. The results and code are shown here.
and immeditaely everyone wanted the code! It turns out that this is the result of my remix of @Zhaoxu Liu / slandarer's entry on the MATLAB Flipbook Mini Hack.
I pointed people to the Flipbook entry but, of course, that just gave the code to render a single frame and people wanted the full code to render the animated gif. That way, they could make personalised versions
I just published a blog post that gives the code used by the team behind the Mini Hack to produce the animated .gifs https://blogs.mathworks.com/matlab/2024/02/16/producing-animated-gifs-from-matlab-flipbook-mini-hack-entries/
Thanks again to @Zhaoxu Liu / slandarer for a great entry that seems like it will live for a long time :)
If you've dabbled in "procedural generation," (algorithmically generating natural features), you may have come across the problem of sphere texturing. How to seamlessly texture a sphere is not immediately obvious. Watch what happens, for example, if you try adding power law noise to an evenly sampled grid of spherical angle coordinates (i.e. a "UV sphere" in Blender-speak):
% Example: how [not] to texture a sphere:
rng(2, 'twister'); % Make what I have here repeatable for you
% Make our radial noise, mapped onto an equal spaced longitude and latitude
% grid.
N = 51;
b = linspace(-1, 1, N).^2;
r = abs(ifft2(exp(6i*rand(N))./(b'+b+1e-5))); % Power law noise
r = rescale(r, 0, 1) + 5;
[lon, lat] = meshgrid(linspace(0, 2*pi, N), linspace(-pi/2, pi/2, N));
[x2, y2, z2] = sph2cart(lon, lat, r);
r2d = @(x)x*180/pi;
% Radial surface texture
subplot(1, 3, 1);
imagesc(r, 'Xdata', r2d(lon(1,:)), 'Ydata', r2d(lat(:, 1)));
xlabel('Longitude (Deg)');
ylabel('Latitude (Deg)');
title('Texture (radial variation)');
% View from z axis
subplot(1, 3, 2);
surf(x2, y2, z2, r);
axis equal
view([0, 90]);
title('Top view');
% Side view
subplot(1, 3, 3);
surf(x2, y2, z2, r);
axis equal
view([-90, 0]);
title('Side view');
The created surface shows "pinching" at the poles due to different radial values mapping to the same location. Furthermore, the noise statistics change based on the density of the sampling on the surface.
How can this be avoided? One standard method is to create a textured volume and sample the volume at points on a sphere. Code for doing this is quite simple:
rng default % Make our noise realization repeatable
% Create our 3D power-law noise
N = 201;
b = linspace(-1, 1, N);
[x3, y3, z3] = meshgrid(b, b, b);
b3 = x3.^2 + y3.^2 + z3.^2;
r = abs(ifftn(ifftshift(exp(6i*randn(size(b3)))./(b3.^1.2 + 1e-6))));
% Modify it - make it more interesting
r = rescale(r);
r = r./(abs(r - 0.5) + .1);
% Sample on a sphere
[x, y, z] = sphere(500);
% Plot
ir = interp3(x3, y3, z3, r, x, y, z, 'linear', 0);
surf(x, y, z, ir);
shading flat
axis equal off
set(gcf, 'color', 'k');
colormap(gray);
The result of evaluating this code is a seamless, textured sphere with no discontinuities at the poles or variation in the spatial statistics of the noise texture:
But what if you want to smooth it or perform some other local texture modification? Smoothing the volume and resampling is not equivalent to smoothing the surficial features shown on the map above.
A more flexible alternative is to treat the samples on the sphere surface as a set of interconnected nodes that are influenced by adjacent values. Using this approach we can start by defining the set of nodes on a sphere surface. These can be sampled almost arbitrarily, though the noise statistics will vary depending on the sampling strategy.
One noise realisation I find attractive can be had by randomly sampling a sphere. Normalizing a point in N-dimensional space by its 2-norm projects it to the surface of an N-dimensional unit sphere, so randomly sampling a sphere can be done very easily using randn() and vecnorm():
N = 5e3; % Number of nodes on our sphere
g=randn(3,N); % Random 3D points around origin
p=g./vecnorm(g); % Projected to unit sphere
The next step is to find each point's "neighbors." The first step is to find the convex hull. Since each point is on the sphere, the convex hull will include each point as a vertex in the triangulation:
k=convhull(p');
In the above, k is an N x 3 set of indices where each row represents a unique triangle formed by a triplicate of points on the sphere surface. The vertices of the full set of triangles containing a point describe the list of neighbors to that point.
What we want now is a large, sparse symmetric matrix where the indices of the columns & rows represent the indices of the points on the sphere and the nth row (and/or column) contains non-zero entries at the indices corresponding to the neighbors of the nth point.
How to do this? You could set up a tiresome nested for-loop searching for all rows (triangles) in k that contain some index n, or you could directly index via:
c=@(x)sparse(k(:,x)*[1,1,1],k,1,N,N);
t=c(1)|c(2)|c(3);
The result is the desired sparse connectivity matrix: a matrix with non-zero entries defining neighboring points.
So how do we create a textured sphere with this connectivity matrix? We will use it to form a set of equations that, when combined with the concept of "regularization," will allow us to determine the properties of the randomness on the surface. Our regularizer will penalize the difference of the radial distance of a point and the average of its neighbors. To do this we replace the main diagonal with the negative of the sum of the off-diagonal components so that the rows and columns are zero-mean. This can be done via:
w=spdiags(-sum(t,2)+1,0,double(t));
Now we invoke a bit of linear algebra. Pretend x is an N-length vector representing the radial distance of each point on our sphere with the noise realization we desire. Y will be an N-length vector of "observations" we are going to generate randomly, in this case using a uniform distribution (because it has a bias and we want a non-zero average radius, but you can play around with different distributions than uniform to get different effects):
Y=rand(N,1);
and A is going to be our "transformation" matrix mapping x to our noisy observations:
Ax = Y
In this case both x and Y are N length vectors and A is just the identity matrix:
A = speye(N);
Y, however, doesn't create the noise realization we want. So in the equation above, when solving for x we are going to introduce a regularizer which is going to penalize unwanted behavior of x by some amount. That behavior is defined by the point-neighbor radial differences represented in matrix w. Our estimate of x can then be found using one of my favorite Matlab assets, the "\" operator:
smoothness = 10; % Smoothness penalty: higher is smoother
x = (A+smoothness*w'*w)\Y; % Solving for radii
The vector x now contains the radii with the specified noise realization for the sphere which can be created simply by multiplying x by p and plotting using trisurf:
p2 = p.*x';
trisurf(k,p2(1,:),p2(2,:),p2(3,:),'FaceC', 'w', 'EdgeC', 'none','AmbientS',0,'DiffuseS',0.6,'SpecularS',1);
light;
set(gca, 'color', 'k');
axis equal
The following images show what happens as you change the smoothness parameter using values [.1, 1, 10, 100] (left to right):
Now you know a couple ways to make a textured sphere: that's the starting point for having a lot of fun with basic procedural planet, moon, or astroid generation! Here's some examples of things you can create based on these general ideas:
The MATLAB command window isn't just for commands and outputs—it can also host interactive hyperlinks. These can serve as powerful shortcuts, enhancing the feedback you provide during code execution. Here are some hyperlinks I frequently use in fprintf statements, warnings, or error messages.
1. Open a website.
msg = "Could not download data from website.";
url = "https://blogs.mathworks.com/graphics-and-apps/";
hypertext = "Go to website"
fprintf(1,'%s <a href="matlab: web(''%s'') ">%s</a>\n',msg,url,hypertext);
Could not download data from website. Go to website
2. Open a folder in file explorer (Windows)
msg = "File saved to current directory.";
directory = cd();
hypertext = "[Open directory]";
fprintf(1,'%s <a href="matlab: winopen(''%s'') ">%s</a>\n',msg,directory,hypertext)
File saved to current directory. [Open directory]
3. Open a document (Windows)
msg = "Created database.csv.";
filepath = fullfile(cd,'database.csv');
hypertext = "[Open file]";
fprintf(1,'%s <a href="matlab: winopen(''%s'') ">%s</a>\n',msg,filepath,hypertext)
Created database.csv. [Open file]
4. Open an m-file and go to a specific line
msg = 'Go to';
file = 'streamline.m';
line = 51;
fprintf(1,'%s <a href="matlab: matlab.desktop.editor.openAndGoToLine(which(''%s''), %d); ">%s line %d</a>', msg, file, line, file, line);
Go to streamline.m line 51
5. Display more text
msg = 'Incomplete data detected.';
extendedInfo = '\tFilename: m32c4r28\n\tDate: 12/20/2014\n\tElectrode: (3,7)\n\tDepth: ???\n';
hypertext = '[Click for more info]';
warning('%s <a href="matlab: fprintf(''%s'') ">%s</a>', msg,extendedInfo,hypertext);
<click>
- Filename: m32c4r28
- Date: 12/20/2014
- Electrode: (3,7)
- Depth: ???
6. Run a function
Similarly, you can also add hyperlinks in figures and apps
And what do you do for Valentine's Day?
which technical support should I contact/ask for the published Simscape example?
Happy year of the dragon.
To enlarge an array with more rows and/or columns, you can set the lower right index to zero. This will pad the matrix with zeros.
m = rand(2, 3) % Initial matrix is 2 rows by 3 columns
mCopy = m;
% Now make it 2 rows by 5 columns
m(2, 5) = 0
m = mCopy; % Go back to original matrix.
% Now make it 3 rows by 3 columns
m(3, 3) = 0
m = mCopy; % Go back to original matrix.
% Now make it 3 rows by 7 columns
m(3, 7) = 0
Can you see them?
I have been procrastinating on schoolwork by looking at all the amazing designs created in the last MATLAB Flipbook Mini Hack! They are just amazing. The voting is over but what are y'all's personal favorites? Mine is the flapping butterfly, it is for sure a creation I plan to share with others in the future!
It is easy to obtain sankey plot like that using my tool:
code is here
You can also see the animated version of the competition here
function dragon24
% Copyright (c) 2024, Zhaoxu Liu / slandarer
baseV=[ -.016,.822; -.074,.809; -.114,.781; -.147,.738; -.149,.687; -.150,.630;
-.157,.554; -.166,.482; -.176,.425; -.208,.368; -.237,.298; -.284,.216;
-.317,.143; -.338,.091; -.362,.037;-.382,-.006;-.420,-.051;-.460,-.084;
-.477,-.110;-.430,-.103;-.387,-.084;-.352,-.065;-.317,-.060;-.300,-.082;
-.331,-.139;-.359,-.201;-.385,-.262;-.415,-.342;-.451,-.418;-.494,-.510;
-.533,-.599;-.569,-.675;-.607,-.753;-.647,-.829;-.689,-.932;-.699,-.988;
-.639,-.905;-.581,-.809;-.534,-.717;-.489,-.642;-.442,-.543;-.393,-.447;
-.339,-.362;-.295,-.296;-.251,-.251;-.206,-.241;-.183,-.281;-.175,-.350;
-.156,-.434;-.136,-.521;-.128,-.594;-.103,-.677;-.083,-.739;-.067,-.813;-.039,-.852];
% 基础比例、上色方式数据
baseV=[0,.82;baseV;baseV(end:-1:1,:).*[-1,1];0,.82];
baseV=baseV-mean(baseV,1);
baseF=1:size(baseV,1);
baseY=baseV(:,2);
baseY=(baseY-min(baseY))./(max(baseY)-min(baseY));
N=30;
baseR=sin(linspace(pi/4,5*pi/6,N))./1.2;
baseR=[baseR',baseR'];baseR(1,:)=[1,1];
baseR(5,:)=[2,.6];
baseR(10,:)=[3.7,.4];
baseR(15,:)=[1.8,.6];
baseT=[zeros(N,1),ones(N,1)];
baseM=zeros(N,2);
baseD=baseM;
ratioT=@(Mat,t)Mat*[cos(t),sin(t);-sin(t),cos(t)];
% 配色数据
CList=[211,56,32;56,105,166;253,209,95]./255;
% CList=bone(4);CList=CList(2:4,:);
% CList=flipud(bone(3));
% CList=lines(3);
% CList=colorcube(3);
% CList=rand(3)
baseC1=CList(2,:)+baseY.*(CList(1,:)-CList(2,:));
baseC2=CList(3,:)+baseY.*(CList(1,:)-CList(3,:));
% 构建图窗
fig=figure('units','normalized','position',[.1,.1,.5,.8],...
'UserData',[98,121,32,115,108,97,110,100,97,114,101,114]);
axes('parent',fig,'NextPlot','add','Color',[0,0,0],...
'DataAspectRatio',[1,1,1],'XLim',[-6,6],'YLim',[-6,6],'Position',[0,0,1,1]);
% 构造龙每个部分句柄
dragonHdl(1)=patch('Faces',baseF,'Vertices',baseV,'FaceVertexCData',baseC1,'FaceColor','interp','EdgeColor','none','FaceAlpha',.95);disp(char(fig.UserData))
for i=2:N
dragonHdl(i)=patch('Faces',baseF,'Vertices',baseV.*baseR(i,:)-[0,i./2.5-.3],'FaceVertexCData',baseC2,'FaceColor','interp','EdgeColor','none','FaceAlpha',.7);
end
set(dragonHdl(5),'FaceVertexCData',baseC1,'FaceAlpha',.7)
set(dragonHdl(10),'FaceVertexCData',baseC1,'FaceAlpha',.7)
set(dragonHdl(15),'FaceVertexCData',baseC1,'FaceAlpha',.7)
for i=N:-1:1,uistack(dragonHdl(i),'top');end
for i=1:N
baseM(i,:)=mean(get(dragonHdl(i),'Vertices'),1);
end
baseD=diff(baseM(:,2));Pos=[0,2];
% 主循环及旋转、运动计算
set(gcf,'WindowButtonMotionFcn',@dragonFcn)
fps=8;
game=timer('ExecutionMode', 'FixedRate', 'Period',1/fps, 'TimerFcn', @dragonGame);
start(game)
% Copyright (c) 2023, Zhaoxu Liu / slandarer
set(gcf,'tag','co','CloseRequestFcn',@clo);
function clo(~,~)
stop(game);delete(findobj('tag','co'));clf;close
end
function dragonGame(~,~)
Dir=Pos-baseM(1,:);
Dir=Dir./norm(Dir);
baseT=(baseT(1:end,:)+[Dir;baseT(1:end-1,:)])./2;
baseT=baseT./(vecnorm(baseT')');
theta=atan2(baseT(:,2),baseT(:,1))-pi/2;
baseM(1,:)=baseM(1,:)+(Pos-baseM(1,:))./30;
baseM(2:end,:)=baseM(1,:)+[cumsum(baseD.*baseT(2:end,1)),cumsum(baseD.*baseT(2:end,2))];
for ii=1:N
set(dragonHdl(ii),'Vertices',ratioT(baseV.*baseR(ii,:),theta(ii))+baseM(ii,:))
end
end
function dragonFcn(~,~)
xy=get(gca,'CurrentPoint');
x=xy(1,1);y=xy(1,2);
Pos=[x,y];
Pos(Pos>6)=6;
Pos(Pos<-6)=6;
end
end
There will be a warning when we try to solve equations with piecewise:
syms x y
a = x+y;
b = 1.*(x > 0) + 2.*(x <= 0);
eqns = [a + b*x == 1, a - b == 2];
S = solve(eqns, [x y]);
% 错误使用 mupadengine/feval_internal
% System contains an equation of an unknown type.
%
% 出错 sym/solve (第 293 行)
% sol = eng.feval_internal('solve', eqns, vars, solveOptions);
%
% 出错 demo3 (第 5 行)
% S=solve(eqns,[x y]);
But I found that the solve function can include functions such as heaviside to indicate positive and negative：
syms x y
a = x+y;
b = floor(heaviside(x)) - 2*abs(2*heaviside(x) - 1) + 2*floor(-heaviside(x)) + 4;
eqns = [a + b*x == 1, a - b == 2];
S = solve(eqns, [x y])
% S =
% 包含以下字段的 struct:
%
% x: -3/2
% y: 11/2
The piecewise function is divided into two sections, which is so complex, so this work must be encapsulated as a function to complete：
function pwFunc=piecewiseSym(x,waypoint,func,pfunc)
% @author : slandarer
gSign=[1,heaviside(x-waypoint)*2-1];
lSign=[heaviside(waypoint-x)*2-1,1];
inSign=floor((gSign+lSign)/2);
onSign=1-abs(gSign(2:end));
inFunc=inSign.*func;
onFunc=onSign.*pfunc;
pwFunc=simplify(sum(inFunc)+sum(onFunc));
end
Function Introduction
- x : Argument
- waypoint : Segmentation point of piecewise function
- func : Functions on each segment
- pfunc : The value at the segmentation point
example
syms x
% x waypoint func pfunc
f=piecewiseSym(x,[-1,1],[-x-1,-x^2+1,(x-1)^3],[-x-1,(x-1)^3]);
For example, find the analytical solution of the intersection point between the piecewise function and f=0.4 and plot it:
syms x
% x waypoint func pfunc
f=piecewiseSym(x,[-1,1],[-x-1,-x^2+1,(x-1)^3],[-x-1,(x-1)^3]);
% solve
S=solve(f==.4,x)
% S =
%
% -7/5
% (2^(1/3)*5^(2/3))/5 + 1
% -15^(1/2)/5
% 15^(1/2)/5
% draw
xx=linspace(-2,2,500);
f=matlabFunction(f);
yy=f(xx);
plot(xx,yy,'LineWidth',2);
hold on
scatter(double(S),.4.*ones(length(S),1),50,'filled')
precedent
syms x y
a=x+y;
b=piecewiseSym(x,0,[2,1],2);
eqns = [a + b*x == 1, a - b == 2];
S=solve(eqns,[x y])
% S =
% 包含以下字段的 struct:
%
% x: -3/2
% y: 11/2
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