I am trying to generate the same plot as the one shown below,
, and I have written the following piece of code in MATLAB,
x1 = [0, 0, 1, 1];
x2 = [0, 1, 0, 1];
Y = [4, 3, 2, 4];
plot3(x1,x2,Y,'o','Color','r','MarkerSize',10, 'MarkerFaceColor', 'r')
hold on
[x y] = meshgrid(0:0.1:2, 0:0.1:2);
z = 1.25 + 2.5 * x + 1.5 * y;
surf(x, y, z,'FaceAlpha',0.5)
xlabel('x1');ylabel('x2');zlabel('y');
hold off
grid on
Would you please tell me how I can plot a line that connects the data point with its corresponding value of the generated surface for the same plot I generated with MATLAB.
Many thanks for your time.
I added a loop within the "hold" portion of your code.
x1 = [0, 0, 1, 1];
x2 = [0, 1, 0, 1];
Y = [4, 3, 2, 4];
plot3(x1,x2,Y,'o','Color','r','MarkerSize',10, 'MarkerFaceColor', 'r')
hold on
[x y] = meshgrid(0:0.1:2, 0:0.1:2);
z = 1.25 + 2.5 * x + 1.5 * y;
surf(x, y, z,'FaceAlpha',0.5)
xlabel('x1');ylabel('x2');zlabel('y');
for ii=1:numel(Y)
plot3( [x1(ii),x1(ii)], [x2(ii),x2(ii)], [Y(ii),1.25+2.5*x1(ii)+1.5*x2(ii)] );
end
hold off
grid on
Also, currently your surface z is hard-coded, therefore the code for the vertical line is hard-coded as well. But once you estimate your parameters for the regression, you could just as easily dynamically adjust the surface and the vertical lines.
Related
I have a unit circle with n roots of unity marked. I would like to be able to rotate, translate, and scale a line resting on the x-axis (between -1 and 1) to connect any pair of marked roots. Currently my code can do this in some cases, but doesn't work in general. I want to avoid hard-coding how the line should move for each possible pair. Here's what I have so far:
clear
%% Roots of unity
n = 10;
roots = zeros(1, n);
for k = 1 : n
roots(k) = exp(2 * k* pi * 1i / n);
end
%% Move line
% Pair of roots the line should connect
point_1 = roots(2);
point_2 = roots(6);
% Coordinates of pair of roots
x1 = real(point_1);
x2 = real(point_2);
y1 = imag(point_1);
y2 = imag(point_2);
d = sqrt((x1-x2)^2+(y1-y2)^2); % Euclidean distance between pair of roots
m = (y1 - y2) / (x1 - x2); % Gradient of line connecting pair of roots
c = y1 - m * x1; % y-intercept of line
int = -c / m; % x-coordinate that the rotation should occur at
shift = [int; 0];
x = linspace(-1, 1, 10); % Initial line lying purely on x-axis
y = 0 * x;
v = [x; y];
theta = atan((y2-shift(2))/(x2-shift(1))); % Angle by which to rotate
rot = [cos(theta), -sin(theta); sin(theta), cos(theta)]; % Rotation matrix
u = v * (d / 2); % Scale initial line
if m < 1e-3 % Horizontal case
shift = [0; 0];
end
w = (rot * (u - shift)) + shift; % Apply rotation
% Another shift that seems necessary
% This is definitely a problematic section
shift_x = w(1, 1) - x2;
shift_y = w(2, 1) - y2;
shift_2 = [shift_x; shift_y];
w = w - shift_2;
%% Plot
fig = figure;
fig.Units = 'inches';
fig.Position = [1, 1, 9, 9];
ax = gca;
tt = title(ax, 'Title');
tt.FontWeight = 'bold';
tt.FontSize = 20;
st = subtitle(ax, sprintf('More text here'));
st.FontAngle = 'italic';
st.FontSize = 15;
hold on
hCircle = viscircles([0, 0], 1, 'Color', 'k');
for i = 1 : n
x_point = real(roots(i));
y_point = imag(roots(i));
hPin = plot(x_point, y_point, 'Marker', 'o', 'MarkerSize', 20, 'MarkerfaceColor', 'red', ...
'MarkerEdgeColor', 'black');
end
% Plot original and shifted line, split into colours so direction is easier to see
plot(v(1,1:4), v(2,1:4), 'b');
plot(v(1,4:7), v(2,4:7), 'r');
plot(v(1,7:end), v(2,7:end), 'g');
plot(w(1,1:4), w(2,1:4), 'b');
plot(w(1,4:7), w(2,4:7), 'r');
plot(w(1,7:end), w(2,7:end), 'g');
For example, keeping point_1 = roots(2); and changing only point_2 = roots(p); works as intended for only p=3, 4, 6, 7, 8.
Any guidance on how to get this working would be greatly appreciated, thanks!
Edit:
To give some more details, basically I have an array of numbers between 0 and 1 (rather than just a line) which I want to plot on the line that would connect two roots. E.g. if my array is x=[0.2, 0.5, 0.9], then I want three points between point_1 and point_2, the first being 0.2d down the connecting line away from point_1, the second 0.5d (i.e. halfway), and the final being 0.9d away.
First of all, since the points you want to connect are complex numbers, it is easier to work with complex coordinate directly.
Roots of unity
I have simplified your code a bit.
Some may raise a flag on naming a variable roots since roots is a built-in matlab function. I am fine with it, as long as the usage does not cause any confusion, namely, don't use roots as a variable and as a function in the same context.
As matlab provides so many built-in functions, it is impossible to avoid name collision unless one knows them all by heart or searches before naming every single variable.
n = 10;
k = 1:n;
roots = exp(2 * k * pi * 1i / n);
Scaling, rotating, and translating
% Pair of roots the line should connect
point_1 = roots(2);
point_2 = roots(6);
d = abs(point_2 - point_1); % distance between pair of roots
theta = angle(point_2 - point_1); % rotation angle
p_on_line = linspace(-1, 1, 10); % Initial line lying on x-axis
p_on_line = p_on_line * d/2; % scale
p_on_line = p_on_line * exp(1i*theta); % rotate
p_on_line = p_on_line + (point_1 - p_on_line(1)); % translate
Plot
I added some scatter points and removed irrevelant parts (e.g. title, fonts).
fig = figure;
fig.Units = 'inches';
fig.Position = [1, 1, 9, 9];
hold on
hCircle = viscircles([0, 0], 1, 'Color', 'k');
hPin = plot(roots, 'o', 'MarkerSize', 20, 'MarkerfaceColor', 'red', ...
'MarkerEdgeColor', 'black');
% Plot line connecting roots
plot(p_on_line(1:4), 'b.-', 'MarkerSize', 20);
plot(p_on_line(4:7), 'r.-', 'MarkerSize', 20);
plot(p_on_line(7:end), 'g.-', 'MarkerSize', 20);
% Plot original line
original_x = linspace(-1, 1, 10);
original_y = zeros(1, 10);
plot(original_x(1:4), original_y(1:4), 'b.-', 'MarkerSize', 20);
plot(original_x(4:7), original_y(4:7), 'r.-', 'MarkerSize', 20);
plot(original_x(7:end), original_y(7:end), 'g.-', 'MarkerSize', 20);
hold off
This should work for all combinations of root pairs.
I would like to plot/draw exactly this shape in MATLAB or OCTAVE. Of course I do know how to plot, and how to create rectangles, using either the plot, the line or the rectangle functions. But I have not yet managed to add this "hole" on the top side of the rectangle. I figure, it's a (half-)circle of radius 0.5 and center point (1.5|2). In OCTAVE, there is a drawCircleArc function, but I don't want to only draw that thing, but also to have the necessary coordinates defining the whole shape for further manipulation.
Here is one way (matlab/octave compatible):
% Specify all polygon points, excluding the semi-circle outline
X = [1, 0, 0, 3, 3, 2];
Y = [2, 2, 0, 0, 2, 2];
% Add semi-circle outline to array of polygon points
t = 0 : -0.01 : -pi;
X = [X, 1.5 + 0.5 * cos(t)];
Y = [Y, 2 + 0.5 * sin(t)];
% Use fill to plot the filled polygon, with desired settings
fill( X, Y, [0.8, 0.8, 0.8], 'linewidth', 1.5 );
axis( [-2, 4, -2, 4] ); axis equal;
As of 2017b you can also use polyshapes and boolean operators.
rect = polyshape([0 3 3 0], [0 0 2 2]);
t = linspace(0, 2*pi, 32);
circ = polyshape(1.5+.5*cos(t), 2+.5*sin(t));
subplot 121, hold on
plot(rect)
plot(circ)
axis equal
shape = subtract(rect, circ);
subplot 122
plot(shape)
axis equal
Consider the polygon with vertices (0, 0), (1, 0), (7/10, 1), (1/2, 1/2), and (3/10, 1). Make a plot of this polygon in Matlab using the fill function. Rotate this polygon by an angle of 100 degrees using matrix-vector multiplication in Matlab with an appropriately chosen rotation matrix R. Make another plot of the rotated polygon using fill.
% Makes original polygon
X = [0 1 7/10 1/2 3/10];
Y = [0 0 1 1/2 1];
norm_poly = fill(X,Y,'k');
thetad = 100;
R = [cosd(thetad) -sind(thetad); sind(thetad) cosd(thetad)];
C = repmat([0 0], 5, 1)';
axis([-10 10 -10 10])
V = get(norm_poly,'Vertices')'; % get the current set of vertices
V = R*(V - C) + C; % do the rotation relative to the centre of the
square
set(norm_poly,'Vertices',V'); % update the vertices
How would I make to different plots to show them? Does the code to rotate make sense and answer all the requirements?
The rotation itself makes sense. To plot multiple things to the same graph use hold on after making the first plot. Alternatively you can make a new figure and plot a new fill there.
P = [0, 1, 7/10, 1/2, 3/10;
0, 0, 1, 1/2, 1];
fill(P(1,:), P(2,:), 'k');
theta = 100;
R = #(t) [cosd(t) -sind(t); sind(t) cosd(t)];
axis([-3 3 -3 3])
grid on
V = R(theta)*P;
hold on;
fill(V(1,:), V(2,:), 'k');
I'm trying to create a figure in matlab that looks like this:
desired figure
I am doing so by: (i) assigning value points to each x,y coordinate, (ii) plotting a surf, and (iii) change the view point so the third axis is not seen. Here is the code:
x = linspace(0, 1, 10);
y = linspace(0, 1, 10);
z = linspace(0, 1, 10);
z = repmat(z, 10, 1);
z = flipud(triu(z));
z(z==0) = nan;
hold off
surf(x, y, z, 'linestyle', 'none')
colormap([linspace(0.39, 1, 20)',linspace(0.58, 0.25, 20)', linspace(0.93, 0.25, 20)']);
colorbar
xlim([x(1) x(end)])
shading interp
view([90 -90])
hold on
plot(x, 1-y, 'linewidth', 2)
I get the following figure: matlab figure I get
As you can see, there a lot of white spaces above the line which I would like to be in color as well. Unfortunately, I cannot add any more grid points as calculating the actual value of the points takes a lot of time (unlike the example above).
Is there a way to have matlab draw colors in those white spaces as well?
Thanks!
You can try to use patch function to create filled polygon.
See http://www.mathworks.com/help/matlab/ref/patch.html
Try the following code:
vert = [0 1;1 1;1 0]; % x and y vertex coordinates
fac = [1 2 3]; % vertices to connect to make triangle
fvc = [1 0 0; 1 1 1; 0 0 1];
patch('Faces',fac,'Vertices',vert,'FaceVertexCData',fvc,'FaceColor','interp');
Result is close:
I was managed to get closer to the desired figure:
close all
x = linspace(0, 1, 10);
y = linspace(0, 1, 10);
%colorbar
xlim([x(1) x(end)])
%Fill rectangle.
vert = [0 0; 1 0; 1 1; 0 1]; % x and y vertex coordinates
fac = [1 2 3 4]; % vertices to connect to make squares
%patch('Faces',fac,'Vertices',vert,'FaceColor','red')
fvc = [1 0 0; 0.6 0.7 1; 0.6 0.7 1; 1 0 0]; %Color of vertices (selected to be close to example image).
patch('Faces',fac,'Vertices',vert,'FaceVertexCData',fvc,'FaceColor','interp')
hold on
%Fill lower triangle with white color.
vert = [0 0;0 1;1 0]; % x and y vertex coordinates
fac = [1 2 3]; % vertices to connect to make triangle
fvc = [1 1 1; 1, 1, 1; 1, 1, 1]; %White color
patch('Faces',fac,'Vertices',vert,'FaceVertexCData',fvc,'FaceColor','interp');
plot(x, 1-y, 'linewidth', 2)
set(gca,'Xtick',[],'Ytick',[]); %Remove tick marks
Result:
Thank you Rotem! I wasn't aware of the patch function and indeed it solved the issue!
The colors on the actual figure I'm trying to achieve are not linear, so I just used patch for all the empty triangles. Here is the adjusted code I use for the simple example (again, this is just a bit more general just to be able to have non linear colors in the area above the curve):
x = linspace(0, 1, 10);
y = linspace(0, 1, 10);
z = linspace(0, 1, 10);
z = repmat(z, 10, 1)+0.1;
z = flipud(triu(z));
z(z==0) = nan;
z = z-0.1;
hold off
surf(x, y, z, 'linestyle', 'none')
colormap([linspace(0.39, 1, 20)',linspace(0.58, 0.25, 20)', linspace(0.93, 0.25, 20)']);
colorbar
xlim([x(1) x(end)])
shading interp
view([90 -90])
hold on
patch_cor_y = kron((length(y):-1:1)', ones(3, 1));
patch_cor_x = kron((1:length(x))', ones(3, 1));
patch_cor = [y(patch_cor_y(2:end-2))', x(patch_cor_x(3:end-1))'];
patch_path = reshape(1:length(patch_cor),3, length(patch_cor)/3)';
patch_col = z(sub2ind(size(z), patch_cor_x(3:end-1), patch_cor_y(2:end-2)));
patch('Faces',patch_path,'Vertices',patch_cor,'FaceVertexCData',patch_col,'FaceColor','interp', 'EdgeColor', 'none');
plot(x, 1-y, 'linewidth', 2)
The figure achieved: figure
I am trying to find a point on the plane that is closest to the origin. When I plot the normal, somehow it is not perpendicular to the plane! Also, the point on the plane closest to origin does not appear correct from the plot. I cannot figure out what is wrong. Any ideas?
c = 2;
x1 = [1, 0, 0] * c;
x2 = [0, 1, 0] * c;
x3 = [0, 0, 1] * c;
x = [x1(1), x2(1), x3(1)];
y = [x1(2), x2(2), x3(2)];
z = [x1(3), x2(3), x3(3)];
figure(1); plot3(x,y,z,'*r'); hold on; grid on;
normal = cross(x1-x2, x1-x3);
% Find all coefficients of plane equation
D = -dot(normal, x1);
range = [-10 10]; [X, Z] = meshgrid(range, range);
Y = (-normal(1) * X - normal(3) * Z - D)/ normal(2);
order = [1 2 4 3]; patch(X(order),Y(order),Z(order),'b');
alpha(0.3);
plot3([x(1), x(3)], [y(1), y(3)], [z(1), z(3)]);
plot3([x(1), x(2)], [y(1), y(2)], [z(1), z(2)]);
x1=x1-x3;
plot3([normal(1), x1(1)], [normal(2), x1(2)], [normal(3), x1(3)], 'k');
%% Get the point on the plane closest point to (0,0,0)
p = normal * (-D / sum(normal.^2,2));
plot3(p(1), p(2), p(3), '*g');
I appreciate your help.
normalize your normal:
normal = normal /norm(normal);
and plot the normal correctly:
plot3([x1(1)+normal(1), x1(1)], [x1(2)+normal(2), x1(2)], [x1(3)+normal(3), x1(3)], 'k');
and for a proper visualization, the axis should be of equal scale:
axis equal
Does not look bad, does it?