Computing the surface between two lines - matlab

I have the following figure, where I plotted two surfaces and I wanted to indicate the intersection of both of them. To do that, I did the following:
zdiff = z1-z2;
C = contours(x,y,zdiff,[0 0]);
xL = C(1, 2:end);
yL = C(2, 2:end);
zL = interp2(x, y, z1, xL, yL);
line(xL, yL, zL, 'Color', 'k', 'LineWidth', 2,'Linestyle','--'); hold on;
line(xL, yL, zeros(size(zL)), 'Color', 'k', 'LineWidth', 2); hold off;
Now, I want to plot the vertical surface between the actual intersection (dash line) and its projection over XY (solid line), but I cannot figure out how to do that. Any ideas?


Another really simple option:
dist = (diff(xL).^2+diff(yL).^2).^0.5; %distance between x,y
cdist = [0, cumsum(dist)]; %cumsum of the distance
area = trapz(cdist,zL); %The area


Why not calculating it manually?
Something like (untested):
Area = 0
for i=1:numel(xL)-1
base = sqrt( (xL(i)-xL(i+1))^2 + (yL(i)-yL(i+1))^2);
Area =Area + base * (zL(i) + zL(i+1))/2;
end;


maybe not pretty but its a oneliner it might do the trick. maybe you have to adjust the format as this code is for (1,N) vectors
xL=(1:100); %size 1 100
yL=(1:100) ;%size 1 100
zL=rand(1,100);%size 1 100
line(xL,yL,zL)
line(xL,yL,zeros(size(zL)))
hold on
surf(repmat(xL,100,1),repmat(yL,100,1),cell2mat(arrayfun(#(x,y) linspace(x,y,100)',zL,zeros(size(zL)),'UniformOutput',false)))


xL=sin((1:30)/10); % Data generation for test only. Use your data
yL=cos((1:30)/10); % Data generation for test only. Use your data
zL=2+xL.*yL; % Data generation for test only. Use your data
surf([xL;xL],[yL;yL],[zeros(size(zL));zL]); % plot the surface

Related

How can I fill an area below a 3D graph in MATLAB?

I created the following 3d plot in MATLAB using the function plot3:
Now, I want to get a hatched area below the "2d sub-graphs" (i.e. below the blue and red curves). Unfortunately, I don't have any idea how to realize that.
I would appreciate it very much if somebody had an idea.

You can do this using the function fill3 and referencing this answer for the 2D case to see how you have to add points on the ends of your data vectors to "close" your filled polygons. Although creating a pattern (i.e. hatching) is difficult if not impossible, an alternative is to simply adjust the alpha transparency of the filled patch. Here's a simple example for just one patch:
x = 1:10;
y = rand(1, 10);
hFill = fill3(zeros(1, 12), x([1 1:end end]), [0 y 0], 'b', 'FaceAlpha', 0.5);
grid on
And here's the plot this makes:
You can also create multiple patches in one call to fill3. Here's an example with 4 sets of data:
nPoints = 10; % Number of data points
nPlots = 4; % Number of curves
data = rand(nPoints, nPlots); % Sample data, one curve per column
% Create data matrices:
[X, Y] = meshgrid(0:(nPlots-1), [1 1:nPoints nPoints]);
Z = [zeros(1, nPlots); data; zeros(1, nPlots)];
patchColor = [0 0.4470 0.7410]; % RGB color for patch edge and face
% Plot patches:
hFill = fill3(X, Y, Z, patchColor, 'LineWidth', 1, 'EdgeColor', patchColor, ...
'FaceAlpha', 0.5);
set(gca, 'YDir', 'reverse', 'YLim', [1 nPoints]);
grid on
And here's the plot this makes:

MATLAB Shading region between SEVERAL curves

There are many questions already on this site for something similar:
MATLAB, Filling in the area between two sets of data, lines in one figure
MATLAB fill area between lines
However, all of the existing questions relate to two curves only. How do you fill a region bounded by several curves that overlap each other?
A crude example would be:
% Create sample data as column vectors.
x = [1 : 100]';
curve1 = x/10;
curve2 = log(x/2) + rand(length(x), 1) - 0.5;
curve3 = log(x) + rand(length(x), 1) + 0.5;
% Plot it.
plot(x, curve1, 'r', 'LineWidth', 2);
hold on;
plot(x, curve2, 'b', 'LineWidth', 2);
plot(x, curve3, 'k', 'LineWidth', 2);
For the shading:
The upper limit would be the black curve followed by the red line.
The lower limit would be the blue curve (briefly), then the red line, followed by the blue curve.
In my actual dataset I have 10 curves which require a similar thing.

If I understand you correctly, you can do this by creating a min and max vectors of the area you want to shade, and use flipud to shade the region with fill
min_data=min([curve1,curve2,curve3],[],2);
max_data=max([curve1,curve2,curve3],[],2);
fill([x;flipud(x)],[min_data;flipud(max_data)],'g')

If I understood you correctly:
basevalue = min([curve1(:) ; curve2(:) ; curve3(:)]);
h = area([curve2 , curve1-curve2 , curve3-curve1],basevalue)
h(1).FaceColor = [1 1 1];
h(2).FaceColor = [0 0.5 0.5];
h(3).FaceColor = [1 1 1];
hold on
plot(x, curve1, 'r', 'LineWidth', 2);
plot(x, curve2, 'b', 'LineWidth', 2);
plot(x, curve3, 'k', 'LineWidth', 2);
ylim([ min([curve1(:) ; curve2(:) ; curve3(:)]); max([curve1(:) ; curve2(:) ; curve3(:)])])
So you need to play with area in a way that is consistent with what you want...

How to create three Y-axis in one graph? [duplicate]

I have 4 sets of values: y1, y2, y3, y4 and one set x. The y values are of different ranges, and I need to plot them as separate curves with separate sets of values on the y-axis.
To put it simple, I need 3 y-axes with different values (scales) for plotting on the same figure.
Any help appreciated, or tips on where to look.

This is a great chance to introduce you to the File Exchange. Though the organization of late has suffered from some very unfortunately interface design choices, it is still a great resource for pre-packaged solutions to common problems. Though many here have given you the gory details of how to achieve this (#prm!), I had a similar need a few years ago and found that addaxis worked very well. (It was a File Exchange pick of the week at one point!) It has inspired later, probably better mods. Here is some example output:
(source: mathworks.com)
I just searched for "plotyy" at File Exchange.
Though understanding what's going on in important, sometimes you just need to get things done, not do them yourself. Matlab Central is great for that.

One possibility you can try is to create 3 axes stacked one on top of the other with the 'Color' properties of the top two set to 'none' so that all the plots are visible. You would have to adjust the axes width, position, and x-axis limits so that the 3 y axes are side-by-side instead of on top of one another. You would also want to remove the x-axis tick marks and labels from 2 of the axes since they will lie on top of one another.
Here's a general implementation that computes the proper positions for the axes and offsets for the x-axis limits to keep the plots lined up properly:
%# Some sample data:
x = 0:20;
N = numel(x);
y1 = rand(1,N);
y2 = 5.*rand(1,N)+5;
y3 = 50.*rand(1,N)-50;
%# Some initial computations:
axesPosition = [110 40 200 200]; %# Axes position, in pixels
yWidth = 30; %# y axes spacing, in pixels
xLimit = [min(x) max(x)]; %# Range of x values
xOffset = -yWidth*diff(xLimit)/axesPosition(3);
%# Create the figure and axes:
figure('Units','pixels','Position',[200 200 330 260]);
h1 = axes('Units','pixels','Position',axesPosition,...
'Color','w','XColor','k','YColor','r',...
'XLim',xLimit,'YLim',[0 1],'NextPlot','add');
h2 = axes('Units','pixels','Position',axesPosition+yWidth.*[-1 0 1 0],...
'Color','none','XColor','k','YColor','m',...
'XLim',xLimit+[xOffset 0],'YLim',[0 10],...
'XTick',[],'XTickLabel',[],'NextPlot','add');
h3 = axes('Units','pixels','Position',axesPosition+yWidth.*[-2 0 2 0],...
'Color','none','XColor','k','YColor','b',...
'XLim',xLimit+[2*xOffset 0],'YLim',[-50 50],...
'XTick',[],'XTickLabel',[],'NextPlot','add');
xlabel(h1,'time');
ylabel(h3,'values');
%# Plot the data:
plot(h1,x,y1,'r');
plot(h2,x,y2,'m');
plot(h3,x,y3,'b');
and here's the resulting figure:

I know of plotyy that allows you to have two y-axes, but no "plotyyy"!
Perhaps you can normalize the y values to have the same scale (min/max normalization, zscore standardization, etc..), then you can just easily plot them using normal plot, hold sequence.
Here's an example:
%# random data
x=1:20;
y = [randn(20,1)*1 + 0 , randn(20,1)*5 + 10 , randn(20,1)*0.3 + 50];
%# plotyy
plotyy(x,y(:,1), x,y(:,3))
%# orginial
figure
subplot(221), plot(x,y(:,1), x,y(:,2), x,y(:,3))
title('original'), legend({'y1' 'y2' 'y3'})
%# normalize: (y-min)/(max-min) ==> [0,1]
yy = bsxfun(#times, bsxfun(#minus,y,min(y)), 1./range(y));
subplot(222), plot(x,yy(:,1), x,yy(:,2), x,yy(:,3))
title('minmax')
%# standarize: (y - mean) / std ==> N(0,1)
yy = zscore(y);
subplot(223), plot(x,yy(:,1), x,yy(:,2), x,yy(:,3))
title('zscore')
%# softmax normalization with logistic sigmoid ==> [0,1]
yy = 1 ./ ( 1 + exp( -zscore(y) ) );
subplot(224), plot(x,yy(:,1), x,yy(:,2), x,yy(:,3))
title('softmax')

Multi-scale plots are rare to find beyond two axes... Luckily in Matlab it is possible, but you have to fully overlap axes and play with tickmarks so as not to hide info.
Below is a nice working sample. I hope this is what you are looking for (although colors could be much nicer)!
close all
clear all
display('Generating data');
x = 0:10;
y1 = rand(1,11);
y2 = 10.*rand(1,11);
y3 = 100.*rand(1,11);
y4 = 100.*rand(1,11);
display('Plotting');
figure;
ax1 = gca;
get(ax1,'Position')
set(ax1,'XColor','k',...
'YColor','b',...
'YLim',[0,1],...
'YTick',[0, 0.2, 0.4, 0.6, 0.8, 1.0]);
line(x, y1, 'Color', 'b', 'LineStyle', '-', 'Marker', '.', 'Parent', ax1)
ax2 = axes('Position',get(ax1,'Position'),...
'XAxisLocation','bottom',...
'YAxisLocation','left',...
'Color','none',...
'XColor','k',...
'YColor','r',...
'YLim',[0,10],...
'YTick',[1, 3, 5, 7, 9],...
'XTick',[],'XTickLabel',[]);
line(x, y2, 'Color', 'r', 'LineStyle', '-', 'Marker', '.', 'Parent', ax2)
ax3 = axes('Position',get(ax1,'Position'),...
'XAxisLocation','bottom',...
'YAxisLocation','right',...
'Color','none',...
'XColor','k',...
'YColor','g',...
'YLim',[0,100],...
'YTick',[0, 20, 40, 60, 80, 100],...
'XTick',[],'XTickLabel',[]);
line(x, y3, 'Color', 'g', 'LineStyle', '-', 'Marker', '.', 'Parent', ax3)
ax4 = axes('Position',get(ax1,'Position'),...
'XAxisLocation','bottom',...
'YAxisLocation','right',...
'Color','none',...
'XColor','k',...
'YColor','c',...
'YLim',[0,100],...
'YTick',[10, 30, 50, 70, 90],...
'XTick',[],'XTickLabel',[]);
line(x, y4, 'Color', 'c', 'LineStyle', '-', 'Marker', '.', 'Parent', ax4)
(source: pablorodriguez.info)

PLOTYY allows two different y-axes. Or you might look into LayerPlot from the File Exchange. I guess I should ask if you've considered using HOLD or just rescaling the data and using regular old plot?
OLD, not what the OP was looking for:
SUBPLOT allows you to break a figure window into multiple axes. Then if you want to have only one x-axis showing, or some other customization, you can manipulate each axis independently.

In your case there are 3 extra y axis (4 in total) and the best code that could be used to achieve what you want and deal with other cases is illustrated above:
clear
clc
x = linspace(0,1,10);
N = numel(x);
y = rand(1,N);
y_extra_1 = 5.*rand(1,N)+5;
y_extra_2 = 50.*rand(1,N)+20;
Y = [y;y_extra_1;y_extra_2];
xLimit = [min(x) max(x)];
xWidth = xLimit(2)-xLimit(1);
numberOfExtraPlots = 2;
a = 0.05;
N_ = numberOfExtraPlots+1;
for i=1:N_
L=1-(numberOfExtraPlots*a)-0.2;
axesPosition = [(0.1+(numberOfExtraPlots*a)) 0.1 L 0.8];
if(i==1)
color = [rand(1),rand(1),rand(1)];
figure('Units','pixels','Position',[200 200 1200 600])
axes('Units','normalized','Position',axesPosition,...
'Color','w','XColor','k','YColor',color,...
'XLim',xLimit,'YLim',[min(Y(i,:)) max(Y(i,:))],...
'NextPlot','add');
plot(x,Y(i,:),'Color',color);
xlabel('Time (s)');
ylab = strcat('Values of dataset 0',num2str(i));
ylabel(ylab)
numberOfExtraPlots = numberOfExtraPlots - 1;
else
color = [rand(1),rand(1),rand(1)];
axes('Units','normalized','Position',axesPosition,...
'Color','none','XColor','k','YColor',color,...
'XLim',xLimit,'YLim',[min(Y(i,:)) max(Y(i,:))],...
'XTick',[],'XTickLabel',[],'NextPlot','add');
V = (xWidth*a*(i-1))/L;
b=xLimit+[V 0];
x_=linspace(b(1),b(2),10);
plot(x_,Y(i,:),'Color',color);
ylab = strcat('Values of dataset 0',num2str(i));
ylabel(ylab)
numberOfExtraPlots = numberOfExtraPlots - 1;
end
end
The code above will produce something like this:

Matlab: Adding third dimenstion to 2D plot

I have the following code to generate me a 2D plot or 2 normal distributions:
res = zeros(2, 320);
index = 1:320;
% assign some data to the res array and then approximate:
PD = fitdist(index','normal', 'frequency', res(1,:)')
pdfNormal = normpdf(index',PD.mu,PD.sigma);
plot(index', pdfNormal, 'Color', 'r', 'LineWidth', 2);
hold on;
PD = fitdist(index','normal', 'frequency', res(2,:)')
pdfNormal = normpdf(index',PD.mu,PD.sigma);
plot(index', pdfNormal, 'Color', 'b', 'LineWidth', 2);
This code generates me then the following picture:
Now I am wondering how I could add a third dimension to this plot? Essentially,
I would like to plot another 2 normal distributions, but this time in the Z-axis,
ie., in the third dimension.
Anyone an idea how I could do that easily?
Thanks so much!

If I understood correctly, you can simply give the plots different z-values. Example:
%# some random data
x = 1:300;
y = zeros(5,300);
for i=1:5
y(i,:) = normpdf(x,100+i*20,10);
end
%# plot
hold on
clr = lines(5);
h = zeros(5,1);
for i=1:5
h(i) = plot(x, y(i,:), 'Color',clr(i,:), 'LineWidth',2);
set(h(i), 'ZData',ones(size(x))*i)
end
zlim([0 6]), box on, grid on
view(3)
hold off

Most efficient way to draw a bunch of 3d lines in matlab

I need to plot a list of 3d lines in matlab. What is the quickest way to do that?
I am currently doing something like
%edges is a MX2 matrix, holding the list of edges
%points are the vertices' coordinates
hold on; %so all the lines will be saved
for i=1:size(edges,1)
a=edges(i,1); %get first point's index
b=edges(i,2); %get second point's index
p=[points(:,a) points(:,b)]; %construct a 3X2 matrix out of the 2 points
plot3(p(1,:),p(2,:),p(3,:)); %plot a line
end
But this is not only slow during the actual loop, but also at the end, the resulting plot is very slow and irresponsive when I try to, for instance, rotate it using the drag & rotate tool.
I know the same plot using opengl etc would run much faster...

You can use the LINE low-level function, using NaN to plot as separate segments:
%# sample graph vertices and edges (similar to your data)
[adj,XYZ] = bucky;
[r c] = find(adj);
edges = [r c]; %# M-by-2 matrix holding the vertex indices
points = XYZ'; %# 3-by-N matrix of points X/Y/Z coordinates
%# build a list of separated lines
e = edges';
e(end+1,:) = 1;
e = e(:);
p = points(:,e);
p(:,3:3:end) = NaN;
figure
h = line(p(1,:), p(2,:), p(3,:));
view(3)
This is very efficient as it creates a single line object. Now you can customize the line, but it is restricted to have one color for the entire thing:
set(h, 'Color',[.4 .4 1], 'Marker','.', 'MarkerSize',10, ...
'MarkerFaceColor','g', 'MarkerEdgeColor','g')
According to the comments, if you want to have each edge in your graph in a specified color, consider the following code instead. It involves using the SURFACE function:
p = p'; %'# transpose the above p for convenience
clr = (1:size(p,1))'; %'# for each edge, color index in current colormap
figure
surface(p(:,[1 1]), p(:,[2 2]), p(:,[3 3]), [clr clr], ...
'EdgeColor','flat', 'FaceColor','none')
colormap( hsv(numel(clr)) ) %# specify your colormap here
view(3)

I think you can do something like this (caution - brain compiled code...)
figure;
patch('faces', edges, 'vertices', points, 'edgecolor', 'b');
axis equal;
Where edges should be an Nx2 matrix of indices and points should be an Mx3 matrix of coordinates (the transpose of your points array).
From my experience, calling patch directly can be significantly faster than repeated calls to plot.
To give some idea, the times to generate 1000 randomly generated line segments, using my (admittedly old!) MATLAB 7.1 are as follows:
Calling patch: 0.03 seconds.
Calling plot: 0.5 seconds.
EDIT: One way to get the edge colour behaving as you want (specifying a single colour per edge) is to introduce duplicate vertices as follows:
This works-around the issue that the edge colour can only be specified indirectly via vertex colour data. If we were to rely only on the vertex colours then all edges sharing a common vertex might end up with the colour assigned to that vertex - check out the 'flat 'edgecolour description here.
%% a "star" shape, so that we can really see what's going on
%% with the edge colours!!
pp = [0,0,0; 1,-1,0; 1,1,0; -1,1,0; -1,-1,0];
ee = [1,2; 1,3; 1,4; 1,5];
%% important - only 1 colour known per edge, not per vertex!!
cc = (1:size(ee,1))';
%% setup a new set of vertices/edges/colours with duplicate vertices
%% so that each edge gets it's correct colour
nnum = 0;
pnew = zeros(2 * size(ee, 1), 3); %% new vertices
enew = zeros(1 * size(ee, 1), 2); %% new edge indices
cnew = zeros(2 * size(ee, 1), 1); %% new edge colours - via vertices
for j = 1 : size(ee, 1)
n1 = ee(j, 1); %% old edge indices
n2 = ee(j, 2);
enew(j, 1) = nnum + 1; %% new edge indicies into pnew
enew(j, 2) = nnum + 2;
pnew(nnum + 1, :) = pp(n1, :); %% create duplicate vertices
pnew(nnum + 2, :) = pp(n2, :);
cnew(nnum + 1) = cc(j); %% map single edge colour onto both vertices
cnew(nnum + 2) = cc(j);
nnum = nnum + 2;
end
%% Draw the set efficiently via patch
tic
figure;
hold on;
patch('faces', enew, 'vertices', pnew, 'facevertexcdata', cnew, ...
'edgecolor', 'flat', 'facecolor', 'none');
plot(pnew(:,1), pnew(:,2), 'b.');
axis equal;
toc
It would be nicer if MATLAB allowed you to directly specify the edge colour data - but it doesn't seem to support that...
Hope this helps.