I need to generate a curve between scatter points then identify the unit normal of the curve at each point. Here is an example of a point cloud
figure
x = [1 2 0 0 1 1 2 3 4 2];
y = [4 6 9 1 1 2 4 9 2 3];
scatter(x,y)
hold on
line(x,y)
xlim([0 4])
ylim([0 10])
NOTE: the 2 points along the y-axis are connected
Instead of a line between the points, I'd like to create a smooth curve. I'm not sure how to do this when points in x and y repeat. An attempt using spline fails. After I know the curve, I need to find the unit normals at each point. How do I go about this?
EDIT:
Basically I want to do what is show here for polyfit in the matlab docs. Assuming that x was unique in my case, this wouldn't be an issue. I could identify the polynomial and then, I believe, determine the unit normals from the polynomial function evaluated at that point. But in my case, the x and y data repeat so a straight forward application doesn't work.
One way to get a smooth path is to treat this as a parametric function and interpolate x and y separately.
x = [1 2 0 0 1 1 2 3 4 2];
y = [4 6 9 1 1 2 4 9 2 3];
t = 1:numel(x);
tq = 1:0.1:t(end);
xq = interp1(t,x,tq,'v5cubic');
yq = interp1(t,y,tq,'v5cubic');
plot(x,y,' ob',xq,yq,'-r');
To estimate the normals you can take the average normal of the two line segments around the sample points. This code is a bit ugly but it gets the job done.
n = zeros(2,numel(x));
for tidx = 1:numel(t)
tt = t(tidx);
idx1 = find(tq <= tt,1,'last');
idx0 = idx1 - 1;
idx2 = idx1 + 1;
if idx0 > 0
n1 = [yq(idx1) - yq(idx0); xq(idx0) - xq(idx1)];
n(:,tidx) = n(:,tidx) + n1/norm(n1);
end
if idx2 <= numel(tq)
n2 = [yq(idx2) - yq(idx1); xq(idx1) - xq(idx2)];
n(:,tidx) = n(:,tidx) + n2/norm(n2);
end
n(:,tidx) = n(:,tidx) / norm(n(:,tidx));
end
plot(x,y,' ob',xq,yq,'-r',[x.' x.'+n(1,:).'].', [y.' y.'+n(2,:).'].',' -k');
axis equal;
If you use pchip instead of v5cubic for the interpolation method then you get more symmetry around the sample points. However, it appears that any sharp turns (90 degrees or greater) are not smoothed.
I would like to draw a 3D histogram (with gnuplot or octave) in order to represent my data.
lets say that I have a data file in the following form:
2 3 4
8 4 10
5 6 7
I'd like to draw nine colored bars (the size of the matrix), in the set [1,3]x[1,3], such that the bar's color is proportional to the bar's height. How can I do this?
Below is a function I implemented that acts as a bar3 replacement (partially).
In my version, the bars are rendered by creating a patch graphics object: we build a matrix of vertex coordinates and a list of faces connecting those vertices.
The idea is to first build a single "3d cube" as a template, then replicate it for as many bars as we have. Each bar is shifted and scaled according to its position and height.
The vertices/faces matrices are constructed in a vectorized manner (look ma, no loops!), and the result is a single patch object drawn for all bars, as opposed to multiple patches one per bar (this is more efficient in terms of graphics performance).
The function could have been implemented by specifying coordinates of connected vertices that form polygons, by using the XData, YData, ZData and CData properties instead of the Vertices and Faces properties. In fact this is what bar3 internally does. Such approach usually requires larger data to define the patches (because we cant have shared points across patch faces, although I didn't care much about that in my implementation). Here is a related post where I tried to explain the structure of the data constructed by bar3.
my_bar3.m
function pp = my_bar3(M, width)
% MY_BAR3 3D bar graph.
%
% M - 2D matrix
% width - bar width (1 means no separation between bars)
%
% See also: bar3, hist3
%% construct patch
if nargin < 2, width = 0.8; end
assert(ismatrix(M), 'Matrix expected.')
% size of matrix
[ny,nx] = size(M);
% first we build a "template" column-bar (8 vertices and 6 faces)
% (bar is initially centered at position (1,1) with width=? and height=1)
hw = width / 2; % half width
[X,Y,Z] = ndgrid([1-hw 1+hw], [1-hw 1+hw], [0 1]);
v = [X(:) Y(:) Z(:)];
f = [
1 2 4 3 ; % bottom
5 6 8 7 ; % top
1 2 6 5 ; % front
3 4 8 7 ; % back
1 5 7 3 ; % left
2 6 8 4 % right
];
% replicate vertices of "template" to form nx*ny bars
[offsetX,offsetY] = meshgrid(0:nx-1,0:ny-1);
offset = [offsetX(:) offsetY(:)]; offset(:,3) = 0;
v = bsxfun(#plus, v, permute(offset,[3 2 1]));
v = reshape(permute(v,[2 1 3]), 3,[]).';
% adjust bar heights to be equal to matrix values
v(:,3) = v(:,3) .* kron(M(:), ones(8,1));
% replicate faces of "template" to form nx*ny bars
increments = 0:8:8*(nx*ny-1);
f = bsxfun(#plus, f, permute(increments,[1 3 2]));
f = reshape(permute(f,[2 1 3]), 4,[]).';
%% plot
% prepare plot
if exist('OCTAVE_VERSION','builtin') > 0
% If running Octave, select OpenGL backend, gnuplot wont work
graphics_toolkit('fltk');
hax = gca;
else
hax = newplot();
set(ancestor(hax,'figure'), 'Renderer','opengl')
end
% draw patch specified by faces/vertices
% (we use a solid color for all faces)
p = patch('Faces',f, 'Vertices',v, ...
'FaceColor',[0.75 0.85 0.95], 'EdgeColor','k', 'Parent',hax);
view(hax,3); grid(hax,'on');
set(hax, 'XTick',1:nx, 'YTick',1:ny, 'Box','off', 'YDir','reverse', ...
'PlotBoxAspectRatio',[1 1 (sqrt(5)-1)/2]) % 1/GR (GR: golden ratio)
% return handle to patch object if requested
if nargout > 0
pp = p;
end
end
Here is an example to compare it against the builtin bar3 function in MATLAB:
subplot(121), bar3(magic(7)), axis tight
subplot(122), my_bar3(magic(7)), axis tight
Note that I chose to color all the bars in a single solid color (similar to the output of the hist3 function), while MATLAB emphasizes the columns of the matrix with matching colors.
It is easy to customize the patch though; Here is an example to match bar3 coloring mode by using indexed color mapping (scaled):
M = membrane(1); M = M(1:3:end,1:3:end);
h = my_bar3(M, 1.0);
% 6 faces per bar
fvcd = kron((1:numel(M))', ones(6,1));
set(h, 'FaceVertexCData',fvcd, 'FaceColor','flat', 'CDataMapping','scaled')
colormap hsv; axis tight; view(50,25)
set(h, 'FaceAlpha',0.85) % semi-transparent bars
Or say you wanted to color the bars using gradient according to their heights:
M = 9^2 - spiral(9);
h = my_bar3(M, 0.8);
% use Z-coordinates as vertex colors (indexed color mapping)
v = get(h, 'Vertices');
fvcd = v(:,3);
set(h, 'FaceVertexCData',fvcd, 'FaceColor','interp')
axis tight vis3d; daspect([1 1 10]); view(-40,20)
set(h, 'EdgeColor','k', 'EdgeAlpha',0.1)
Note that in the last example, the "Renderer" property of the figure will affect the appearance of the gradients. In MATLAB, the 'OpenGL' renderer will interpolate colors along the RGB colorspace, whereas the other two renderers ('Painters' and 'ZBuffer') will interpolate across the colors of the current colormap used (so the histogram bars would look like mini colorbars going through the jet palette, as opposed to a gradient from blue at the base to whatever the color is at the defined height as shown above). See this post for more details.
I've tested the function in Octave 3.6.4 and 3.8.1 both running on Windows, and it worked fine. If you run the examples I showed above, you'll find that some of the advanced 3D features are not yet implemented correctly in Octave (this includes transparency, lighting, and such..). Also I've used functions not available in Octave like membrane and spiral to build sample matrices, but those are not essential to the code, just replace them with your own data :)
Solution using only functions available in OCTAVE, tested with octave-online
This solution generates a surface in a similar way to the internals of Matlabs hist3d function.
In brief:
creates a surface with 4 points with the "height" of each
value, which are plotted at each bin edge.
Each is surrounded by zeros, which are also plotted at each bin edge.
The colour is set to be based on the bin values and is applied to
the 4 points and the surrounding zeros. (so that the edges and tops of the 'bars' are coloured to match the "height".)
For data given as a matrix containing bin heights (bin_values in the code):
Code
bin_values=rand(5,4); %some random data
bin_edges_x=[0:size(bin_values,2)];
x=kron(bin_edges_x,ones(1,5));
x=x(4:end-2);
bin_edges_y=[0:size(bin_values,1)];
y=kron(bin_edges_y,ones(1,5));
y=y(4:end-2);
mask_z=[0,0,0,0,0;0,1,1,0,0;0,1,1,0,0;0,0,0,0,0;0,0,0,0,0];
mask_c=ones(5);
z=kron(bin_values,mask_z);
c=kron(bin_values,mask_c);
surf(x,y,z,c)
Output
I don't have access to Octave, butI believe this should do the trick:
Z = [2 3 4
8 4 10
5 6 7];
[H W] = size(Z);
h = zeros( 1, numel(Z) );
ih = 1;
for ix = 1:W
fx = ix-.45;
tx = ix+.45;
for iy = 1:W
fy = iy-.45;
ty = iy+.45;
vert = [ fx fy 0;...
fx ty 0;...
tx fy 0;...
tx ty 0;...
fx fy Z(iy,ix);...
fx ty Z(iy,ix);...
tx fy Z(iy,ix);...
tx ty Z(iy,ix)];
faces = [ 1 3 5;...
5 3 7;...
7 3 4;...
7 8 4;...
5 6 7;...
6 7 8;...
1 2 5;...
5 6 2;...
2 4 8;...
2 6 8];
h(ih) = patch( 'faces', faces, 'vertices', vert, 'FaceVertexCData', Z(iy,ix),...
'FaceColor', 'flat', 'EdgeColor','none' );
ih = ih+1;
end
end
view( 60, 45 );
colorbar;
I think the following should do the trick. I didn't use anything more sophisticated than colormap, surf and patch, which to my knowledge should all work as-is in Octave.
The code:
%# Your data
Z = [2 3 4
8 4 10
5 6 7];
%# the "nominal" bar (adjusted from cylinder())
n = 4;
r = [0.5; 0.5];
m = length(r);
theta = (0:n)/n*2*pi + pi/4;
sintheta = sin(theta); sintheta(end) = sqrt(2)/2;
x0 = r * cos(theta);
y0 = r * sintheta;
z0 = (0:m-1)'/(m-1) * ones(1,n+1);
%# get data for current colormap
map = colormap;
Mz = max(Z(:));
mz = min(Z(:));
% Each "bar" is 1 surf and 1 patch
for ii = 1:size(Z,1)
for jj = 1:size(Z,2)
% Get color (linear interpolation through current colormap)
cI = (Z(ii,jj)-mz)*(size(map,1)-1)/(Mz-mz) + 1;
fC = floor(cI);
cC = ceil(cI);
color = map(fC,:) + (map(cC,:) - map(fC,:)) * (cI-fC);
% Translate and rescale the nominal bar
x = x0+ii;
y = y0+jj;
z = z0*Z(ii,jj);
% Draw the bar
surf(x,y,z, 'Facecolor', color)
patch(x(end,:), y(end,:), z(end,:), color)
end
end
Result:
How I generate the "nominal bar" is based on code from MATLAB's cylinder(). One cool thing about that is you can very easily make much more funky-looking bars:
This was generated by changing
n = 4;
r = [0.5; 0.5];
into
n = 8;
r = [0.5; 0.45; 0.2; 0.1; 0.2; 0.45; 0.5];
Have you looked at this tutorial on bar3?
Adapting it slightly:
Z=[2 3 4
8 4 10
5 6 7]; % input data
figure;
h = bar3(Z); % get handle to graphics
for k=1:numel(h),
z=get(h(k),'ZData'); % old data - need for its NaN pattern
nn = isnan(z);
nz = kron( Z(:,k),ones(6,4) ); % map color to height 6 faces per data point
nz(nn) = NaN; % used saved NaN pattern for transparent faces
set(h(k),'CData', nz); % set the new colors
end
colorbar;
And here's what you get at the end:
I would like to insert a rectangle into my matlab figure to highlight a specific region:
x = [0 1 2 2 3 4 5 6 7 8 9 10];
y = [0 1 2 4 3 4 5 6 7 8 9 10];
fh = figure(1);
plot(x,y)
xlim([0 10]);
ylim([0 10]);
I can do this by using the annotation function and defining the left bottom width height of the rectangle.
I am wondering, however, can this be done according to the x and y values from the figure in question? For the example shown, for example I would like to draw a rectangle from x = 1.5 y = 1.5 with a height of 3 and a width of two. This is my attempt:
% define location of lbwh in terms of x and y values
l = 1.5;
b = 1.5;
w = 2;
h = 3;
% convert factor of 1
xx = xlim;
l = l./xx(2);
b = b./xx(2);
w = w./xx(2);
h = h./xx(2);
annotation('rectangle','position',[l,b,w,h]);
The problem is that the position I'm providing is in terms of the (0,0) position in the plot and not the bottom left hand of the figure window. how can I correct this?
One way would be to just create a rectangle from line graphs:
plot([l,l,l+w,l+w,l],[b,b+h,b+h,b,b], 'r', 'LineWidth', 2)
I have two matrices A and B of the same size. Each can contain NaNs at some places.
I visualize some measure C for the difference between A and B in the following way:
C = (A - B) ./ ((A + B) ./ 2) ;
figure(1); clf;
imagesc(C); colorbar;
I'd like to change the current presentation in a way so that:
If isnan(A(i,j)) and ~isnan(B(i,j)) ---> white in the color map
If ~isnan(A(i,j)) and isnan(B(i,j)) ---> black in the color map
If isnan(A(i,j)) and isnan(B(i,j)) ---> gray in the color map
otherwise ---> color according to C(i,j) value [as is now]
The colors above don't really matter as long as it is distinguishable.
I see there are similar ideas (here, for example) but not exactly what I need...
Any ideas?
Many thanks!!!
Perhaps there are better solutions out there but I can come out with one here. Essentially, I'm creating an RGB representation of the image to show it. So I picked a colormap with the number of colors I wanted at first. Then, from the data, convert them to index and use in2rgb() to get the RGB image. Then, I can get the bin size of each color and label the color bar appropriately.
% Randomly generate some data for demonstration
A = [1 nan nan; 1 2 3; 4 5 6];
B = [nan 0 nan; 4 3 2; 1 2 1];
C = (A - B) ./ ((A + B) ./ 2);
% Number of colors you want to use
ncolor = 8;
data_colormap = [jet(ncolor); 1 1 1; 0 0 0; 0.5 0.5 0.5];
data_range = [min(C(:)) max(C(:))];
data_ind = (C - data_range(1)) / (data_range(2) - data_range(1)) * (ncolor - 1) + 1;
% Assign indices > ncolor for the special cases
data_ind(isnan(A)) = ncolor + 1; % isnan(A) assign to white
data_ind(isnan(B)) = ncolor + 2; % isnan(A) assign to black
data_ind(isnan(A) & isnan(B)) = ncolor + 3; % isnan(A) + isnan(B)
% Get the RGB representation
img = ind2rgb(round(data_ind), data_colormap);
imagesc(img)
% Custom labels for the colorbar
bin_size = (data_range(2)-data_range(1)) / ncolor;
caxis([data_range(1) data_range(2) + 3*bin_size])
colormap(data_colormap)
ax = colorbar;
yticks = get(ax, 'YTick');
yticks = yticks(yticks < data_range(2));
yticklabels = num2cell(yticks);
% Pad another 3 custom labels
yticks = [yticks, data_range(2)+[bin_size 2*bin_size 3*bin_size]-0.5*bin_size];
yticklabels = [yticklabels 'isnan(A)', 'isnan(B)', 'both'];
set(ax, 'YTick', yticks, 'YTickLabel', yticklabels)
For some reason imtransform function ignores translation part by default.
If I add additional space with XData and YData as it said in manual, I will handle only simple cases (i.e. translation only).
So, how to apply full-featured affine transform in Matlab?
I = imread('cameraman.png');
imshow(I);
% does not translate
xform = [1 2 0; 2 1 0; 100 0 1];
T = maketform('affine',xform);
I2 = imtransform(I,T);
figure, imshow(I2)
% translates but cuts some portion of an image
xform = [1 2 0; 2 1 0; 100 0 1];
T = maketform('affine',xform);
I2 = imtransform(I,T,'XData',[1 size(I,2)+xform(3,1)],'YData',[1 size(I,1)+xform(3,2)]);
figure, imshow(I2)
So I found I should apply transform to image range too.
After that I can decide, what to do if an image corner is not at the beginning of coordinates.
I = imread('cameraman.png');
XData=[1 size(I,2)];
YData=[1 size(I,1)];
imshow(I);
xform = [1 2 0; 2 1 0; 100 0 1];
T = maketform('affine',xform);
[XData1, YData1] = tformfwd(T, XData, YData);
if XData1(1)>1
XData1(1)=1;
end
if YData1(1)>1
YData1(1)=1;
end
I2 = imtransform(I,T,'XData',XData1,'YData',YData1);
figure, imshow(I2)