How to add a color-dependent legend to scatter3 plot?

I have a 3D histogram via scatter3, but I wish to add a legend to state the frequency signified by the color. How do I do this?

Also, I would appreciate any simplifications you could suggest to my code below.

%%Plot a scatter3 histogram of the shifts.
xdata = tumorshifts(:,1); ydata = tumorshifts(:,2); 
zdata = tumorshifts(:,3); 
size = 10*shiftno;
for loop = 1:length(size)
  if isequal(shiftno(loop),1)
      size(loop) = size(loop)/10;
  end
end
color = zeros(length(shiftno),3); 
values = unique(shiftno);
% Resource: http://www.wolframalpha.com/input/?i=orange+RGB
%  http://www.wolframalpha.com/input/?i=576+nm+light+to+RGB
for loop = 1:length(color)
      if shiftno(loop) == values(1)
  color(loop,1) = 130; color(loop,2) = 130; color(loop,3) = 130; % grey
  elseif shiftno(loop) == values(2)
  color(loop,1) =  41; color(loop,2) =   0; color(loop,3) = 255; % 452 nm
  elseif shiftno(loop) == values(3)
  color(loop,1) =   0; color(loop,2) = 214; color(loop,3) =  69; % 514 nm
  elseif shiftno(loop) == values(4)
  color(loop,1) = 132; color(loop,2) = 252; color(loop,3) =   0; % 576 nm
  elseif shiftno(loop) == values(5) 
  color(loop,1) = 255; color(loop,2) =   8; color(loop,3) =   0; % 638 nm
  elseif shiftno(loop) == values(6) 
  color(loop,1) = 158; color(loop,2) =   0; color(loop,3) =   0; % crimson
  end
end
scatter3(xdata,ydata,zdata,size,color/255)
axis equal
title(['Histogram of ',num2str(length(unique(elektapatients.StudyID))),...
     ' Elekta Patients'' Daily Shifts'])
xlabel('Left [mm]')
ylabel('Superior [mm]')
zlabel('Posterior [mm]')

Answer 1

[Walter Roberson]

%%Plot a scatter3 histogram of the shifts.
xdata = tumorshifts(:,1); ydata = tumorshifts(:,2); 
zdata = tumorshifts(:,3); 
pointsize = 10*shiftno;
for loop = 1:length(pointsize)
  if shiftno(loop) == 1
     pointsize(loop) = pointsize(loop)/10;
  end
end
color = zeros(length(shiftno),3); 
values = unique(shiftno);
% Resource: http://www.wolframalpha.com/input/?i=orange+RGB
%  http://www.wolframalpha.com/input/?i=576+nm+light+to+RGB

cmap = [130, 130, 130;    %grey
         41,   0, 255;    %452 nm
          0, 214,  69;    %514 nm
        132, 252,   0;    %576 nm
        255,   8,   0;    %638 nm
        158,   0,   0];   %crimson
for loop = 1:length(color)
  switch shiftno(loop)
    case values(1): color(loop, :) = cmap(1,:);   % grey
    case values(2): color(loop, :) = cmap(2,:);   % 452 nm
    case values(3): color(loop, :) = cmap(3,:);   % 514 nm
    case values(4): color(loop, :) = cmap(4,:);   % 576 nm
    case values(5): color(loop, :) = cmap(5,:);   % 638 nm
    case values(6): color(loop, :) = cmap(6,:); % crimson
  end
end

scatter3(xdata, ydata, zdata, pointsize, color/255)

axis equal
title(['Histogram of ', num2str(length(unique(elektapatients.StudyID))),...
     ' Elekta Patients'' Daily Shifts'])
xlabel('Left [mm]')
ylabel('Superior [mm]')
zlabel('Posterior [mm]')

hold on
for K = 1 : size(cmap, 1)
  H(K) = scatter3(nan, nan, nan, K*10, cmap(K,:));
end
legend(H, {'grey', '452 nm', '514 nm', '576 nm', '638 nm', 'crimson'});

Note that size had to be renamed because you need the MATLAB size() function later.

Going from if/elseif to switch/case was just for cleaner code.

You might want to adjust the point size for the legend purposes.

Notice the trick here of using nan to create scatter points that will not show up. The points will exist and will have the proper color but they will not be rendered. This is done in order to get the individual handles of those scatter plots so that they can have individual legends generated. Any one scatter3() plot results in a single graphics handle and that would only permit a single legend entry. You need to create different handles for each entry you want to make.

[Daniel Bridges]

What are the differences between isequal and == ?

This comment from doc isequal makes me think == additionally compares handles, making me think isequal is executed more quickly: "When comparing handle objects, use == to test whether objects have the same handle. Use isequal to determine if objects with different handles have equal property values."

MATLAB R2016a doesn't allow this use of : to put the statement on the same line as the case expression: "Error: The expression to the left of the equals sign is not a valid target for an assignment." (It is red-underlining the equals sign between color and cmap in the Editor. Erasing the colon and putting the statement in the following line resolves it.) Thank you for clarifying the logic of switch/case usage.

Here is the result with the new code:

%%Plot a scatter3 histogram of the shifts.
xdata = tumorshifts(:,1); ydata = tumorshifts(:,2); 
zdata = tumorshifts(:,3); 
pointsize = 10*shiftno;
for loop = 1:length(pointsize)
  if isequal(shiftno(loop),1)
      pointsize(loop) = pointsize(loop)/10;
  end
end
color = zeros(length(shiftno),3); 
values = unique(shiftno);
% Resource: http://www.wolframalpha.com/input/?i=orange+RGB
%  http://www.wolframalpha.com/input/?i=576+nm+light+to+RGB
cmap = [130, 130, 130;    % grey
        0, 255,   0;    % 545 nm lime green
       41,   0, 104;    % 390 nm dark purple
      255, 113,   0;    % 623 nm orange
        0,  54, 249;    % 468 nm deep blue
      158,   0,   0];   % 700 nm crimson
for loop = 1:length(color)
  switch shiftno(loop)
      case values(1)
          color(loop,:) = cmap(1,:); % grey
      case values(2)
          color(loop,:) = cmap(2,:); % 452 nm
      case values(3)
          color(loop,:) = cmap(3,:); % 514 nm
      case values(4)
          color(loop,:) = cmap(4,:); % 576 nm
      case values(5)
          color(loop,:) = cmap(5,:); % 638 nm
      case values(6)
          color(loop,:) = cmap(6,:); % crimson
  end
end
scatter3(xdata,ydata,zdata,pointsize,color/255)
axis equal
title(['Histogram of ',num2str(length(unique(elektapatients.StudyID))),...
     ' Elekta Patients'' Daily Shifts'])
xlabel('Left [mm]')
ylabel('Superior [mm]')
zlabel('Posterior [mm]')
%%add a legend to the scatter3 histogram
hold on
for loop = 1:size(cmap,1)
  VectorOfHandles(loop) = scatter3(nan,nan,nan,loop*10,cmap(loop,:)/255);
end
legend(VectorOfHandles,{num2str(values(1)),num2str(values(2)),...
                      num2str(values(3)),num2str(values(4)),...
                      num2str(values(5)),num2str(values(6))});
hold off

[Walter Roberson]

"When comparing handle objects, use == to test whether objects have the same handle. Use isequal to determine if objects with different handles have equal property values."