1、离散热力图
function out = scatplot(x,y,method,radius,N,n,po,ms)
% Scatter plot with color indicating data density
%
% USAGE:
% out = scatplot(x,y,method,radius,N,n,po,ms)
% out = scatplot(x,y,dd)
%
% DESCRIPTION:
% Draws a scatter plot with a colorscale
% representing the data density computed
% using three methods
%
% INPUT VARIABLES:
% x,y - are the data points
% method - is the method used to calculate data densities:
% 'circles' - uses circles with a determined area
% centered at each data point
% 'squares' - uses squares with a determined area
% centered at each data point
% 'voronoi' - uses voronoi cells to determin data densities
% default method is 'voronoi'
% radius - is the radius used for the circles or squares
% used to calculate the data densities if
% (Note: only used in methods 'circles' and 'squares'
% default radius is sqrt((range(x)/30)^2 + (range(y)/30)^2)
% N - is the size of the square mesh (N x N) used to
% filter and calculate contours
% default is 100
% n - is the number of coeficients used in the 2-D
% running mean filter
% default is 5
% (Note: if n is length(2), n(2) is tjhe number of
% of times the filter is applied)
% po - plot options:
% 0 - No plot
% 1 - plots only colored data points (filtered)
% 2 - plots colored data points and contours (filtered)
% 3 - plots only colored data points (unfiltered)
% 4 - plots colored data points and contours (unfiltered)
% default is 1
% ms - uses this marker size for filled circles
% default is 4
%
% OUTPUT VARIABLE:
% out - structure array that contains the following fields:
% dd - unfiltered data densities at (x,y)
% ddf - filtered data densities at (x,y)
% radius - area used in 'circles' and 'squares'
% methods to calculate densities
% xi - x coordenates for zi matrix
% yi - y coordenates for zi matrix
% zi - unfiltered data densities at (xi,yi)
% zif - filtered data densities at (xi,yi)
% [c,h] = contour matrix C as described in
% CONTOURC and a handle H to a contourgroup object
% hs = scatter points handles
%
%Copy-Left, Alejandro Sanchez-Barba, 2005
if nargin==0
scatplotdemo
return
end
if nargin<3 | isempty(method)
method = 'vo';
end
if isnumeric(method)
gsp(x,y,method,2)
return
else
method = method(1:2);
end
if nargin<4 | isempty(n)
n = 5; %number of filter coefficients
end
if nargin<5 | isempty(radius)
radius = sqrt((range(x)/30)^2 + (range(y)/30)^2);
end
if nargin<6 | isempty(po)
po = 1; %plot option
end
if nargin<7 | isempty(ms)
ms = 4; %markersize
end
if nargin(x(k)-r) & x(y(k)-r) & y<(y(k)+r) );
end %for
area = (2*r)^2;
dd = dd/area;
case 'ci'
for k=1:Ld
dd(k) = sum( sqrt((x-x(k)).^2 + (y-y(k)).^2) < r );
end
area = pi*r^2;
dd = dd/area;
case 'vo' %----- Using voronoi cells ------
[v,c] = voronoin([x,y]);
for k=1:length(c)
%If at least one of the indices is 1,
%then it is an open region, its area
%is infinity and the data density is 0
if all(c{k}>1)
a = polyarea(v(c{k},1),v(c{k},2));
dd(k) = 1/a;
end %if
end %for
end %switch
return
%~~~~~~~~~~ Graf Scatter Plot ~~~~~~~~~~~
function varargout = gsp(x,y,c,ms)
%Graphs scattered poits
map = colormap;
ind = fix((c-min(c))/(max(c)-min(c))*(size(map,1)-1))+1;
h = [];
%much more efficient than matlab's scatter plot
for k=1:size(map,1)
if any(ind==k)
h(end+1) = line('Xdata',x(ind==k),'Ydata',y(ind==k), ...
'LineStyle','none','Color',map(k,:), ...
'Marker','.','MarkerSize',ms);
end
end
if nargout==1
varargout{1} = h;
end
return
clear,clc; x = normrnd(10,1,1000,1); y = x * 3 + normrnd(10,1,1000,1); scatplot(double(x),double(y))
效果如下：
2、绘制3D球体
function scatter3sph(X,Y,Z,varargin)
%SCATTER3SPH (X,Y,Z) Makes a 3d scatter plot with 3D spheres
% SCATTER3SPH is like scatter3 only drawing spheres instead
% of flat circles, at coordinates specified by vectors X, Y, Z. All three
% vectors have to be of the same length.
% SCATTER3SPH(X,Y,Z) draws the spheres with the default size and color.
% SCATTER3SPH(X,Y,Z,'size',S) draws the spheres with sizes S. If length(S)= 1
% the same size is used for all spheres.
% SCATTER3SPH(X,Y,Z,'color',C) draws the spheres with colors speciffied in a
% N-by-3 matrix C as RGB values.
% SCATTER3SPH(X,Y,Z,'transp',T) applies transparency level 'T' to the spheres
% T= 0 => transparent, T= 1 => opaque.
% Parameter names can be abreviated to 3 letters. For example: 'siz' or
% 'col'. Case is irrelevant.
%
% Example
% %Coordinates
% X= 100*rand(9,1); Y= 100*rand(9,1); Z= 100*rand(9,1);
%
% %Colors: 3 blue, 3 red and 3 green
% C= ones(3,1)*[0 0 1];
% C= [C;ones(3,1)*[1 0 0]];
% C= [C;ones(3,1)*[0 1 0]];
%
% %Sizes
% S= 5+10*rand(9,1);
%
% scatter3sph(X,Y,Z,'size',S,'color',C,'trans',0.3);
% axis vis3d
%-- Some checking...
if nargin < 3 error('Need at least three arguments'); return; end
if mean([length(X),length(Y),length(Z)]) ~= length(X) error ('Imput vectors X, Y, Z are of different lengths'); return; end
%-- Defaults
C= ones(length(X),1)*[0 0 1];
S= 0.1*max([X;Y;Z])*ones(length(X),1);
nfacets= 15;
transp= 0.5;
%-- Extract optional arguments
for j= 1:2:length(varargin)
string= lower(varargin{j});
switch string(1:min(3,length(string)))
case 'siz'
S= varargin{j+1};
if length(S) == 1
S= ones(length(X),1)*S;
elseif length(S) < length(X)
error('The vector of sizes must be of the same length as coordinate vectors (or 1)');
return
end
case 'col'
C= varargin{j+1};
if size(C,2) < 3 error('Colors matrix must have 3 columns'); return; end
if size(C,1) == 1
C= ones(length(X),1)*C(1:3);
elseif size(C,1) < length(X)
error('Colors matrix must have the same number of rows as length of coordinate vectors (or 1)');
return
end
case 'fac'
nfacets= varargin{j+1};
case 'tra'
transp= varargin{j+1};
otherwise
error('Unknown parameter name. Allowed names: ''size'', ''color'', ''facets'', ''transparency'' ');
end
end
%-- Sphere facets
[sx,sy,sz]= sphere(nfacets);
%--- Correct potential distortion
maxax= max([range(X), range(Y), range(Z)]);
ratios= [range(X)/maxax, range(Y)/maxax, range(Z)/maxax];
sx= sx*ratios(1);
sy= sy*ratios(2);
sz= sz*ratios(3);
%-- Plot spheres
hold on
for j= 1:length(X)
surf(sx*S(j)+X(j), sy*S(j)+Y(j), sz*S(j)+Z(j),...
'LineStyle','none',...
'FaceColor',C(j,:),...
'FaceAlpha',transp);
end
daspect([ratios(1), ratios(2), ratios(3)]);
light('Position',[1 1 1],'Style','infinit','Color',[1 1 1]);
lighting gouraud;
view(30,30)
clear,clc; X= 100*rand(9,1); Y= 100*rand(9,1); Z= 100*rand(9,1); C= ones(3,1)*[0 0 1]; C= [C;ones(3,1)*[1 0 0]]; C= [C;ones(3,1)*[0 1 0]]; S= 5+10*rand(20,1); scatter3sph(X,Y,Z,'size',S,'color',C,'trans',0.3); axis vis3d grid on
3、matlab绘制复杂矢量图
function hh = quiverwcolorbar(varargin)
% Melissa Day 5/24/2013
% Upgrade of Andrew Diamond's quiverc2wcmap to generate a quiver plot
% with arrows colored according to vector magnitude.
% Functional differences from quiverc2wcmap:
% 1) Allows user to specify colormap boundaries using 'bound': changes
% colorbar axes AND corresponding vector coloring
% (much more useful for intercomparison of datasets)
% 2) Improved fidelity to magnitude colors in large datasets
% (at a cost of increased computation time...)
% Uses some improvements from DS's vfield_color
% 3) Small clarifications added
% Example:
% x = rand(1,50).*100;
% y = rand(1,50).*100;
% u = rand(1,50) .* 10;
% v = rand(1,50) .* 10;
% scale = 0;
% figure; quiverwcolorbar(x',y',u',v',scale); %compare to:
% figure; quiverwcolorbar(x',y',u',v',scale,'bounds',[0 10]);
%----------------
% function hh = quiverc2wcmap(varargin)
% Andrew Diamond 3/17/2005
% This is based off of Tobias H鰂fken which was based off of Bertrand Dano
% keeping with their main intent to show a color w/r to magnitude quiver plot
% while maintaining a large amount of quiver API backwards compatability.
% Functional differences from quiverc2:
% 1) This works under 6.5.1
% 2) It handles NaNs
% 3) It draws a colormap that is w/r to the quiver magnitudes (hard coded to
% 20 segments of the colormap as per quiverc2 - seems fine for a quiver).
% 4) Various bug fixes (I think)
% In order to do this I needed some small hacks on 6.5.1's quiver to take a
% color triplet. I have included as part of this file in a subfunction below.
%----------------
% Comments from quiverc2
% changed Tobias H鰂fken 3-14-05
% totally downstripped version of the former
% split input field into n segments and do a quiver qhich each of them
% Modified version of Quiver to plots velocity vectors as arrows
% with components (u,v) at the points (x,y) using the current colormap
% Bertrand Dano 3-3-03
% Copyright 1984-2002 The MathWorks, Inc.
% changed T. H鰂fken 14.03.05, for high data resolution
% using fixed color "spacing" of 20
%QUIVERC Quiver color plot.
% QUIVERC(X,Y,U,V) plots velocity vectors as arrows with components (u,v)
% at the points (x,y). The matrices X,Y,U,V must all be the same size
% and contain corresponding position and velocity components (X and Y
% can also be vectors to specify a uniform grid). QUIVER automatically
% scales the arrows to fit within the grid.
%
% QUIVERC(U,V) plots velocity vectors at equally spaced points in
% the x-y plane.
%
% QUIVERC(U,V,S) or QUIVER(X,Y,U,V,S) automatically scales the
% arrows to fit within the grid and then stretches them by S. Use
% S=0 to plot the arrows without the automatic scaling.
%
% QUIVERC(...,LINESPEC) uses the plot linestyle specified for
% the velocity vectors. Any marker in LINESPEC is drawn at the base
% instead of an arrow on the tip. Use a marker of '.' to specify
% no marker at all. See PLOT for other possibilities.
%
% QUIVERC(...,'filled') fills any markers specified.
%
% H = QUIVERC(...) returns a vector of line handles.
%
% Example:
% [x,y] = meshgrid(-2:.2:2,-1:.15:1);
% z = x .* exp(-x.^2 - y.^2); [px,py] = gradient(z,.2,.15);
% contour(x,y,z), hold on
% quiverc(x,y,px,py), hold off, axis image
%
% See also FEATHER, QUIVER3, PLOT.
% Clay M. Thompson 3-3-94
% Copyright 1984-2002 The MathWorks, Inc.
% $Revision: 5.21 $ $Date: 2002/06/05 20:05:16 $
%-------------------------------------------------------------
nin = nargin; %number of inputs
% error(nargchk(2,5,nin));
error(nargchk(2,7,nin)); %added +2 to maxargs to account for 'bounds' add
% Check numeric input arguments
if nin= 5) % quiver(x,y,u,v,s) or quiver(x,y,u,v,s,'bounds',[start end])
if(isscalar(varargin{5}))
scale = varargin{5};
end
end
%-------------Define matrix of vector magnitudes-------------
% Define matrix of vector magnitudes
vr = sqrt(u.^2+v.^2);
% From quiverc2wcmap:
% if data has Nan, don't let it contaminate the computations that segment the
% data; I could just do this with vr and then get clever with the indices but
% this make for easy debugging and as this is a graphics routine the computation
% time is completely irrelevant.
nonNaNind = find(~isnan(vr(:)));
xyuvvrNN = [x(nonNaNind),y(nonNaNind),u(nonNaNind),v(nonNaNind),vr(nonNaNind)];
[xyuvvrNNs, xyuvvrNNsi] = sortrows(xyuvvrNN,5);
% From quiverc2wcmap, no longer necessary
% n = 20; %number of colors
% CC = colormap;
% iCCs=round(linspace(1,size(CC,1),n));
% iData = round(linspace(0,size(xyuvvrNNs,1),n+1));
% figure;
%-------------Generate colorbar-------------
% Includes a clever way to generate (and subsequently hide) an image that
% is required for colorbar without running out of memory for large datasets.
%
% Condensed comments from quiverc2wcmap:
% In 6.5.1 if you ever want a colorbar tick marks to reflect real data ranges
% (versus just the indices of a colormap) then there apparently has to be an
% image somewhere in the figure. Of course, I don't want an image but I figured
% I just make it invisible and then draw the quiver plot over it.
% Unfortunately, it seems that colorbar uses caxis to retrive the data range in
% the image and for invisible images it always seems to be 0 UNLESS you
% explictly reset the caxis.
% This will work but then the axis will be oversized to accomodate the image
% because images have their first and last vitual "pixels" CENTERED around the
% implicit or explict xmin,xmax,ymin,ymax (as per imagesc documentation) but the
% start and end of each of these "pixels" is +/- half a unit where the unit
% corresponds to subdividing the limits by the number of pixels (-1). Given
% that formula and given my invisible 2x2 image for which it is desired to
% diplay in an axis that ISN'T oversized (i.e. min(x), max(x), min(y),max(y)) it
% is possible to solve for the limits (i.e. an artifically reduced limit)
% that need to be specified for imagesc to make its final oversized axis to be the
% non oversized axis that we really want.
% xa,xb,ya,yb compenstates for the axis extention given by imagesc to make
% pixels centered at the limit extents (etc.). Note, this "easy"
% formula would only work for 2x2 pixel images.
xs = min(x); %x(1);
xf = max(x); %x(end)
xa = (3 * xs + xf)/4;
xb = (3 * xf + xs)/4;
ys = min(y); %y(1);
yf = max(y); %y(end)
ya = (3 * ys + yf)/4;
yb = (3 * yf + ys)/4;
% Determine magnitude min/max (which is reflected in colorbar)
colormin = min(xyuvvrNNs(:,5)); %column 5 is NaN-cleared vr
colormax = max(xyuvvrNNs(:,5));
% Allow user to edit bounds using "'bounds',[colormin colormax]" input
for k=1:nin
if (k~=nin) && (length(varargin{k})==6) && strcmp(varargin{k},'bounds')
bounds = varargin{k+1};
if isempty(bounds), error('Specify colormap boundaries'); end
colormin = bounds(1);
colormax = bounds(2);
end
end
% mapbounds = reshape(xyuvvrNNs([1,end;1,end],5),2,2); %from quiverc2wcmap
mapbounds = [colormin colormax; colormin colormax];
h=imagesc([xa,xb],[ya,yb],mapbounds);
set(h,'visible','off');
% Prep colorbar
rang = (colormax-colormin)/colormax;
ticknum = 6; %if you want to toggle number of ticks on colorbar
incr = rang./(ticknum-1);
B = [colormin/colormax:incr:1];
B = B.*colormax;
C = sprintf(['%4.2e',repmat([' \n%4.2e'], 1, ticknum)],B);
C = str2num(C);
caxis([colormin colormax])
colorbar('EastOutside','ytick',B,'yticklabel',C,...
'ticklength',[0.04 0.1],'YLim',[B(1) B(ticknum)],'FontSize',20)
% In quiverc2wcmap this loop plotted for each color level (n=20) and was very
% fast, but I found it did not plot some large data sets with enough color
% accuracy. Switched the loop to examine each data point individually.
% Takes longer but I'm more confident that the colors are correct. Note:
% much of this overhaul was inspired by DS's vfield_color.
hold on;
cmap = jet(64); %toggle type of colormap
CC = colormap(cmap);
cm_stepsize = (colormax-colormin)/length(CC);
for it=1:size(xyuvvrNNs,1) %takes ~13 seconds for a 8730-point dataset
% Some quiverc2wcmap fragments for reference:
% for it=1:n %10x faster, but may not be accurate
% c = CC(iCCs(it),:); %colormap([1:64](it),:) %ie "This RGB color row ="
% si = iData(it)+1; %[1:size(data)](it)+1; %ie "This start row"
% ei = iData(it+1); %[1:size(data)](it+1); %ie "This end row"
% hh=quiver(xyuvvrNNs(si:ei,1),xyuvvrNNs(si:ei,2),...
% xyuvvrNNs(si:ei,3),xyuvvrNNs(si:ei,4),scale*it/n,'Color',c)
cm_index = floor( (xyuvvrNNs(it,5) - colormin) / ( cm_stepsize ) ) + 1;
if cm_index == 1 %in case colormin is zero
c = CC(cm_index,:);
elseif cm_index > length(CC) %in case max(xyuvvrNNs) > colormax
cm_index = length(CC);
c = CC(cm_index,:);
elseif cm_index <= 0 %in case min(xyuvvrNNs) < colormin
cm_index = 1;
c = CC(cm_index,:);
else
cm_index = cm_index-1;
c = CC(cm_index,:);
end
hh=quiver(xyuvvrNNs(it,1),xyuvvrNNs(it,2),...
xyuvvrNNs(it,3),xyuvvrNNs(it,4),scale,'Color',c);
end
%----------Rest of document is from quiverc2wcmap---------------
% This is Matlab's 6.5.1 quiver. I figure that ensures a fair amouint of backward
% compatibility but I needed to hack it to allow a 'Color' property. Obviously
% a person could do more.
function hh = quiver(varargin)
%QUIVER Quiver plot.
% QUIVER(X,Y,U,V) plots velocity vectors as arrows with components (u,v)
% at the points (x,y). The matrices X,Y,U,V must all be the same size
% and contain corresponding position and velocity components (X and Y
% can also be vectors to specify a uniform grid). QUIVER automatically
% scales the arrows to fit within the grid.
%
% QUIVER(U,V) plots velocity vectors at equally spaced points in
% the x-y plane.
%
% QUIVER(U,V,S) or QUIVER(X,Y,U,V,S) automatically scales the
% arrows to fit within the grid and then stretches them by S. Use
% S=0 to plot the arrows without the automatic scaling.
%
% QUIVER(...,LINESPEC) uses the plot linestyle specified for
% the velocity vectors. Any marker in LINESPEC is drawn at the base
% instead of an arrow on the tip. Use a marker of '.' to specify
% no marker at all. See PLOT for other possibilities.
%
% QUIVER(...,'filled') fills any markers specified.
%
% H = QUIVER(...) returns a vector of line handles.
%
% Example:
% [x,y] = meshgrid(-2:.2:2,-1:.15:1);
% z = x .* exp(-x.^2 - y.^2); [px,py] = gradient(z,.2,.15);
% contour(x,y,z), hold on
% quiver(x,y,px,py), hold off, axis image
%
% See also FEATHER, QUIVER3, PLOT.
% Clay M. Thompson 3-3-94
% Copyright 1984-2002 The MathWorks, Inc.
% $Revision: 5.21 $ $Date: 2002/06/05 20:05:16 $
% Arrow head parameters
alpha = 0.33; % Size of arrow head relative to the length of the vector
beta = 0.33; % Width of the base of the arrow head relative to the length
autoscale = 1; % Autoscale if ~= 0 then scale by this.
plotarrows = 1; % Plot arrows
sym = '';
filled = 0;
ls = '-';
ms = '';
col = 'b';
nin = nargin;
ColorSpecInd = find(strcmpi(varargin, 'color'));
if(length(ColorSpecInd)==1 & nin > ColorSpecInd)
col = varargin{ColorSpecInd+1};
varargin = varargin([1:ColorSpecInd-1,ColorSpecInd+2:nin]);
nin = nin-2;
end
% Parse the string inputs
while isstr(varargin{nin}),
vv = varargin{nin};
if ~isempty(vv) & strcmp(lower(vv(1)),'f')
filled = 1;
nin = nin-1;
else
[l,c,m,msg] = colstyle(vv);
if ~isempty(msg),
error(sprintf('Unknown option "%s".',vv));
end
if ~isempty(l), ls = l; end
if ~isempty(c), col = c; end
if ~isempty(m), ms = m; plotarrows = 0; end
if isequal(m,'.'), ms = ''; end % Don't plot '.'
nin = nin-1;
end
end
error(nargchk(2,5,nin));
% Check numeric input arguments
if nin0
len = sqrt((u.^2 + v.^2)/del);
maxlen = max(len(:));
else
maxlen = 0;
end
if maxlen>0
autoscale = autoscale*0.9 / maxlen;
else
autoscale = autoscale*0.9;
end
u = u*autoscale; v = v*autoscale;
end
ax = newplot;
next = lower(get(ax,'NextPlot'));
hold_state = ishold;
% Make velocity vectors
x = x(:).'; y = y(:).';
u = u(:).'; v = v(:).';
uu = [x;x+u;repmat(NaN,size(u))];
vv = [y;y+v;repmat(NaN,size(v))];
% h1 = plot(uu(:),vv(:),[col ls]);
h1 = plot(uu(:),vv(:),ls,'Color',col);
if plotarrows,
% Make arrow heads and plot them
hu = [x+u-alpha*(u+beta*(v+eps));x+u; ...
x+u-alpha*(u-beta*(v+eps));repmat(NaN,size(u))];
hv = [y+v-alpha*(v-beta*(u+eps));y+v; ...
y+v-alpha*(v+beta*(u+eps));repmat(NaN,size(v))];
hold on
% h2 = plot(hu(:),hv(:),[col ls]);
h2 = plot(hu(:),hv(:),ls,'Color',col);
else
h2 = [];
end
if ~isempty(ms), % Plot marker on base
hu = x; hv = y;
hold on
% h3 = plot(hu(:),hv(:),[col ms]);
h3 = plot(hu(:),hv(:),ls,'Color',col);
if filled, set(h3,'markerfacecolor',get(h1,'color')); end
else
h3 = [];
end
if ~hold_state, hold off, view(2); set(ax,'NextPlot',next); end
if nargout>0, hh = [h1;h2;h3]; end
function retval = isscalar(m)
retval = prod(size(m)) == 1;
clear，clc; x = rand(1,100).*100; y = rand(1,100).*100; u = rand(1,100) .* 10; v = rand(1,100) .* 10; scale = 0; figure; quiverwcolorbar(x',y',u',v',scale); figure; quiverwcolorbar(x',y',u',v',scale,'bounds',[0 10]);
4、精细化作图工具箱
因为是数据文件只能加群：【matlab&&python资源共享】：获取panel-2.14.rar文件
4、matlab绘制维恩图
function varargout = venn (varargin)
%VENN Plot 2- or 3- circle area-proportional Venn diagram
%
% venn(A, I)
% venn(Z)
% venn(..., F)
% venn(..., 'ErrMinMode', MODE)
% H = venn(...)
% [H, S] = venn(...)
% [H, S] = venn(..., 'Plot', 'off')
% S = venn(..., 'Plot', 'off')
% [...] = venn(..., P1, V1, P2, V2, ...)
%
%venn(A, I) by itself plots circles with total areas A, and intersection
%area(s) I. For two-circle venn diagrams, A is a two element vector of circle
%areas [c1 c2] and I is a scalar specifying the area of intersection between
%them. For three-circle venn diagrams, A is a three element vector [c1 c2 c3],
%and I is a four element vector [i12 i13 i23 i123], specifiying the
%two-circle intersection areas i12, i13, i23, and the three-circle
%intersection i123.
%
%venn(Z) plots a Venn diagram with zone areas specified by the vector Z.
%For a 2-circle venn diagram, Z is a three element vector [z1 z2 z12]
%For a 3-circle venn, Z is a 7 element vector [z1 z2 z3 z12 z13 z23 z123]
%
%venn(..., F) specifies optional optimization options. VENN uses FMINBND to
%locate optimum pair-wise circle distances, and FMINSEARCH to optimize
%overall three-circle alignment. F is a structure with fields specifying
%optimization options for these functions. F may be a two-element array of
%structures, in which case the first structure is used for FMINBND
%function calls, and the second structure is used for FMINSEARCH function
%calls.
%
%venn(..., 'ErrMinMode', MODE)
%Used for 3-circle venn diagrams only. MODE can be 'TotalError' (default),
%'None', or 'ChowRodgers'. When ErrMinMode is 'None', the positions and
%sizes of the three circles are fixed by their pairwise-intersections,
%which means there may be a large amount of error in the area of the three-
%circle intersection. Specifying ErrMinMode as 'TotalError' attempts to
%minimize the total error in all four intersection zones. The area of the
%three circles are kept constant in proportion to their populations. The
%'ChowRodgers' mode uses the the method proposed by Chow and Rodgers
%[Ref. 1] to draw 'nice' three-circle venn diagrams which appear more
%visually representative of the desired areas, although the actual areas of
%the circles are allowed to deviate from requested values.
%
%H = venn(...) returns a two- or three- element vector to the patches
%representing the circles.
%
%[H, S] = venn(...) returns a structure containing descriptive values
%computed for the requested venn diagram. S is a structure with the
%following fields, where C is the number of circles (N = 2 or 3), Z is
%the number of zones (Z = 3 or 7), and I is the number of intersection
%areas (1 or 4)
%
% Radius C-element vector of circle radii
%
% Position C*2 array of circle centers
%
% ZoneCentroid Z*2 array of zone centroids (Can be used for labeling)
%
% CirclePop C-element vector of supplied circle populations.
% (I.e., the 'true' circle areas)
%
% CircleArea C-element of actual circle areas
%
% CircleAreaError = (CircleArea-CirclePop)/CirclePop
%
% IntersectPop I-element vector of supplied intersection populations
% (I.e., the 'true' intersection areas)
%
% IntersectArea I-element vector of actual intersection areas
%
% IntersectError = (IntersectArea-IntersectPop)/IntersectPop
%
% ZonePop Z-element vector of supplied zone populations. (I.e.
% 'true' zone areas
%
% ZoneArea Z-element vector of actual zone areas.
%
% ZoneAreaError = (ZoneArea-ZonePop)/ZonePop
%
%
%[H, S] = venn(..., 'Plot', 'off')
%S = venn(..., 'Plot', 'off')
%Returns a structure of computed values, without plotting the diagram. This
%which can be useful when S is used to draw custom venn diagrams or for
%exporting venn diagram data to another application. When Plot is set to off,
%the handles vector H is returned as an empty array. Alternatively, the command
%S = venn(..., 'Plot', 'off) will return only the output structure.
%
%[...] = venn(..., P1, V1, P2, V2, ...)
%Specifies additional patch settings in standard Matlab parameter/value
%pair syntax. Parameters can be any valid patch parameter. Values for patch
%parameters can either be single values, or a cell array of length LENGTH(A),
%in which case each value in the cell array is applied to the corresponding
%circle in A.
%
%Examples
%
% %Plot a simple 2-circle venn diagram with custom patch properties
% figure, axis equal, axis off
% A = [300 200]; I = 150;
% venn(A,I,'FaceColor',{'r','y'},'FaceAlpha',{1,0.6},'EdgeColor','black')
%
% %Compare ErrMinModes
% A = [350 300 275]; I = [100 80 60 40];
% figure
% subplot(1,3,1), h1 = venn(A,I,'ErrMinMode','None');
% axis image, title ('No 3-Circle Error Minimization')
% subplot(1,3,2), h2 = venn(A,I,'ErrMinMode','TotalError');
% axis image, title ('Total Error Mode')
% subplot(1,3,3), h3 = venn(A,I,'ErrMinMode','ChowRodgers');
% axis image, title ('Chow-Rodgers Mode')
% set([h1 h2], 'FaceAlpha', 0.6)
%
% %Using the same areas as above, display the error optimization at each
% iteration. Get the output structure.
% F = struct('Display', 'iter');
% [H,S] = venn(A,I,F,'ErrMinMode','ChowRodgers','FaceAlpha', 0.6);
%
% %Now label each zone
% for i = 1:7
% text(S.ZoneCentroid(i,1), S.ZoneCentroid(i,2), ['Zone ' num2str(i)])
% end
%
%See also patch, bar, optimset, fminbdn, fminsearch
%
%Copyright (C) 2008 Darik Gamble, University of Waterloo.
%dgamble@engmail.uwaterloo.ca
%
%References
%1. S Chow and P Rodgers. Extended Abstract: Constructing Area-Proportional
% Venn and Euler Diagrams with Three Circles. Presented at Euler Diagrams
% Workshop 2005. Paris. Available online:
% http://www.cs.kent.ac.uk/pubs/2005/2354/content.pdf
%
%2. S Chow and F Ruskey. Drawing Area-Proportional Venn and Euler Diagrams.
% Lecture Notes in Computer Science. 2004. 2912: 466-477. Springer-Verlag.
% Available online: http://www.springerlink.com/content/rxhtlmqav45gc84q/
%
%3. MP Fewell. Area of Common Overlap of Three Circles. Australian Government
% Department of Defence. Defence Technology and Science Organisation. 2006.
% DSTO-TN-0722. Available online:
% http://dspace.dsto.defence.gov.au/dspace/bitstream/1947/4551/4/DSTO-TN-0722.PR.pdf
%Variable overview
% A0, A Desired and actual circle areas
% A = [A1 A2] or [A1 A2 A3]
% I0, I Desired and actual intersection areas
% I = I12 or [I12 I13 I23 I123]
% Z0, Z Desired and actual zone areas
% Z = [Z1 Z2 Z12] or [Z1 Z2 Z3 Z12 Z13 Z23 Z123]
% x, y Circle centers
% x = [x1 x2] or [x1 x2 x3]
% r Circle radii
% r = [r1 r2] or [r1 r2 r3]
% d Pair-wise distances between circles
% d = d12 or [d12 d13 d23]
%Parse input arguments and preallocate settings
[A0, I0, Z0, nCirc, fminOpts, vennOpts, patchOpts] = parseArgsIn (varargin);
[d, x, y, A, I, Z] = preallocVectors (nCirc);
zoneCentroids = []; %Will only be calculated if needed
%Circle Radii
r = sqrt(A0/pi);
%Determine distance between first circle pair
d(1) = circPairDist(r(1), r(2), I0(1), fminOpts(1));
%Position of second circle is now known
x(2) = d(1);
%First intersection area
I(1) = areaIntersect2Circ(r(1), r(2), d(1));
if nCirc==3
%Pairwise distances for remaining pairs 1&3 and 2&3
d(2) = circPairDist(r(1), r(3), I0(2), fminOpts(1)); %d13
d(3) = circPairDist(r(2), r(3), I0(3), fminOpts(1)); %d23
%Check triangle inequality
srtD = sort(d);
if ~(srtD(end)<(srtD(1)+srtD(2)))
error('venn:triangleInequality', 'Triangle inequality not satisfied')
end
%Guess the initial position of the third circle using the law of cosines
alpha = acos( (d(1)^2 + d(2)^2 - d(3)^2) / (2 * d(1) * d(2)) );
x(3) = d(2)*cos(alpha);
y(3) = d(2)*sin(alpha);
%Each pair-wise intersection fixes the distance between each pair
%of circles, so technically there are no degrees of freedom left in
%which to adjust the three-circle intersection. We can either try
%moving the third circle around to minimize the total error, or
%apply Chow-Rodgers
switch vennOpts.ErrMinMode
case 'TotalError'
%Minimize total intersection area error by moving the third circle
pos = fminsearch(@threeCircleAreaError, [x(3) y(3)], fminOpts(2));
x(3) = pos(1);
y(3) = pos(2);
case 'ChowRodgers'
%note that doChowRodgersSearch updates x and y in this
%workspace as a nested fcn
doChowRodgersSearch;
end
%Make sure everything is 'up to date' after optimization
update3CircleData;
end
%Are we supposed to plot?
if vennOpts.Plot
if isempty(vennOpts.Parent)
vennOpts.Parent = gca;
end
hVenn = drawCircles(vennOpts.Parent, x, y, r, patchOpts.Parameters, patchOpts.Values);
else
hVenn = [];
end
%Only determine zone centroids if they're needed
%Needed for output structure
nOut = nargout;
if (nOut==1 && ~vennOpts.Plot) || nOut==2
if nCirc == 2
%Need to calculate new areas
A = A0; %Areas never change for 2-circle venn
Z = calcZoneAreas(2, A, I);
zoneCentroids = zoneCentroids2(d, r, Z);
else
zoneCentroids = zoneCentroids3(x, y, d, r, Z);
end
end
%Figure out output arguments
if nOut==1
if vennOpts.Plot
varargout{1} = hVenn;
else
varargout{1} = getOutputStruct;
end
elseif nOut==2
varargout{1} = hVenn;
varargout{2} = getOutputStruct;
end
function err = threeCircleAreaError (pos)
x3 = pos(1);
y3 = pos(2);
%Calculate distances
d(2) = sqrt(x3^2 + y3^2); %d13
d(3) = sqrt((x3-d(1))^2 + y3^2); %d23
%Calculate intersections
%Note: we're only moving the third circle, so I12 is not changing
I(2:3) = areaIntersect2Circ (r(1:2), r([3 3]), d(2:3)); %I13 and I23
I(4) = areaIntersect3Circ (r, d); %I123
%Replace 0 (no intersection) with infinite error
I(I==0) = Inf;
%Error
err = sum(abs((I-I0)./I0));
end
function doChowRodgersSearch
%Adapted from Ref. [1]
%Initialize an index matrix to select all 7choose2 zone pairs (21 pairs)
idx = nchoosek(1:7, 2);
%Which zone-zone pairs are considered equal?
%Zones within 10% of each other considered equal
zonePairAreas0 = Z0(idx);
%Percent difference in population between the two members of a pair
ar0 = 2*abs(zonePairAreas0(:,1)-zonePairAreas0(:,2))./sum(zonePairAreas0, 2)*100;
eqPairCutoff = 10;
pairIsEq = ar0<=eqPairCutoff;
%Calculate allowable range for pairs of zones considered unequal
if any(~pairIsEq)
%Sort zone areas
[zUneqAreas0, zUneqArea***tIdx] = sort(zonePairAreas0(~pairIsEq,:), 2);
%Make a real index array out of the inconvenient index sort returns
n = sum(~pairIsEq);
zUneqArea***tIdx = sub2ind([n,2], [1:n; 1:n]', zUneqArea***tIdx);
%rp = (largepopulation/smallpopulation)-1
rp = zUneqAreas0(:,2)./zUneqAreas0(:,1)-1;
rpMin = 1 + 0.3*rp;
rpMax = 1 + 2*rp;
end
%Preallocate zone error vector
zoneErr = zeros(1,21);
%Initialize independent parameters to search over
guessParams = [r(1) x(2) r(2) x(3) y(3) r(3)];
%Search!
pp = fminsearch(@chowRodgersErr, guessParams, fminOpts(2));
[r(1) x(2) r(2) x(3) y(3) r(3)] = deal(pp(1), pp(2), pp(3), pp(4), pp(5), pp(6));
function err = chowRodgersErr (p)
%params = [x2 r2 x3 y3 r3]
[r(1), x(2), r(2), x(3), y(3), r(3)] = deal(p(1), p(2), p(3), p(4), p(5), p(6));
%After changing x2, r2, x3, y3, and r3, update circle areas,
%distances, intersection areas, zone areas
update3CircleData;
if any(pairIsEq)
%For zone pairs considered equal, error is equal to square of the
%distance beyond the cutoff; 0 within cutoff
zAreas = Z(idx(pairIsEq,:));
ar = 2*abs(zAreas(:,1)-zAreas(:,2))./sum(zAreas, 2)*100;
isWithinRange = ar<eqPairCutoff;
ar(isWithinRange) = 0;
ar(~isWithinRange) = ar(~isWithinRange) - eqPairCutoff;
%Amplify error for equal zones with unequal areas
eqZoneUneqAreaErrorGain = 10;
ar(~isWithinRange) = ar(~isWithinRange)*eqZoneUneqAreaErrorGain;
zoneErr(pairIsEq) = ar.^2;
end
if any(~pairIsEq)
%For zone pairs considered unequal, error is equal to square of
%the distance from the allowable range of rp
%rp = (largepopulation/smallpopulation)-1
zUneqPairAreas = Z(idx(~pairIsEq,:));
%Sort based on the population sizes (determined by parent
%function doChowRodgersSearch)
zUneqPairAreas = zUneqPairAreas(zUneqArea***tIdx);
rp = zUneqPairAreas(:,2)./zUneqPairAreas(:,1)-1;
lessThanMin = rprpMax;
rp(~lessThanMin & ~moreThanMax) = 0;
%Determine how far out of range errors are
rp(lessThanMin) = rp(lessThanMin) - rpMin(lessThanMin);
rp(moreThanMax) = rp(moreThanMax) - rpMax(moreThanMax);
%Consider the case where rp < rpMin to be more
%erroneous than the case where rp > rpMax
tooSmallErrorGain = 10;
rp(lessThanMin) = rp(lessThanMin)*tooSmallErrorGain;
zoneErr(~pairIsEq) = rp.^2;
end
%Total error
err = sum(zoneErr);
end %chowRodgersErr
end %doChowRodgersSearch
function update3CircleData
%Circle areas
A = pi*r.^2;
%Calculate distances
d(1) = abs(x(2)); %d12
d(2) = sqrt(x(3)^2 + y(3)^2); %d13
d(3) = sqrt((x(3)-d(1))^2 + y(3)^2); %d23
%Calculate actual intersection areas
I(1:3) = areaIntersect2Circ (r([1 1 2]), r([2 3 3]), d); %I12, I13, I23
I(4) = areaIntersect3Circ (r, d); %I123
%Calculate actual zone areas
Z = calcZoneAreas(3, A, I);
end
function S = getOutputStruct
S = struct(...
'Radius' ,r ,...
'Position' ,[x' y'] ,...
'ZoneCentroid' ,zoneCentroids ,...
'CirclePop' ,A0 ,...
'CircleArea' ,A ,...
'CircleAreaError' ,(A-A0)./A0 ,...
'IntersectPop' ,I0 ,...
'IntersectArea' ,I ,...
'IntersectError' ,(I-I0)./I0 ,...
'ZonePop' ,Z0 ,...
'ZoneArea' ,Z ,...
'ZoneAreaError' ,(Z-Z0)./Z0 );
end
end %venn
function D = circPairDist (rA, rB, I, opts)
%Returns an estimate of the distance between two circles with radii rA and
%rB with area of intersection I
%opts is a structure of FMINBND search options
D = fminbnd(@areadiff, 0, rA+rB, opts);
function dA = areadiff (d)
intersectArea = areaIntersect2Circ (rA, rB, d);
dA = abs(I-intersectArea)/I;
end
end
function hCirc = drawCircles(hParent, xc, yc, r, P, V)
hAx = ancestor(hParent, 'axes');
nextplot = get(hAx, 'NextPlot');
%P and V are cell arrays of patch parameter/values
xc = xc(:); yc = yc(:); %Circle centers
r = r(:); %Radii
n = length(r);
%Independent parameter
dt = 0.05;
t = 0:dt:2*pi;
%Origin centered circle coordinates
X = r*cos(t);
Y = r*sin(t);
hCirc = zeros(1,n);
c = {'r', 'g', 'b'}; %default colors
fa = {0.6, 0.6, 0.6}; %default face alpha
tag = {'Circle1', 'Circle2', 'Circle3'}; %default tag
for i = 1:n
xx = X(i,:)+xc(i);
yy = Y(i,:)+yc(i);
hCirc(i) = patch (xx, yy, c{i}, 'FaceAlpha', fa{i}, 'Parent', hParent, 'Tag', tag{i});
if i==1
set(hAx, 'NextPlot', 'add');
end
end
set(hAx, 'NextPlot', nextplot);
%Custom patch parameter values
if ~isempty(P)
c = cellfun(@iscell, V);
%Scalar parameter values -- apply to all circles
if any(~c)
set(hCirc, {P{~c}}, {V{~c}});
end
%Parameters values with one value per circle
if any(c)
%Make sure all vals are column cell arrays
V = cellfun(@(val) (val(:)), V(c), 'UniformOutput', false);
set(hCirc, {P{c}}, [V{:}])
end
end
end %plotCircles
function A = areaIntersect2Circ (r1, r2, d)
%Area of Intersection of 2 Circles
%Taken from [2]
alpha = 2*acos( (d.^2 + r1.^2 - r2.^2)./(2*r1.*d) );
beta = 2*acos( (d.^2 + r2.^2 - r1.^2)./(2*r2.*d) );
A = 0.5 * r1.^2 .* (alpha - sin(alpha)) ...
+ 0.5 * r2.^2 .* (beta - sin(beta));
end
function [A, x, y, c, trngArea] = areaIntersect3Circ (r, d)
%Area of common intersection of three circles
%This algorithm is taken from [3].
% Symbol Meaning
% T theta
% p prime
% pp double prime
%[r1 r2 r3] = deal(r(1), r(2), r(3));
%[d12 d13 d23] = deal(d(1), d(2), d(3));
%Intersection points
[x,y,sinTp,cosTp] = intersect3C (r,d);
if any(isnan(x)) || any(isnan(y))
A = 0;
%No three circle intersection
return
end
%Step 6. Use the coordinates of the intersection points to calculate the chord lengths c1,
%c2, c3:
i1 = [1 1 2];
i2 = [2 3 3];
c = sqrt((x(i1)-x(i2)).^2 + (y(i1)-y(i2)).^2)';
%Step 7: Check whether more than half of circle 3 is included in the circular triangle, so
%as to choose the correct expression for the area
lhs = d(2) * sinTp;
rhs = y(2) + (y(3) - y(2))/(x(3) - x(2))*(d(2)*cosTp - x(2));
if lhs < rhs
sign = [-1 -1 1];
else
sign = [-1 -1 -1];
end
%Calculate the area of the three circular segments.
ca = r.^2.*asin(c/2./r) + sign.*c/4.*sqrt(4*r.^2 - c.^2);
trngArea = 1/4 * sqrt( (c(1)+c(2)+c(3))*(c(2)+c(3)-c(1))*(c(1)+c(3)-c(2))*(c(1)+c(2)-c(3)) );
A = trngArea + sum(ca);
end
function [x, y, sinTp, cosTp] = intersect3C (r, d)
%Calculate the points of intersection of three circles
%Adapted from Ref. [3]
%d = [d12 d13 d23]
%x = [x12; x13; x23]
%y = [y12; y13; y23]
% Symbol Meaning
% T theta
% p prime
% pp double prime
x = zeros(3,1);
y = zeros(3,1);
%Step 1. Check whether circles 1 and 2 intersect by testing d(1)
if ~( ((r(1)-r(2))<d(1)) && (d(1)<(r(1)+r(2))) )
%x = NaN; y = NaN;
%bigfix: no returned values for sinTp, cosTp
[x, y, sinTp, cosTp] = deal(NaN);
return
end
%Step 2. Calculate the coordinates of the relevant intersection point of circles 1 and 2:
x(1) = (r(1)^2 - r(2)^2 + d(1)^2)/(2*d(1));
y(1) = 0.5/d(1) * sqrt( 2*d(1)^2*(r(1)^2 + r(2)^2) - (r(1)^2 - r(2)^2)^2 - d(1)^4 );
%Step 3. Calculate the values of the sines and cosines of the angles tp and tpp:
cosTp = (d(1)^2 + d(2)^2 - d(3)^2) / (2 * d(1) * d(2));
cosTpp = -(d(1)^2 + d(3)^2 - d(2)^2) / (2 * d(1) * d(3));
sinTp = (sqrt(1 - cosTp^2));
sinTpp = (sqrt(1 - cosTpp^2));
%Step 4. Check that circle 3 is placed so as to form a circular triangle.
cond1 = (x(1) - d(2)*cosTp)^2 + (y(1) - d(2)*sinTp)^2 < r(3)^2;
cond2 = (x(1) - d(2)*cosTp)^2 + (y(1) + d(2)*sinTp)^2 >r(3)^2;
if ~(cond1 && cond2)
x = NaN; y = NaN;
return
end
%Step 5: Calculate the values of the coordinates of the relevant intersection points involving
%circle 3
xp13 = (r(1)^2 - r(3)^2 + d(2)^2) / (2 * d(2));
%yp13 = -0.5 / d(2) * sqrt( 2 * d(2)^2 * (r(2)^2 + r(3)^2) - (r(1)^2 - r(3)^2)^2 - d(2)^4 );
yp13 = -0.5 / d(2) * sqrt( 2 * d(2)^2 * (r(1)^2 + r(3)^2) - (r(1)^2 - r(3)^2)^2 - d(2)^4 );
x(2) = xp13*cosTp - yp13*sinTp;
y(2) = xp13*sinTp + yp13*cosTp;
xpp23 = (r(2)^2 - r(3)^2 + d(3)^2) / (2 * d(3));
ypp23 = 0.5 / d(3) * sqrt( 2 * d(3)^2 * (r(2)^2 + r(3)^2) - (r(2)^2 - r(3)^2)^2 - d(3)^4 );
x(3) = xpp23*cosTpp - ypp23*sinTpp + d(1);
y(3) = xpp23*sinTpp + ypp23*cosTpp;
end
function z = calcZoneAreas(nCircles, a, i)
%Uses simple set addition and subtraction to calculate the zone areas
%with circle areas a and intersection areas i
if nCircles==2
%a = [A1 A2]
%i = I12
%z = [A1-I12, A2-I12, I12]
z = [a(1)-i, a(2)-i, i];
elseif nCircles==3
%a = [A1 A2 A3]
%i = [I12 I13 I23 I123]
%z = [A1-I12-I13+I123, A2-I12-I23+I123, A3-I13-I23+I123, ...
% I12-I123, I13-I123, I23-I123, I123];
z = [a(1)-i(1)-i(2)+i(4), a(2)-i(1)-i(3)+i(4), a(3)-i(2)-i(3)+i(4), ...
i(1)-i(4), i(2)-i(4), i(3)-i(4), i(4)];
else
error('')
%This error gets caught earlier in the stack w. better error msgs
end
end
function [Cx, Cy, aiz] = centroid2CI (x, y, r)
%Finds the centroid of the area of intersection of two circles.
%Vectorized to find centroids for multiple circle pairs
%x, y, and r are nCirclePairs*2 arrays
%Cx and Cy are nCirclePairs*1 vectors
%Centroid of the area of intersection of two circles
n = size(x,1);
xic = zeros(n,2);
az = zeros(n,2);
dx = x(:,2)-x(:,1);
dy = y(:,2)-y(:,1);
d = sqrt(dx.^2 + dy.^2);
%Translate the circles so the first is at (0,0) and the second is at (0,d)
%By symmetry, all centroids are located on the x-axis.
%The two circles intersect at (xp, yp) and (xp, -yp)
xp = 0.5*(r(:,1).^2 - r(:,2).^2 + d.^2)./d;
%Split the inner zone in two
%Right side (Area enclosed by circle 1 and the line (xp,yp) (xp,-yp)
%Angle (xp,yp) (X1,Y1) (xp,-yp)
alpha = 2*acos(xp./r(:,1));
%Area and centroid of the right side of the inner zone
[xic(:,1) az(:,1)] = circleChordVals (r(:,1), alpha);
%Angle (xp,yp) (X2,Y2) (xp,-yp)
alpha = 2*acos((d-xp)./r(:,2));
%Area and centroid of the left side of the inner zone
[xic(:,2) az(:,2)] = circleChordVals (r(:,2), alpha);
xic(:,2) = d - xic(:,2);
%Thus the overall centroid & area of the inner zone
aiz = sum(az,2);
Cx = sum(az.*xic,2)./aiz;
%Now translate the centroid back based on the original positions of the
%circles
theta = atan2(dy, dx);
Cy = Cx.*sin(theta) + y(:,1);
Cx = Cx.*cos(theta) + x(:,1);
end
function centroidPos = zoneCentroids2 (d, r, Z)
centroidPos = zeros(3,2);
%Find the centroids of the three zones in a 2-circle venn diagram
%By symmetry, all centroids are located on the x-axis.
%First, find the x-location of the middle (intersection) zone centroid
%Centroid of the inner zone
centroidPos(3,1) = centroid2CI([0 d], [0 0], r);
%Now, the centroid of the left-most zone is equal to the centroid of
%the first circle (0,0) minus the centroid of the inner zone
centroidPos(1,1) = -centroidPos(3,1)*Z(3)/Z(1);
%Similarly for the right-most zone; the second circle has centroid at x=d
centroidPos(2,1) = (d*(Z(2)+Z(3)) - centroidPos(3,1)*Z(3))/Z(2);
end
function centroidPos = zoneCentroids3 (x0, y0, d, r, Z)
Z = Z(:);
%Get area, points of intersection, and chord lengths
[act, xi, yi, c, atr] = areaIntersect3Circ (r, d);
atr = atr(:);
r = r(:);
%Area and centroid of the triangle within the circular triangle is
xtr = sum(xi/3);
ytr = sum(yi/3);
%Now find the centroids of the three segments surrounding the triangle
i = [1 2; 1 3; 2 3];
xi = xi(i); yi = yi(i);
[xcs, ycs, acs] = circSegProps (r(:), x0(:), y0(:), xi, yi, c(:));
%Overall centroid of the circular triangle
xct = (xtr*atr + sum(xcs.*acs))/act;
yct = (ytr*atr + sum(ycs.*acs))/act;
%Now calculate the centroids of the three two-pair intersection zones
%(Zones 12 13 23)
%Entire zone centroid/areas
%x, y, and r are nCirclePairs*2 arrays
%Cx and Cy are nCirclePairs*1 vectors
i = [1 2; 1 3; 2 3];
[x2c, y2c, a2c] = centroid2CI (x0(i), y0(i), r(i));
%Minus the three-circle intersection zone
xZI2C = (x2c.*a2c - xct*act)./(a2c-act);
yZI2C = (y2c.*a2c - yct*act)./(a2c-act);
x0 = x0(:);
y0 = y0(:);
%Finally, the centroids of the three circles minus the intersection
%areas
i1 = [4 4 5]; i2 = [5 6 6];
j1 = [1 1 2]; j2 = [2 3 3];
x1C = (x0*pi.*r.^2 - xZI2C(j1).*Z(i1) - xZI2C(j2).*Z(i2) - xct*act)./Z(1:3);
y1C = (y0*pi.*r.^2 - yZI2C(j1).*Z(i1) - yZI2C(j2).*Z(i2) - yct*act)./Z(1:3);
%Combine and return
centroidPos = [x1C y1C; xZI2C yZI2C; xct yct];
end
function [x, a] = circleChordVals (r, alpha)
%For a circle centered at (0,0), with angle alpha from the x-axis to the
%intersection of the circle to a vertical chord, find the x-centroid and
%area of the region enclosed between the chord and the edge of the circle
%adapted from http://mathworld.wolfram.com/CircularSegment.html
a = r.^2/2.*(alpha-sin(alpha)); %Area
x = 4.*r/3 .* sin(alpha/2).^3 ./ (alpha-sin(alpha)); %Centroid
end
function [xc, yc, area] = circSegProps (r, x0, y0, x, y, c)
%Translate circle to (0,0)
x = x-[x0 x0];
y = y-[y0 y0];
%Angle subtended by chord
alpha = 2*asin(0.5*c./r);
%adapted from http://mathworld.wolfram.com/CircularSegment.html
area = r.^2/2.*(alpha-sin(alpha)); %Area
d = 4.*r/3 .* sin(alpha/2).^3 ./ (alpha-sin(alpha)); %Centroid
%Perpindicular bisector of the chord
m = -(x(:,2)-x(:,1))./(y(:,2)-y(:,1));
%angle of bisector
theta = atan(m);
%centroids
xc = d.*cos(theta);
yc = d.*sin(theta);
%Make sure we're on the correct side
%Point of intersection of the perp. bisector and the circle perimeter
xb = (x(:,1)+x(:,2))/2;
xc(xb<0) = xc(xb<0)*-1;
yc(xb<0) = yc(xb0
if isstruct(args{1})
%FMIN search options
f = args{1};
nIn = nIn - 1;
if nIn>0, args = args(2:end); end
if length(f) == 1
%Just double up
fminOpts = [f f];
elseif length(f) == 2
%ok
fminOpts = f;
else
error('venn:parseArgsIn', 'FMINOPTS must be a 1 or 2 element structure array.')
end
else
%Use defaults
fminOpts = [optimset('fminbnd'), optimset('fminsearch')];
end
else
%Use defaults
fminOpts = [optimset('fminbnd'), optimset('fminsearch')];
end
%If there's an even number of args in remaining
if nIn>0
if mod(nIn, 2)==0
%Parameter/Value pairs
p = args(1:2:end);
v = args(2:2:end);
[vennOpts, patchOpts] = parsePVPairs (p, v, nZones);
else
error('venn:parseArgsIn', 'Parameter/Value options must come in pairs')
end
else
vennOpts = defaultVennOptions;
patchOpts = struct('Parameters', [], 'Values', []);
end
end %parseArgsIn
function [vennOpts, patchOpts] = parsePVPairs (p, v, nZones)
p = lower(p);
%Break up P/V list into Venn parameters and patch parameters
vennParamNames = {'plot', 'errminmode', 'parent'};
[isVennParam, idx] = ismember(p, vennParamNames);
idx = idx(isVennParam);
%vennParams = p(isVennParam);
vennVals = v(isVennParam);
%First do Patch options
patchOpts.Parameters = p(~isVennParam);
patchOpts.Values = v(~isVennParam);
%Now do Venn options
vennOpts = defaultVennOptions;
%PLOT
i = find(idx==1, 1);
if i
plot = lower(vennVals{i});
if islogical(plot)
vennOpts.Plot = plot;
else
if ischar(plot) && any(strcmp(plot, {'on', 'off'}))
vennOpts.Plot = strcmp(plot, 'on');
else
error('venn:parsePVPairs', 'Plot must be ''on'', ''off'', or a logical value.')
end
end
end
%ERRMINMODE
i = find(idx==2, 1);
if i
mode = lower(vennVals{i});
okModes = {'None', 'TotalError', 'ChowRodgers'};
[isOkMode, modeIdx] = ismember(mode, lower(okModes));
if isOkMode
vennOpts.ErrMinMode = okModes{modeIdx};
else
error('venn:parsePVPairs', 'ErrMinMode must be None, TotalError, or ChowRodgers')
end
end
%PARENT
i = find(idx==5, 1);
if i
h = v{i};
if length(h)==1 && ishandle(h)
vennOpts.Parent = h;
else
error('venn:parsePVPairs', 'Parent must be a valid scalar handle')
end
end
end %parsePVPairs
function [A0, I0, Z0] = parseInputAreas (A0, I0, Z0)
%Switch to row vectors
A0 = A0(:)';
I0 = I0(:)';
Z0 = Z0(:)';
if isempty(Z0)
%A0 and I0 supplied
Z0 = calcZoneAreas (length(A0), A0, I0);
else
%Z0 supplied
switch length(Z0)
case 3
A0 = Z0(1:2)+Z0(3);
I0 = Z0(3);
case 7
A0 = Z0(1:3)+Z0([4 4 5])+Z0([5 6 6])+Z0(7);
I0 = [Z0(4:6)+Z0(7) Z0(7)];
otherwise
error('')
end
end
end
function vennOpts = defaultVennOptions
vennOpts = struct(...
'Plot' ,true ,...
'Labels' ,[] ,...
'PopLabels' ,false ,...
'DrawLabels' ,false ,...
'Parent' ,[] ,...
'Offset' ,[0 0] ,...
'ErrMinMode' ,'TotalError' );
end
function [d, x, y, A, I, Z] = preallocVectors (nCirc)
%Initialize position vectors
x = zeros(1, nCirc);
y = zeros(1, nCirc);
if nCirc==2
d = 0;
I = 0;
A = zeros(1,2);
Z = zeros(1,3);
else %nCirc==3
d = zeros(1,3);
I = zeros(1,4);
A = zeros(1,3);
Z = zeros(1,7);
end
end
clear,clc
%Plot a simple 2-circle venn diagram with custom patch properties
figure, axis equal, axis off
A = [300 200]; I = 150;
venn(A,I,'FaceColor',{'r','y'},'FaceAlpha',{1,0.6},'EdgeColor','black')
%Compare ErrMinModes
A = [350 300 275]; I = [100 80 60 40];
figure
subplot(1,3,1), h1 = venn(A,I,'ErrMinMode','None');
axis image, title ('No 3-Circle Error Minimization')
subplot(1,3,2), h2 = venn(A,I,'ErrMinMode','TotalError');
axis image, title ('Total Error Mode')
subplot(1,3,3), h3 = venn(A,I,'ErrMinMode','ChowRodgers');
axis image, title ('Chow-Rodgers Mode')
set([h1 h2], 'FaceAlpha', 0.6)
5、颜色条
function varargout = contourfnu(x,y,data,v,cmap,pos_colorbar,overticklabel,method,ninterp,nancolor)
% non-uniform contourf/imagesc/colorbar
%
% Input variables
% x : x-coordinates of grid, vector or 2d matrix
% y : y-coordinates of grid, vector or 2d matrix
% If x and y are vectors, then length(x)==size(z,2) and length(y)==size(Z,1).
% If x and y are 2d matrix, they are generated by meshgrid
% data : 2d matrix to be ploted
%
% Optional:
% v : vector of contour levels (default:linspace(datamin,datamax,10))
% cmap : color map array (default:jet)
% pos_colorbar : 'none', or location with respect to the axes (default:'eastoutside')
% overticklabel : whether or not label the overrange ticks at colorbar (default:true)
% method : imagesc, contourf, contour or pcolor (default:imagesc)
% ninterp : repeatedly interp times in each dimension (default:0)
% nancolor : axis backgroud color
%
% Output variable
% hout : structure with handles
% .h plot handle
% .c contour matrix (method='contourf')
% .hc colorbar handle (pos_colorbar~='none')
datamax = max(data(:));
datamin = min(data(:));
if(~exist('v','var')||isempty(v)), v = linspace(datamin,datamax,10); end
if(~exist('cmap','var')||isempty(cmap)), cmap = jet; end
if(~exist('pos_colorbar','var')||isempty(pos_colorbar)), pos_colorbar = 'eastoutside'; end
if(~exist('overticklabel','var')||isempty(overticklabel)), overticklabel = true; end
if(~exist('method','var')||isempty(method)), method = 'imagesc'; end
if(~exist('ninterp','var')||isempty(ninterp)), ninterp = 0; end
if(ninterp>0)
data=interp2(data,ninterp);
if( strcmp(method,'contourf')||strcmp(method,'contour')||strcmp(method,'pcolor') )
if( isvector(x)&&isvector(y) ) % vector to meshgrid
[x,y] = meshgrid(x,y);
end
x = interp2(x,ninterp);
y = interp2(y,ninterp);
end
end
if( strcmp(method,'imagesc')&&~isvector(x) ) % meshgrid to vector
x = x(1,:);
y = y(:,1);
end
if(isrow(v)), v = v'; end
v = sort(v);
% extendmin = dataminv(end);
if(dataminv(end))
v = [v;inf];
end
nlev = length(v);
% piecewise linear mapping, v -> 1:nlev, data -> 1 to nlev
z = zeros(size(data));
for i=1:nlev-1
if( i==1 && v(i)==-inf )
index = data=v(end-1);
z(index) = i+(data(index)-v(end-1))/(datamax-v(end-1));
else
index = data>=v(i) & data0
varargout{1} = hout;
end
实例代码
% Case 1
n = 50;
x = 1:n;
y = 1:n;
data = peaks(n).^4;
contour_levels = [0.5, 10, 100, 500, 1000 ];
contour_levels2 = [0,contour_levels,5000];
% % Case 2
% x=1:0.5:5;
% y=1:0.5:10;
% [x,y] = meshgrid(x,y);
% data = x.^2+exp(y);
% data(end-5:end,end-3:end) = nan;
% data(end-2:end,end-2:end) = inf;
% contour_levels = [5,20,100,1000,10000];
% contour_levels2 = [0,contour_levels,50000];
figure('position',[1,1,1150,800])
subplot(331)
contourf(x,y,data)
colorbar,colormap(jet)
title('original linear cmap')
subplot(332)
contourfnu(x,y,data,contour_levels)
title('imagesc default')
subplot(333)
contourfnu(x,y,data,contour_levels,[],[],[],'contourf')
title('contourf default')
subplot(334)
contourfnu(x,y,data,contour_levels,[],[],false)
title('imagesc overticklabel=false')
subplot(335)
cmap = jet;
cmap(1,:) = [1,1,1]; %white
contourfnu(x,y,data,contour_levels,cmap,[],false)
title('imagesc FirstColorWhite')
subplot(336)
contourfnu(x,y,data,contour_levels2)
title('imagesc AnotherContourLevels')
subplot(337)
contourfnu(x,y,data,contour_levels,[],[],[],[],2)
title('imagesc interp')
subplot(338)
contourfnu(x,y,data,[-inf,contour_levels2,inf],[],[],false)
title('imagesc InfInLevels')
subplot(339)
contourfnu(x,y,data,contour_levels2,[],'southoutside')
title('imagesc PosCbar=''southoutside''')