matlab小结
最近，有做一个图像处理的项目，总结出一些有用的maltlab小工具。
1. Numsubplot
在进行分析的时候，有时候可能需要多图打印，numsubplot还是挺方便的。使用可以看注释部分
function [p,n]=numSubplots(n)
% function [p,n]=numSubplots(n)
%
% Purpose
% Calculate how many rows and columns of sub-plots are needed to
% neatly display n subplots.
%
% Inputs
% n - the desired number of subplots.
%
% Outputs
% p - a vector length 2 defining the number of rows and number of
% columns required to show n plots.
% [ n - the current number of subplots. This output is used only by
% this function for a recursive call.]
%
%
%
% Example: neatly lay out 13 sub-plots
% >> p=numSubplots(13)
% p =
% 3 5
% for i=1:13; subplot(p(1),p(2),i), pcolor(rand(10)), end
%
%
% Rob Campbell - January 2010
while isprime(n) & n>4,
n=n+1;
end
p=factor(n);
if length(p)==1
p=[1,p];
return
end
while length(p)>2
if length(p)>=4
p(1)=p(1)*p(end-1);
p(2)=p(2)*p(end);
p(end-1:end)=[];
else
p(1)=p(1)*p(2);
p(2)=[];
end
p=sort(p);
end
%Reformat if the column/row ratio is too large: we want a roughly
%square design
while p(2)/p(1)>2.5
N=n+1;
[p,n]=numSubplots(N); %Recursive!
end
2. Winrose
a. 可以用于绘制风玫瑰图，也就是风向变量和风速变量 b. 也可以用于绘制单一变量的玫瑰图，比如角度玫瑰图
function [figure_handle,colorSeq,barX,barY,count,speeds,directions,Table] = WindRose(direction,speed,varargin)
% WindRose Draw a Wind Rose knowing direction and speed
%
% [figure_handle,count,speeds,directions,Table] = WindRose(direction,speed);
% [figure_handle,count,speeds,directions,Table] = WindRose(direction,speed,'parameter1',value1,...);
%
% figure_handle is the handle of the figure containing the chart
% count is the frequency for each speed (ncolumns = nspeeds) and for each direction (nrows = ndirections).
% speeds is a 1 by n vector containing the values for the speed intervals
% directions is a m by 1 vector containing the values in which direction intervals are centered
% Table is a (4+m) by (3+m) cell array (excel-ready), containing Frequencies for each direction and for each speed.
%
% User can specify direction angle meaning North and East winds, so
% the graphs is shown in the desired reference
%
% Example
% d = 360 * rand(10000,1); % My reference is North = 0? East = 90?
% v = 30*rand(10000,1);
%
% [figure_handle,count,speeds,directions,Table] = WindRose(d,v,'anglenorth',0,'angleeast',90,'freqlabelangle',45);
%
% PARAMETER CLASS DEFAULT VALUE DESCRIPTION
%------------------------------------------------------------------------------------------------------------------------------------------------------------
% 'centeredin0' Logical. true Is first angular bin centered in 0 (-5 to 5)? -> CeteredIn0 = true // or does it start in 0 (0 to 10)? -> CeteredIn0 = false.
% 'ndirections' Numeric. 36 Number of direction bins (subdivisions) to be shown.
% 'freqround' Numeric. 1 Maximum frquency value will be rounded to the first higher whole multiple of FrequenciesRound. Only applies if 'maxfrequency' is specified.
% 'nfreq' Numeric. 5 Draw this number of circles indicating frequency.
% 'speedround' Numeric. [] (auto) Maximum wind speed will be rounded to the first higher whole multiple of WindSpeedRound.
% 'nspeeds' Numeric. [] (auto) Draw this number of windspeeds subdivisions (bins). Default is 6 if 'speedround' is specified. Otherwise, default is automatic.
% 'maxfrequency' Numeric. [] (auto) or 6 Set the value of the maximum frequency circle to be displayed. Be careful, because bins radius keep the original size.
% 'freqlabelangle' Numeric. [] (auto) Angle in which frequecy labels are shown. If this value is empty, frequency labels will NOT be shown. Trigonometric reference. 0=Right, 90=Up.
% 'titlestring' Cell/String. {'Wind Rose';' '} Figure title. It is recommended to include an empty line below the main string.
% 'lablegend' String. 'Wind speeds in m/s' String that will appear at the top of the legend. Can be empty.
% 'cmap' String. 'jet' String with the name of a colormap function. If you put inv before the name of the funcion, colors will be flipped (e.g. 'invjet', 'invautum', 'invbone', ...). Use any of the built-in functions (autumn, bone, colorcube, cool, copper, flag, gray, hot, hsv, jet, lines, pink, prism, spring, summer, white, winter). See doc colormap for more information.
% 'height' Numeric. 2/3*screensize Figure inner height in pixels. Default is 2/3 of minimum window dimension;
% 'width' Numeric. 2/3*screensize Figure inner width in pixels.
% 'figcolor' Color Code. 'w' Figure color, any admitted matlab color format. Default is white.
% 'textcolor' Color Code. 'k' Text and axis color, any admitted matlab color format. Default is black.
% 'labels' CellString {'N','S','E','W'} Specify North South East West in a cell array of strings.
% 'labelnorth' String. 'N' Label to indicate North. Be careful if you specify 'labels' and 'labelnorth'. Last parameter specified will be the one used.
% 'labelsouth' String. 'S' Label to indicate South. Be careful if you specify 'labels' and 'labelsouth'. Last parameter specified will be the one used.
% 'labeleast' String. 'E' Label to indicate East. Be careful if you specify 'labels' and 'labeleast' . Last parameter specified will be the one used.
% 'labelwest' String. 'W' Label to indicate West. Be careful if you specify 'labels' and 'labelwest' . Last parameter specified will be the one used.
% 'titlefontweight' String. 'bold' Title font weight. You can use 'normal','bold','light','demi'
% 'legendvariable' String. 'W_S' Variable abbreviation that appears inside the legend. You can use TeX sequences.
% 'anglenorth' Numeric. 90 Direction angle meaning North wind. Default is 90 for North (trigonometric reference). If you specify 'north' angle, you need to specify 'east' angle, so the script knows how angles are referenced.
% 'angleeast' Numeric. 0 Direction angle meaning East wind. Default is 0 for East (counterclockwise). If you specify 'east' angle, you need to specify 'north' angle, so the script knows how angles are referenced.
% 'minradius' Numeric 1/30 Minimum radius of the wind rose, relative to the maximum frequency radius. An empty circle of this size appears if greater than 0.
% 'legendtype' Numeric 2 Legend type continuous = 1, separated boxes = 2
%
%
% by Daniel Pereira - dpereira@s2msolutions.com
%
% 2014/Jul/14 - First version
%% Check funciton call
if nargin<2
error('WindRose needs at least two inputs');
elseif mod(length(varargin),2)~=0
error('Inputs must be paired: WindRose(Speed,Direction,''PropertyName'',PropertyValue,...)');
elseif ~isnumeric(speed) || ~isnumeric(speed)
error('Speed and Direction must be numeric arrays.');
elseif ~isequal(size(speed),size(direction))
error('Speed and Direction must be the same size.');
end
%% Default parameters
SCS = get(0,'screensize');
CeteredIn0 = true;
ndirections = 36;
FrequenciesRound = 1;
NFrequencies = 5;
WindSpeedRound = [];
NSpeeds = [];
circlemax = [];
FreqLabelAngle = [];
TitleString = {'Wind Rose';' '};
%lablegend = 'Wind Speeds in m/s';
lablegend = 'flow angle in °';
colorfun = 'jet';
height = min(SCS(3:4))*2/3;
width = min(SCS(3:4))*2/3;
figcolor = '[1,1,1]';
TextColor = '[0,0,0]';
% label.N = 'N';
% label.S = 'S';
% label.W = 'W';
% label.E = 'E';
label.N = '90°';
label.S = '270°';
label.W = '180°';
label.E = '0°';
titlefontweight = 'bold';
legendvariable = 'W_S';
RefN = 90;
RefE = 0;
min_radius = 1/30;
LegendType = 2;
%% User-.specified parameters
for i=1:2:numel(varargin)
switch lower(varargin{i})
case 'centeredin0'
CeteredIn0 = varargin{i+1};
case 'ndirections'
ndirections = varargin{i+1};
case 'freqround'
FrequenciesRound = varargin{i+1};
case 'nfreq'
NFrequencies = varargin{i+1};
case 'speedround'
WindSpeedRound = varargin{i+1};
case 'nspeeds'
NSpeeds = varargin{i+1};
case 'freqlabelangle'
FreqLabelAngle = varargin{i+1};
case 'titlestring'
TitleString = varargin{i+1};
case 'lablegend'
lablegend = varargin{i+1};
case 'cmap'
colorfun = varargin{i+1};
case 'height'
height = varargin{i+1};
case 'width'
width = varargin{i+1};
case 'figcolor'
figcolor = varargin{i+1};
case 'textcolor'
TextColor = varargin{i+1};
case 'min_radius'
min_radius = varargin{i+1};
case 'maxfrequency'
circlemax = varargin{i+1};
case 'titlefontweight'
titlefontweight = varargin{i+1};
case 'legendvariable'
legendvariable = varargin{i+1};
case 'legendtype'
LegendType = varargin{i+1};
case 'labelnorth'
label.N = varargin{i+1};
case 'labelsouth'
label.S = varargin{i+1};
case 'labeleast'
label.E = varargin{i+1};
case 'labelwest'
label.W = varargin{i+1};
case 'labels'
label.N = varargin{i+1}{1};
label.S = varargin{i+1}{2};
label.E = varargin{i+1}{3};
label.W = varargin{i+1}{4};
case 'anglenorth'
k = any(arrayfun(@(x) strcmpi(x,'angleeast'),varargin));
if ~k
error('Reference angles need to be specified for AngleEAST and AngleNORTH directions');
end
case 'angleeast'
k = find(arrayfun(@(x) strcmpi(x,'anglenorth'),varargin));
if isempty(k)
error('Reference angles need to be specified for AngleEAST and AngleNORTH directions');
else
RefE = varargin{i+1};
RefN = varargin{k+1};
end
if abs(RefN-RefE)~=90
error('The angles specified for north and east must differ in 90 degrees');
end
otherwise
error([varargin{i} ' is not a valid property for WindRose function.']);
end
end
speed = reshape(speed,[],1); % Convert wind speed into a column vector
direction = reshape(direction,[],1); % Convert wind direction into a column vector
NumberElements = numel(direction); % Coun the actual number of elements, to consider winds = 0 when calculating frequency.
dir = mod((RefN-direction)/(RefN-RefE)*90,360); % Ensure that the direction is between 0 and 360?
speed = speed(speed>0); % Only show winds higher than 0. 縒hy? See next comment.
dir = dir(speed>0); % Wind = 0 does not have direction, so it cannot appear in a wind rose, but the number of appeareances must be considered.
figure_handle = figure('color',figcolor,'units','pixels','position',[SCS(3)/2-width/2 SCS(4)/2-height/2 width height],'menubar','none','toolbar','none');
%% Bin Directions
N = linspace(0,360,ndirections+1); % Create ndirections direction intervals (ndirections+1 edges)
N = N(1:end-1); % N is the angles in which direction bins are centered. We do not want the 360 to appear, because 0 is already appearing.
n = 180/ndirections; % Angle that should be put backward and forward to create the angular bin, 1st centered in 0
if ~CeteredIn0 % If user does not want the 1st bin to be centered in 0?
N = N+n; % Bin goes from 0 to 2n (N to N+2n), instead of from -n to n (N-n to N+n), so Bin is not centered in 0 (N) angle, but in the n (N+n) angle
end
%% Wind speeds/velocities
if ~isempty(WindSpeedRound)
if isempty(NSpeeds); NSpeeds = 6; end % Default value for NSpeeds if not user specified
vmax = ceil(max(speed)/WindSpeedRound)*WindSpeedRound; % Max wind speed rounded to the nearest whole multiple of WindSpeedRound (Use round or ceil as desired)
if vmax==0; vmax=WindSpeedRound; end; % If max wind speed is 0, make max wind to be WindSpeedRound, so wind speed bins are correctly shown.
vwinds = linspace(0,vmax,NSpeeds); % Wind speeds go from 0 to vmax, creating the desired number of wind speed intervals
else
figure2 = figure('visible','off'); plot(speed); % Plot wind speed
vwinds = get(gca,'ytick'); delete(figure2); % Yaxis will automatically make divisions or us.
if ~isempty(NSpeeds)
vwinds = linspace(min(vwinds),max(vwinds),NSpeeds);
end
end
%% Histogram in each direction + Draw
count = PivotTableCount(N,n,vwinds,speed,dir,NumberElements); % For each direction and for each speed, value of the radius that the windorose must reach (Accumulated in speed).
if isempty(circlemax)
circlemax = ceil(max(max(count))/FrequenciesRound)*FrequenciesRound; % Round highest frequency to closest whole multiple of theFrequenciesRound (Use round or ceil as desired)
end
min_radius = min_radius*circlemax;
DrawPatches(N,n,vwinds,count,colorfun,figcolor,min_radius);% Draw the windrose, knowing the angles, the range for each direction, the speed ranges, the count (frequency) values and the colormap used.
%% Constant frequecy circles and x-y axes + Draw + Labels
[x,y] = cylinder(1,50); x = x(1,:); y = y(1,:); % Get x and y for a unit-radius circle
circles = linspace(0,circlemax,NFrequencies+1); circles = circles(2:end);% Radii of the circles that must be drawn (frequencies). We do not want to spend time drawing radius=0.
radius = circles + min_radius;
radiusmax = circlemax + min_radius;
plot(x'*radius,y'*radius,':','color',TextColor); % Draw circles
plot(x*radiusmax,y*radiusmax,'-','color',TextColor); % Redraw last circle
axisangles = 0:30:360; axisangles = axisangles(1:end-1); % Angles in which to draw the radial axis (trigonometric reference)
R = [min_radius;radiusmax];
plot(R*cosd(axisangles),R*sind(axisangles),':','color',TextColor); % Draw radial axis, in the specified angles
FrequecyLabels(circles,radius,FreqLabelAngle,TextColor); % Display frequency labels
CardinalLabels(radiusmax,TextColor,label); % Display N, S, E, W
%% Title and Legend
title(TitleString,'color',TextColor,'fontweight',titlefontweight); % Display a title
set(gca,'outerposition',[0 0 1 1]); % Check that the current axis fills the figure.
if LegendType==2
leyenda = CreateLegend(vwinds,lablegend,legendvariable); % Create a legend cell string
l = legend(leyenda,'location','southwest'); % Display the legend wherever (position is corrected)
PrettyLegend(l,TextColor); % Display the legend in a good position
elseif LegendType==1
disp(vwinds);
caxis([vwinds(1) vwinds(end)]);
colorbar('YTick',vwinds);
end
%% Outputs
[count,speeds,directions,Table,colorSeq,barX,barY] = CreateOutputs(count,vwinds,N,n,RefN,RefE);
function count = PivotTableCount(N,n,vwinds,speed,dir,NumberElements)
count = zeros(length(N),length(vwinds));
for i=1:length(N)
d1 = mod(N(i)-n,360); % Direction 1 is N-n
d2 = N(i)+n; % Direction 2 is N+n
if d1>d2 % If direction 1 is greater than direction 2 of the bin (d1 = -5 = 355, d2 = 5)
cond = or(dir>=d1,dir<d2); % The condition is satisfied whenever d>=d1 or d<d2
else % For the rest of the cases,
cond = and(dir>=d1,dir<d2); % Both conditions must be met for the same bin
end
counter = histc(speed(cond),vwinds); % If vmax was for instance 25, counter will have counts for these intervals: [>=0 y <5] [>=5 y <10] [>=10 y <15] [>=15 y <20] [>=20 y <25] [>=25]
if isempty(counter); counter = zeros(1,size(count,2)); end % If counter is empty for any reason, set the counts to 0.
count(i,:) = cumsum(counter); % Computing cumsum will make count to have the counts for [<5] [<10] [<15] [<20] [<25] [>=25] (cumulative count, so we have the radius for each speed)
end
count = count/NumberElements*100; % Frequency in percentage
function DrawPatches(N,n,vwinds,count,colorfun,figcolor,min_radius)
inv = strcmp(colorfun(1:3),'inv'); % INV = First three letters in cmap are inv
if inv; colorfun = colorfun(4:end); end % if INV, cmap is the rest, excluding inv
color = feval(colorfun,256); % Create color map
color = interp1(linspace(1,length(vwinds),256),color,1:length(vwinds));% Get the needed values.
if inv; color = flipud(color); end; % if INV, flip upside down the colormap
plot(0,0,'.','color',figcolor,'markeredgecolor',figcolor,'markerfacecolor',figcolor); % This will create an empty legend entry.
hold on; axis square; axis off;
for i=1:length(N)
for j=length(vwinds)👎1
if j>1
r(1) = count(i,j-1);
else
r(1) = 0; % For the first case, radius is 0
end
r(2) = count(i,j);
r = r+min_radius;
alpha = linspace(-n,n,100)+N(i);
x1 = r(1) * sind(fliplr(alpha));
y1 = r(1) * cosd(fliplr(alpha));
x = [x1 r(2)*sind(alpha)]; % Create circular sectors
y = [y1 r(2)*cosd(alpha)];
fill(x,y,color(j,:),'edgecolor',hsv2rgb(rgb2hsv(color(j,:)).*[1 1 0.7])); % Draw them in the specified coloe. Edge is slightly darker.
%text(x(1),y(1),num2str(count(i,j))); %% add label
end
end
function FrequecyLabels(circles,radius,angulo,TextColor)
s = sind(angulo); c = cosd(angulo); % Get the positions in which labels must be placed
if c>0; ha = 'left'; elseif c<0; ha = 'right'; else ha = 'center'; end % Depending on the sign of the cosine, horizontal alignment should be one or another
if s>0; va = 'bottom'; elseif s<0; va = 'top'; else va = 'middle'; end % Depending on the sign of the sine , vertical alignment should be one or another
for i=1:length(circles)
text(radius(i)*c,radius(i)*s,[num2str(circles(i)) '%'],'HorizontalAlignment',ha,'verticalalignment',va,'color',TextColor); % display the labels for each circle
end
rmin = radius(1)-abs(diff(radius(1:2)));
if rmin>0
if c>0; ha = 'right'; elseif c<0; ha = 'left'; else ha = 'center'; end % Depending on the sign of the cosine, horizontal alignment should be one or another
if s>0; va = 'top'; elseif s<0; va = 'bottom'; else va = 'middle'; end % Depending on the sign of the sine , vertical alignment should be one or another
text(rmin*c,rmin*s,'0%','HorizontalAlignment',ha,'verticalalignment',va,'color',TextColor); % display the labels for each circle
end
function CardinalLabels(circlemax,TextColor,labels)
text( circlemax,0,[' ' labels.E],'HorizontalAlignment','left' ,'verticalalignment','middle','color',TextColor); % East label
text( circlemax*cos(30*pi/180),circlemax*sin(30*pi/180),[' 30°'],'HorizontalAlignment','left' ,'verticalalignment','middle','color',TextColor); % East label
text( circlemax*cos(60*pi/180),circlemax*sin(60*pi/180),[' 60°'],'HorizontalAlignment','left' ,'verticalalignment','middle','color',TextColor);
text( (circlemax+3)*cos(120*pi/180),(circlemax+3)*sin(120*pi/180),['120°'],'HorizontalAlignment','left' ,'verticalalignment','middle','color',TextColor);
text( (circlemax+4)*cos(150*pi/180),(circlemax+4)*sin(150*pi/180),['150°'],'HorizontalAlignment','left' ,'verticalalignment','middle','color',TextColor);
text( (circlemax+4)*cos(210*pi/180),(circlemax+4)*sin(210*pi/180),['210°'],'HorizontalAlignment','left' ,'verticalalignment','middle','color',TextColor);
text( (circlemax+3)*cos(240*pi/180),(circlemax+3)*sin(240*pi/180),['240°'],'HorizontalAlignment','left' ,'verticalalignment','middle','color',TextColor);
text( circlemax*cos(300*pi/180),circlemax*sin(300*pi/180),[' 300°'],'HorizontalAlignment','left' ,'verticalalignment','middle','color',TextColor);
text( circlemax*cos(330*pi/180),circlemax*sin(330*pi/180),[' 330°'],'HorizontalAlignment','left' ,'verticalalignment','middle','color',TextColor);
text(-circlemax,0,[labels.W ' '],'HorizontalAlignment','right' ,'verticalalignment','middle','color',TextColor); % West label
text(0, circlemax,labels.N ,'HorizontalAlignment','center','verticalalignment','bottom','color',TextColor); % North label
text(0,-circlemax,labels.S ,'HorizontalAlignment','center','verticalalignment','top' ,'color',TextColor); % South label
xlim([-circlemax circlemax]);
ylim([-circlemax circlemax]);
function leyenda = CreateLegend(vwinds,lablegend,legendvariable)
leyenda = cell(length(vwinds),1); % Initialize legend cell array
for j=1:length(vwinds)
if j==length(vwinds) % When last index is reached
string = sprintf('%s %s %g',legendvariable,'\geq',vwinds(j)); % Display wind <= max wind
else % For the rest of the indices
string = sprintf('%g %s %s < %g',vwinds(j),'\leq',legendvariable,vwinds(j+1)); % Set v1 <= v2 < v1
end
string = regexprep(string,'0 \leq','0 <'); % Replace "0 <=" by "0 <", because wind speed = 0 is not displayed in the graph.
leyenda{length(vwinds)-j+1} = string;
end
leyenda = [lablegend; leyenda]; % Add the title for the legend
function PrettyLegend(l,TextColor)
set(l,'units','normalized','box','off'); % Do not display the box
POS = get(l,'position'); % get legend position (width and height)
set(l,'position',[0 1-POS(4) POS(3) POS(4)],'textcolor',TextColor); % Put the legend in the upper left corner
uistack(l,'bottom'); % Put the legend below the axis
function [count,speeds,directions,Table,colorSeq,barX,barY] = CreateOutputs(count,vwinds,N,n,RefN,RefE)
count = [count(:,1) diff(count,1,2)]; % Count had the accumulated frequencies. With this line, we get the frequency for each single direction and each single speed with no accumulation.
speeds = vwinds; % Speeds are the same as the ones used in the Wind Rose Graph
directions = mod(RefN - N'/90*(RefN-RefE),360); % Directions are the directions in which the sector is centered. Convert function reference to user reference
vwinds(end+1) = inf; % Last wind direction is inf (for creating intervals)
[directions,i] = sort(directions); % Sort directions in ascending order
count = count(i,:); % Sort count in the same way.
wspeeds = cell(1,length(vwinds)-1);
for i=1:(length(vwinds)-1)
if vwinds(i) == 0; s1 = '('; else s1 = '['; end % If vwinds(i) =0 interval is open, because count didn't compute windspeed = 0.
wspeeds{i} = [s1 num2str(vwinds(i)) ' , ' num2str(vwinds(i+1)) ')'];% Create wind speed intervals
end
wdirs = cell(length(directions),1);
for i=1:length(directions)
wdirs{i} = sprintf('[%g , %g)',mod(directions(i)-n,360),directions(i)+n); % Create widn direction intervals
end
% countMark = find(count == max(max(count)));
% countColumnLength = length(directions);
% foundIndex = countMark -countColumnLength * floor(countMark/countColumnLength);
% colorSeq = [mod(directions(foundIndex)-n,360),directions(foundIndex)+n];
WindZeroFreqency = 100-sum(sum(count)); % Wind speed = 0 appears 100-sum(total) % of the time. It does not have direction.
WindZeroFreqency = WindZeroFreqency*(WindZeroFreqency/100>eps); % If frequency/100% is lower than eps, do not show that value.
Table = [{'Frequencies (%)'},{''},{'Wind Speed Interval'},repmat({''},1,numel(wspeeds));'Direction Interval (?','Direction ~',wspeeds,'TOTAL';[wdirs num2cell(directions) num2cell(count) num2cell(sum(count,2))]]; % Create table cell. Ready to xlswrite.
Table(end+1,:) = [{'[0 , 360)','TOTAL'},num2cell(sum(count,1)),{sum(sum(count))}];
Table(end+1,1:2) = {'No Direction', 'Wind Speed = 0'}; % Show Wind Speed = 0 on table.
%% find max count
colorBar1 = sum(count,2);
foundIndex = find(colorBar1 == max(colorBar1));
colorSeq = [mod(directions(foundIndex)-n,360),directions(foundIndex)+n];
barIndex = find(colorBar1>0);
barX = [];
barY = [];
for i = 1:length(barIndex)
barX(i) = directions(i);
barY(i) = colorBar1(i);
end
%bp = bar(barX,barY);
%bp(1).LineWidth = 3;
%bp(foundIndex).EdgeColor = 'red';
Table{end,end} = WindZeroFreqency;
3. 多项式拟合
可以自己更改n为不同的多项式
function [t,y1,a]=getfitLine(x,y,TapeLine)
n=5;
p = polyfit(x,y,n);
for i=1:n+1
a(i)= p(i);
end
t = linspace(x(1),x(length(x)),TapeLine);
if n==1;
y1=a(1)*t+a(2);
elseif n==2;
y1=a(1)*t.^2+a(2)*t+a(3);
elseif n==3;
y1 = a(1)*t.^3 + a(2)*t.^2 + a(3)*t + a(4);
elseif n==4;
y1 = a(1)*t.^4 + a(2)*t.^3 + a(3)*t.^2 + a(4)*t+a(5);
elseif n==5
y1= a(1)*t.^5+a(2)*t.^4+a(3)*t.^3+a(4)*t.^2+a(5)*t+a(6);
end
end
4. 不错的在图片中绘制箭头
function hn=arrow3(p1,p2,s,w,h,ip,alpha,beta)
% ARROW3 (R13)
% ARROW3(P1,P2) draws lines from P1 to P2 with directional arrowheads.
% P1 and P2 are either nx2 or nx3 matrices. Each row of P1 is an
% initial point, and each row of P2 is a terminal point.
%
% ARROW3(P1,P2,S,W,H,IP,ALPHA,BETA) can be used to specify properties
% of the line, initial point marker, and arrowhead. S is a character
% string made with one element from any or all of the following 3
% columns:
%
% Color Switches LineStyle LineWidth
% ------------------ ------------------- --------------------
% k blacK (default) - solid (default) 0.5 points (default)
% y Yellow : dotted 0 no lines
% m Magenta -. dashdot / LineWidthOrder
% c Cyan -- dashed
% r Red * LineStyleOrder _______ __
% g Green ^ |
% b Blue / \ |
% w White Arrowhead / \ Height
% a Asparagus / \ |
% d Dark gray / \ |
% e Evergreen /___ ___\ __|__
% f Firebrick | | | |
% h Hot pink |-- Width --|
% i Indigo | | | |
% j Jade | |
% l Light gray | |
% n Nutbrown | |
% p Pear | |
% q kumQuat Line -->| |<--LineWidth
% s Sky blue | |
% t Tawny | |
% u bUrgundy | |
% v Violet | |
% z aZure | |
% x random Initial / \
% o colorOrder Point -->( )<--IP
% | magnitude Marker \_ _/
%
% -------------------------------------------------------------
% Color Equivalencies
% -------------------------------------------------------------
% ColorOrder Arrow3 | Simulink Arrow3
% ---------- ---------- | ---------- ----------
% Color1 Blue | LightBlue aZure
% Color2 Evergreen | DarkGreen Asparagus
% Color3 Red | Orange kumQuat
% Color4 Sky blue | Gray Light gray
% Color5 Violet |
% Color6 Pear |
% Color7 Dark gray |
% -------------------------------------------------------------
%
% The components of S may be specified in any order. Invalid
% characters in S will be ignored and replaced by default settings.
%
% Prefixing the color code with '_' produces a darker shade, e.g.
% '_t' is dark tawny; prefixing the color code with '^' produces a
% lighter shade, e.g. '^q' is light kumquat. The relative brightness
% of light and dark color shades is controlled by the scalar parameter
% BETA. Color code prefixes do not affect black (k), white (w), or
% the special color switches (xo|).
%
% ColorOrder may be achieved in two fashions: The user may either
% set the ColorOrder property (using RGB triples) or define the
% global variable ColorOrder (using a string of valid color codes).
% If the color switch is specified with 'o', and the global variable
% ColorOrder is a string of color codes (color switches less 'xo|',
% optionally prefixed with '_' or '^'), then the ColorOrder property
% will be set to the sequence of colors indicated by the ColorOrder
% variable. The color sequence 'bersvpd' matches the default
% ColorOrder property. If the color switch is specified with 'o', and
% the global variable ColorOrder is empty or invalid, then the current
% ColorOrder property will be used. Note that the ColorOrder variable
% takes precedence over the ColorOrder property.
%
% The magnitude color switch is used to visualize vector magnitudes
% in conjunction with a colorbar. If the color switch is specified
% with '|', colors are linearly interpolated from the current ColorMap
% according to the length of the associated line. This option sets
% CLim to [MinM,MaxM], where MinM and MaxM are the minimum and maximum
% magnitudes, respectively.
%
% The current LineStyleOrder property will be used if LineStyle is
% specified with '*'. MATLAB cycles through the line styles defined
% by the LineStyleOrder property only after using all colors defined
% by the ColorOrder property. If however, the global variable
% LineWidthOrder is defined, and LineWidth is specified with '/',
% then each line will be drawn with sequential color, linestyle, and
% linewidth.
%
% W (default = 1) is a vector of arrowhead widths; use W = 0 for no
% arrowheads. H (default = 3W) is a vector of arrowhead heights. If
% vector IP is neither empty nor negative, initial point markers will
% be plotted with diameter IP; for default diameter W, use IP = 0.
% The units of W, H and IP are 1/72 of the PlotBox diagonal.
%
% ALPHA (default = 1) is a vector of FaceAlpha values ranging between
% 0 (clear) and 1 (opaque). FaceAlpha is a surface (arrowhead and
% initial point marker) property and does not affect lines. FaceAlpha
% is not supported for 2D rendering.
%
% BETA (default = 0.4) is a scalar that controls the relative
% brightness of light and dark color shades, ranging between 0 (no
% contrast) and 1 (maximum contrast).
%
% Plotting lines with a single color, linestyle, and linewidth is
% faster than plotting lines with multiple colors and/or linestyles.
% Plotting lines with multiple linewidths is slower still. ARROW3
% chooses renderers that produce the best screen images; exported
% or printed plots may benefit from different choices.
%
% ARROW3(P1,P2,S,W,H,'cone',...) will plot cones with bases centered
% on P1 in the direction given by P2. In this instance, P2 is
% interpreted as a direction vector instead of a terminal point.
% Neither initial point markers nor lines are plotted with the 'cone'
% option.
%
% HN = ARROW3(P1,P2,...) returns a vector of handles to line and
% surface objects created by ARROW3.
%
% ARROW3 COLORS will plot a table of named colors with default
% brightness. ARROW3('colors',BETA) will plot a table of named
% colors with brightness BETA.
%
% ARROW3 attempts to preserve the appearance of existing axes. In
% particular, ARROW3 will not change XYZLim, View, or CameraViewAngle.
% ARROW3 does not, however, support stretch-to-fill scaling. AXIS
% NORMAL will restore the current axis box to full size and remove any
% restrictions on the scaling of units, but will likely result in
% distorted arrowheads and initial point markers. See
% (arrow3_messes_up_my_plots.html).
%
% If a particular aspect ratio or variable limit is required, use
% DASPECT, PBASPECT, AXIS, or XYZLIM commands before calling ARROW3.
% Changing limits or aspect ratios after calling ARROW3 may alter the
% appearance of arrowheads and initial point markers. ARROW3 sets
% XYZCLimMode to manual for all plots, sets DataAspectRatioMode to
% manual for linear plots, and sets PlotBoxAspectRatioMode to manual
% for log plots and 3D plots. CameraViewAngleMode is also set to
% manual for 3D plots.
%
% ARROW3 UPDATE will restore the appearance of arrowheads and
% initial point markers that have become corrupted by changes to
% limits or aspect ratios. ARROW3('update',SF) will redraw initial
% point markers and arrowheads with scale factor SF. If SF has one
% element, SF scales W, H and IP. If SF has two elements, SF(1)
% scales W and IP, and SF(2) scales H. If SF has three elements,
% SF(1) scales W, SF(2) scales H, and SF(3) scales IP. All sizes are
% relative to the current PlotBox diagonal.
%
% ARROW3 UPDATE COLORS will update the magnitude coloring of
% arrowheads, initial point markers, and lines to conform to the
% current ColorMap.
%
% HN = ARROW3('update',...) returns a vector of handles to updated
% objects.
%
% EXAMPLES:
%
% % 2D vectors
% arrow3([0 0],[1 3])
% arrow3([0 0],[1 2],'-.e')
% arrow3([0 0],[10 10],'--x2',1)
% arrow3(zeros(10,2),50*rand(10,2),'x',1,3)
% arrow3(zeros(10,2),[10*rand(10,1),500*rand(10,1)],'u')
% arrow3(10*rand(10,2),50*rand(10,2),'x',1,[],1)
%
% % 3D vectors
% arrow3([0 0 0],[1 1 1])
% arrow3(zeros(20,3),50*rand(20,3),'--x1.5',2)
% arrow3(zeros(100,3),50*rand(100,3),'x',1,3)
% arrow3(zeros(10,3),[10*rand(10,1),500*rand(10,1),50*rand(10,1)],'a')
% arrow3(10*rand(10,3),50*rand(10,3),'x',[],[],0)
%
% % 3D animation
% t=(0:pi/40:8*pi)'; u=cos(t); v=sin(t);
% plot3(20*t,u,v)
% axis([0,600,-1.5,1.5,-1.5,1.5])
% grid on, view(35,25)
% hold on
% pbaspect([1.8,1.4,1])
% arrow3(zeros(3),diag([500,1.5,1.5]),'l',0.7,[],0)
% p=[20*t,u,v]; inc=4:1:length(t);
% p2=p(inc,:); p1=p(inc-1,:);
% hn=arrow3(p1(1,:),p2(1,:),'0_b',0.7);
% for i=2:1:length(p1)
% delete(hn)
% hn=arrow3(p1(i,:),p2(i,:),'0_b',0.7);
% pause(0.01)
% end
% hold off
%
% % Cone plot
% t=(pi/8:pi/8:2*pi)'; p1=[cos(t) sin(t) t]; p2=repmat([0 0 1],16,1);
% arrow3(p1,p2,'x',2,4,'cone'), hold on
% plot3(p1(:,1),p1(:,2),p1(:,3)), hold off
% pause % change cone size
% arrow3('update',[1,2])
%
% % Just for fun
% arrow3(zeros(100,3),50*rand(100,3),'x',8,4,[],0.95)
% light('position',[-10 -10 -10],'style','local')
% light('position',[60,60,60]), lighting gouraud
%
% % ColorOrder variable, color code prefixes, and Beta
% global ColorOrder, ColorOrder='^ui^e_hq^v';
% theta=[0:pi/22:pi/2]';
% arrow3(zeros(12,2),[cos(theta),sin(theta)],'1.5o',1.5,[],[],[],0.5)
%
% % ColorOrder property, LineStyleOrder, and LineWidthOrder
% global ColorOrder, ColorOrder=[];
% set(gca,'ColorOrder',[1,0,0;0,0,1;0.25,0.75,0.25;0,0,0])
% set(gca,'LineStyleOrder',{'-','--','-.',':'})
% global LineWidthOrder, LineWidthOrder=[1,2,4,8];
% w=[1,2,3,4]; h=[4,6,4,2];
% arrow3(zeros(4,2),[10*rand(4,1),500*rand(4,1)],'o*/',w,h,0)
%
% % Magnitude coloring
% colormap spring
% arrow3(20*randn(20,3),50*randn(20,3),'|',[],[],0)
% set(gca,'color',0.7*[1,1,1])
% set(gcf,'color',0.5*[1,1,1]), grid on, colorbar
% pause % change the ColorMap and update colors
% colormap hot
% arrow3('update','colors')
%
% % LogLog plot
% set(gca,'xscale','log','yscale','log');
% axis([1e2,1e8,1e-2,1e-1]); hold on
% p1=repmat([1e3,2e-2],15,1);
% q1=[1e7,1e6,1e5,1e4,1e3,1e7,1e7,1e7,1e7,1e7,1e7,1e6,1e5,1e4,1e3];
% q2=1e-2*[9,9,9,9,9,7,5,4,3,2,1,1,1,1,1]; p2=[q1',q2'];
% global ColorOrder, ColorOrder=[];
% set(gca,'ColorOrder',rand(15,3))
% arrow3(p1,p2,'o'), grid on, hold off
%
% % SemiLogX plot
% set(gca,'xscale','log','yscale','linear');
% axis([1e2,1e8,1e-2,1e-1]); hold on
% p1=repmat([1e3,0.05],15,1);
% q1=[1e7,1e6,1e5,1e4,1e3,1e7,1e7,1e7,1e7,1e7,1e7,1e6,1e5,1e4,1e3];
% q2=1e-2*[9,9,9,9,9,7,5,4,3,2,1,1,1,1,1]; p2=[q1',q2'];
% arrow3(p1,p2,'x'), grid on, hold off
%
% % SemiLogY plot
% set(gca,'xscale','linear','yscale','log');
% axis([2,8,1e-2,1e-1]); hold on
% p1=repmat([3,2e-2],17,1);
% q1=[7,6,5,4,3,7,7,7,7,7,7,7,7,6,5,4,3];
% q2=1e-2*[9,9,9,9,9,8,7,6,5,4,3,2,1,1,1,1,1]; p2=[q1',q2'];
% set(gca,'LineStyleOrder',{'-','--','-.',':'})
% arrow3(p1,p2,'*',1,[],0), grid on, hold off
%
% % Color tables
% arrow3('colors') % default color table
% arrow3('colors',0.3) % low contrast color table
% arrow3('colors',0.5) % high contrast color table
%
% % Update initial point markers and arrowheads
% % relative to the current PlotBox diagonal
% arrow3('update') % redraw same size
% arrow3('update',2) % redraw double size
% arrow3('update',0.5) % redraw half size
% arrow3('update',[0.5,2,1]) % redraw W half size,
% % H double size, and
% % IP same size
%
% See also (arrow3_examples.html), (arrow3_messes_up_my_plots.html).
% Copyright(c)2002-2011 Version 5.14
% Tom Davis (tdavis@metzgerwillard.com)
% Jeff Chang
% Revision History:
%
% 07/27/11 - Added animation example. (TD)
% 05/13/09 - Corrected spelling errors (TD)
% 03/16/08 - Updated contact information (TD)
% 10/23/07 - Corrected zero magnitude exclusion (TD)
% 09/08/07 - Added cone plot option; removed adaptive grid
% spacing; corrected scale factor; removed "nearly"
% tight limits (TD)
% 07/24/07 - Ignore zero-magnitude input (TD)
% 07/08/07 - Modified named colors to match named Simulink
% colors; added light and dark shades for basic
% colors (ymcrgb) (TD)
% 07/01/07 - Modified named colors to match default ColorOrder
% colors (TD)
% 06/24/07 - Error checking for empty P1, P2 (TD)
% 06/17/07 - Trim colors,W,H,IP,ALPHA to LENGTH(P1) (TD)
% 05/27/07 - Magnitude coloring and documentation revision (TD)
% 03/10/07 - Improved code metrics (TD)
% 02/21/07 - Preserve existing axis appearance;
% use relative sizes for W, H, and IP;
% removed version checking; minor bug fixes (TD)
% 01/09/04 - Replaced calls to LINSPACE, INTERP1, and
% COLORMAP (TD)
% 12/17/03 - Semilog examples, CAXIS support, magnitude
% coloring, and color updating; use CData instead
% of FaceColor; minor bug fixes (TD)
% 07/17/03 - Changed 2D rendering from OpenGL to ZBuffer;
% defined HN for COLORS and UPDATE options (TD)
% 02/27/03 - Replaced calls to RANDPERM, VIEW, REPMAT, SPHERE,
% and CYLINDER; added ZBuffer for log plots, RESET
% for CLA and CLF, and ABS for W and H (TD)
% 02/01/03 - Added UPDATE scale factor and MATLAB version
% checking, replaced call to CROSS (TD)
% 12/26/02 - Added UserData and UPDATE option (TD)
% 11/16/02 - Added more named colors, color code prefix,
% global ColorOrder, ALPHA , and BETA (TD)
% 10/12/02 - Added global LineWidthOrder,
% vectorized W, H and IP (TD)
% 10/05/02 - Changed CLF to CLA for subplot support,
% added ColorOrder and LineStyleOrder support (TD)
% 04/27/02 - Minor log plot revisions (TD)
% 03/26/02 - Added log plot support (TD)
% 03/24/02 - Adaptive grid spacing control to trade off
% appearance vs. speed based on size of matrix (JC)
% 03/16/02 - Added "axis tight" for improved appearance (JC)
% 03/12/02 - Added initial point marker (TD)
% 03/03/02 - Added aspect ratio support (TD)
% 03/02/02 - Enhanced program's user friendliness (JC)
% (lump Color, LineStyle, and LineWidth together)
% 03/01/02 - Replaced call to ROTATE (TD)
% 02/28/02 - Modified line plotting,
% added linewidth and linestyle (TD)
% 02/27/02 - Minor enhancements on 3D appearance (JC)
% 02/26/02 - Minor enhancements for speed (TD&JC)
% 02/26/02 - Optimize PLOT3 and SURF for speed (TD)
% 02/25/02 - Return handler, error handling, color effect,
% generalize for 2D/3D vectors (JC)
% 02/24/02 - Optimize PLOT3 and SURF for speed (TD)
% 02/23/02 - First release (JC&TD)
%-------------------------------------------------------------------------
% Error Checking
global LineWidthOrder ColorOrder
if nargin<8 || isempty(beta), beta=0.4; end
beta=abs(beta(1)); if nargout, hn=[]; end
if strcmpi(p1,'colors') % plot color table
if nargin>1, beta=abs(p2(1)); end
LocalColorTable(1,beta); return
end
fig=gcf; ax=gca;
if strcmpi(p1,'update'), ud=get(ax,'UserData'); % update
LocalLogCheck(ax);
if size(ud,2)<13, error('Invalid UserData'), end
set(ax,'UserData',[]); sf=[1,1,1]; flag=0;
if nargin>1
if strcmpi(p2,'colors'), flag=1; % update colors
elseif ~isempty(p2) % update surfaces
sf=p2(1)*sf; n=length(p2(:));
if n>1, sf(2)=p2(2); if n>2, sf(3)=p2(3); end, end
end
end
H=LocalUpdate(fig,ax,ud,sf,flag); if nargout, hn=H; end, return
end
InputError=['Invalid input, type HELP ',upper(mfilename),...
' for usage examples'];
if nargin<2, error(InputError), end
[r1,c1]=size(p1); [r2,c2]=size(p2);
if c1<2 || c1>3 || r1*r2==0, error(InputError), end
if r1~=r2, error('P1 and P2 must have same number of rows'), end
if c1~=c2, error('P1 and P2 must have same number of columns'), end
p=sum(abs(p2-p1),2)~=0; cone=0;
if nargin>5 && ~isempty(ip) && strcmpi(ip,'cone') % cone plot
cone=1; p=sum(p2,2)~=0;
if ~any(p), error('P2 cannot equal 0'), end
set(ax,'tag','Arrow3ConePlot');
elseif ~any(p), error('P1 cannot equal P2')
end
if ~all(p)
warning('Arrow3:ZeroMagnitude','Zero magnitude ignored')
p1=p1(p,:); p2=p2(p,:); [r1,c1]=size(p1);
end
n=r1; Zeros=zeros(n,1);
if c1==2, p1=[p1,Zeros]; p2=[p2,Zeros];
elseif ~any([p1(:,3);p2(:,3)]), c1=2; end
L=get(ax,'LineStyleOrder'); C=get(ax,'ColorOrder');
ST=get(ax,'DefaultSurfaceTag'); LT=get(ax,'DefaultLineTag');
EC=get(ax,'DefaultSurfaceEdgeColor');
if strcmp(get(ax,'nextplot'),'add') && strcmp(get(fig,'nextplot'),'add')
Xr=get(ax,'xlim'); Yr=get(ax,'ylim'); Zr=get(ax,'zlim');
[xs,ys,xys]=LocalLogCheck(ax); restore=1;
if xys, mode='auto';
if any([p1(:,3);p2(:,3)]), error('3D log plot not supported'), end
if (xs && ~all([p1(:,1);p2(:,1)]>0)) || ...
(ys && ~all([p1(:,2);p2(:,2)]>0))
error('Nonpositive log data not supported')
end
else mode='manual';
if strcmp(get(ax,'WarpToFill'),'on')
warning('Arrow3:WarpToFill',['Stretch-to-fill scaling not ',...
'supported;\nuse DASPECT or PBASPECT before calling ARROW3.']);
end
end
set(ax,'XLimMode',mode,'YLimMode',mode,'ZLimMode',mode,...
'CLimMode','manual');
else restore=0; cla reset; xys=0; set(fig,'nextplot','add');
if c1==2, azel=[0,90]; else azel=[-37.5,30]; end
set(ax,'UserData',[],'nextplot','add','View',azel);
end
%-------------------------------------------------------------------------
% Style Control
[vc,cn]=LocalColorTable(0); prefix=''; OneColor=0;
if nargin<3, [c,ls,lw]=LocalValidateCLSW;% default color, linestyle/width
else
[c,ls,lw]=LocalValidateCLSW(s);
if length(c)>1, if sum('_^'==c(1)), prefix=c(1); end, c=c(2); end
if c=='x' % random named color (less white)
[ignore,i]=sort(rand(1,23)); c=cn(i,:); %#ok
elseif c=='o' % ColorOrder
if length(ColorOrder)
[c,failed]=LocalColorMap(lower(ColorOrder),vc,cn,beta);
if failed, ColorOrderWarning=['Invalid ColorOrder ',...
'variable, current ColorOrder property will be used'];
warning('Arrow3:ColorOrder',ColorOrderWarning)
else C=c;
end
end, c=C;
elseif c=='|', map=get(fig,'colormap'); % magnitude coloring
M=(p1-p2); M=sqrt(sum(M.*M,2)); minM=min(M); maxM=max(M);
if maxM-minM<1, minM=0; end
set(ax,'clim',[minM,maxM]); c=LocalInterp(minM,maxM,map,M);
elseif ~sum(vc==c), c='k'; ColorWarning=['Invalid color switch, ',...
'default color (black) will be used'];
warning('Arrow3:Color',ColorWarning)
end
end
if length(c)==1 % single color
c=LocalColorMap([prefix,c],vc,cn,beta); OneColor=1;
end
set(ax,'ColorOrder',c); c=LocalRepmat(c,[ceil(n/size(c,1)),1]);
if ls~='*', set(ax,'LineStyleOrder',ls); end % LineStyleOrder
if lw=='/' % LineWidthOrder
if length(LineWidthOrder)
lw=LocalRepmat(LineWidthOrder(:),[ceil(n/length(LineWidthOrder)),1]);
else lw=0.5; LineWidthOrderWarning=['Undefined LineWidthOrder, ',...
'default width (0.5) will be used'];
warning('Arrow3:LineWidthOrder',LineWidthOrderWarning)
end
end
if nargin<4 || isempty(w), w=1; end % width
w=LocalRepmat(abs(w(:)),[ceil(n/length(w)),1]);
if nargin<5 || isempty(h), h=3*w; end % height
h=LocalRepmat(abs(h(:)),[ceil(n/length(h)),1]);
if nargin>5 && ~isempty(ip) && ~cone % ip
ip=LocalRepmat(ip(:),[ceil(n/length(ip)),1]);
i=find(ip==0); ip(i)=w(i);
else ip=-ones(n,1);
end
if nargin<7 || isempty(alpha), alpha=1; end
a=LocalRepmat(alpha(:),[ceil(n/length(alpha)),1]); % FaceAlpha
%-------------------------------------------------------------------------
% Log Plot
if xys
units=get(ax,'units'); set(ax,'units','points');
pos=get(ax,'position'); set(ax,'units',units);
if strcmp(get(ax,'PlotBoxAspectRatioMode'),'auto')
set(ax,'PlotBoxAspectRatio',[pos(3),pos(4),1]);
end
par=get(ax,'PlotBoxAspectRatio');
set(ax,'DataAspectRatio',[par(2),par(1),par(3)]);
% map coordinates onto unit square
q=[p1;p2]; xr=Xr; yr=Yr;
if xs, xr=log10(xr); q(:,1)=log10(q(:,1)); end
if ys, yr=log10(yr); q(:,2)=log10(q(:,2)); end
q=q-LocalRepmat([xr(1),yr(1),0],[2*n,1]);
dx=xr(2)-xr(1); dy=yr(2)-yr(1);
q=q*diag([1/dx,1/dy,1]);
q1=q(1:n,:); q2=q(n+1:end,:);
else xs=0; ys=0; dx=0; dy=0; xr=0; yr=0;
end
%-------------------------------------------------------------------------
% Line
if ~cone
set(ax,'DefaultLineTag','arrow3');
if length(lw)==1
if lw>0
if OneColor && ls(end)~='*' && n>1 % single color, linestyle/width
P=zeros(3*n,3); i=1:n;
P(3*i-2,:)=p1(i,:); P(3*i-1,:)=p2(i,:); P(3*i,1)=NaN;
H1=plot3(P(:,1),P(:,2),P(:,3),'LineWidth',lw);
else % single linewidth
H1=plot3([p1(:,1),p2(:,1)]',[p1(:,2),p2(:,2)]',...
[p1(:,3),p2(:,3)]','LineWidth',lw);
end
else H1=[];
end
else % use LineWidthOrder
ls=LocalRepmat(cellstr(L),[ceil(n/size(L,1)),1]);
H1=Zeros;
for i=1:n
H1(i)=plot3([p1(i,1),p2(i,1)],[p1(i,2),p2(i,2)],...
[p1(i,3),p2(i,3)],ls{i},'Color',c(i,:),'LineWidth',lw(i));
end
end
else % cone plot
P=zeros(3*n,3); i=1:n;
P(3*i-2,:)=p1(i,:); P(3*i-1,:)=p1(i,:); P(3*i,1)=NaN;
H1=plot3(P(:,1),P(:,2),P(:,3));
end
%-------------------------------------------------------------------------
% Scale
if ~restore, axis tight, end
ar=get(ax,'DataAspectRatio'); ar=sqrt(3)*ar/norm(ar);
set(ax,'DataAspectRatioMode','manual');
if xys, sf=1;
else xr=get(ax,'xlim'); yr=get(ax,'ylim'); zr=get(ax,'zlim');
sf=norm(diff([xr;yr;zr],1,2)./ar')/72;
end
%-------------------------------------------------------------------------
% UserData
c=c(1:n,:); w=w(1:n); h=h(1:n); ip=ip(1:n); a=a(1:n);
set(ax,'UserData',[get(ax,'UserData');p1,p2,c,w,h,ip,a]);
%-------------------------------------------------------------------------
% Arrowhead
whip=sf*[w,h,ip];
if xys, whip=whip*sqrt(2)/72; p1=q1; p2=q2; end
w=whip(:,1); h=whip(:,2); ip=whip(:,3);
if cone % cone plot
delete(H1), H1=[];
p2=p2./LocalRepmat(sqrt(sum(p2.*p2,2)),[1,3]);
p2=p1+p2.*LocalRepmat(ar,[n,1]).*LocalRepmat(h,[1,3]);
end
W=(p1-p2)./LocalRepmat(ar,[n,1]);
W=W./LocalRepmat(sqrt(sum(W.*W,2)),[1,3]); % new z direction
U=[-W(:,2),W(:,1),Zeros];
N=sqrt(sum(U.*U,2)); i=find(N<eps); j=length(i);
U(i,:)=LocalRepmat([1,0,0],[j,1]); N(i)=ones(j,1);
U=U./LocalRepmat(N,[1,3]); % new x direction
V=[W(:,2).*U(:,3)-W(:,3).*U(:,2),... % new y direction
W(:,3).*U(:,1)-W(:,1).*U(:,3),...
W(:,1).*U(:,2)-W(:,2).*U(:,1)];
m=20; % surface grid spacing
set(ax,'DefaultSurfaceTag','arrow3','DefaultSurfaceEdgeColor','none');
r=[0;1]; theta=(0:m)/m*2*pi; Ones=ones(1,m+1);
x=r*cos(theta); y=r*sin(theta); z=r*Ones;
G=surface(x/2,y/2,z); dar=diag(ar);
X=get(G,'XData'); Y=get(G,'YData'); Z=get(G,'ZData');
H2=Zeros; [j,k]=size(X);
for i=1:n % translate, rotate, and scale
H2(i)=copyobj(G,ax);
xyz=[w(i)*X(:),w(i)*Y(:),h(i)*Z(:)]*[U(i,:);V(i,:);W(i,:)]*dar;
x=reshape(xyz(:,1),j,k)+p2(i,1);
y=reshape(xyz(:,2),j,k)+p2(i,2);
z=reshape(xyz(:,3),j,k)+p2(i,3);
LocalSetSurface(xys,xs,ys,dx,dy,xr,yr,...
x,y,z,a(i),c(i,:),H2(i),2,m+1);
end
delete(G);
%-------------------------------------------------------------------------
% Initial Point Marker
if any(ip>0)
theta=(-m:2:m)/m*pi; phi=(-m:2:m)'/m*pi/2; cosphi=cos(phi);
x=cosphi*cos(theta); y=cosphi*sin(theta); z=sin(phi)*Ones;
G=surface(x*ar(1)/2,y*ar(2)/2,z*ar(3)/2);
X=get(G,'XData'); Y=get(G,'YData'); Z=get(G,'ZData');
H3=zeros(n,1);
for i=1:n % translate
if ip(i)>0
H3(i)=copyobj(G,ax);
x=p1(i,1)+X*ip(i); y=p1(i,2)+Y*ip(i); z=p1(i,3)+Z*ip(i);
LocalSetSurface(xys,xs,ys,dx,dy,xr,yr,...
x,y,z,a(i),c(i,:),H3(i),m+1,m+1);
end
end, delete(G);
else H3=[];
end
%-------------------------------------------------------------------------
% Finish
if restore, xr=Xr; yr=Yr; zr=Zr;
if xys, set(ax,'DataAspectRatioMode','auto'); end
else
axis tight
xr=get(ax,'xlim'); yr=get(ax,'ylim'); zr=get(ax,'zlim');
set(ax,'nextplot','replace');
end
azel=get(ax,'view');
if abs(azel(2))==90, renderer='ZBuffer'; else renderer='OpenGL'; c1=3; end
set(fig,'Renderer',renderer);
set(ax,'LineStyleOrder',L,'ColorOrder',C,'DefaultLineTag',LT,...
'DefaultSurfaceTag',ST,'DefaultSurfaceEdgeColor',EC,...
'xlim',xr,'ylim',yr,'zlim',zr,'clim',get(ax,'CLim'));
if c1==3, set(ax,'CameraViewAngle',get(ax,'CameraViewAngle'),...
'PlotBoxAspectRatio',get(ax,'PlotBoxAspectRatio'));
end
if nargout, hn=[H1(:);H2(:);H3(:)]; end
%-------------------------------------------------------------------------
% Local Functions
%-------------------------------------------------------------------------
% Update
function H=LocalUpdate(fig,ax,ud,sf,flag)
global ColorOrder
p1=ud(:,1:3); p2=ud(:,4:6); c=ud(:,7:9); a=ud(:,13);
w=sf(1)*ud(:,10); h=sf(2)*ud(:,11); ip=sf(3)*ud(:,12);
H=get(ax,'children'); tag=get(H,'tag'); type=get(H,'type');
delete(H(strcmp(tag,'arrow3') & strcmp(type,'surface')));
set(fig,'nextplot','add'); set(ax,'nextplot','add'); H1=[];
if flag, map=get(fig,'colormap'); % update colors
M=(p1-p2); M=sqrt(sum(M.*M,2)); minM=min(M); maxM=max(M);
H1=H(strcmp(tag,'arrow3') & strcmp(type,'line'));
MagnitudeWarning=['Cannot perform magnitude coloring on lines ',...
'that\nwere drawn with a single color, linestyle, and linewidth'];
if length(H1)>1
for i=1:length(H1) % update line colors
x=get(H1(i),'xdata'); y=get(H1(i),'ydata'); z=get(H1(i),'zdata');
if length(x)>2 % multiple lines
warning('Arrow3:Magnitude',MagnitudeWarning), continue
end
m=sqrt((x(1)-x(2))^2+(y(1)-y(2))^2+(z(1)-z(2))^2);
c=LocalInterp(minM,maxM,map,m); set(H1(i),'color',c);
end
elseif length(H1)==1
warning('Arrow3:Magnitude',MagnitudeWarning)
end
c=LocalInterp(minM,maxM,map,M);
end
set(ax,'ColorOrder',c); % update surfaces
ColorOrder=[];
if strcmp(get(ax,'tag'),'Arrow3ConePlot')
H=arrow3(p1,p2,'o' ,w,h,'cone',a); % update cones
else H=arrow3(p1,p2,'o0',w,h, ip,a);
end, H=[H1(:);H(:)];
set(ax,'nextplot','replace');
%-------------------------------------------------------------------------
% SetSurface
function LocalSetSurface(xys,xs,ys,dx,dy,xr,yr,x,y,z,a,c,H,n,m)
if xys
x=x*dx+xr(1); y=y*dy+yr(1);
if xs, x=10.^x; end
if ys, y=10.^y; end
end
cd=zeros(n,m,3); cd(:,:,1)=c(1); cd(:,:,2)=c(2); cd(:,:,3)=c(3);
set(H,'XData',x,'YData',y,'ZData',z,'CData',cd,'FaceAlpha',a);
%-------------------------------------------------------------------------
% ColorTable
function [vc,cn]=LocalColorTable(n,beta)
vc='kymcrgbadefhijlnpqstuvzw'; % valid color codes
% k y m c
cn=[0.00,0.00,0.00; 1.00,1.00,0.00; 1.00,0.00,1.00; 0.00,1.00,1.00;
% r g b a
1.00,0.00,0.00; 0.00,1.00,0.00; 0.00,0.00,1.00; 0.42,0.59,0.24;
% d e f h
0.25,0.25,0.25; 0.00,0.50,0.00; 0.70,0.13,0.13; 1.00,0.41,0.71;
% i j l n
0.29,0.00,0.51; 0.00,0.66,0.42; 0.50,0.50,0.50; 0.50,0.20,0.00;
% p q s t
0.75,0.75,0.00; 1.00,0.50,0.00; 0.00,0.75,0.75; 0.80,0.34,0.00;
% u v z w
0.50,0.00,0.13; 0.75,0.00,0.75; 0.38,0.74,0.99; 1.00,1.00,1.00];
% Named Simulink Colors (zaql)
% LightBlue = 0.38 0.74 0.99 = aZure
% DarkGreen = 0.42 0.59 0.24 = Asparagus
% Orange = 1.00 0.50 0.00 = kumQuat
% Gray = 0.50 0.50 0.50 = Light gray
%
% Default ColorOrder Property Colors (bersvpd)
% Color1 = 0.00 0.00 1.00 = Blue
% Color2 = 0.00 0.50 0.00 = Evergreen
% Color3 = 1.00 0.00 0.00 = Red
% Color4 = 0.00 0.75 0.75 = Sky blue
% Color5 = 0.75 0.00 0.75 = Violet
% Color6 = 0.75 0.75 0.00 = Pear
% Color7 = 0.25 0.25 0.25 = Dark gray
if n, clf reset % plot color table
name={'blacK','Yellow','Magenta','Cyan',...
'Red','Green','Blue','Asparagus',...
'Dark gray','Evergreen','Firebrick','Hot pink',...
'Indigo','Jade','Light gray','Nutbrown',...
'Pear','kumQuat','Sky blue','Tawny',...
'bUrgundy','Violet','aZure','White'};
c=['yptn';'gjae';'czsb';'hmvi';'qrfu';'wldk'];
set(gcf,'DefaultAxesXTick',[],'DefaultAxesYTick',[],...
'DefaultAxesXTickLabel',[],'DefaultAxesYTickLabel',[],...
'DefaultAxesXLim',[0,0.75],'DefaultAxesYLim',[0,0.75],...
'DefaultRectangleEdgeColor','none');
for i=1:24, subplot(4,6,i); box on
j=find(vc==c(i)); title(name{j});
dark=LocalBrighten(cn(j,:),-beta);
light=LocalBrighten(cn(j,:),beta);
rectangle('Position',[0,0.00,0.75,0.25],'FaceColor',dark);
rectangle('Position',[0,0.25,0.75,0.25],'FaceColor',cn(j,:));
rectangle('Position',[0,0.50,0.75,0.25],'FaceColor',light);
rectangle('Position',[0,0.00,0.75,0.75],'EdgeColor','k');
if rem(i,6)==1
set(gca,'YTickLabel',{'dark','normal','light'},...
'YTick',[0.125,0.375,0.625]);
if i==19
text(0,-0.25,['{\bf\itARROW3} Named Color Table ',...
'( \beta = ',num2str(beta),' )']);
end
end
end
end
%-------------------------------------------------------------------------
% ColorMap
function [C,failed]=LocalColorMap(c,vc,cn,beta)
n=length(c); failed=0; C=zeros(n,3); i=1; j=1;
while 1
if ~sum([vc,'_^']==c(i)), failed=1; break, end
if sum('_^'==c(i))
if i+1>n, failed=1; break, end
if ~sum(vc==c(i+1)), failed=1; break, end
cc=cn(vc==c(i+1),:); gamma=beta;
if c(i)=='_', gamma=-beta; end
C(j,:)=LocalBrighten(cc,gamma); i=i+2;
else C(j,:)=cn(vc==c(i),:); i=i+1;
end
if i>n, break, end, j=j+1;
end
if n>j, C(j+1:n,:)=[]; end
%-------------------------------------------------------------------------
% Brighten
function C=LocalBrighten(c,beta)
if sum([c==0,c==1])==3 && sum(c==0)<3 && sum(c==1)<3
if beta<0
C=(1+beta)*c;
else
C=c; C(C==0)=beta;
end
else
C=c.^((1-min(1-sqrt(eps),abs(beta)))^sign(beta));
end
%-------------------------------------------------------------------------
% Repmat
function B=LocalRepmat(A,siz)
if length(A)==1, B(prod(siz))=A; B(:)=A; B=reshape(B,siz);
else [m,n]=size(A); mind=(1:m)'; nind=(1:n)';
mind=mind(:,ones(1,siz(1))); nind=nind(:,ones(1,siz(2)));
B=A(mind,nind);
end
%-------------------------------------------------------------------------
% Interp
function v=LocalInterp(xmin,xmax,y,u)
[m,n]=size(y); h=(xmax-xmin)/(m-1); p=length(u); v=zeros(p,n);
k=min(max(1+floor((u-xmin)/h),1),m-1); s=(u-xmin)/h-k+1;
for j=1:n, v(:,j)=y(k,j)+s.*(y(k+1,j)-y(k,j)); end
v(v<0)=0; v(v>1)=1;
%-------------------------------------------------------------------------
% Check for supported log scales
function [xs,ys,xys]=LocalLogCheck(ax)
xs=strcmp(get(ax,'xscale'),'log');
ys=strcmp(get(ax,'yscale'),'log');
zs=strcmp(get(ax,'zscale'),'log');
if zs, error('Z log scale not supported'), end
xys=xs+ys;
if xys, azel=get(ax,'view');
if abs(azel(2))~=90, error('3D log plot not supported'), end
end
%-------------------------------------------------------------------------
% Generate valid value for color, linestyle and linewidth
function [c,ls,lw]=LocalValidateCLSW(s)
if nargin<1, c='k'; ls='-'; lw=0.5;
else
% identify linestyle
if findstr(s,'--'), ls='--'; s=strrep(s,'--','');
elseif findstr(s,'-.'), ls='-.'; s=strrep(s,'-.','');
elseif findstr(s,'-'), ls='-'; s=strrep(s,'-','');
elseif findstr(s,':'), ls=':'; s=strrep(s,':','');
elseif findstr(s,'*'), ls='*'; s=strrep(s,'*','');
else ls='-';
end
% identify linewidth
tmp=double(s);
tmp=find(tmp>45 & tmp<58);
if length(tmp)
if any(s(tmp)=='/'), lw='/'; else lw=str2double(s(tmp)); end
s(tmp)='';
else lw=0.5;
end
% identify color
if length(s), s=lower(s);
if length(s)>1, c=s(1:2);
else c=s(1); end
else c='k';
end
end
5. 误差带
有时候可能输入平均值，和上下线误差，该程序比内置的errorbar更好用一些function errorbare(sty,x,y,xbar,ybar,symbol)
% ERRORBARE Enhanced Errorbar Function.
% ERRORBARE(STY,X,Y,Xbar,Ybar,symbol)
% It can draw errorbar along X/Y/Dual axis
% in normal,semilog,loglog coordinate system,
% and adjust length of top line automatically,
% can also control dotstyle and color in the same way with errorbar.
%
% If the lower and upper error range of x/y is different, they should be
% input as [lower,upper] if x/y is a column vector;
% for a row vector, they should be [lower;uper].
%
% parameter STY include 12 types:
% v,h,d,vlogx,hlogx,dlogx,vlogy,hlogy,
% dlogy,vlogd,hlogd,dlogd
% where
% v stands for vertical errorbar，
% h draws horizontal errorbar，
% d means dual direction,
% logx corresponding to semilogx，can use preffix v/h/d
% logy corresponding to semilogy，can use preffix v/h/d
% logd corresponding to loglog，can use preffix v/h/d
% 误差棒函数增强版
% ERRORBARE(STY,X,Y,Xbar,Ybar,symbol)
% 可在各个坐标系中沿X轴，Y轴方向，或者两轴方向绘制误差棒，
% 能够根据所选坐标类型调整端点线长。
% 增加对误差棒的线型控制，用法与原errorbar函数中相同
%
% 若上下限范围不同，X为列向量时应按照
% [下限,上限] 的格式输入，若为行向量则为 [下限;上限]
%
% STY 参数包括 v,h,d,vlogx,hlogx,dlogx,vlogy,hlogy,
% dlogy,vlogd,hlogd,dlogd 共12种
% v 表示误差棒垂直，
% h 表示误差棒水平，
% d (dual) 显示双轴误差，
% logx 对应 semilogx，前缀 v,h,d 意义同上
% logy 对应 semilogy，前缀 v,h,d 意义同上
% logd 对应 loglog，前缀 v,h,d 意义同上
% For example,
% x = 1:10;
% y = sin(x)+2;
% e = std(y)*ones(size(x));
% errorbare(x,y,e) % use function "errorbar" directly
% errorbare(x,y,e,'or')
% errorbare('v',x,y,e) % "e" is error of "y"
% errorbare('v',x,y,[e;2*e]) % try different error limits
% errorbare('hlogx',x,y,e) % "e" is error of "x" here，
% errorbare('d',x,y,e,e)
% errorbare('d',x,y,e,e,'or')
% errorbare('dlogd',x,y,e,e)
%
% by Henry Sting Email: henrysting@hotmail.com
% $Revision: 1.2 $ $Date: 2010-2-8 $
lx=[];ux=[];ly=[];uy=[]; % 误差棒上下限
xl=[];xr=[];yl=[];yr=[]; % 端点短线左右限
if ~isstr(sty)
if nargin == 3
errorbar(sty,x,y)
return
elseif nargin == 4
errorbar(sty,x,y,xbar)
return
elseif nargin > 4
error('Please assign adopted coordinate system with symbol parameters.')
end
elseif isstr(sty)
if size(x)~=size(y)
error('Coordinate array should be equal.')
end
if nargin == 4
symbol='ob';
if length(x)~=length(xbar)
error('Format of Xbar is illegal.')
end
if sty(1) == 'v'
ybar=xbar;xbar=[];
elseif sty(1) == 'h'
ybar=[];
elseif sty(1) == 'd'
error('Parameters are not enough.')
else
error('Symbol parameter is illegal.')
end
elseif nargin == 5 & ~isstr(ybar)
symbol='ob';
if length(x)~=length(xbar)
error('Format of Xbar is illegal.')
elseif length(y)~=length(ybar)
error('Format of Ybar is illegal.')
end
elseif nargin == 5 & isstr(ybar)
symbol=ybar;ybar=[];
if length(x)~=length(xbar)
error('Format of Xbar is illegal.')
end
if sty(1) == 'v'
ybar=xbar;xbar=[];
elseif sty(1) == 'h'
ybar=[];
elseif sty(1) == 'd'
error('Parameters are not enough.')
else
error('Symbol parameter is illegal.')
end
elseif nargin == 6
if length(x)~=length(xbar)
error('Format of Xbar is illegal.')
elseif length(y)~=length(ybar)
error('Format of Ybar is illegal.')
end
if ~isstr(symbol)
error('Symbol should be string')
end
end
end
[ls,col,mark,msg] = colstyle(symbol); if ~isempty(msg), error(msg); end
symbol = [ls mark col]; % Use marker only on data part
esymbol = ['-' col]; % Make sure bars are solid
% 转换为列距阵
[a,b]=size(x);
if a < b
x=x';y=y';xbar=xbar';ybar=ybar';
c=a;a=b;b=c;
end
%% 处理上下限不等
[xa,xb]=size(xbar);
if xb==1
ux=xbar;lx=xbar;
elseif xb==2
lx=xbar(:,1);ux=xbar(:,2);
end
[ya,yb]=size(ybar);
if yb==1
uy=ybar;ly=ybar;
elseif yb==2
ly=ybar(:,1);uy=ybar(:,2);
end
%% 描点
dx=(max(x(:))-min(x(:)))/100;
dy=(max(y(:))-min(y(:)))/100;
logn=10;
if length(sty) == 1
xl = x-dx; xr = x+dx; yl = y-dy; yr = y+dy; % 定义端点短线长度
plot(x,y,symbol);hold on
elseif length(sty) == 5 & sty(2:5) == 'logx'
dx=(log(max(x(:)))-log(min(x(:))))/100;
xl = x/logn^dx;xr = x*logn^dx;yl = y-dy; yr = y+dy;
semilogx(x,y,symbol);hold on
elseif length(sty) == 5 & sty(2:5) == 'logy'
dy=(log(max(y(:)))-log(min(y(:))))/100;
yl = y/logn^dy;yr = y*logn^dy;xl = x-dx; xr = x+dx;
semilogy(x,y,symbol);hold on
elseif length(sty) == 5 & sty(2:5) == 'logd'
dx=(log(max(x(:)))-log(min(x(:))))/100;
dy=(log(max(y(:)))-log(min(y(:))))/100;
xl = x/logn^dx;xr = x*logn^dx; yl = y/logn^dy;yr = y*logn^dy;
loglog(x,y,symbol);hold on
end
%% 纵向
if sty(1) == 'v' | sty(1) == 'd'
vx = zeros(a*9,b);
vx(1:9:end,:) = x;
vx(2:9:end,:) = x;
vx(3:9:end,:) = NaN;
vx(4:9:end,:) = xl;
vx(5:9:end,:) = xr;
vx(6:9:end,:) = NaN;
vx(7:9:end,:) = xl;
vx(8:9:end,:) = xr;
vx(9:9:end,:) = NaN;
vy = zeros(a*9,b);
vy(1:9:end,:) = y-ly;
vy(2:9:end,:) = y+uy;
vy(3:9:end,:) = NaN;
vy(4:9:end,:) = y-ly;
vy(5:9:end,:) = y-ly;
vy(6:9:end,:) = NaN;
vy(7:9:end,:) = y+uy;
vy(8:9:end,:) = y+uy;
vy(9:9:end,:) = NaN;
plot(vx,vy,esymbol,'markersize',20)
end
%% 横向
if sty(1) == 'h' | sty(1) == 'd'
hx = zeros(a*9,b);
hx(1:9:end,:) = x-lx;
hx(2:9:end,:) = x+ux;
hx(3:9:end,:) = NaN;
hx(4:9:end,:) = x-lx;
hx(5:9:end,:) = x-lx;
hx(6:9:end,:) = NaN;
hx(7:9:end,:) = x+ux;
hx(8:9:end,:) = x+ux;
hx(9:9:end,:) = NaN;
hy = zeros(a*9,b);
hy(1:9:end,:) = y;
hy(2:9:end,:) = y;
hy(3:9:end,:) = NaN;
hy(4:9:end,:) = yl;
hy(5:9:end,:) = yr;
hy(6:9:end,:) = NaN;
hy(7:9:end,:) = yl;
hy(8:9:end,:) = yr;
hy(9:9:end,:) = NaN;
plot(hx,hy,esymbol,'markersize',20)
end
6. 一种matlab编程配置写法
配置文件 Initial.db
0%%%%%%Configure
0.01
0.99
0.01
0.99
0%%%%%%getLine
100
15
0
30
90
50
0%%%%%HSV
0
25
170
255
30
170
30
170
0%%%%pile process cut
100 %[100~200]
0.8 %[0~1]
0.73 %[0~1]
0.47 %[0~0.5]
读取部分的核心部分，最终返回一个x_coordinate.
function [x_coordinate] = readConfTest(filename)
RowNumber=getRowFromFile(filename);
f = fopen(filename) ;
tline = cell(1, RowNumber) ;
for i = 1 : RowNumber
tline{i} = fgetl(f);
y = sscanf( tline{i} , '%f') ;
x_coordinate(i)=y;
end
end
function row=getRowFromFile(filename)
fid=fopen(filename,'rt'); % t是告诉fread是这里文本文件
row=1;
while ~feof(fid)
% 一次性读取10000字符，计算其中的回车个数，其中10是回车的ASCII编码
% '*char'表示每次读取一个字符，*表示输出也是字符
% 放心fread现在已经可以自动识别中文了，万一还是识别不了，
% 请在fopen中指定文件编码格式，比如gbk
row=row+sum(fread(fid,10000,'*char')==char(10));
% 下面还有一个类似的方法，但是效率低很多，大概是上面的一半
% 'char'表示每次读取一个字符，但是默认输出double，
% 也就是说读取char然后转换double中间有转换能快吗？
% row=row+sum(fread(fid,10000,'char')==10);
end
fclose(fid);
%row=row+1;
end
7. Cell and array
a. 调用cell数据的方式是{} 区分于array（使用[]创建array）的()调用数组数据。
令狐冲
Engineer of offshore wind turbine technique research
My research interests include distributed energy, wind turbine power generation technique , Computational fluid dynamic and programmable matter.