基于MATLAB实现的单摆仿真+使用说明文档.rar

% ARROWH Draws a solid 2D arrow head in current plot. % % ARROWH(X,Y,COLOR,SIZE,LOCATION) draws a solid arrow head into % the current plot to indicate a direction. X and Y must contain % a pair of x and y coordinates ([x1 x2],[y1 y2]) of two points: % % The first point is only used to tell (in conjunction with the % second one) the direction and orientation of the arrow -- it % will point from the first towards the second. % % The head of the arrow will be located in the second point. An % example of use is plot([0 2],[0 4]); ARROWH([0 1],[0 2],'b') % % You may also give two vectors of same length > 2. The routine % will then choose two consecutive points from "about" the middle % of each vectors. Useful if you don't want to worry each time % about where to put the arrows on a trajectory. If x1 and x2 % are the vectors x1(t) and x2(t), simply put ARROWH(x1,x2,'r') % to have the right direction indicated in your x2 = f(x1) phase % plane. % % (x2,y2) % --o % \ | % \| % % % o % (x1,y1) % % Please note that the following optional arguments need -- if % you want to use them -- to be given in that exact order. You % may pass on empty vectors "[]" to skip arguments you don't want % to set (if you want to access "later" arguments...). % % The COLOR argument is quite the same as for plots, i.e. either % a string like 'r' or an RGB value vector like [1 0 0]. If you % only want the outlines of the head (in other words a non-solid % arrow head), prefix the color string by 'e' or the color vector % by 0, e.g. to get only a red outline use 'er' or [0 1 0 0]. % % The SIZE argument allows you to tune the size of the arrows. If % SIZE is a scalar, it scales the arrow proportionally. SIZE can % also be a two element vector, where the first element is the % overall scale (in percent), the second one controls the width % of the arrow head (again, in percent). % % The LOCAITON argument can be used to tweak the position of the % arrow head. If a time series of x and y coordinates are given, % you can use this argument to place the arrow head for instance % at 20% along the line. It can be a vector, if you want to have % more than one arrow head drawn. % % Both SIZE and LOCATION arguments must also be given in percent, % where 100 means standard size, 50 means half size, respectively % 100 means end of the vector, 0 beginning of it. Note that those % "locations" correspond to the cardinal position "inside" the % vector, in other words the "index-wise" position. % % This little tool is mainely intended to be used for indicating % "directions" on trajectories -- just give two consecutive times % and the corresponding values of a flux and the proper direction % of the trajectory will be shown on the plot. You may also pass % on two solution vectors, as described above. % % Note, that the arrow heads only look good in the original axis % settings (as in when the routine was actually started). If you % zoom in afterwards, the triangle will get distorted. % % HANDLES = ARROWH(...) will give you a vector with the handles % to the patches created by this function (if you want to modify % them later on, for instance). % % Examples of use: % x1 = [0:.2:2]; x2 = [0:.2:2]; plot(x1,x2); hold on; % arrowh(x1,x2,'r',[],20); % passing entire vectors % arrowh([0 1],[0 1],'eb',[300,75]); % passing 2 points % arrowh([0 1],[0 1],'eb',[300,75],25); % head closer to (x1,y1) % Author: Florian Knorn % Email: florian@knorn.org % Version: 1.14 % Filedate: Jun 18th, 2008 % % History: 1.14 - LOCATION now also works with lines % 1.13 - Allow for non-solid arrow heads % 1.12 - Return handle(s) of created patches % 1.11 - Possibility to change width % 1.10 - Buxfix % 1.09 - Possibility to chose *several* locations % 1.08 - Possibility to chose location % 1.07 - Choice of color % 1.06 - Bug fixes % 1.00 - Release % % ToDos: - Keep proportions when zooming or resizing; has to % be done with callback functions, I guess. % % Bugs: None discovered yet, those discovered were fixed % % Thanks: Thanks also to Oskar Vivero for using my humble % little program in his great MIMO-Toolbox. % % If you have suggestions for this program, if it doesn't work % for your "situation" or if you change something in it -- please % send me an email! This is my very first "public" program and % I'd like to improve it where I can -- your help is kindely % appreciated! Thank you! function handle = arrowh(x,y,clr,ArSize,Where) %-- errors if nargin < 2 error('Please give enough coordinates !'); end if (length(x) < 2) || (length(y) < 2), error('X and Y vectors must each have "length" >= 2 !'); end if (x(1) == x(2)) && (y(1) == y(2)), error('Points superimposed - cannot determine direction !'); end if nargin <= 2 clr = 'b'; end if nargin <= 3 ArSize = [100,100]; end handle = []; %-- check if variables left empty, deal width ArSize and Color if isempty(clr) clr = 'b'; nonsolid = false; elseif ischar(clr) if strncmp('e',clr,1) % for non-solid arrow heads nonsolid = true; clr = clr(2); else nonsolid = false; end elseif isvector(clr) if length(clr) == 4 && clr(1) == 0 % for non-solid arrow heads nonsolid = true; clr = clr(2:end); else nonsolid = false; end else error('COLOR argument of wrong type (must be either char or vector)'); end if nargin <= 4 if (length(x) == length(y)) && (length(x) == 2) Where = 100; else Where = 50; end end if isempty(ArSize) ArSize = [100,100]; end if length(ArSize) == 2 ArWidth = 0.75*ArSize(2)/100; % .75 to make arrows it a bit slimmer else ArWidth = 0.75; end ArSize = ArSize(1); %-- determine and remember the hold status, toggle if necessary if ishold, WasHold = 1; else WasHold = 0; hold on; end %-- start for-loop in case several arrows are wanted for Loop = 1:length(Where) %-- if vectors "longer" then 2 are given we're dealing with time series if (length(x) == length(y)) && (length(x) > 2), j = floor(length(x)*Where(Loop)/100); %-- determine that location if j >= length(x), j = length(x) - 1; end if j == 0, j = 1; end x1 = x(j); x2 = x(j+1); y1 = y(j); y2 = y(j+1); else %-- just two points given - take those x1 = x(1); x2 = (1-Where/100)*x(1)+Where/100*x(2); y1 = y(1); y2 = (1-Where/100)*y(1)+Where/100*y(2); end %-- get axe ranges and their norm OriginalAxis = axis; Xextend = abs(OriginalAxis(2)-OriginalAxis(1)); Yextend = abs(OriginalAxis(4)-OriginalAxis(3)); %-- determine angle for the rotation of the triangle if x2 == x1, %-- line vertical, no need to calculate slope if y2 > y1, p = pi/2; else p= -pi/2; end else %-- line not vertical, go ahead and calculate slope %-- using normed differences (looks better like that) m = ( (y2 - y1)/Yextend ) / ( (x2 - x1)/Xextend ); if x2 > x1, %-- now calculate the resulting angle p = atan(m); else p = atan(m) + pi; end end %-- the arrow is made of a transformed "template triangle". %-- it will be created, rotated, moved, resized and shifted. %-- the template triangle (it points "east", centered in (0,0)): xt = [1 -sin(pi/6) -sin(pi/6)]; yt = ArWidth*[0 cos(pi/6) -cos(pi/6)]; %-- rotate it by the angle determined above: xd = []; yd = []; for i=1:3 xd(i) = cos(p)*xt(i) - sin(p)*yt(i); yd(i) = sin(p)*xt(i) + cos(p)*yt(i); end %-- move the triangle so that its "head" lays in (0,0): xd = xd - cos(p); yd = yd - sin(p); %-- stretch/deform the triangle to look good on the current axes: xd = xd*Xextend*ArSize/10000; yd = yd*Yextend*ArSize/10000; %-- move the triangle to the location where it's needed xd = xd + x2; yd = yd + y2; %-- draw the actual triangle handle(Loop) = p