厦门大学数学科学学院：《高等代数》课程教学资源（应用与实验）MATLAB Lecture 8 - Graphics-Curve

MATLAB Lecture 8 School of Mathematical Sciences Xiamen Univer http://gdjpkc.xmu.edu.cn MATLAB Lecture 8-Graphics-Curve 绘图 Ref: MATLAB- Graphics- Basic Plotting Commands Vocabulary: plot绘图 轴 display显示 annotate注释 curve/ curved line曲线 explicit显式 implicit隐式 parameter参数 polar coordinates极坐标 boldface黑体 grid网格 tite标题 figure图形 legend图例 radian 弧度 radius半径 ● Some functions plot ezplot polar plot title xlabel ylabel *figure biplot grid on *grid off ● Graphics MATLAB provides a variety of functions for displaying vector data as line plots, as well as functions for annotating and printing these graphs t The representation of curve and surface The representation of curve on plane Explicit scheme y=f(x) Implicit formula: F(x, y)=0 x=x(1) Parameter representation Polar coordinates representation: p=f(e) Tabulation, say table of trigonometric function, experimental data etc Figure, say sine curve, experimental curve etc The representation of curve in space Explicit scheme: z=f(x,y) Implicit formula: F(x, y, z)=0 x=x(u, v) Parameter representation: y=y(u, v) (,v) Data form,x={x},y={y},z={n},=1,2,…,m,j=1,2,…,n

MATLAB Lecture 8  School of Mathematical Sciences Xiamen University  http://gdjpkc.xmu.edu.cn  Lec8­1 MATLAB Lecture 8 ­ Graphics ­ Curve 绘图 Ref: MATLAB→Graphics→Basic  Plotting  Commands l Vocabulary: plot  绘图 x­axis x 轴 display  显示 annotate 注释 curve/curved line  曲线 explicit 显式 implicit 隐式 parameter 参数 polar coordinates  极坐标 boldface 黑体 grid  网格 title 标题 figure 图形 legend  图例 radian  弧度 radius  半径 l Some functions plot  ezplot  polar plot3  title xlabel  ylabel  *figure *legend *subplot  *grid on *grid off l Graphics MATLAB provides a variety of functions for displaying vector data as line plots, as well as  functions for annotating and printing these graphs.  ² The representation of curve and surface ¸ The representation of curve on plane Explicit scheme: y = f(x) Implicit formula: F(x,y) = 0  Parameter representation:  ( ) ( ) x x t  y y t Ï = Ì Ó = Polar coordinates representation:  r = f (q ) Tabulation, say table of trigonometric function, experimental data etc.  Figure, say sine curve, experimental curve etc.  ¸ The representation of curve in space Explicit scheme: z = f(x,y) Implicit formula: F(x,y,z) = 0  Parameter representation:  ( , ) ( , ) ( , ) x x u v  y y u v  z z u v Ï = Ô Ì = Ô = Ó Data form,  { }, { }, { }, 1, 2,..., , 1, 2,..., i j ij x = x y = y z = z i = m j = n .  Graphics

MATLAB Lecture 8 School of Mathematical Sciences Xiamen University http://gdjpkc.xmu.edu.cn 2 Basic plotting Commands Plotting st The process of constructing a basic graph to meet your presentation graphics requirements is outlined in the following table. The table shows seven typical steps and some example code for each If you are performing analysis only, you may want to view various graphs just to explore your data. In this case, steps I and 3 may be all you need. If you are creating presentation graphics, you may want to fine-tune your graph by positioning it on the page, setting line styles and colors, adding annotations, and making other such Improvements I Typic 1. Prepare your data X=0:0.2:12 yl= bessel(l, x) 2. Select a window and position a plot figure(1) region within the window subplot(2, 2, 1) 3.Call elementary plotting function h=plot(x,yl, x,y2, x, y3); elect line and marker characteris- set(h Line Width, 2, 'Line Style"), ('",-,".) set(h, 'Color, f'r, g; b)) 5. Set axis limits, tick marks, and grid axis([0 12-0.]) grid 6. Annotate the graph with axis xlabel(Time,") labels. legend. and text ylabel('Amplitude legend(h, First, 'Second, Third) tle( Bessel Functions) yⅸx]=min(yl1) text(x(ix),y, First Min \ rightarrow Horizontalali 7. Export graph print-depsc-tiff-r200 myplot Plot plot(X, Y): plots vector Y versus vector X. If X or Y is a matrix, then the vector is plotted versus the rows or columns of the matrix, whichever line up It can be used to plot of a curve expressed in explicit scheme or parameter 123456};y=[1-1.52-3-17] Lec8-2

MATLAB Lecture 8  School of Mathematical Sciences Xiamen University  http://gdjpkc.xmu.edu.cn  Lec8­2  ² Basic Plotting Commands  ¸ Plotting Steps  The process of constructing a basic graph to meet your presentation graphics  requirements is outlined in the following table. The table shows seven typical steps and  some example code for each.  If you are performing analysis only, you may want to view various graphs just to explore your data.  In this  case,  steps  1  and  3  may be all you need.  If you are creating  presentation graphics,  you may want  to fine­tune your graph by  positioning it on the page,  setting line styles  and colors,  adding annotations,  and making other such  improvements.  Step  Typical Code 1. Prepare your data  x = 0:0.2:12; y1 = bessel(1,x);  y2 = bessel(2,x);  y3 = bessel(3,x);  2. Select a window and position a plot  region within the window  figure(1) subplot(2,2,1) 3. Call elementary plotting function  h = plot(x,y1,x,y2,x,y3);  4. Select line and marker characteris￾tics  set(h,'LineWidth',2,{'LineStyle'},{'­­';':';'­.'})  set(h,{'Color'},{'r';'g';'b'})  5. Set axis limits, tick marks, and grid  lines  axis([0 12 ­0.5 1]) grid on  6.  Annotate the graph with axis labels, legend, and text  xlabel('Time') ylabel('Amplitude') legend(h,'First','Second','Third') title('Bessel Functions') [y,ix] = min(y1);  text(x(ix),y,'First Min \rightarrow',...  'HorizontalAlignment','right')  7. Export graph  print ­depsc ­tiff ­r200 myplot  ¸ Plot function  plot(X,Y): plots vector Y versus vector X. If X or Y is a matrix, then the vector is plotted  versus the rows or columns of the matrix, whichever line up.  It  can be used to  plot  of a curve expressed  in  explicit scheme or parameter representation.  >> x = [1 2 3 4 5 6]; y = [1 ­1.5 2 ­3 ­1 7];  >> plot(x, y);

MATLAB Lecture 8 School of Mathematical Sciences Xiamen Univer http:/gdjpkc.xmu.edu.cn File dit yiew Insert Tools Desktop Indos Help →日舀回长日国口 >a=16;149162536] ploa);% plot six lines(1,1)(2,4),(3,9);(4,16),(5,25);(6,36) Eile Edit Vie Insert Tools Desktop Window Help D日每令骨回日国回 Plot sin x over [0, 2T ]with title and grid >>t=0:pi/100:2°pi plot(t,y) > title( Plot of sinx vs x) %titled Plot of sinx vs x >xlabel('x #a'); ylabel('sinx) %adds text beside the X-axis Y-axis on the current axis grid on

MATLAB Lecture 8  School of Mathematical Sciences Xiamen University  http://gdjpkc.xmu.edu.cn  Lec8­3  >> a =[1:6; 1 4 9 16 25 36];  >> plot(a);  %plot six lines (1, 1); (2, 4); (3, 9); (4, 16); (5, 25); (6, 36) Plotsin x over [0, 2p ] with title and grid.  >> t = 0:pi/100:2*pi; >> y = sin(t);  >> plot(t,y) >> title (‘Plot of sinx vs x’) %titled ‘Plot of sinx vs x’ >> xlabel(‘x  轴’); ylabel(‘sinx’) % adds text beside the X­axis & Y­axis …  on the current axis >> grid on

MATLAB Lecture 8 School of Mathematical Sciences Xiamen University http:/gdjpkc.xmu.edu.cn File Edit yiew Insert Tool: Desktop Lindow Help →日回长日国 一 Plot of sinx vsxytitle x轴)一a5 Plot the curve with x= asin mt, y=a cos nt over t E[0, 2T while a=8, m=2 and >t= linspace( 0, 2*pi); generates a row vector of 100 linearly equally spaced points between 0 and 2 T >X=a°sin(m*t); >y=a°cos(n°t) plot(x, y, 'b-7) color blue, line style"- FIgure 1 File Edit view Insert Tools Desktop Window Help y DG副舀心回|国| 10 10 Lec8-4

MATLAB Lecture 8  School of Mathematical Sciences Xiamen University  http://gdjpkc.xmu.edu.cn  Lec8­4  Plot the curve with x = a sin mt, y = a cos nt over t Œ[0, 2p ] while a=8,  m=2  and  n=5.  >> t = linspace(0,2*pi);  % generates a row vector of 100 linearly equally spaced…  points between 0 and 2p .  >> a=8;  >> m=2;  >> n=5;  >> x = a*sin(m*t);  >> y = a*cos(n*t); >> plot (x, y, ‘b­’) % color blue, line style ‘­’

MATLAB Lecture 8 School of Mathematical Sciences Xiamen Univer http://gdjpkc.xmu.edu.cn v Polar Plots polar(THETA, RHO)makes a plot using polar coordinates of the angle THETA,in radians versus the radius rho g=0.5 >> theta= linspace(0, 2*pi, 51) %generates 51 linearly equally spaced points polar(theta, gain, r-') %color red, line style solid title('\bf Gain versus angle \theta):%boldface, Theta will be display as 8 9Figure I Eile Edit Lie Insert Tools Desktop lindow Help theta Ezplot Function--Easy to use function plotter It is usually used to plot a curve expressed in implicit formula ezplot( FUn) plots the function FUN(X) over the default domain-2 pi<X<2 pi ezplot(FUN, [A, BD plots FUN(X)over A<X<B Plot the function x2-2x+1, over x∈[-2x,2丌 eplo(x^2-2*x+1) Figure 1 Edt互 N Insert o1s正 estep Rindos He D母↓间平日口

MATLAB Lecture 8  School of Mathematical Sciences Xiamen University  http://gdjpkc.xmu.edu.cn  Lec8­5  ¸ Polar Plots polar(THETA,  RHO) makes  a plot  using polar coordinates  of the angle THETA,  in  radians, versus the radius RHO. >> g=0.5;  >> theta = linspace(0,2*pi,51);  %generates 51 linearly equally spaced points…  between 0 and 2p .  >> gain = 2*g*(1+cos(theta)); >> polar (theta, gain, ‘r­’) %color red, line style solid‘­’ >> title (‘\bf Gain versus angle \theta’);  %boldface, \theta will be display as q ¸ Ezplot Function ­­ Easy to use function plotter It is usually used to plot a curve expressed in implicit formula.  ezplot(FUN) plots the function FUN(X) over the default domain ­2*pi > ezplot('x^2 ­ 2*x + 1');

MATLAB Lecture 8 School of Mathematical Sciences Xiamen University tp: /gdjpkc. xmu. edu.cn Plot x+y=2, over x,yE[-2, 2 > ezplot(x.*4+y4-2~43,[-44]) 口佥日舀日回长日 v Plot 3 Function Plot lines and points in 3-D space plot(x,y, z), where x, y and z are three vectors of the same length, plots a line in 3-space through the points whose coordinates are the elements of x, y and z plot(X,Y, Z), where X, Y and Z are three matrices of the same size, plots several lines obtained from the columns of x.y and Z Various line types, plot symbols and colors may be obtained with plot(X,Y, Z, s) where s is a 1, 2 or 3 character string made from the characters listed under the plot command >t=0pi/50:10*pi; plot(sin(t), cos(t), t); Figure I Eile Edit yie Insert Ioos Desktop window Belp Lec8-6

MATLAB Lecture 8  School of Mathematical Sciences Xiamen University  http://gdjpkc.xmu.edu.cn  Lec8­6  Plot 4 4 4  x + y = 2 , over x, y Œ[-2, 2].  >> ezplot(‘x.*4+ y.^4­2^4’, [­4,4]) ¸ Plot3 Function  Plot lines and points in 3­D space.  plot3(x,y,z), where x, y and z are three vectors of the same length, plots a line in 3­space through the points whose coordinates are the elements of x, y and z.  plot3 (X,Y,Z), where X, Y and Z are three matrices of the same size, plots several lines  obtained from the columns of X, Y and Z.  Various line types, plot symbols and colors may be obtained with plot3 (X,Y,Z,s) where s  is a 1,  2  or 3  character string made from  the characters  listed under the  plot3  command.  >> t = 0:pi/50:10*pi; >> plot3(sin(t),cos(t),t);

MATLAB Lecture 8 School of Mathematical Sciences Xiamen Univer tp: /gdjpkc. xmu. edu.cn t=0:pi/30:9*pi;a=20;c=3 >x=at *sin(t); y=a*t *cos(t):z=c*t; > plot(x,y, z, 'mo) magenta, line type circle View Insert Icols Qeakte? Lindow ulp 的回日m曰 Compare ezplot3(20t. sin(t), 20*t *cos(t), 3 t, [0 9*pi],'mo) y2=coS(x); > plot(x, yl, b-'): %blue color solid(-) line style hold on: %after this command, all additional plots will be laid on top of the previously existing plot le > hold off, %switches plotting behavior back to the default situation, in which A new plot replaces the previous one >>x=-pi: pi/20: pi; >yl=sin(x);

MATLAB Lecture 8  School of Mathematical Sciences Xiamen University  http://gdjpkc.xmu.edu.cn  Lec8­7  >> t = 0:pi/30:9*pi; a = 20; c = 3;  >> x = a*t.*sin(t); y = a*t.*cos(t); z = c*t; >> plot3(x,y,z,’mo’) %color magenta, line type circle Compare >> ezplot3('20*t.*sin(t)','20*t.*cos(t)','3*t',[0 9*pi],’mo’) ² Plotting Multiple Plots on the Same Axes  >> x = ­pi:pi/20:pi; >> y1 = sin(x);  >> y2 = cos(x);  >> plot (x, y1, ‘b­’ );  %blue color solid(­) line style >> hold on; %after this command, all additional plots will be laid on top of the ..  previously existing plots.  >> plot (x, y2, ‘k­­’);  %black color dashed(­­) line style  >> hold off;  %switches plotting behavior back to the default situation, in which …  A new plot replaces the previous one >> legend (‘sin x’, ‘cosx’); Or >> x = ­pi:pi/20:pi; >> y1 = sin(x);

MATLAB Lecture 8 School of Mathematical Sciences Xiamen Univer tp: /gdjpkc. xmu. edu.cn >>y2=c0s(x) plot(x, yl, b-',x, y2, k--) >legend (sin x',cosx) =4线:口口 Create Multiple Figures >figure(1) %figure window 1 >x=00.05:2 > plot(x, yD) > figure(2) %create another figure window plot(x, y2); 小 Figute2 tile Eat fie Insert Tools lesktog LiadesHelp Eile Rtt ye sert Tools Desktop Yindo yule 日舀回←日■ 舀代费回长日目日回 0204 subplot(2, 1, 1) %create 2 X lsubplots in current figure, arranged in 2 rows and I column, and selects subplot I to receive all current plotting commands

MATLAB Lecture 8  School of Mathematical Sciences Xiamen University  http://gdjpkc.xmu.edu.cn  Lec8­8  >> y2 = cos(x);  >> plot (x, y1, ‘b­’, x, y2, ‘k­­’);  >> legend (‘sin x’, ‘cosx’) ² Create Multiple Figures  >> figure(1) %figure window 1  >> x = 0:0.05:2; >> y1 = exp(x) ;  >> plot (x, y1); >> figure (2) %create another figure window 2  >> y2 = exp(­x);  >> plot (x, y2);  ² Subplots  >> subplot(2,1,1) %create 2×1subplots in current figure, arranged in 2 rows …  and 1 column, and selects subplot 1 to receive all current …  plotting commands  >> x = ­pi:pi/20:pi;

MATLAB Lecture 8 School of Mathematical Sciences Xiamen Univer http://gdjpkc.xmu.edu.cn lot(x, y) tle(窗口1标题”) >> subplot(2, 1, 2) %create 2 X lsubplots in current figure, arranged in 2 rows and I column, and selects subplot 2 to receive all current plotting command >>y=cos(-X) > plot(x, y); te(窗口2标题) D回俄回长日阻■口 窗口2标题 Some examples clear; x0: pi/20: 2. " pi, y= sin(x) y1=cos(2*x): plot(x, y, --rs', linewidth, 2, markeredgecolor', k, ' markerfacecolor, 'g, 'markersize, 10) hold > plot(x,yl, -ko, markeredgecolor','k, markerfacecolor,'T, markersize, 10) >legend(sinx,"cos2x') Bile Edit View Insert Fools Desktop lindow Help Lec8-9

MATLAB Lecture 8  School of Mathematical Sciences Xiamen University  http://gdjpkc.xmu.edu.cn  Lec8­9  >> y = sin(x);  >> plot (x, y);  >> title (‘窗口 1  标题’); >> subplot(2,1,2) %create 2×1subplots in current figure, arranged in 2 rows …  and 1 column, and selects subplot 2 to receive all current …  plotting commands  >> x = ­pi:pi/20:pi; >> y = cos(­x);  >> plot (x, y);  >> title (‘窗口 2  标题’);  ² Some examples >> clear; x=0:pi/20:2.*pi; y= sin(x);  >> y1=cos(2.*x);  >> plot(x,y,'­­rs','linewidth',2,'markeredgecolor','k','markerfacecolor','g','markersize',10) >> hold on  >> plot(x,y1,'­ko','markeredgecolor','k','markerfacecolor','r','markersize',10) >> legend (‘sinx’, ‘cos2x’)

MATLAB Lecture 8 School of Mathematical Sciences Xiamen Univer http://gdjpkc.xmu.edu.cn A curve fitting example(曲线拟合) > High boy=[155,1.58,1.6,1.64,1.66,1.68,1.7,1.73,1.78,1.8,1.82,1.85 >> Weight boy={60,57,57,65,63,64,70,65,68,76,72,78 > plot( High boy, Weight boy, 'b* >> hold on >Everage boy=polyfit( High boy, Weight boy, 1) >>X1,5: 0.1: 1.9, boy line=Everage boy(1)x+ Everage boy (2) plot(x, boy line, ' g-,linewidth, 1.2); 旧囟 File Edit View Insert Tools Desktop Window Help 3 D日舀心Q回日国 Appendix Various line types, plot symbols and colors may be obtained with PLoT(X,Y, S)where S is a character string made from one element from any or all the following 3 columns point X-mark dashdot magenta star (none)no line diamond triangle(up) triangle(left) triangle(right) pentagram You can use a subset of TeX commands embedded in the string to produce special characters such as Greek letters and mathematical symbols. The following table lists these characters and the character sequences used to define them Lec8-I0

MATLAB Lecture 8  School of Mathematical Sciences Xiamen University  http://gdjpkc.xmu.edu.cn  Lec8­10  A curve fitting example (曲线拟合) >> High_boy=[1.55, 1.58, 1.6, 1.64, 1.66, 1.68, 1.7, 1.73, 1.78, 1.8, 1.82, 1.85];  >> Weight_boy=[60, 57, 57, 65, 63, 64, 70, 65, 68, 76, 72, 78];  >> plot(High_boy, Weight_boy, 'b*') >> hold on;  >> Everage_boy=polyfit(High_boy, Weight_boy, 1) >> x=1.5:0.1:1.9; boy_line=Everage_boy(1)* x + Everage_boy(2) >> plot(x, boy_line, 'g­', 'linewidth', 1.2);  ² Appendix Various line types, plot symbols and colors may be obtained with PLOT(X,Y,S) where S is a character string made from one element from any or all the following 3 columns: b  blue .  point  ­ solid  g  green  o  circle  :  dotted  r red  x  x­mark  ­.  dashdot  c cyan  +  plus  ­­ dashed  m  magenta  *  star (none) no line y  yellow  s  square k  black  d  diamond  v  triangle(down) ^ triangle (up)   triangle(right)  p  pentagram  h  hexagram  You can use a subset  of TeX  commands  embedded in  the string to produce special  characters such  as  Greek letters  and mathematical symbols.  The following table lists these characters and the character sequences used to define them