Image 2 Symbol_image(將圖片變成符號組成的圖片)

% 省略了很多MATLAB的GUI宣告(Source Code不完整)
% 在GUI裡使用了一個axes
x = imread('test.bmp');
n = 7;
z = zeros(ceil([length(x(:,1,1))/n,length(x(1,:,1))/n]));
y = ones(ceil([length(x(:,1,1))/n,length(x(1,:,1))/n])*n)*255;
y(1:size(x,1),1:size(x,2)) = rgb2gray(x);
z = z';  y = y';
u = char(z);
for i = 1:length(y(:,1))/n
      for j = 1:length(y(1,:))/n
            z(i,j) = mean(mean(y((i-1)*n+1:i*n,(j-1)*n+1:j*n)));
      end
end
mi = min(z(:));
d = (max(z(:)) - mi)/6;        %level = 6
u(find(z < mi+d)) = '@';
u(find(z >= mi+d & z < mi+2*d)) = 'm';
u(find(z >= mi+2*d & z < mi+3*d)) = 'n';
u(find(z >= mi+3*d & z < mi+4*d)) = 'v';
u(find(z >= mi+4*d & z < mi+5*d)) = '/';
u(find(z >= mi+5*d)) = '.';
set(handles.figure1,'Position',[90 50 size(z,1) size(z,2)/3]);
set(handles.axes1,'Position',[0 0 size(z,1) size(z,2)/3]);
drawnow;
for i = 1:length(u(:,1))
      for j = 1:length(u(1,:))
            text((i)/length(u(:,1)),(length(u(1,:))-j)/length(u(1,:)),u(i,j),'fontsize',4);
      end
end
axis off
im = getframe(handles.figure1); % 擷取畫面
[filename, pathname] = uiputfile({'*.bmp','BMP-files (*.bmp)';'*.jpg','JPEG (*.jpg)';'*.tif','TIF (*.tif)';'*.*','All Files (*.*)'},'Pick a file');
imwrite(uint8(im.cdata),[pathname filename]);

原圖

結果

Plot -- Inverse Trigonometric Function

%========================================
% sin^-1(x)
%========================================
close all
figure,
x=-pi:0.1:pi;
y=sin(x);
plot(x,y,'--b')
x=[-pi/2:0.1:pi/2 pi/2];
y=sin(x);
hold on
plot(x,y,'b','LineWidth',3)
hold off
axis([-3.5 3.5 -1.5 1.5])
line( [0 0], [-1.5 1.5], 'color', 'm');
line( [-3.5 3.5], [0 0], 'color', 'm');
line( [-pi/2 -pi/2], [-1.05 0.05], 'color', 'r');
line( [pi/2 pi/2], [-0.05 1.05], 'color', 'r');
gtext('\fontname{Times New Roman}\fontsize{14}{\itx}')
gtext('\fontname{Times New Roman}\fontsize{14}{\ity}')
gtext('(0,0)')
gtext('\fontname{Times New Roman}\fontsize{10}\rm-{\it\pi} /2')
gtext('\fontname{Times New Roman}\fontsize{10}\rm{\it\pi} /2')
gtext('\fontname{Times New Roman}\fontsize{10}\rm(-{\it\pi} /2,-1)')
gtext('\fontname{Times New Roman}\fontsize{10}\rm({\it\pi} /2,1)')
gtext('\fontname{Times New Roman}\fontsize{14}{\itf}\rm({\itx}) = sin\itx')

x=-pi:0.1:pi;
y=sin(x);
figure, plot(x,y,'--b')
x=[-pi/2:0.1:pi/2 pi/2];
y=sin(x);
hold on
plot(x,y,'b','LineWidth',3)
x=-1:0.1:1;
y=asin(x);
plot(x,y,'g','LineWidth',3)
x=-2:0.1:2;
y=x;
plot(x,y,'--c')
hold off
axis([-2 2 -2 2])
line( [0 0], [-2 2], 'color', 'm');
line( [-2 2], [0 0], 'color', 'm');
line( [-pi/2 -pi/2], [-1.05 0.05], 'color', 'r');
line( [-1 -1], [-pi/2-0.05 0.05], 'color', 'b');
line( [pi/2 pi/2], [-0.05 1.05], 'color', 'r');
line( [1 1], [-0.05 pi/2+0.05], 'color', 'b');
line( [-1.05 0.05], [-pi/2 -pi/2], 'color', 'b');
line( [-0.05 1.05], [pi/2 pi/2], 'color', 'b');
gtext('\fontname{Times New Roman}\fontsize{12}{\itx}')
gtext('\fontname{Times New Roman}\fontsize{12}{\ity}')
gtext('(0,0)')
gtext('\fontname{Times New Roman}\fontsize{10}\rm-{\it\pi} /2')
gtext('\fontname{Times New Roman}\fontsize{10}\rm{\it\pi} /2')
gtext('\fontname{Times New Roman}\fontsize{10}\rm(-{\it\pi} /2,-1)')
gtext('\fontname{Times New Roman}\fontsize{10}\rm({\it\pi} /2,1)')
gtext('\fontname{Times New Roman}\fontsize{12}{\itf}\rm({\itx}) = sin\itx')
gtext('\fontname{Times New Roman}\fontsize{10}\rm-{\it\pi} /2')
gtext('\fontname{Times New Roman}\fontsize{10}\rm{\it\pi} /2')
gtext('\fontname{Times New Roman}\fontsize{10}\rm(-1,-{\it\pi} /2)')
gtext('\fontname{Times New Roman}\fontsize{10}\rm(1,{\it\pi} /2)')
gtext('-1')
gtext('1')
gtext('\fontname{Times New Roman}\fontsize{12}{\itf}\rm({\itx}) = sin^{-1}\itx')

%========================================
% cos^-1(x)
%========================================
close all
figure,
x=-pi/2:0.1:3*pi/2;
y=cos(x);
plot(x,y,'--b')
x=[0:0.1:pi pi];
y=cos(x);
hold on
plot(x,y,'b','LineWidth',3)
hold off
axis([-0.5 3.5 -1.5 1.5])
line( [0 0], [-1.5 1.5], 'color', 'm');
line( [-3.5 3.5], [0 0], 'color', 'm');
line( [-0.5 0.05], [1 1], 'color', 'r');
line( [pi pi], [-1.05 0.05], 'color', 'r');
line( [pi/2 pi/2], [-0.05 0.05], 'color', 'r');
gtext('\fontname{Times New Roman}\fontsize{12}{\itx}')
gtext('\fontname{Times New Roman}\fontsize{12}{\ity}')
gtext('(0,0)')
gtext('\fontname{Times New Roman}\fontsize{10}\rm{\it\pi} /2')
gtext('\fontname{Times New Roman}\fontsize{10}\rm{\it\pi}')
gtext('(0,1)')
gtext('\fontname{Times New Roman}\fontsize{10}\rm({\it\pi},-1)')
gtext('\fontname{Times New Roman}\fontsize{12}{\itf}\rm({\itx}) = cos\itx')
x=-2:0.1:3*pi/2;
y=cos(x);
figure, plot(x,y,'--b')
x=[0:0.1:pi pi];
y=cos(x);
hold on
plot(x,y,'b','LineWidth',3)
x=-1:0.1:1;
y=acos(x);
plot(x,y,'g','LineWidth',3)
x=-2:0.1:4;
y=x;
plot(x,y,'--c')
hold off
axis([-2 4 -2 4])
line( [0 0], [-2 4], 'color', 'm');
line( [-2 4], [0 0], 'color', 'm');
line( [-2 0.1], [1 1], 'color', 'r');
line( [pi pi], [-1.1 0.1], 'color', 'r');
line( [pi/2 pi/2], [-0.1 0.1], 'color', 'r');
line( [-0.1 0.1], [pi/2 pi/2], 'color', 'r');
line( [-2 -0.9], [pi pi], 'color', 'b');
line( [-1 -1], [-0.1 pi+0.1], 'color', 'b');
line( [1 1], [-0.1 0.1], 'color', 'b');
gtext('\fontname{Times New Roman}\fontsize{12}{\itx}')
gtext('\fontname{Times New Roman}\fontsize{12}{\ity}')
gtext('(0,0)')
gtext('-1')
gtext('1')
gtext('\fontname{Times New Roman}\fontsize{10}\rm({\it\pi} /2,0)')
gtext('\fontname{Times New Roman}\fontsize{10}\rm{\it\pi}')
gtext('\fontname{Times New Roman}\fontsize{10}\rm({\it\pi},-1)')
gtext('\fontname{Times New Roman}\fontsize{10}\rm(-1,{\it\pi})')
gtext('\fontname{Times New Roman}\fontsize{10}\rm(0,{\it\pi} /2)')
gtext('\fontname{Times New Roman}\fontsize{12}{\itf}\rm({\itx}) = cos\itx')
gtext('\fontname{Times New Roman}\fontsize{12}{\itf}\rm({\itx}) = cos^{-1}\itx')

%========================================
% tan^-1(x)
%========================================
close all
figure,
x=[-pi/2+0.05:0.1:pi/2];
y=tan(x);
plot(x,y,'b','LineWidth',3)
axis([-10 10 -10 10])
line( [0 0], [-10 10], 'color', 'm');
line( [-10 10], [0 0], 'color', 'm');
line( [-pi/2 -pi/2], [-10 0.2], 'color', 'r');
line( [pi/2 pi/2], [-0.2 10], 'color', 'r');
gtext('\fontname{Times New Roman}\fontsize{12}{\itx}')
gtext('\fontname{Times New Roman}\fontsize{12}{\ity}')
gtext('(0,0)')
gtext('\fontname{Times New Roman}\fontsize{10}\rm-{\it\pi} /2')
gtext('\fontname{Times New Roman}\fontsize{10}\rm{\it\pi} /2')
gtext('\fontname{Times New Roman}\fontsize{12}{\itf}\rm({\itx}) = tan\itx')
x=[-pi/2+0.05:0.1:pi/2];
y=tan(x);
figure, plot(x,y,'b','LineWidth',3)
hold on
x=-10:0.1:10;
y=atan(x);
plot(x,y,'g','LineWidth',3)
x=-10:0.1:10;
y=x;
plot(x,y,'--c')
hold off
axis([-10 10 -10 10])
line( [0 0], [-10 10], 'color', 'm');
line( [-10 10], [0 0], 'color', 'm');
line( [-pi/2 -pi/2], [-10 0.2], 'color', 'r');
line( [pi/2 pi/2], [-0.2 10], 'color', 'r');
line( [-10 0.2], [-pi/2 -pi/2], 'color', 'b');
line( [-0.2 10], [pi/2 pi/2], 'color', 'b');
gtext('\fontname{Times New Roman}\fontsize{12}{\itx}')
gtext('\fontname{Times New Roman}\fontsize{12}{\ity}')
gtext('(0,0)')
gtext('\fontname{Times New Roman}\fontsize{10}\rm-{\it\pi} /2')
gtext('\fontname{Times New Roman}\fontsize{10}\rm{\it\pi} /2')
gtext('\fontname{Times New Roman}\fontsize{12}{\itf}\rm({\itx}) = tan\itx')
gtext('\fontname{Times New Roman}\fontsize{10}\rm-{\it\pi} /2')
gtext('\fontname{Times New Roman}\fontsize{10}\rm{\it\pi} /2')
gtext('\fontname{Times New Roman}\fontsize{12}{\itf}\rm({\itx}) = tan^{-1}\itx')

%========================================
% cot^-1(x)
%========================================
close all
figure,
x=[0.05:0.1:pi];
y=cot(x);
plot(x,y,'b','LineWidth',3)
axis([-10 10 -10 10])
line( [0 0], [-10 10], 'color', 'm');
line( [-10 10], [0 0], 'color', 'm');
line( [pi pi], [-10 0.2], 'color', 'r');
line( [pi/2 pi/2], [-0.2 0.2], 'color', 'r');
gtext('\fontname{Times New Roman}\fontsize{12}{\itx}')
gtext('\fontname{Times New Roman}\fontsize{12}{\ity}')
gtext('(0,0)')
gtext('\fontname{Times New Roman}\fontsize{10}\rm{\it\pi} /2')
gtext('\fontname{Times New Roman}\fontsize{10}\rm{\it\pi}')
gtext('\fontname{Times New Roman}\fontsize{12}{\itf}\rm({\itx}) = cot\itx')
x=[0.05:0.1:pi];
y=cot(x);
figure, plot(x,y,'b','LineWidth',3)
hold on
x=-10:0.1:-0.1;
y=acot(x)+pi;
x2=0:0.1:10;
y=[y acot(x2)];
plot([x x2],y,'g','LineWidth',3)
x=-10:0.1:10;
y=x;
plot(x,y,'--c')
hold off
axis([-10 10 -10 10])
line( [0 0], [-10 10], 'color', 'm');
line( [-10 10], [0 0], 'color', 'm');
line( [pi pi], [-10 0.2], 'color', 'r');
line( [-10 0.2], [pi pi], 'color', 'b');
gtext('\fontname{Times New Roman}\fontsize{12}{\itx}')
gtext('\fontname{Times New Roman}\fontsize{12}{\ity}')
gtext('(0,0)')
gtext('\fontname{Times New Roman}\fontsize{10}\rm{\it\pi}')
gtext('\fontname{Times New Roman}\fontsize{12}{\itf}\rm({\itx}) = cot\itx')
gtext('\fontname{Times New Roman}\fontsize{10}\rm{\it\pi}')
gtext('\fontname{Times New Roman}\fontsize{12}{\itf}\rm({\itx}) = cot^{-1}\itx')

%========================================
% sec^-1(x) ------nonunique
%========================================
close all
figure,
x=[-pi/2+0.05:0.1:pi/2-0.05];
y=sec(x);
plot(x,y,'--b')
hold on
x3 = x-3*pi;  y=sec(x3);  plot(x3,y,'--b')
x2 = x-2*pi;  y=sec(x2);  plot(x2,y,'--b')
x1 = x-pi;    y=sec(x1);  plot(x1,y,'--b')
x3 = x+3*pi;  y=sec(x3);  plot(x3,y,'--b')
x2 = x+2*pi;  y=sec(x2);  plot(x2,y,'--b')
x1 = x+pi;    y=sec(x1);  plot(x1,y,'--b')
x=[0:0.1:pi/2-0.05];
y=sec(x);
plot(x,y,'b','LineWidth',3)
x=[pi/2+0.05:0.1:pi pi];
y=sec(x);
plot(x,y,'b','LineWidth',3)
axis([-10 10 -10 10])
hold off
line( [0 0], [-10 10], 'color', 'm');
line( [-10 10], [0 0], 'color', 'm');
line( [5*pi/2 5*pi/2], [-10 10], 'color', 'r');
line( [3*pi/2 3*pi/2], [-10 10], 'color', 'r');
line( [pi/2 pi/2], [-10 10], 'color', 'r');
line( [-5*pi/2 -5*pi/2], [-10 10], 'color', 'r');
line( [-3*pi/2 -3*pi/2], [-10 10], 'color', 'r');
line( [-pi/2 -pi/2], [-10 10], 'color', 'r');
line( [-0.5 0.5], [1 1], 'color', 'r');
line( [-0.4 pi+0.4], [-1 -1], 'color', 'r');
line( [pi pi], [-1.4 0.4], 'color', 'r');
line( [2*pi 2*pi], [-0.4 1.4], 'color', 'r');
line( [-pi -pi], [-1.4 0.4], 'color', 'r');
gtext('\fontname{Times New Roman}\fontsize{12}{\itx}')
gtext('\fontname{Times New Roman}\fontsize{12}{\ity}')
gtext('(0,0)')
gtext('1')
gtext('-1')
gtext('\fontname{Times New Roman}\fontsize{10}\rm{\it\pi} /2')
gtext('\fontname{Times New Roman}\fontsize{10}\rm{\it\pi}')
gtext('\fontname{Times New Roman}\fontsize{10}\rm3{\it\pi} /2')
gtext('\fontname{Times New Roman}\fontsize{10}\rm2{\it\pi}')
gtext('\fontname{Times New Roman}\fontsize{10}\rm-{\it\pi} /2')
gtext('\fontname{Times New Roman}\fontsize{10}\rm-{\it\pi}')
gtext('\fontname{Times New Roman}\fontsize{12}{\itf}\rm({\itx}) = sec\itx')
figure,
x=[-pi/2+0.05:0.1:pi/2-0.05];
y=sec(x);
plot(x,y,'--b')
hold on
x3 = x-3*pi;  y=sec(x3);  plot(x3,y,'--b')
x2 = x-2*pi;  y=sec(x2);  plot(x2,y,'--b')
x1 = x-pi;    y=sec(x1);  plot(x1,y,'--b')
x3 = x+3*pi;  y=sec(x3);  plot(x3,y,'--b')
x2 = x+2*pi;  y=sec(x2);  plot(x2,y,'--b')
x1 = x+pi;    y=sec(x1);  plot(x1,y,'--b')
x=[0:0.1:pi/2-0.05];
y=sec(x);
plot(x,y,'b','LineWidth',3)
x=[pi/2+0.05:0.1:pi pi];
y=sec(x);
plot(x,y,'b','LineWidth',3)
x=[-10:0.1:-1];
y=asec(x);
plot(x,y,'g','LineWidth',3)
x=[1:0.1:10];
y=asec(x);
plot(x,y,'g','LineWidth',3)
x=-10:0.1:10;
y=x;
plot(x,y,'--c')
hold off
line( [0 0], [-10 10], 'color', 'm');
line( [-10 10], [0 0], 'color', 'm');
line( [pi/2 pi/2], [-10 10], 'color', 'r');
line( [-0.5 0.5], [1 1], 'color', 'r');
line( [-0.4 pi+0.4], [-1 -1], 'color', 'r');
line( [pi pi], [-1.4 0.4], 'color', 'r');
line( [-10 0.4], [pi pi], 'color', 'b');
line( [-1 -1], [-0.4 pi+0.4], 'color', 'b');
line( [1 1], [-0.4 0.4], 'color', 'b');
axis([-10 10 -10 10])
gtext('\fontname{Times New Roman}\fontsize{12}{\itx}')
gtext('\fontname{Times New Roman}\fontsize{12}{\ity}')
gtext('(0,0)')
gtext('1')
gtext('-1')
gtext('\fontname{Times New Roman}\fontsize{10}\rm{\it\pi} /2')
gtext('\fontname{Times New Roman}\fontsize{10}\rm{\it\pi}')
gtext('-1')
gtext('1')
gtext('\fontname{Times New Roman}\fontsize{10}\rm{\it\pi}')
gtext('\fontname{Times New Roman}\fontsize{12}{\itf}\rm({\itx}) = sec\itx')
gtext('\fontname{Times New Roman}\fontsize{12}{\itf}\rm({\itx}) = sec^{-1}\itx')

%========================================
% csc^-1(x) ------nonunique
%========================================
close all
figure,
x=[0.05:0.1:pi-0.05];
y=csc(x);
plot(x,y,'--b')
hold on
x3 = x-3*pi;  y=csc(x3);  plot(x3,y,'--b')
x2 = x-2*pi;  y=csc(x2);  plot(x2,y,'--b')
x1 = x-pi;    y=csc(x1);  plot(x1,y,'--b')
x3 = x+3*pi;  y=csc(x3);  plot(x3,y,'--b')
x2 = x+2*pi;  y=csc(x2);  plot(x2,y,'--b')
x1 = x+pi;    y=csc(x1);  plot(x1,y,'--b')
x=[0:0.1:pi/2 pi/2];
y=csc(x);
plot(x,y,'b','LineWidth',3)
x=[-pi/2:0.1:-0.05 -0.05];
y=csc(x);
plot(x,y,'b','LineWidth',3)
axis([-10 10 -10 10])
hold off
line( [0 0], [-10 10], 'color', 'm');
line( [-10 10], [0 0], 'color', 'm');
line( [5*pi/2 5*pi/2], [-10 10], 'color', 'r');
line( [3*pi/2 3*pi/2], [-10 10], 'color', 'r');
line( [pi/2 pi/2], [-10 10], 'color', 'r');
line( [-5*pi/2 -5*pi/2], [-10 10], 'color', 'r');
line( [-3*pi/2 -3*pi/2], [-10 10], 'color', 'r');
line( [-pi/2 -pi/2], [-10 10], 'color', 'r');
line( [-0.5 0.5], [1 1], 'color', 'r');
line( [-0.4 pi+0.4], [-1 -1], 'color', 'r');
line( [pi pi], [-1.4 0.4], 'color', 'r');
line( [2*pi 2*pi], [-0.4 1.4], 'color', 'r');
line( [-pi -pi], [-1.4 0.4], 'color', 'r');
gtext('\fontname{Times New Roman}\fontsize{12}{\itx}')
gtext('\fontname{Times New Roman}\fontsize{12}{\ity}')
gtext('\fontname{Times New Roman}\fontsize{12}{\itf}\rm({\itx}) = csc\itx')

繪製反函數圖形(Inverse Function)

x=-3.5:0.1:3.5;
y=x.^2-1;
plot(x,y,'--b')
x=-3:0.1:-1;
y=x.^2-1;
hold on
plot(x,y,'b','LineWidth',1.5)
axis([-3.5 3.5 -1.5 10])
line( [0 0], [-1.5 10], 'color', 'm');
line( [-3.5 3.5], [0 0], 'color', 'm');
line( [-1 -1], [-0.5 0.2], 'color', 'r');
line( [-3 -3], [-0.5 9], 'color', 'r');
gtext('(0,0)')
gtext('-3')
gtext('-1')
gtext('(-3,8)')
gtext('(0,-1)')
gtext('\fontname{Times New Roman}\fontsize{14}{\itf}\rm({\itx}) = {\itx}^2-1')

x=-4:0.1:-1;
y=x.^2-1;
%subplot(1,2,2),
figure, plot(x,y,'b','LineWidth',1.5)
hold on
x=0:0.1:10;
y=-sqrt(x+1);
plot(x,y,'g','LineWidth',1.5)
x=-4:0.1:10;
y=x;
plot(x,y,'--c')
hold off
axis([-4 10 -4 10])
line( [0 0], [-4 10], 'color', 'm');
line( [-4 10], [0 0], 'color', 'm');
line( [-1 -1], [-0.5 0.2], 'color', 'r');
line( [-3 -3], [-0.5 9], 'color', 'r');
line( [-0.5 0.2], [-1 -1], 'color', 'r');
line( [-0.5 9], [-3 -3], 'color', 'r');
gtext('(0,0)')
gtext('-3')
gtext('-1')
gtext('-1')
gtext('-3')
gtext('(-3,8)')
gtext('(-1,0)')
gtext('(0,-1)')
gtext('(8,-3)')
mystr = '$f(x) = x^2-1$';
h = text('string',mystr,'interpreter','latex',...
            'fontsize',14,'units','norm','pos',[0.11 0.7]);
mystr = '$f^{-1}(x) = -\sqrt{x+1}$';
h = text('string',mystr,'interpreter','latex',...
            'fontsize',14,'units','norm','pos',[0.63 0.16]);

繪圖之水平座標與垂直座標刻度設定

Example:

n = [-100:100];
x = cos(0.1*pi*n);
Hx = stem(n,x,'r--','filled');
set(Hx,'markersize',2);
axis([-110, 110,-2,2]);
xtick = [-100:18:100];
ytick = [-2:0.5:2];
set(gca,'XTickMode','manual','XTick',xtick);
set(gca,'YTickMode','manual','YTick',ytick);
xlabel('n','FontSize',10);
ylabel('x(n)','FontSize',10);

其中水平座標刻度設定

xtick = [刻度由此開始:刻度間隔:刻度結束]

垂直座標刻度設定亦同

ytick = [刻度由此開始:刻度間隔:刻度結束]