Polar Chart（极坐标图）：
- Snip20180214_15.png
例：蜗牛线（蚌线、蚶线）
theta = linspace(0, 2*pi);
r = 1 + 2*cos(theta);
subplot(2,2,1);
line1 = polar(theta, r);
set(line1, 'LineWidth', 0.8, 'Color','m');
title('r = a + b cos\theta（a < b 时）（左右型）');
r = 2 + cos(theta);
subplot(2,2,3);
line2 = polar(theta, r);
set(line2, 'LineWidth', 0.8, 'Color','m');
title('r = a + b cos\theta（a > b 时）（左右型）');
r = 1 + 2*sin(theta);
subplot(2,2,2);
line3 = polar(theta, r);
set(line3, 'LineWidth', 0.8, 'Color','m');
title('r = a + b sin\theta（a < b 时）（上下型）');
r = 2 + sin(theta);
subplot(2,2,4);
line4 = polar(theta, r);
set(line4, 'LineWidth', 0.8, 'Color','m');
title('r = a + b sin\theta（a > b 时）（上下型）');
蜗牛线.jpg
例：心脏线
theta = linspace(0, 2*pi);
r = 1 + sin(theta);
subplot(2,2,1);
line1 = polar(theta, r);
set(line1, 'LineWidth', 0.8, 'Color','r');
title('r = a + a sin\theta（上型）');
r = 1 - sin(theta);
subplot(2,2,2);
line2 = polar(theta, r);
set(line2, 'LineWidth', 0.8, 'Color','r');
title('r = a - a sin\theta（下型）');
r = 1 + cos(theta);
subplot(2,2,3);
line3 = polar(theta, r);
set(line3, 'LineWidth', 0.8, 'Color','r');
title('r = a + a cos\theta（右型）');
r = 1 - cos(theta);
subplot(2,2,4);
line4 = polar(theta, r);
set(line4, 'LineWidth', 0.8, 'Color','r');
title('r = a - a cos\theta（左型）');
心脏线.jpg
例：伯努利双纽线
theta = 0 : pi/200 : 2*pi;
r = sqrt( 1^2 * sin(2*theta) );
subplot(1,2,1);
line1 = polar(theta, r);
set(line1, 'LineWidth', 1, 'Color','m');
title('r^2 = a^2 sin2\theta');
r = sqrt( 1^2 * cos(2*theta) );
subplot(1,2,2);
line2 = polar(theta, r);
set(line2, 'LineWidth', 1, 'Color','m');
title('r^2 = a^2 cos2\theta');
伯努利双纽线.jpg
例：阿基米德螺线
theta = 0 : pi/200 : 16*pi;
r = theta;
line = polar(theta, r);
set(line, 'LineWidth', 2, 'Color','m');
t = title('r = \theta');
set(t, 'FontSize',18);
阿基米德螺线.jpg
例：对数螺线
theta = 0 : pi/500 : 50*pi;
r = 0.0000000000001 * exp(0.2*theta);
line = polar(theta, r);
set(line, 'LineWidth', 2, 'Color','b');
t = title('r = a e^{b\theta}');
set(t, 'FontSize',18);
对数螺线.jpg
例：双曲螺线
theta = 0 : 0.2 : 6*pi;
r = 3./(theta);
line = polar(theta, r);
set(line, 'LineWidth', 1, 'Color','b');
t = title('r = a/\theta');
set(t, 'FontSize',18);
双曲螺线.jpg
例：费马螺线
theta = 0 : 0.01 : 4*pi;
a = 4;
r1 = a * sqrt(theta);
r2 = -a * sqrt(theta);
line1 = polar(theta, r1, '-r');
hold on
line2 = polar(theta, r2, '-b');
set(line1, 'LineWidth', 2);
set(line2, 'LineWidth', 2);
legend('r = a \theta^{1/2}', 'r = -a \theta^{1/2}');
费马螺线.jpg
例：玫瑰线
theta = linspace(0, 2*pi);
a = 2;
r = a * sin(2*theta);
subplot(2,2,1);
line1 = polar(theta, r);
set(line1, 'LineWidth', 1, 'Color','r');
t = title('r = a sin(2\theta) 四瓣玫瑰');
set(t, 'FontSize',16);
r = a * sin(4*theta);
subplot(2,2,2);
line2 = polar(theta, r);
set(line2, 'LineWidth', 1, 'Color','r');
t = title('r = a sin(4\theta) 八瓣玫瑰');
set(t, 'FontSize',16);
r = a * sin(3*theta);
subplot(2,2,3);
line3 = polar(theta, r);
set(line3, 'LineWidth', 1, 'Color','b');
t = title('r = a sin(3\theta) 三瓣玫瑰');
set(t, 'FontSize',16);
r = a * sin(5*theta);
subplot(2,2,4);
line4 = polar(theta, r);
set(line4, 'LineWidth', 1, 'Color','b');
t = title('r = a sin(5\theta) 五瓣玫瑰');
set(t, 'FontSize',16);
玫瑰线.jpg
三度空间曲面
例：抛物线锅
x = -3.5 : 0.1 : 3.5; y = -3.5 : 0.1 : 3.5;
[X,Y] = meshgrid(x,y);
Z = X.^2 + Y.^2;
surf(X,Y,Z);
set(gca,'FontSize', 16);
zlabel('z');
xlim([-4 4]); xlabel('x');
ylim([-4 4]); ylabel('y');
colormap(jet);
legend('z = x^2 + y^2');
axis normal;
抛物线锅.jpg
例：球（Sphere）
sphere(50);
axis equal tight;
colormap(jet);
shading flat;
axis vis3d off;
light('Position',[1 3 2]);
light('Position',[-3 -1 3]);
material shiny;
view(-45,20);
t1 = title('(x-a)^2 + (y-b)^2 + (z-c)^2 = r^2 //(a,b,c)为球心');
set(t1, 'FontSize',16);
球（Sphere）.jpg
例：椭球（Ellipsoid）
xc = 0; yc = 0; zc = 0; xr = 6; yr = 3; zr = 2;
[x,y,z] = ellipsoid(xc,yc,zc,xr,yr,zr);
surf(x, y, z)
axis equal tight;
colormap(jet);
shading flat;
axis vis3d off;
light('Position',[1 3 2]);
light('Position',[-3 -1 3]);
material shiny;
set(gcf,'Color',[1 1 1]);
view(-45,20);
t1 = title('(x-xc)^2/xr^2 + (y-yc)^2/yr^2 + (z-zc)^2/zr^2 = 1');
set(t1, 'FontSize',16);
椭球（Ellipsoid）.jpg
例：椭圆双曲面（Elliptic Hyperboloid）
syms x y z;
a = 1; b = 2; c = 3;
subplot(1,3,1);
fimplicit3(x^2./a^2 + y^2./b^2 - z^2./c^2 - 1);
axis equal;
colormap(jet);
t1 = title('x^2/a^2 + y^2/b^2 - z^2/c^2 = 1');
set(t1, 'FontSize',16);
subplot(1,3,2);
fimplicit3(x^2./a^2 + y^2./b^2 - z^2./c^2);
axis equal;
colormap(jet);
t2 = title('x^2/a^2 + y^2/b^2 - z^2/c^2 = 0');
set(t2, 'FontSize',16);
subplot(1,3,3);
fimplicit3(x^2./a^2 + y^2./b^2 - z^2./c^2 + 1);
axis equal;
colormap(jet);
t3 = title('x^2/a^2 + y^2/b^2 - z^2/c^2 = -1');
set(t3, 'FontSize',16);
椭圆双曲面（Elliptic Hyperboloid）.jpg
例：椭圆抛物面（Elliptic Paraboloid）
syms x y z;
a = 1; b = 2;
fimplicit3(x^2./a^2 + y^2./b^2 - z*0.5);
axis equal;
colormap(jet);
t1 = title('z = x^2/a^2 + y^2/b^2');
set(t1, 'FontSize',16);
椭圆抛物面（Elliptic Paraboloid）.jpg
例：双曲抛物面 Hyperbolic Paraboloid (画法一：马鞍)
x = -3.5 : 0.2 : 3.5; y = -3.5 : 0.2 : 3.5;
[X,Y] = meshgrid(x,y);
a = 2; b = 2;
Z = (Y.^2)./(b^2) - (X.^2)./(a^2);
surf(X,Y,Z);
set(gca,'FontSize', 16);
zlabel('z');
xlim([-4 4]); xlabel('x');
ylim([-4 4]); ylabel('y');
colormap(jet);
t1 = title('z = y^2/b^2 - x^2/a^2');
set(t1, 'FontSize',16);
axis normal;
双曲抛物面 Hyperbolic Paraboloid（画法1）.jpg
例：双曲抛物面 Hyperbolic Paraboloid (画法二：洋芋片)
syms x y z;
a = 1; b = 2;
fimplicit3(y^2./b^2 - x^2./a^2 - z*0.5);
axis equal;
colormap(jet);
t1 = title('z = y^2/b^2 - x^2/a^2');
set(t1, 'FontSize',16);
双曲抛物面 Hyperbolic Paraboloid（画法2）.jpg
