close all;clear all;

%% 椭球体、椭圆锥体、单叶双曲面、双叶双曲面

[X,Y] = meshgrid(-5:0.1:5,-5:0.1:5);

figure()

Z = 2*sqrt(25 - X.^2 - Y.^2).*(X.^2 + Y.^2<=25);

waterfall(X,Y,Z);

hold on;

Z = 2*-sqrt(25 - X.^2 - Y.^2).*(X.^2 + Y.^2<=25);

waterfall(X,Y,Z)

hold off;

hidden off;

xlabel('x');

ylabel('y');

zlabel('z');

title('椭球体：x^2+y^2+z^2/2^2=25');

figure()

Z = sqrt(X.^2 + Y.^2).*(X.^2 + Y.^2<=25) + 5*(X.^2 + Y.^2>25);

Z2 = -sqrt(X.^2 + Y.^2).*(X.^2 + Y.^2<=25) -5*(X.^2 + Y.^2>25);

waterfall(X,Y,Z);

hold on;

waterfall(X,Y,Z2);

hold off;

colormap('winter');

hidden off;

xlabel('x');

ylabel('y');

zlabel('z');

title('椭圆锥体：z^2=x^2+y^2,z<=25');

figure()

Z = sqrt(X.^2 + Y.^2-4).*(X.^2 + Y.^2>=4).*(X.^2 + Y.^2<=16) + 4*(X.^2 + Y.^2>16);

waterfall(X,Y,Z);

hold on;

Z = -sqrt(X.^2 + Y.^2-4).*(X.^2 + Y.^2>=4).*(X.^2 + Y.^2<=16) - 4*(X.^2 + Y.^2>16);

waterfall(X,Y,Z);

hold off;

colormap('winter');

hidden off;

xlabel('x');

ylabel('y');

zlabel('z');

title('单叶双曲面：z^2=x^2+y^2-4,-4<=z<=4');

figure()

Z = sqrt(X.^2 + Y.^2+4).*(X.^2 + Y.^2<=21) + 5*(X.^2 + Y.^2>21);

waterfall(X,Y,Z);

hold on;

Z = -sqrt(X.^2 + Y.^2+4).*(X.^2 + Y.^2<=21) - 5*(X.^2 + Y.^2>21);

waterfall(X,Y,Z);

hold off;

colormap('winter');

hidden off;

xlabel('x');

ylabel('y');

zlabel('z');

title('单叶双曲面：z^2=x^2+y^2+4,x^2+y^2<=21');

%% 椭圆锥面、双曲柱面、椭圆抛物面、双曲抛物面、抛物柱面

figure()

X = -5:0.1:5;

Y = sqrt(25-X.^2);

Y = Y';

Y2 = -sqrt(25-X.^2);

Y2 = Y2';

Z = 1.*((X.^2+Y.^2)<=25);

Z2 = -1.*((X.^2+Y.^2)<=25);

waterfall(X,Y,Z);

hold on;

waterfall(X,Y2,Z);

waterfall(X,Y,Z2);

waterfall(X,Y2,Z2);

hold off;

colormap('winter');

hidden off;

xlabel('x');

ylabel('y');

zlabel('z');

title('椭圆柱面：x^2/5^2+y^2/5^2=1,-1=

figure()

X = -5:0.1:5;

Y = sqrt(X.^2-4).*(X.^2>=4);

Y = Y';

Y2 = -sqrt(X.^2-4).*(X.^2>=4);

Y2 = Y2';

Z = 1.*((X.^2-Y.^2)>=4);

Z2 = -1.*((X.^2-Y.^2)>=4);

waterfall(X,Y,Z);

hold on;

waterfall(X,Y2,Z);

waterfall(X,Y,Z2);

waterfall(X,Y2,Z2);

hold off;

colormap('winter');

hidden off;

xlabel('x');

ylabel('y');

zlabel('z');

title('双曲柱面：x^2/2^2-y^2/2^2=1,-1=

figure()

[X,Y] = meshgrid(-5:0.1:5,-5:0.1:5);

Z = (X.^2 + Y.^2).*(X.^2 + Y.^2<=25) + 25.*(X.^2 + Y.^2>25);

waterfall(X,Y,Z);

hidden off;

xlabel('x');

ylabel('y');

zlabel('z');

title('椭圆抛物面：x^2/5^2+y^2/5^2=z');

figure()

[X,Y] = meshgrid(-5:0.1:5,-5:0.1:5);

Z = (X.^2 - Y.^2 - 1).*(X.^2 - Y.^2>=1);

waterfall(X,Y,Z);

hold on;

waterfall(X,Y,-Z);

hidden off;

xlabel('x');

ylabel('y');

zlabel('z');

title('椭圆双曲面：z=x^2-y^2-1');椭球体

椭圆锥体

单叶双曲面

双叶双曲面

椭圆柱面

双曲柱面

椭圆抛物面

椭圆双曲面