Calc 3 Lab - 2/26/15

*************************************************
DUAL HELIX
*************************************************
syms t;
t=linspace(0,4*pi,101);

x = cos(t);
y = sin(t);
z = t;
plot3(x,y,z,'r','LineWidth',2);
view([1 1 1])
xlabel('x'); ylabel('y'); zlabel('z');
hold on;

x = 2*cos(t);
y = 2*sin(t);
z = t;
plot3(x,y,z,'b','LineWidth',5);
view([1 1 1]);
grid on;


*************************************************
Rainbow Helixes
*************************************************


syms t;
t=linspace(0,4*pi,2);

x = cos(t);
y = sin(t);
z = t;
clf;
plot3(x,y,z,'r','LineWidth',2);
view([1 1 1])
xlabel('x'); ylabel('y'); zlabel('z');
grid on;
hold on;

x = 1.2*cos(t);
y = 1.2*sin(t);
z = t;
plot3(x,y,z,'green','LineWidth',3);
hold on;
view([1 1 1]);
grid on;

x = 1.3*cos(t);
y = 1.3*sin(t);
z = t;
plot3(x,y,z,'yellow','LineWidth',3);
hold on;
view([1 1 1]);
grid on;

x = 1.4*cos(t);
y = 1.4*sin(t);
z = t;
plot3(x,y,z,'c','LineWidth',4);
hold on;
view([1 1 1]);
grid on;

x = 1.6*cos(t);
y = 1.6*sin(t);
z = t;
plot3(x,y,z,'m','LineWidth',4);
hold on;
view([1 1 1]);
grid on;

x = 1.8*cos(t);
y = 1.8*sin(t);
z = t;
plot3(x,y,z,'black','LineWidth',4);
hold on;
view([1 1 1]);
grid on;

x = 2*cos(t);
y = 2*sin(t);
z = t;
plot3(x,y,z,'b','LineWidth',6);
hold on;
view([1 1 1]);
grid on;


*************************************************
Upside Down Parachute
*************************************************
syms x y;
clf;
x=linspace(-2,2,-5);
y=linspace(-2,2,-5);
[x,y]=meshgrid(x,y);
z=x.^2+y.^2;
surf(x,y,z);
view([1 1 1]);
xlabel('x');
ylabel('y');
zlabel('z');
title('First Octant View of z = x^2 + y^2');