Section 10.6 - 3D Surfaces

(We'll use a = 3, b= 2, c = 1 for the following surfaces.  Maple Commands are at the bottom of webpage)

1. Ellipsoid  x^2/a^2+y^2/b^2+z^2/c^2 = 1Plot     

2. Cone  z^2/c^2 = x^2/a^2+y^2/b^2

Plot


 

3. Elliptic Paraboloid  z/c = x^2/a^2+y^2/b^2Plot

 

4. Hyperboloid of One Sheet 1/9*x^2+1/4*y^2-z^2 = 1Plot

5. Hyperbolic Paraboloid  z/c = x^2/a^2-y^2/b^2Plot

 

6. Hyperboloid of Two Sheets -1/9*x^2-1/4*y^2+z^2 = 1 Plot

 


Maple Command - 1) Ellipsoid

with(plots)
plot3d({[3*r*cos(theta), 2*r*sin(theta), sqrt(1-r^2)], [3*r*cos(theta), 2*r*sin(theta), -sqrt(1-r^2)]}, r = 0 .. 1, theta = 0 .. 2*Pi, axes = normal, labels = [x, y, z])
plot3d({[3*r*cos(theta), 2*r*sin(theta), sqrt(1-r^2)], [3*r*cos(theta), 2*r*sin(theta), -sqrt(1-r^2)]}, r = 0 .. 1, theta = 0 .. 2*Pi, axes = normal, labels = [x, y, z])
plot3d({[3*r*cos(theta), 2*r*sin(theta), sqrt(1-r^2)], [3*r*cos(theta), 2*r*sin(theta), -sqrt(1-r^2)]}, r = 0 .. 1, theta = 0 .. 2*Pi, axes = normal, labels = [x, y, z])


Maple Command - 2) Cone

plot3d({[3*r*cos(theta), 2*r*sin(theta), r], [3*r*cos(theta), 2*r*sin(theta), -r]}, r = 0 .. 1, theta = 0 .. 2*Pi, axes = normal, labels = [x, y, z])
plot3d({[3*r*cos(theta), 2*r*sin(theta), r], [3*r*cos(theta), 2*r*sin(theta), -r]}, r = 0 .. 1, theta = 0 .. 2*Pi, axes = normal, labels = [x, y, z])
plot3d({[3*r*cos(theta), 2*r*sin(theta), r], [3*r*cos(theta), 2*r*sin(theta), -r]}, r = 0 .. 1, theta = 0 .. 2*Pi, axes = normal, labels = [x, y, z])

Maple Command - 3) Elliptic Paraboloid
plot3d([3*r*cos(theta), 2*r*sin(theta), r^2], r = 0 .. 1, theta = 0 .. 2*Pi, axes = boxed, labels = [x, y, z])
plot3d([3*r*cos(theta), 2*r*sin(theta), r^2], r = 0 .. 1, theta = 0 .. 2*Pi, axes = boxed, labels = [x, y, z])

Maple Command - 4) Hyperboloid of One Sheet
plot3d({[3*r*cos(theta), 2*r*sin(theta), -sqrt(r^2-1)], [3*r*cos(theta), 2*r*sin(theta), sqrt(r^2-1)]}, r = 1 .. 3, theta = 0 .. 2*Pi, axes = normal, labels = [x, y, z])
plot3d({[3*r*cos(theta), 2*r*sin(theta), -sqrt(r^2-1)], [3*r*cos(theta), 2*r*sin(theta), sqrt(r^2-1)]}, r = 1 .. 3, theta = 0 .. 2*Pi, axes = normal, labels = [x, y, z])
plot3d({[3*r*cos(theta), 2*r*sin(theta), -sqrt(r^2-1)], [3*r*cos(theta), 2*r*sin(theta), sqrt(r^2-1)]}, r = 1 .. 3, theta = 0 .. 2*Pi, axes = normal, labels = [x, y, z])
Maple Command - 5) Hyperbolic Paraboloid
plot3d([3*r*cos(theta), 2*r*sin(theta), r^2*cos(2*theta)], r = 0 .. 10, theta = 0 .. 2*Pi, axes = normal, labels = [x, y, z])
plot3d([3*r*cos(theta), 2*r*sin(theta), r^2*cos(2*theta)], r = 0 .. 10, theta = 0 .. 2*Pi, axes = normal, labels = [x, y, z])
Maple Command - 6) Hyperboloid of Two Sheets
plot3d({[3*r*cos(theta), 2*r*sin(theta), sqrt(r^2+1)], [3*r*cos(theta), 2*r*sin(theta), -sqrt(r^2+1)]}, r = 1 .. 3, theta = 0 .. 2*Pi, axes = normal, labels = [x, y, z])
plot3d({[3*r*cos(theta), 2*r*sin(theta), sqrt(r^2+1)], [3*r*cos(theta), 2*r*sin(theta), -sqrt(r^2+1)]}, r = 1 .. 3, theta = 0 .. 2*Pi, axes = normal, labels = [x, y, z])
plot3d({[3*r*cos(theta), 2*r*sin(theta), sqrt(r^2+1)], [3*r*cos(theta), 2*r*sin(theta), -sqrt(r^2+1)]}, r = 1 .. 3, theta = 0 .. 2*Pi, axes = normal, labels = [x, y, z])