3.5 Space Curves in Matlab

252 Chapter 3 Plotting in Matlab
these components in the view(ax,el)
in your script to obtain an identical
view. Label the axes and provide
a title that includes the name
the conic section that is the intersection
of the given plane and the
right circular cone.
7. Sketch the plane z = 1/2 over the
domain
D = {(x, y) : −1 ≤ x, y ≤ 1}.
8. Sketch the plane z = 0.4y + 0.5
over the domain
D = {(x, y) : −1 ≤ x, y ≤ 1}.
9. Sketch the plane z = y+0.25 over
the domain
D = {(x, y) : −1 ≤ x, y ≤ 1}.
10. Sketch the plane x = 0.5 over
the domain
D = {(y, z) : −1 ≤ y, z ≤ 1}.
11. Sketch the torus defined by the
parametric equations
x = (7 + 2 cos u) cos v
y = (7 + 2 cos u) sin v
z = 3 sin u.
Set the EdgeColor to a shade of gray
and add transparency by setting both
FaceAlpha and EdgeAlpha equal
to 0.5. Set the axis equal. Use Matlab’s
line command to superimpose
the torus knot having parmetric equations
x = (7 + 2 cos 5t) cos 2t
y = (7 + 2 cos 5t) sin 2t
z = 3 sin 5t
over the time domain 0 ≤ t ≤ 2π.
Use handle graphics to set the Color
of the torus knot to a color of your
choice and set the LineWidth to a
thickness of 2 points.
12. Sketch the torus defined by the
parametric equations
x = (8 + 2 cos u) cos v
y = (8 + 2 cos u) sin v
z = 3 sin u.
Set the EdgeColor to a shade of gray
and add transparency by setting both
FaceAlpha and EdgeAlpha equal
to 0.5. Set the axis equal. Use Matlab’s
line command to superimpose
the torus knot having parmetric equations
x = (8 + 2 cos 11t) cos 3t
y = (8 + 2 cos 11t) sin 3t
z = 3 sin 11t
over the time domain 0 ≤ t ≤ 2π.
Use handle graphics to set the Color
of the torus knot to a color of your
choice and set the LineWidth to a
thickness of 2 points.
13. Sketch the cone defined by the
parametric equations
x = r cos θ
y = r sin θ
z = r
where 0 ≤ r ≤ 1 and 0 ≤ θ ≤ 2π.
Set the EdgeColor to a shade of gray