Trivial cases Sphere–cylinder intersection

1 trivial cases

1.1 sphere lies entirely within cylinder
1.2 sphere touches cylinder in 1 point
1.3 sphere centered on cylinder axis

trivial cases
sphere lies entirely within cylinder

if



a
+
r
<
r


{\displaystyle a+r<r}

, sphere lies entirely in interior of cylinder. intersection empty set.

sphere touches cylinder in 1 point

if sphere smaller cylinder (



r
<
r


{\displaystyle r<r}

) ,



a
+
r
=
r


{\displaystyle a+r=r}

, sphere lies in interior of cylinder except 1 point. intersection single point



(
r
,
0
,
0
)


{\displaystyle (r,0,0)}

.

sphere centered on cylinder axis

if center of sphere lies on axis of cylinder,



a
=
0


{\displaystyle a=0}

. in case, intersection consists of 2 circles of radius



r


{\displaystyle r}

. these circles lie in planes

z
=
±



r

2


−

r

2




;


{\displaystyle z=\pm {\sqrt {r^{2}-r^{2}}};}

if



r
=
r


{\displaystyle r=r}

, intersection single circle in plane



z
=
0


{\displaystyle z=0}

.