### 27.3.3 Finding an intersection point of two objects in space

See Section 26.5.6 for single points of intersection of objects in the plane.

The single_inter or line_inter command finds an intersection point of two geometric objects.

- single_inter takes two mandatory arguments and one optional argument.
  - obj1, obj2, two geometric objects.
  - Optionally, pt, a point or list of points.
  line_inter(obj1,obj2⟨,pt⟩) returns one of the points of intersection of obj1 and obj2.

  If pt is a single point, then the command returns the point of intersection closest to pt.

  If pt is a list of points, then the command tries to return a point not in pt.

#### Examples

A:=single_inter(plane(point(0,1,1),point(1,0,1),point(1,1,0)), line(point(0,0,0),point(1,1,1))):; coordinates(A)

⎡
⎢
⎢
⎣

2
3

,

2
3

,

2
3

⎤
⎥
⎥
⎦

B:=single_inter(sphere(point(0,0,0),1),line(point(0,0,0),point(1,1,1))):; coordinates(B)

⎡
⎢
⎢
⎣

√

3

3

,

√

3

3

,

√

3

3

⎤
⎥
⎥
⎦

B1:=single_inter(sphere(point(0,0,0),1),line(point(0,0,0),point(1,1,1)),point(-1,0,0)):; coordinates(B1)

⎡
⎢
⎢
⎣

−

√

3

3

,−

√

3

3

,−

√

3

3

⎤
⎥
⎥
⎦

C:=single_inter(sphere(point(0,0,0),1),line(point(1,0,0),point(1,1,1))):; coordinates(C)

| ⎡ ⎣ | 1,0,0 | ⎤ ⎦

C1:=single_inter(sphere(point(0,0,0),1),line(point(1,0,0),point(1,1,1)),[point(1,0,0)]):; coordinates(C1)

⎡
⎢
⎢
⎣

1
3

,

2
3

,

2
3

⎤
⎥
⎥
⎦