See Section 13.6.7 for points of intersection of objects in the plane.
The inter command finds the intersection of two geometric objects in ℝ3.
Examples.
| LA:=inter(plane(point(0,1,1),point(1,0,1),point(1,1,0)),line(point(0,0,0),point(1,1,1))):; |
| coordinates(LA) |
| ⎡ ⎢ ⎢ ⎣ | ⎡ ⎢ ⎢ ⎣ |
| , |
| , |
| ⎤ ⎥ ⎥ ⎦ | ⎤ ⎥ ⎥ ⎦ |
| LB:=inter(sphere(point(0,0,0),1),line(point(0,0,0),point(1,1,1))):; |
| coordinates(LB) |
| ⎡ ⎢ ⎢ ⎣ | ⎡ ⎢ ⎢ ⎣ |
| , |
| , |
| ⎤ ⎥ ⎥ ⎦ | , | ⎡ ⎢ ⎢ ⎣ | − |
| ,− |
| ,− |
| ⎤ ⎥ ⎥ ⎦ | ⎤ ⎥ ⎥ ⎦ |
| ⎡ ⎢ ⎢ ⎣ |
| , |
| , |
| ⎤ ⎥ ⎥ ⎦ |
| LB1:=inter(sphere(point(0,0,0),1),line(point(0,0,0),point(1,1,1)),point(1/2,1/2,1/2)) |
| coordinates(LB1) |
| ⎡ ⎢ ⎢ ⎣ |
| , |
| , |
| ⎤ ⎥ ⎥ ⎦ |