I am doing visual SLAM and learning about Bundle Adjustment. So I started reading about bundles and pencils in geometry and I understood the main concept:
In geometry, a pencil is a family of geometric objects with a common property, for example the set of lines that pass through a given point in a plane, or the set of circles that pass through two given points in a plane. The common characteristic is that the pencil is completely determined by any two of its members.
But the following confused me:
Analogously, a set of geometric objects that are determined by any three of its members is called a bundle. Thus, the set of all lines through a point in three-space is a bundle of lines... source
Two intersecting lines in 3D-space specify a point (x,y,z) which we can then use to find all other lines that go through that point. So why isn't "the set of all lines through a point in three-space" a pencil instead of a bundle? In other words why is it that at least 3 lines going through the point are needed to specify all other lines going through the same point? shouldn't two be enough?