bookshelf/Common/Geometry/Line.lean

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import Common.Geometry.Point
/-! # Common.Geometry.Line
A representation of a line in the two-dimensional Cartesian plane.
-/
namespace Geometry
/--
A `Line` is represented in vector form (not to be confused with `Vector`).
It is completely characterized by a point `P` on the line in question and a
direction vector `dir` parallel to the line. Such a line is represented by
equation
```
\vec{r} = \vec{OP} + t\vec{d},
```
where `O` denotes the origin and `t ∈ `.
-/
structure Line where
p : Point
dir : ×
end Geometry