geometry Representing Lines Point and Direction
Example
One can describe a line in arbitrary dimensions as
X = A + t*D
where A and D are both vectors of suitably many dimensions. So in 2d this would be
x = Ax + t*Dx
y = Ay + t*Dy
Now as t assumes any real value, this equation will produce all points along the line. The representation is not unique, though: any point along the line may be used as starting point A, and any multiple of the vector D represents the same direction.
