Tutorial by Examples

One can describe a line in the plane as y = a*x + b so that the line is essentially controlled by two parameters a, b. For a given line, the choice of these parameters is unique. But vertical lines cannot be described like this.

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 uniq...

Given a pair of points A and B in a vector space of arbitrary dimension, one can describe the line between them as X = A + t*(B - A) = (1 - t)*A + t*B so in 2d this would be x = Ax + t*(Bx - Ax) = (1 - t)*Ax + t*Bx y = Ay + t*(By - Ay) = (1 - t)*Ay + t*By As t assumes any real value, this w...

A line in the plane can be described as a*x + b*y + c = 0 This uses a three-element parameter vector [a, b, c] to describe the line. Sometimes the constant term c is moved to the right hand side of the equation instead. The representation is not unique, since the length of that vector is arbitra...