I want to know if the cross Ratio depends upon the ordering of the points around a particular point . I am calculating the cross ratio as :
CR = A(1,2,3)*A(1,4,5)/(A(1,2,4)*A(1,3,5)
where A is the area of the triangle formed using the given numbering of the points as coordinates.
I'd denote the cross ratio you compute as $(2,4;3,5)_1$, the cross ratio of $2,4;3,5$ as seen from point $1$. It depends on the lines joining $1$ to $2,3,4,5$, so you might as well consider this a cross ratio of concurrent lines, which is dual to a cross ratio of collinear points. The order of $2,3,4,5$ does matter, see this answer for the effects of changing that order. It does however not depend on the position of the points on these lines. In particular, you can move a point $2,3,4,5$ to the other half of its line, on the other side of point $1$, and you will still obtain the same cross ratio. So depending on what exactly you mean by “ordering of the points”, this should help answering your question.
