To determine if the transformation T involves a reflection, consider the initial points |
p1 = (x1, y1), p2 = (x2, y2), and p3 = (x3, y3), |
and their images |
Viewing these as points in the xy-plane in 3-dimensional space, we form the cross-products |
(p2 - p1) x
(p3 - p1) =
0i - 0j + |
(q2 - q1) x
(q3 - q1) =
0i - 0j + |
If both vectors point in the same direction, the orientation of the triple of image points is the same as that of the triple of initial points, so T does not involve a reflection. |
If the vectors point in opposite directions, T does inolve a reflection. |
Return to Finding IFS Rules from Images of Points.