Patent ID: 7619749

Claim:
A measuring method for measuring a free form surface having non-rotational symmetry by using a computer to align a first surface with a second surface, said first surface being a computer generated theoretical model of a free form surface or being a computer generated model of a free form surface generated from a plurality of measured points and said second surface being the measured free form surface, wherein P(x i ,y i ,z i ) is any point on the first surface and Q(x′ i ,y′ i ,z′ i ) is any point on the second surface, said first surface and said second surface being separated by a first-degree separation, a second-degree separation, and a third-degree separation, said measuring method comprising the steps of: minimizing the first-degree separation by the steps of: selecting at least one feature point from each of the first surface and the second surface; adjusting a coordinate of the second surface to minimize a distance between said at least one feature point of each of the first surface and the second surface to be below a predetermined threshold value θ; minimizing the second-degree separation by the steps of dividing the first surface into a plurality of first zones, each first zone having at least one first coordinate defining said first zone; dividing the second surface into a plurality of second zones, each second zone having at least one second coordinate defining said second zone; for the plurality of first zones, repeating the steps of: a) obtaining distances between the at least one first coordinate and each of the plurality of second zones; b) comparing the distances obtained in step a) to determine a pair of corresponding zones on the first and the second surfaces having a minimum distance obtained in step a); until all zones on the first and the second surfaces are paired; determining the distances between each pair of corresponding zones on the first and the second surfaces; obtaining a summation of the distances between each pair of corresponding zones; adjusting the coordinate of the second surface to minimize the summation of the distances between each pair of corresponding zones to be below a predetermined threshold value ε; minimizing the third-degree separation by the steps of: minimizing a transfer matrix T to be below a predetermined threshold value λ by adjusting at least one pair of parameters along a direction, one of said parameters relating to translation and the other parameter relating to rotation along the direction.