🚀 go-pugleaf

In article <9311090618.AA27135@relay1.UU.NET> nicnet!GISD!pkv@UUNET.UU.NET
(Prabhat K Vaish) writes:
>1. Why do we need 4 or more points to correctly define the
transformation.

Theoretically, you don't. Three pts are sufficient to solve a first order
transformation eqn. Might be a requirement of your software....

>2. How does accuraccy of tranformation improves with more no of points,
when
>    only 3 points can be used to define affine transformations.

The degree of the transformation, N, is limited by the number of
calibration points (a set of known (u,v) coordinates and their
corresponding (x,y) values). Three calibration points are needed for a
first degree transformation; at least six points are needed for second
degree equations. Bear in mind, however, that higher order eqns. are prone
to develop  undulations in their surface and become unstable.

An example:
                                T -1([uc, vc]k, [xc, yc]k, x,y) -> u,v                  (1)
                 N

The bracketed pairs represent arrays of k calibration points where

                                        k    (N+1)(N+2)/2                                       (2)

This approach requires additional calibration points, ideally balanced in
both the x and y directions, so that the requirement of Equation (2) is
met.

Useful References

Evenden, G. I., 1990. Cartographic Projection Procedures for the Unix
Environment - A User's Manual. Woods Hole, Massachusetts: U.S. Geological
Survey Open-File Report 90-284, 63p.

Evenden, G. I., 1991. Notes on a Method to Transform Digitized Coordinates
to Geographic Coordinates. Woods Hole, Massachusetts:, U.S. Geological
Survey Open-File Report 91-17, 5p.


Rob Thieler                                | rthieler@rogue.geo.duke.edu
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