HELP FIRST_ORDER_FLOW                               David Young
                                                    April 1994

LIB * FIRST_ORDER_FLOW provides one procedure that just returns the flow
vector for a given set of first-order flow parameters and a position in
the image. See CSRP 313 for further details.

first_order_flow(x, y, xc, yc, D, R, S, Theta) -> (vx, vy)
        x and y are the coordinates of the point in the image at which
        the flow is to be calculated.

        xc and yc are the coordinates of the fixed point (the point
        where the flow is zero).

        D, R and S give the amounts of dilation, rotation and shear
        shear. Theta gives the direction of shear expansion (one of the
        principal axes of shear) relative to the x-axis. To avoid
        repeated calls to sin and cos, Theta can be a structure such as
        list, pair or vector containing the cosine and sine of the
        angle, with the cosine first.

        The results vx and vy are the components of the optic flow
        vector at the point specified.

The equation used is:

       -  -       -     - -          - -      - -      -
       |vx|       |c  -s| |D+S    -R | | c   s| |x - xc|
       |  |   =   |     | |          | |      | |      |
       |vy|       |s   c| | R     D-S| |-s   c| |y - yc|
       -  -       -     - -          - -      - -      -

where

            c = cos(Theta)
            s = sin(Theta)

See also * WARP_2D.


--- $popvision/help/first_order_flow
--- Copyright University of Sussex 1994. All rights reserved.
