Determine the complement of a double precision window with respect to a specified interval.
VARIABLE I/O DESCRIPTION -------- --- -------------------------------------------------- left, right I Left, right endpoints of complement interval. window I Input window. result O Complement of window with respect to [left,right].
left, right are the left and right endpoints of the complement interval. window is the window to be complemented. window must be declared as a double precision SpiceCell.
result is the output window, containing the complement of window with respect to the interval from left to right. If the output window is not large enough to contain the result, as many intervals as will fit are returned. result must be declared as a double precision SpiceCell. result must be distinct from window.
Mathematically, the complement of a window contains those points that are not contained in the window. That is, the complement of the set of closed intervals [ a(0), b(0) ], [ a(1), b(1) ], ..., [ a(n), b(n) ] is the set of open intervals ( -inf, a(0) ), ( b(0), a(1) ), ..., ( b(n), +inf ) Because ANSI C offers no satisfactory representation of infinity, we must take the complement with respect to a finite interval. In addition, ANSI C offers no satisfactory floating point representation of open intervals. Therefore, the complement of a floating point window is closure of the set theoretical complement. In short, the floating point complement of the window [ a(0), b(0) ], [ a(1), b(1) ], ..., [ a(n), b(n) ] with respect to the interval from left to right is the intersection of the windows ( -inf, a(0) ), ( b(0), a(1) ), ..., ( b(n), +inf ) and [ left, right ] Note that floating point intervals of measure zero (singleton intervals) in the original window are replaced by gaps of measure zero, which are filled. Thus, complementing a floating point window twice does not necessarily yield the original window.
Let window contain the intervals [ 1, 3 ] [ 7, 11 ] [ 23, 27 ] Then the floating point complement of window with respect to [2,20] contains the intervals [ 3, 7 ] [ 11, 20 ] and the complement with respect to [ 0, 100 ] contains [ 0, 1 ] [ 3, 7 ] [ 11, 23 ] [ 27, 100 ]
1) If either input window does not have double precision type, the error SPICE(TYPEMISMATCH) is signaled. 2) If left is greater than right, the error SPICE(BADENDPOINTS) is signaled.
N.J. Bachman (JPL) H.A. Neilan (JPL) W.L. Taber (JPL) I.M. Underwood (JPL)
-CSPICE Version 1.0.0, 27-AUG-2002 (NJB) (HAN) (WLT) (IMU)
complement a d.p. window