FUNCTION enclose_cregion_in_pregion

(* SCHEMA step_merged_ap_schema; *)
-- IN AP242
FUNCTION enclose_cregion_in_pregion
      (crgn : cartesian_complex_number_region;
       centre : complex_number_literal ) : polar_complex_number_region;
      FUNCTION angle
         (a : REAL ) : REAL;
         REPEAT WHILE a > 3.14159;
            a := a - 2 * 3.14159;
         END_REPEAT;
         REPEAT WHILE a <= -3.14159;
            a := a + 2 * 3.14159;
         END_REPEAT;
         RETURN (a);
      END_FUNCTION;
      FUNCTION strictly_in
         (z : REAL;
          zitv : real_interval ) : LOGICAL;
         RETURN ((NOT min_exists(zitv) OR (z > real_min(zitv))) AND (NOT max_exists(zitv) OR (z < real_max(zitv))));
      END_FUNCTION;
      PROCEDURE angle_minmax
         (ab : REAL;
          a : REAL;
          a_in : BOOLEAN;
          VAR amin : REAL;
          VAR amax : REAL;
          VAR amin_in : BOOLEAN;
          VAR amax_in : BOOLEAN );
         a := angle(a - ab);
         IF amin = a THEN
            amin_in := amin_in OR a_in;
         END_IF;
         IF amin > a THEN
            amin := a;
            amin_in := a_in;
         END_IF;
         IF amax = a THEN
            amax_in := amax_in OR a_in;
         END_IF;
         IF amax < a THEN
            amax := a;
            amax_in := a_in;
         END_IF;
      END_PROCEDURE;
      PROCEDURE range_max
         (r : REAL;
          incl : BOOLEAN;
          VAR rmax : REAL;
          VAR rmax_in : BOOLEAN );
         IF rmax = r THEN
            rmax_in := rmax_in OR incl;
         END_IF;
         IF rmax < r THEN
            rmax := r;
            rmax_in := incl;
         END_IF;
      END_PROCEDURE;
      PROCEDURE range_min
         (r : REAL;
          incl : BOOLEAN;
          VAR rmin : REAL;
          VAR rmin_in : BOOLEAN );
         IF rmin = r THEN
            rmin_in := rmin_in OR incl;
         END_IF;
         IF (rmin < 0) OR (rmin > r) THEN
            rmin := r;
            rmin_in := incl;
         END_IF;
      END_PROCEDURE;
   LOCAL
      xitv : real_interval;
      yitv : real_interval;
      is_xmin : BOOLEAN;
      is_xmax : BOOLEAN;
      is_ymin : BOOLEAN;
      is_ymax : BOOLEAN;
      xmin : REAL := 0;
      xmax : REAL := 0;
      ymin : REAL := 0;
      ymax : REAL := 0;
      xc : REAL := 0;
      yc : REAL := 0;
      xmin_in : BOOLEAN := FALSE;
      xmax_in : BOOLEAN := FALSE;
      ymin_in : BOOLEAN := FALSE;
      ymax_in : BOOLEAN := FALSE;
      rmin : REAL := -1;
      rmax : REAL := -1;
      amin : REAL := 4;
      amax : REAL := -4;
      rmax_exists : BOOLEAN := TRUE;
      outside : BOOLEAN := TRUE;
      rmin_in : BOOLEAN := FALSE;
      rmax_in : BOOLEAN := FALSE;
      amin_in : BOOLEAN := FALSE;
      amax_in : BOOLEAN := FALSE;
      ab : REAL := 0;
      a : REAL := 0;
      r : REAL := 0;
      incl : BOOLEAN;
      ritv : real_interval;
      aitv : finite_real_interval;
      minclo : open_closed := open;
      maxclo : open_closed := open;
   END_LOCAL;
      IF NOT EXISTS(crgn) OR NOT EXISTS(centre) THEN
         RETURN (?);
      END_IF;
      xitv := crgn.real_constraint;
      yitv := crgn.imag_constraint;
      xc := centre.real_part;
      yc := centre.imag_part;
      is_xmin := min_exists(xitv);
      is_xmax := max_exists(xitv);
      is_ymin := min_exists(yitv);
      is_ymax := max_exists(yitv);
      IF is_xmin THEN
         xmin := real_min(xitv);
         xmin_in := min_included(xitv);
      END_IF;
      IF is_xmax THEN
         xmax := real_max(xitv);
         xmax_in := max_included(xitv);
      END_IF;
      IF is_ymin THEN
         ymin := real_min(yitv);
         ymin_in := min_included(yitv);
      END_IF;
      IF is_ymax THEN
         ymax := real_max(yitv);
         ymax_in := max_included(yitv);
      END_IF;
      rmax_exists := ((is_xmin AND is_xmax) AND is_ymin) AND is_ymax;
      IF is_xmin AND (xc <= xmin) THEN
         ab := 0;
      ELSE
         IF is_ymin AND (yc <= ymin) THEN
            ab := 0.500000 * 3.14159;
         ELSE
            IF is_ymax AND (yc >= ymax) THEN
               ab := -0.500000 * 3.14159;
            ELSE
               IF is_xmax AND (xc >= xmax) THEN
                  ab := 3.14159;
               ELSE
                  outside := FALSE;
               END_IF;
            END_IF;
         END_IF;
      END_IF;
      IF NOT outside AND NOT rmax_exists THEN
         RETURN (?);
      END_IF;
      IF (is_xmin AND (xc <= xmin)) AND strictly_in(yc, yitv) THEN
         rmin := xmin - xc;
         rmin_in := xmin_in;
      ELSE
         IF (is_ymin AND (yc <= ymin)) AND strictly_in(xc, xitv) THEN
            rmin := ymin - yc;
            rmin_in := ymin_in;
         ELSE
            IF (is_ymax AND (yc >= ymax)) AND strictly_in(xc, xitv) THEN
               rmin := yc - ymax;
               rmin_in := ymax_in;
            ELSE
               IF (is_xmax AND (xc >= xmax)) AND strictly_in(yc, yitv) THEN
                  rmin := xc - xmax;
                  rmin_in := xmax_in;
               END_IF;
            END_IF;
         END_IF;
      END_IF;
      IF is_xmin THEN
         IF is_ymin THEN
            r := sqrt((xmin - xc) ** 2 + (ymin - yc) ** 2);
            incl := xmin_in AND ymin_in;
            IF rmax_exists THEN
               range_max( r, incl, rmax, rmax_in );
            END_IF;
            IF outside THEN
               IF r > 0 THEN
                  range_min( r, incl, rmin, rmin_in );
                  a := angle(atan2(ymin - yc, xmin - xc) - ab);
                  IF xc = xmin THEN
                     incl := xmin_in;
                  END_IF;
                  IF yc = ymin THEN
                     incl := ymin_in;
                  END_IF;
                  angle_minmax( ab, a, incl, amin, amax, amin_in, amax_in );
               ELSE
                  rmin := 0;
                  rmin_in := xmin_in AND ymin_in;
                  amin := angle(0 - ab);
                  amin_in := ymin_in;
                  amax := angle(0.500000 * 3.14159 - ab);
                  amax_in := xmin_in;
               END_IF;
            END_IF;
         ELSE
            IF xc <= xmin THEN
               angle_minmax( ab, -0.500000 * 3.14159, (xc = xmin) AND xmin_in, amin, amax, amin_in, amax_in );
            END_IF;
         END_IF;
         IF NOT is_ymax AND (xc <= xmin) THEN
            angle_minmax( ab, 0.500000 * 3.14159, (xc = xmin) AND xmin_in, amin, amax, amin_in, amax_in );
         END_IF;
      END_IF;
      IF is_ymin THEN
         IF is_xmax THEN
            r := sqrt((xmax - xc) ** 2 + (ymin - yc) ** 2);
            incl := xmax_in AND ymin_in;
            IF rmax_exists THEN
               range_max( r, incl, rmax, rmax_in );
            END_IF;
            IF outside THEN
               IF r > 0 THEN
                  range_min( r, incl, rmin, rmin_in );
                  a := angle(atan2(ymin - yc, xmax - xc) - ab);
                  IF xc = xmax THEN
                     incl := xmax_in;
                  END_IF;
                  IF yc = ymin THEN
                     incl := ymin_in;
                  END_IF;
                  angle_minmax( ab, a, incl, amin, amax, amin_in, amax_in );
               ELSE
                  rmin := 0;
                  rmin_in := xmax_in AND ymin_in;
                  amin := angle(0.500000 * 3.14159 - ab);
                  amin_in := ymin_in;
                  amax := angle(3.14159 - ab);
                  amax_in := xmax_in;
               END_IF;
            END_IF;
         ELSE
            IF yc <= ymin THEN
               angle_minmax( ab, 0, (yc = ymin) AND ymin_in, amin, amax, amin_in, amax_in );
            END_IF;
         END_IF;
         IF NOT is_xmin AND (yc <= ymin) THEN
            angle_minmax( ab, 3.14159, (yc = ymin) AND ymin_in, amin, amax, amin_in, amax_in );
         END_IF;
      END_IF;
      IF is_xmax THEN
         IF is_ymax THEN
            r := sqrt((xmax - xc) ** 2 + (ymax - yc) ** 2);
            incl := xmax_in AND ymax_in;
            IF rmax_exists THEN
               range_max( r, incl, rmax, rmax_in );
            END_IF;
            IF outside THEN
               IF r > 0 THEN
                  range_min( r, incl, rmin, rmin_in );
                  a := angle(atan2(ymax - yc, xmax - xc) - ab);
                  IF xc = xmax THEN
                     incl := xmax_in;
                  END_IF;
                  IF yc = ymax THEN
                     incl := ymax_in;
                  END_IF;
                  angle_minmax( ab, a, incl, amin, amax, amin_in, amax_in );
               ELSE
                  rmin := 0;
                  rmin_in := xmax_in AND ymax_in;
                  amin := angle(-3.14159 - ab);
                  amin_in := ymax_in;
                  amax := angle(-0.500000 * 3.14159 - ab);
                  amax_in := xmax_in;
               END_IF;
            END_IF;
         ELSE
            IF xc >= xmax THEN
               angle_minmax( ab, 0.500000 * 3.14159, (xc = xmax) AND xmax_in, amin, amax, amin_in, amax_in );
            END_IF;
         END_IF;
         IF NOT is_ymin AND (xc >= xmax) THEN
            angle_minmax( ab, -0.500000 * 3.14159, (xc = xmax) AND xmax_in, amin, amax, amin_in, amax_in );
         END_IF;
      END_IF;
      IF is_ymax THEN
         IF is_xmin THEN
            r := sqrt((xmin - xc) ** 2 + (ymax - yc) ** 2);
            incl := xmin_in AND ymax_in;
            IF rmax_exists THEN
               range_max( r, incl, rmax, rmax_in );
            END_IF;
            IF outside THEN
               IF r > 0 THEN
                  range_min( r, incl, rmin, rmin_in );
                  a := angle(atan2(ymax - yc, xmin - xc) - ab);
                  IF xc = xmin THEN
                     incl := xmin_in;
                  END_IF;
                  IF yc = ymax THEN
                     incl := ymax_in;
                  END_IF;
                  angle_minmax( ab, a, incl, amin, amax, amin_in, amax_in );
               ELSE
                  rmin := 0;
                  rmin_in := xmin_in AND ymax_in;
                  amin := angle(0.500000 * 3.14159 - ab);
                  amin_in := ymax_in;
                  amax := angle(3.14159 - ab);
                  amax_in := xmin_in;
               END_IF;
            END_IF;
         ELSE
            IF yc >= ymax THEN
               angle_minmax( ab, 3.14159, (yc = ymax) AND ymax_in, amin, amax, amin_in, amax_in );
            END_IF;
         END_IF;
         IF NOT is_xmax AND (yc >= ymax) THEN
            angle_minmax( ab, 0, (yc = ymax) AND ymax_in, amin, amax, amin_in, amax_in );
         END_IF;
      END_IF;
      IF outside THEN
         amin := angle(amin + ab);
         IF amin = 3.14159 THEN
            amin := -3.14159;
         END_IF;
         amax := angle(amax + ab);
         IF amax <= amin THEN
            amax := amax + 2 * 3.14159;
         END_IF;
      ELSE
         amin := -3.14159;
         amin_in := FALSE;
         amax := 3.14159;
         amax_in := FALSE;
      END_IF;
      IF amin_in THEN
         minclo := closed;
      END_IF;
      IF amax_in THEN
         maxclo := closed;
      END_IF;
      aitv := make_finite_real_interval(amin, minclo, amax, maxclo);
      minclo := open;
      IF rmin_in THEN
         minclo := closed;
      END_IF;
      IF rmax_exists THEN
         maxclo := open;
         IF rmax_in THEN
            maxclo := closed;
         END_IF;
         ritv := make_finite_real_interval(rmin, minclo, rmax, maxclo);
      ELSE
         ritv := make_real_interval_from_min(rmin, minclo);
      END_IF;
      RETURN (make_polar_complex_number_region(centre, ritv, aitv));
END_FUNCTION;

Referenced By

Defintion enclose_cregion_in_pregion is references by the following definitions:
DefinitionType
 compatible_complex_number_regions FUNCTION
 subspace_of FUNCTION


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2017-01-19T11:17:24-05:00