FUNCTION enclose_cregion_in_pregion
(* SCHEMA FUNCTIONAL_DATA_AND_SCHEMATIC_REPRESENTATION_MIM_LF; *)
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 > PI;
a := a - 2.0 * PI;
END_REPEAT;
REPEAT WHILE a <= -PI;
a := a + 2.0 * PI;
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 < 0.0) 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 := 0.0;
xmax : REAL := 0.0;
ymin : REAL := 0.0;
ymax : REAL := 0.0;
xc : REAL := 0.0;
yc : REAL := 0.0;
xmin_in : BOOLEAN := FALSE;
xmax_in : BOOLEAN := FALSE;
ymin_in : BOOLEAN := FALSE;
ymax_in : BOOLEAN := FALSE;
rmin : REAL := -1.0;
rmax : REAL := -1.0;
amin : REAL := 4.0;
amax : REAL := -4.0;
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 := 0.0;
a : REAL := 0.0;
r : REAL := 0.0;
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 := 0.0;
ELSE
IF is_ymin AND (yc <= ymin) THEN
ab := 0.5 * PI;
ELSE
IF is_ymax AND (yc >= ymax) THEN
ab := -0.5 * PI;
ELSE
IF is_xmax AND (xc >= xmax) THEN
ab := PI;
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 > 0.0 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 := 0.0;
rmin_in := xmin_in AND ymin_in;
amin := angle(0.0 - ab);
amin_in := ymin_in;
amax := angle(0.5 * PI - ab);
amax_in := xmin_in;
END_IF;
END_IF;
ELSE
IF xc <= xmin THEN
angle_minmax(ab, -0.5 * PI, (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, 0.5 * PI, (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 > 0.0 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 := 0.0;
rmin_in := xmax_in AND ymin_in;
amin := angle(0.5 * PI - ab);
amin_in := ymin_in;
amax := angle(PI - ab);
amax_in := xmax_in;
END_IF;
END_IF;
ELSE
IF yc <= ymin THEN
angle_minmax(ab, 0.0, (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, PI, (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 > 0.0 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 := 0.0;
rmin_in := xmax_in AND ymax_in;
amin := angle(-PI - ab);
amin_in := ymax_in;
amax := angle(-0.5 * PI - ab);
amax_in := xmax_in;
END_IF;
END_IF;
ELSE
IF xc >= xmax THEN
angle_minmax(ab, 0.5 * PI, (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, -0.5 * PI, (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 > 0.0 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 := 0.0;
rmin_in := xmin_in AND ymax_in;
amin := angle(0.5 * PI - ab);
amin_in := ymax_in;
amax := angle(PI - ab);
amax_in := xmin_in;
END_IF;
END_IF;
ELSE
IF yc >= ymax THEN
angle_minmax(ab, PI, (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, 0.0, (yc = ymax) AND ymax_in, amin, amax, amin_in,
amax_in);
END_IF;
END_IF;
IF outside THEN
amin := angle(amin + ab);
IF amin = PI THEN
amin := -PI;
END_IF;
amax := angle(amax + ab);
IF amax <= amin THEN
amax := amax + 2.0 * PI;
END_IF;
ELSE
amin := -PI;
amin_in := FALSE;
amax := PI;
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:
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2012-03-27T17:17:33-04:00