FUNCTION enclose_pregion_in_cregion

(* SCHEMA Ap242_managed_model_based_3d_engineering_mim_LF; *)

FUNCTION enclose_pregion_in_cregion(prgn : polar_complex_number_region)
                                   : cartesian_complex_number_region;
  PROCEDURE nearest_good_direction(acart    : REAL;
                                   aitv     : finite_real_interval;
                                   VAR a    : REAL;
                                   VAR a_in : BOOLEAN);
    a := acart;                    a_in := TRUE;
    IF      a < aitv.min THEN
      -- a+2.0*PI > aitv.min automatically!
      IF a+2.0*PI < aitv.max THEN                               RETURN;  END_IF;
      IF a+2.0*PI = aitv.max THEN  a_in := max_included(aitv);  RETURN;  END_IF;
    ELSE IF a = aitv.min THEN      a_in := min_included(aitv);  RETURN;
    ELSE IF a < aitv.max THEN                                   RETURN;
    ELSE IF a = aitv.max THEN      a_in := max_included(aitv);  RETURN;
    END_IF;  END_IF;  END_IF;  END_IF;
    IF COS(acart - aitv.max) >= COS(acart - aitv.min) THEN
      a := aitv.max;               a_in := max_included(aitv);
    ELSE
      a := aitv.min;               a_in := min_included(aitv);
    END_IF;
  END_PROCEDURE;
  LOCAL
    xc, yc, xmin, xmax, ymin, ymax : REAL := 0.0;
    ritv, xitv, yitv : real_interval;
    aitv : finite_real_interval;
    xmin_exists, xmax_exists, ymin_exists, ymax_exists : BOOLEAN;
    xmin_in, xmax_in, ymin_in, ymax_in : BOOLEAN := FALSE;
    a, r : REAL := 0.0;
    a_in : BOOLEAN := FALSE;
    min_clo, max_clo : open_closed := open;
  END_LOCAL;
  IF NOT EXISTS (prgn) THEN  RETURN (?);  END_IF;
  -- Extract elementary input data
  xc := prgn.centre.real_part;
  yc := prgn.centre.imag_part;
  ritv := prgn.distance_constraint;
  aitv := prgn.direction_constraint;
  -- Determine xmin data
  nearest_good_direction(PI,aitv,a,a_in);
  IF COS(a) >= 0.0 THEN
    xmin_exists := TRUE;
    xmin := xc + real_min(ritv)*COS(a);
    xmin_in := a_in AND (min_included(ritv) OR (COS(a) = 0.0));
  ELSE
    IF max_exists(ritv) THEN
      xmin_exists := TRUE;
      xmin := xc + real_max(ritv)*COS(a);
      xmin_in := a_in AND max_included(ritv);
    ELSE
      xmin_exists := FALSE;
    END_IF;
  END_IF;
  -- Determine xmax data
  nearest_good_direction(0.0,aitv,a,a_in);
  IF COS(a) <= 0.0 THEN
    xmax_exists := TRUE;
    xmax := xc + real_min(ritv)*COS(a);
    xmax_in := a_in AND (min_included(ritv) OR (COS(a) = 0.0));
  ELSE
    IF max_exists(ritv) THEN
      xmax_exists := TRUE;
      xmax := xc + real_max(ritv)*COS(a);
      xmax_in := a_in AND max_included(ritv);
    ELSE
      xmax_exists := FALSE;
    END_IF;
  END_IF;
  -- Determine ymin data
  nearest_good_direction(-0.5*PI,aitv,a,a_in);
  IF SIN(a) >= 0.0 THEN
    ymin_exists := TRUE;
    ymin := yc + real_min(ritv)*SIN(a);
    ymin_in := a_in AND (min_included(ritv) OR (SIN(a) = 0.0));
  ELSE
    IF max_exists(ritv) THEN
      ymin_exists := TRUE;
      ymin := yc + real_max(ritv)*SIN(a);
      ymin_in := a_in AND max_included(ritv);
    ELSE
      ymin_exists := FALSE;
    END_IF;
  END_IF;
  -- Determine ymax data
  nearest_good_direction(0.5*PI,aitv,a,a_in);
  IF SIN(a) <= 0.0 THEN
    ymax_exists := TRUE;
    ymax := yc + real_min(ritv)*SIN(a);
    ymax_in := a_in AND (min_included(ritv) OR (SIN(a) = 0.0));
  ELSE
    IF max_exists(ritv) THEN
      ymax_exists := TRUE;
      ymax := yc + real_max(ritv)*SIN(a);
      ymax_in := a_in AND max_included(ritv);
    ELSE
      ymax_exists := FALSE;
    END_IF;
  END_IF;
  -- Construct result
  IF NOT (xmin_exists OR xmax_exists OR ymin_exists OR ymax_exists) THEN
    RETURN (?);  -- No finite boundaries exist
  END_IF;
  -- Construct real_constraint
  IF xmin_exists THEN
    IF xmin_in THEN  min_clo := closed;  ELSE  min_clo := open;  END_IF;
    IF xmax_exists THEN
      IF xmax_in THEN  max_clo := closed;  ELSE  max_clo := open;  END_IF;
      xitv := make_finite_real_interval(xmin,min_clo,xmax,max_clo);
    ELSE
      xitv := make_real_interval_from_min(xmin,min_clo);
    END_IF;
  ELSE
    IF xmax_exists THEN
      IF xmax_in THEN  max_clo := closed;  ELSE  max_clo := open;  END_IF;
      xitv := make_real_interval_to_max(xmax,max_clo);
    ELSE
      xitv := the_reals;
    END_IF;
  END_IF;
  -- Construct imag_constraint
  IF ymin_exists THEN
    IF ymin_in THEN  min_clo := closed;  ELSE  min_clo := open;  END_IF;
    IF ymax_exists THEN
      IF ymax_in THEN  max_clo := closed;  ELSE  max_clo := open;  END_IF;
      yitv := make_finite_real_interval(ymin,min_clo,ymax,max_clo);
    ELSE
      yitv := make_real_interval_from_min(ymin,min_clo);
    END_IF;
  ELSE
    IF ymax_exists THEN
      IF ymax_in THEN  max_clo := closed;  ELSE  max_clo := open;  END_IF;
      yitv := make_real_interval_to_max(ymax,max_clo);
    ELSE
      yitv := the_reals;
    END_IF;
  END_IF;
  -- Construct cartesian region
  RETURN (make_cartesian_complex_number_region(xitv,yitv));
END_FUNCTION;  -- enclose_pregion_in_cregion

Referenced By

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2012-03-27T17:20:10-04:00