Online Appendix 1

The following is an example of a complete plan fragment for a line-segment that is generated
by the system. One end-point of the line-segment is fixed and a new constraint that needs to
be satisfied is that the second end-point be on a given one-dimensional locus. The solution 
involves rotation of the line-segment about the fixed end-point followed by a scale operation.
This example is given to provide a feel for the complexity of the plan fragment library and 
the justification for automating its construction. 

Problem Specification:
----------------------

Geom-Type: line-segment
----------
Name: $lseg
-----
Invariants: (INVARIANT-POINT $LSEG (>> $LSEG END1) $GLB-COORDS1)
-----------           
To-be-achieved: ((1D-CONSTRAINED-POINT $LSEG (>> $LSEG END1) $1D-LOCUS3))
---------------

Skeletal solution produced by Phase I:
-------------------------------------- 
(rotate $LSEG (>> $LSEG END1) ?ANY-AXIS ?ANY-AMT)
(scale $LSEG 
       (>> $LSEG END1) 
       (TIMES (>> (v- (0D-INTERSECTION 
			(LINE-LOCUS (>> $LSEG END2) (>> $LSEG DIRECTION)) 
			$1D-LOCUS4) 
		      END2) 
		  MAGNITUDE) 
	      (COSINE (ANGLE-BETWEEN 
		  	(>> (v- (0D-INTERSECTION 
			    	  (LINE-LOCUS (>> $LSEG END2) (>> $LSEG DIRECTION)) 
			    	  $1D-LOCUS4) 
		                END2) 
		      	     DIRECTION) 
			(>> $LSEG DIRECTION)))))


Complete plan fragment generated by Phase II:
---------------------------------------------

void pf_02111_end2_1d(Cgeom& selected_geom, Sconstraint *new_constraint)
{
  Clseg chosen(selected_geom);
  Solution cur_sln, next_sln;
  Sdirect LLdirec7343874; Spoint LLthru_point7343874; int S_ZDflag917984 = 0; 
  int S_ZDmotion917984; int S_ZDint917984; int S_ZDinterval917984; 
  Cgeom *ZDlocus2917984; Cgeom *ZDlocus1917984; Spoint Vto_point50999; 
  Spoint Vfrom_point50999; Cvector *SUBvector250998; Sdirect ABangle21342; 
  Sdirect ABangle11342; double CIarg67; Sdirect LLdirec9090; 
  Spoint LLthru_point9090; int S_ZDflag1136 = 0; int S_ZDmotion1136; 
  int S_ZDint1136; int S_ZDinterval1136; Cgeom *ZDlocus21136; 
  Cgeom *ZDlocus11136; Spoint Vto_point63; Spoint Vfrom_point63; 
  Cvector *SUBvector162; double Tscalar35; double Tscalar25; 
  double Tscalar15; int end; double scale_amount; 
  Spoint scale_point; double var_angle22; int R_angle_flag22 = 0; 
  int R_angle_motion22; int R_angle_int22; int R_angle_interval22; 
  double rot_radians; Spoint rot_point; Spoint trans_point2;
  SSignature *ssign = new SSignature; SSignature *ss;
  Sconstraint *temp_constraint = new Sconstraint;
  Cgeom new_geom(*new_constraint->cgm);

*temp_constraint = *new_constraint;
  ssign->next = NULL;
  ssign->sconstraint = temp_constraint;
  ssign->sigNo = 101111;
  
  init_sln(&cur_sln);
  cur_sln.trans_count = 0;
  init_sln(&next_sln);
  next_sln.rot_loc = 1;
  
  next_sln.rot_count = 1;
  rot_point = get_point(&chosen, END1, &next_sln, R);
  next_sln.rot_point = rot_point;
  /**** rot_axis is ignored here ****/
  R_angle_interval22 = count_angles();
  R_angle_motion22 = 9999999;for (R_angle_int22 = 0; R_angle_int22 < R_angle_interval22; R_angle_int22++)
  {
    if ((R_angle_motion22 <= cur_sln.motion) && (R_angle_flag22 > 1)) 
       break;
    else if (R_angle_motion22 > cur_sln.motion)
    {
      R_angle_motion22 = cur_sln.motion;
      R_angle_flag22++;
      }
    var_angle22 = get_angles(R_angle_interval22, R_angle_int22);
    rot_radians = var_angle22;
    next_sln.rot_amount = rot_radians;
    next_sln.scl_loc = 2;
    
    next_sln.scl_count = 1;
    scale_point = get_point(&chosen, END1, &next_sln, S);
    end = END1;
    next_sln.scl_point = scale_point;
    Vfrom_point63 = get_point(&chosen, END2, &next_sln, S);
    LLthru_point9090 = get_point(&chosen, END2, &next_sln, S);
    LLdirec9090 = get_direction(&chosen, &next_sln, S);
    Clseg LLline9090(&LLthru_point9090, 100, &LLdirec9090);
    ZDlocus11136 = &LLline9090;
    ZDlocus21136 = &new_geom;
    S_ZDinterval1136 = count_0d_intersection(ZDlocus11136, ZDlocus21136);
    if (next_sln.scl_count) 
     next_sln.scl_count *= S_ZDinterval1136;
    else 
     next_sln.scl_count = S_ZDinterval1136;
    S_ZDmotion1136 = 9999999;for (S_ZDint1136 = 0; S_ZDint1136 < S_ZDinterval1136; S_ZDint1136++)
    {
      if ((S_ZDmotion1136 <= cur_sln.motion) && (S_ZDflag1136 > 1)) 
         break;
      else if (S_ZDmotion1136 > cur_sln.motion)
      {
        S_ZDmotion1136 = cur_sln.motion;
        S_ZDflag1136++;
        }
      Vto_point63 = get_0d_intersection(ZDlocus11136, ZDlocus21136, S_ZDinterval1136, S_ZDint1136, &next_sln);
      Cvector Vvect63(&Vfrom_point63, &Vto_point63);
      SUBvector162 = &Vvect63;
      Tscalar15 = SUBvector162->magnitude();
      Vfrom_point50999 = get_point(&chosen, END2, &next_sln, S);
      LLthru_point7343874 = get_point(&chosen, END2, &next_sln, S);
      LLdirec7343874 = get_direction(&chosen, &next_sln, S);
      Clseg LLline7343874(&LLthru_point7343874, 100, &LLdirec7343874);
      ZDlocus1917984 = &LLline7343874;
      ZDlocus2917984 = &new_geom;
      S_ZDinterval917984 = count_0d_intersection(ZDlocus1917984, ZDlocus2917984);
      if (next_sln.scl_count) 
       next_sln.scl_count *= S_ZDinterval917984;
      else 
       next_sln.scl_count = S_ZDinterval917984;
      S_ZDmotion917984 = 9999999;for (S_ZDint917984 = 0; S_ZDint917984 < S_ZDinterval917984; S_ZDint917984++)
      {
        if ((S_ZDmotion917984 <= cur_sln.motion) && (S_ZDflag917984 > 1)) 
           break;
        else if (S_ZDmotion917984 > cur_sln.motion)
        {
          S_ZDmotion917984 = cur_sln.motion;
          S_ZDflag917984++;
          }
        Vto_point50999 = get_0d_intersection(ZDlocus1917984, ZDlocus2917984, S_ZDinterval917984, S_ZDint917984, &next_sln);
        Cvector Vvect50999(&Vfrom_point50999, &Vto_point50999);
        SUBvector250998 = &Vvect50999;
        ABangle11342 = *(SUBvector250998->direction());
        ABangle21342 = get_direction(&chosen, &next_sln, S);
        CIarg67 = compute_angle_between(&ABangle21342, &ABangle11342, &next_sln);
        Tscalar25 = compute_cosinv(CIarg67, end);
        Tscalar35 = get_length(&chosen, &next_sln, S);
        scale_amount = Tscalar15 * Tscalar25 + Tscalar35;
        next_sln.scl_amount = scale_amount;
            measure_motion(&next_sln, &chosen);
        if (next_sln.motion < cur_sln.motion)
        {
          cur_sln = next_sln;
        }
      }
    }
  }

if (!cur_sln.rot_count || !cur_sln.scl_count || !cur_sln.trans_count) 
 { 
printf("No action taken\n");
printf("no other planFrags to use\n");
}
else 
{
  chosen.geomRotate(&cur_sln.rot_point, &(cur_sln.normal), cur_sln.rot_amount);
  chosen.geomScale(&cur_sln.scl_point, cur_sln.scl_amount);
  for(ss=&(selected_geom.geomSignature); ss && ss->next; ss = ss->next);
  ss->next = ssign;
  selected_geom.assignPts(chosen.end1(),chosen.end2(),chosen.end2(),LSEG);
}
}