radius  OIB.  From  BC,  erect  a  perpendicular bisector.  The  point  of  intersection  02   between this  bisector  and  the  radius  OIB  is  the  center for   the   arc   BC.   Draw   the   radius   02C,   and erect  a  perpendicular  bisector  from  CD.  The point   of   intersection   03   of   this   bisector   and the   extension   of   02C   is   the   center   for   the arc  CD. To  continue  the  curve  from  D  to  E,  you  must reverse the direction of curvature. Draw the radius 03D,  and  erect  a  perpendicular  bisector  from  DE on   the   opposite   side   of   the   curve   from   those previously   erected.   The   point   of   intersection   of this bisector and the extension of 03D is the center of  the  arc  DE. REVERSE,   OR   OGEE,   CURVE A  reverse,  or  ogee,  curve  is  composed  of  two consecutive   tangent   circular   arcs   that   curve   in opposite   directions, Figure  4-41  shows  a  method  of  connecting  two parallel  lines  by  a  reverse  curve  tangent  to  the lines.  The  problem  is  to  construct  a  reverse  curve tangent  to  the  upper  line  at  A  and  to  the  lower line  at  B. Connect  A  and  B  by  a  straight  line  AB.  Select on AB point C where you want to have the reverse curve   change   direction.   Erect   perpendicular bisectors  from  BC  and  CA,  and  erect  perpen- diculars  from  B  and  A.  The  points  of  inter- section   between   the   perpendiculars   (01 and  02) are  the  centers  for  the  arcs  BC  and  CA. Figure  4-42  shows  a  method  of  constructing a   reverse   curve   tangent   to   three   intersecting straight  lines.  The  problem  is  to  draw  a  reverse Figure 4-41.—Reverse curve connecting and tangent to two parallel lines. Figure 4-42.—Reverse curve tangent to three intersecting straight lines. curve  tangent  to  the  three  lines  that  intersect  at points  A  and  B.  Select  on  AB  point  C  where  you want  the  reverse  curve  to  change  direction.  Lay off  from  A  a  distance  equal  to  AC  to  establish point   D.   Erect   a   perpendicular   from   D   and another  from  C.  The  point  of  intersection  of  these perpendiculars   (01)  is  the  center  of  the  arc DC. Lay  off  from  B  a  distance  equal  to  CB to  establish  point  E.  Erect  a  perpendicular  from E,  and  extend   OIC  to  intersect  it.  The  point of   intersection   (02)   is   the   center   of   the arc   CE. NONCIRCULAR  CURVES The  basic  uniform  noncircular  curves  are  the ellipse,   the   parabola,   and   the   hyperbola.   These curves  are  derived  from  conic  sections  as  shown in  figure  4-43.  The  circle  itself  (not  shown,  but a  curve  formed  by  a  plane  passed  through  a  cone perpendicular  to  the  vertical  axis)  is  also  derived from  a  conic  section. This  section  describes  methods  of  constructing the   ellipse   only.   Methods   of   constructing   the hyperbola  are  given  in  Engineering  Drawing  by French  and  Vierck  and  in  Architectural   Graphic Standards. Of   the   many   different   ways   to   construct an   ellispe,   the   three   most   common   are   as follows:  the  pin-and-string  method,  the  four- center  method,  and  the  concentric-circle  method. The   method   you   should   use   will   depend on  the  size  of  the  ellipse  and  where  it  is  to be  used. 4-14