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CLPPG3

       SUBROUTINE  CLPPG3 (P1,P2, XVERTX,INCX, YVERTX,INCY, ZVERTX,INCZ,
      X                    NVERTX, ALPHA,NALPHA)
 C$    (3-Dimensional Clip to General Polygon)
 C$    Clip  a   line  segment   defined  by   its  endpoints   in
 C$    3-dimensional coordinates to a general (convex or  concave)
 C$    polygon defined by its vertices.  The clipping may  produce
 C$    zero or more line segments defined by a vector ALPHA(*)  of
 C$    parameter pairs such that points are defined by P(ALPHA)  =
 C$    P1 + ALPHA(I)*(P2 - P1).
 C$
 C$    The input arguments are:
 C$
 C$    P1(*)..........(x,y,z) coordinates of first point.
 C$    P2(*)..........(x,y,z) coordinates of second point.
 C$    XVERTX(*)......x coordinates of polygon vertices.
 C$    INCX...........Increment between successive coordinates in
 C$                   XVERTX(*) (normally 1).
 C$    YVERTX(*)......y coordinates of polygon vertices.
 C$    INCY...........Increment between successive coordinates in
 C$                   YVERTX(*) (normally 1).
 C$    ZVERTX(*)......z coordinates of polygon vertices.
 C$    INCZ...........Increment between successive coordinates in
 C$                   ZVERTX(*) (normally 1).
 C$    NVERTX.........Number of polygon vertices.  Vertex NVERTX
 C$                   is implicitly connected to vertex 1 to close
 C$                   the polygon.
 C$
 C$    The output arguments are:
 C$
 C$    ALPHA(*).......Parameters   for   the   endpoints  of  line
 C$                   segments    in    the    parametric     line
 C$                   representation (1-ALPHA)*P1 + ALPHA*P2.   On
 C$                   output, values will be in strictly ascending
 C$                   order, each pair defining a visible segment.
 C$                   The array must be large enough to contain at
 C$                   least 2*NVERTX values.
 C$    NALPHA.........Number of parameters returned in ALPHA(*).
 C$                   The output value is always even.
 C$
 C$    If an  increment  INCX,  INCY, or  INCZ  is  negative,  the
 C$    starting vertex is taken as  (1-NVERTX)*INC + 1 instead  of
 C$    1, so that the array is stepped through in reverse order.
 C$
 C$    The polygon vertices are assumed to be arranged so that the
 C$    interior lies  to the  left of  each line  segment  between
 C$    vertices i  and  i+1.  Thus,  reversing  the order  of  the
 C$    vertices will exchange the exterior and interior.  The  set
 C$    of alpha's returned will be correct only if the polygon  is
 C$    an interior  one.   Determination  of whether  a  point  is
 C$    inside or outside  requires counting edges  to the left  of
 C$    the point, and the parity of the count is odd for an inside
 C$    point in  an interior  polygon, and  even for  an  exterior
 C$    polygon.   Thus,  the  interior/exterior  character  of   a
 C$    polygon cannot be determined  without examining all of  its
 C$    edges.  This routine can be used for this determination  if
 C$    a tiny line  segment just  inside the visible  side of  one
 C$    edge is passed for clipping.  If NALPHA = 0 on return,  the
 C$    polygon is an exterior polygon.  If NALPHA = 2, it must  be
 C$    an interior polygon.
 C$
 C$    Clipping  against  an  exterior  polygon  may  be  done  by
 C$    reversing  the  order  of   the  vertices  explicitly,   or
 C$    implicitly with negative  INCX, INCY,  INCZ parameters,  in
 C$    order  to  get  an   interior  polygon,  then  taking   the
 C$    complement of the  set of  alpha's returned  to obtain  the
 C$    exterior line segments.  This could be used to advantage in
 C$    a mapping application  to clip  against regions  containing
 C$    embedded islands.
 C$
 C$    Although the z coordinates are specified, the edge  normals
 C$    are defined to have z = 0 (i.e., the polygon is assumed  to
 C$    lie in the xy plane).   However, the z coordinates  **are**
 C$    used in determining whether the line segment intersects  an
 C$    edge.
 C$    (17-SEP-81)