Boundary Paths

A boundary path has the general form

START(a,b) segment TO (c,d) ...

where (a,b) and (c,d) are the physical coordinates of the ends of the segment, and segment is either LINE, SPLINE or ARC.

The path continues with a connected series of segments, each of which moves the segment to a new point.  The end point of one segment becomes the start point of the next segment.

A path ends whenever the next input item cannot be construed as a segment, or when it is closed by returning to the start point.  The closing segment may simply end at the start point, or it can explicitly reference CLOSE, which will cause the current path to be continued to meet the starting point:

... segment TO CLOSE.

or

... segment  CLOSE.

[Note: In prior versions, return to start was signaled by the word FINISH.  This form is still accepted by FlexPDE 5, but is deprecated because of ambiguous implications. ]

Line Segments

Line segments take the form

LINE TO (x,y)

When successive LINE segments are used, the reserved word LINE does not have to be repeated, as in the following: 

LINE TO (x1,y1) TO (x2,y2) TO (x3,y3) TO ...

Spline Segments

Spline segments are syntactically similar to Line segments

SPLINE TO (x,y) TO (x2,y2) TO (x3,y3) TO ...

A cubic spline will be fit to the listed points. The first point of the spline will be either the START point or the ending point of the previous segment.  The last point of the spline will be the last point stated in the chain of TO(,) points.

The fitted spline will have zero curvature at the end points, so it is a good idea to begin and end with closely spaced points to establish the proper endpoint directions.  [4.1]

Arc Segments

Arc segments create either circular or elliptical arcs, and take one of the following the forms:

ARC TO (x1,y1) to (x2,y2)

ARC ( RADIUS = R ) to (x,y)

ARC ( CENTER = x1,y1 ) to (x2,y2)

ARC ( CENTER = x1,y1 ) ANGLE=angle

Here angle is an angle measured in degrees, following  the standard convention that positive angles rotate counter-clockwise and negative angles rotate clockwise. The coordinate point at the end of the arc is determined by the radius swept out by the angle.   To specify the angle in radians, follow the radian value by the qualifier RADIANS.

When the form ARC (CENTER=x1,y1) to (x2,y2) is used and the center (x1,y1) is not equidistant from the start and end points, an elliptical arc segment is generated with major and minor axes along the X and Y coordinate directions.

Example:

START(0,0)

LINE TO (10,0) TO (10,10) TO (0,10) TO CLOSE

Named Paths

Names can be assigned to paths.  When names are assigned to paths they take the form of a quoted string and must be placed immediately after the reserved word START:

START  "namedpath"  ( <x> , <y> )

Assigned path names are useful when boundary or line-related integrals are desired or for establishing paths over which ELEVATION plots are desired.