PK_ERROR_code_t     PK_CURVE_make_bcurve
(
--- received arguments ---
PK_CURVE_t          curve,         --- curve
PK_INTERVAL_t       range,         --- parameter bounds: required part of curve
PK_LOGICAL_t        cubic,         --- force cubic BCURVE
PK_LOGICAL_t        non_rational,  --- force non_rational BCURVE
double              tolerance,     --- for approximate result

--- returned arguments ---
PK_BCURVE_t  *const b_curve,       --- created BCURVE
PK_LOGICAL_t *const exact          --- whether b_curve is exact
)


This function creates a bcurve which is coincident with the given parametric
interval of the given curve.


Specific Errors:

    PK_ERROR_cant_make_bspline      failed to create equivalent geometry
                                    (SERIOUS)
    PK_ERROR_tolerances_too_tight   tolerance is too tight
    PK_ERROR_zero_interval          range has zero extent



The created BCURVE will be exactly coincident with the given curve if
possible.  Where this is not possible, the maximum distance between curve and
result will be limited by tolerance.  The function will usually achieve
this condition but this is not guaranteed.

When the curve is being approximated, and excessive subdivision of the
curve has failed to achieve the requested tolerance, then the function will
fail with the error PK_ERROR_tolerances_too_tight.  A looser tolerance may
allow the function to succeed.

Representations of lines and the rational forms of circles and ellipses are
exact.  When the representation of a bcurve is changed it will, in general,
only be exact when the order is not decreased.  The returned argument exact
is set to PK_LOGICAL_true if the result is exact, otherwise to
PK_LOGICAL_false.

If cubic is set to PK_LOGICAL_true, then the resulting bcurve is forced to
be cubic.  If `non-rational' is set to PK_LOGICAL_true, then the resulting
bcurve is forced to be non-rational.

The form of the created curve depends upon the given values of cubic and
`non-rational' as follows:

        |  false       true       true     false   | cubic
curve   |  false       false      true     true    | non_rational
--------|-----------|----------|--------|----------|
line    |  linear   |  cubic   | cubic  |  linear  |
        |           |          |        |          |
circle  | rational  | rational | cubic  |  cubic   |
        |  cubic    |  cubic   |        |          |
        |           |          |        |          |
ellipse | rational  | rational | cubic  |  cubic   |
        |  cubic    |  cubic   |        |          |
        |           |          |        |          |
bcurve  | no change |  cubic   | cubic  | rational |
        |           |          |        | to cubic |
        |           |          |        |          |
others* |  cubic    |  cubic   | cubic  |  cubic   |
--------|-----------|----------|--------|----------|

* If an intersection curve or spcurve lies on a bsurf and coincides with a
constant parameter line on that bsurf, the equivalent bcurve will be
extracted from the surface.  In this case, the options will apply to the
extracted bcurve and so exact representations will be possible in certain
cases.