|
Comparison_result
|
fo (
ArrTraits::Point_2 p
,
ArrTraits::X_monotone_curve_2 xcv
,
Arr_curve_end ce
)
|
| |
Given a point p, an x-monotone curve xcv, and an
enumeration ce that specifies either the minimum or the
maximum end of the curve where the curve has a vertical asymptote,
compares the x-coordinate of p and the x-coordinate of the
limit of the curve at its specificed end. The variable xcv
identifies the parametric curve C(t) = (X(t),Y(t)) defined over an
open or half-open interval with endpoints 0 and 1. The
enumeration ce identifies an open end d ∈ {0,1} of C.
Formally, compares the x-coordinate of p and
lim t → d X(t). Returns SMALLER, EQUAL, or
LARGER accordingly.
| Precondition: | parameter_space_in_y_2(xcv, ce) ≠
ARR_INTERIOR.
|
| Precondition: | If the parameter space is unbounded, C has a vertical
asymptote at its d-end; that is,
parameter_space_in_x_2(xcv, ce) = ARR_INTERIOR. |
|
|
|
Comparison_result
|
|
| |
Given two x-monotone curves xcv1 and xcv2 and two
indices ce1 and ce2 that specify either the minimum
or the maximum ends of xcv1 and xcv2, respectively,
where the curves have vertical asymptotes, compares the
x-coordinates of the limits of the curves at their specificed
ends. The variables xcv1 and xcv2 identify the
parametric curves C1(t) = (X1(t),Y1(t)) and
C2(t) = (X2(t),Y2(t)), respectively, defined over open or
half-open intervals with endpoints 0 and 1. The indices
ce1 and ce2 identify open ends d1 ∈ {0,1} and
d2 ∈ {0,1} of C1 and C2, respectively. Formally,
compares lim t → d1 X1(t) and
lim t → d2 X2(t). Returns SMALLER, EQUAL,
or LARGER accordingly.
| Precondition: | parameter_space_in_y_2(xcv1, ce1) ≠
ARR_INTERIOR.
|
| Precondition: | parameter_space_in_y_2(xcv2, ce2) ≠
ARR_INTERIOR.
|
| Precondition: | If the parameter space is unbounded, C1 has a vertical
asymptote at its respective end; that is,
parameter_space_in_x_2(xcv1, ce1) =
ARR_INTERIOR.
|
| Precondition: | If the parameter space is unbounded, C2 has a vertical
asymptote at its respective end; that is,
parameter_space_in_x_2(xcv2, ce2) =
ARR_INTERIOR. |
|
