mirror of https://github.com/CGAL/cgal
applied Ron's suggestions, in particular
VLine-> StatusLine get_ -> ""
This commit is contained in:
Eric Berberich
parent
870f584a7a
commit
78f0a33847
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@ -1,25 +1,34 @@
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\begin{ccRefConcept}{CurveAnalysis_2::CurveVerticalLine_1}
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\begin{ccRefConcept}{CurveAnalysis_2::StatusLine_1}
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\ccDefinition
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The \ccc{CurveVerticalLine_1} concept is meant to provide information
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The \ccc{StatusLine_1} concept is meant to provide information
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about the intersections of a curve with a vertical line at a given
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finite $x$-coordinate. Note that a curve can have a vertical line component
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at this coordinate and non-vertical components may intersect
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the vertical line respectively.
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the status line respectively.
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With the help of the concept's methods one is able
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to compute the local topology of the curve at the given vertical line.
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Note that vertical lines at $x = \pm\infty$ are not allowed, since different
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events (curve ends going to infinity with different non-horizontal asymptotes)
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would have equal $y$-coordinate ($\pm\infty$), which confuses more than it
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helps. Note in addition that curve ends approaching the vertical asymptote
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to compute the local topology of the curve
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at the given vertical line $x = x_0$ for some finite $x_0$.
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A status line an $x_0$ smaller than any $x$-coordinate of a curve's
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status lines captures the topology of the curve when approaching $x = -\infty$.
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An analogue arguments holds for $x_0$ larger than any $x$-coordinate
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of a curve's status lines and $x = +\infty$.
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%at the given vertical line.
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%Note that vertical lines at $x = \pm\infty$ are not allowed, since different
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%events (curve ends going to infinity with different non-horizontal asymptotes)
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%would have equal $y$-coordinate ($\pm\infty$), which confuses more than it
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%helps.
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Note in addition that curve ends approaching the vertical asymptote
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introduce an event (depending on whether approaching $+\infty$ or $-\infty$ -
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but the event with coordinates $(x,-\infty)$, resp. $(x,+\infty)$, occur
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only once, if they occur, and they imply not to be associated with
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a instance of \ccc{Algebraic_real_2}.
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an instance of \ccc{Algebraic_real_2}.
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\ccTypes
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\ccNestedType{size_type}{A instance of a size type, e.g., \ccc{int}}
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\ccNestedType{Algebraic_real_1}{A model of the concept
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\ccc{AlgebraicKernel_d_1::AlgebraicReal_1}.}
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@ -38,48 +47,52 @@ a instance of \ccc{Algebraic_real_2}.
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a component
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}
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\ccMethod{unsigned int number_of_events();}{
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\ccMethod{size_type number_of_events();}{
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returns number of distinct and finite intersections of a curve with a
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(intended) vertical line ignoring a real vertical line component
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of the curve at the given $x$-coordinate.
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the vertical line $x = x_0$ ignoring a real vertical line component
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of the curve at $x_0$.
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}
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\ccMethod{Algebraic_real_2 get_algebraic_real_2(int j);}{
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\ccMethod{Algebraic_real_2 algebraic_real_2(size_type j);}{
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returns an object of type \ccc{Algebraic_real_2} for the $j$-th event
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\ccPrecond{$0 \leq j < \mbox{num\_events()}$}.
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}
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\ccMethod{std::pair< unsigned int, unsigned int >
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get_number_of_incident_branches(int j);}{
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\ccMethod{std::pair< size_type, size_type >
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number_of_incident_branches(size_type j);}{
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returns the number of branches of the curve connected to $j$-th event
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immediately to the left,
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to the right, respectively, as a pair of \ccc{unsigned int} ignoring
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to the right, respectively, as a pair of \ccc{size_type} ignoring
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vertical curve components at the given $x$-coordinate.
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\ccPrecond{$0 \leq j < \mbox{num\_events()}$}
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}
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\ccMethod{std::pair< unsigned int, unsigned int >
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get_number_of_branches_approaching_minus_infinity();}{
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\ccMethod{std::pair< size_type, size_type >
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number_of_branches_approaching_minus_infinity();}{
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returns the number of vertical asymptotes at $x$
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of the curve approaching $y=-\infty$
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from left and right. A vertical line being component of the curve is ignored.
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}
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\ccMethod{std::pair< unsigned int, unsigned int >
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get_number_of_branches_approaching_plus_infinity();}{
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\ccMethod{std::pair< size_type, size_type >
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number_of_branches_approaching_plus_infinity();}{
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returns the number of vertical asymptotes at $x$
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of the curve approaching $y=+\infty$
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from left and right. A vertical line being component of the curve is ignored.
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}
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\ccMethod{bool has_f_fy_intersection();}{
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returns \ccc{true} if the curve $f$ has an intersection with $f_y$ at $x$
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}
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\ccMethod{bool is_event();}{
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returns \ccc{true} if curve has vertical line component or
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curve $f$ has intersection with $f_y$ at $x$
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returns \ccc{true} if one of \ccc{has_f_fy_intersection()} or
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\ccc{covers_line()} evaluates to \ccc{true}.
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}
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\end{ccRefConcept}
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\begin{ccRefConcept}{AlgebraicKernel_d_2::CurveAnalysis_2}
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\begin{ccRefConcept}{AlgebraicKernelWithAnalysis_d_2::CurveAnalysis_2}
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\footnote{There is no need
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for curves to be algebraic, hence the generic name. Only the number
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of events must be finite.}
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@ -91,9 +104,9 @@ concept is meant to provide tools to analyse a single
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curve. An analysis is meant to describe the curve's interesting points and how
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they are connected. The analysis searches for {\it events}. Events only
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occur at a finite number of $x$-coordinates. Each such coordinate defines
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a \ccc{CurveVerticalLine_1} of an event. These coordinates also define open
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a \ccc{StatusLine_1} of an event. These coordinates also define open
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{\it intervals} on the $x$-axis. Different
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\ccc{CurveVerticalLine_1} at values within one
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\ccc{StatusLine_1} at values within one
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such interval only differ in the values of the \ccc{Algebraic_real_2} entries.
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Topological information are equal for all $x$-coordinate inside such an
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open interval.
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@ -104,6 +117,8 @@ open interval.
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\ccTypes
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\ccNestedType{size_type}{A instance of a size type, e.g., \ccc{int}}
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\ccNestedType{Algebraic_real_1}{A model of the concept
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\ccc{AlgebraicKernel_d_1::AlgebraicReal_1}.}
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@ -114,7 +129,7 @@ open interval.
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\ccc{AlgebraicKernel_d_2::Polynomial_2}.}
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\ccNestedType{Curve_vertical_line_1}{A model of the concept
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\ccc{CurveAnalysis_2::CurveVerticalLine_1}.}
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\ccc{CurveAnalysis_2::StatusLine_1}.}
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\ccCreation
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\ccCreationVariable{fo}
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@ -139,48 +154,48 @@ open interval.
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\ccAccessFunctions
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\ccMethod{Polynomial_2 get_polynomial_2();}{
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\ccMethod{Polynomial_2 polynomial_2();}{
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returns the defining polynomial of the analysis
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}
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\ccMethod{unsigned int number_of_vertical_lines_with_event();}{
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\ccMethod{size_type number_of_status_lines_with_event();}{
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returns number of vertical lines that encode an event
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}
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\ccMethod{Curve_vertical_line_1 vertical_line_at_event(int i);}{
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returns an instance of \ccc{CurveVerticalLine_1} at the $i$-th event
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\ccMethod{Status_line_1 status_line_at_event(size_type i);}{
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returns an instance of \ccc{StatusLine_1} at the $i$-th event
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}
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\ccMethod{Curve_vertical_line_1 vertical_line_of_interval(int i);}{
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returns an instance of \ccc{CurveVerticalLine_1} of the $i$-th interval
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\ccMethod{Status_line_1 status_line_of_interval(size_type i);}{
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returns an instance of \ccc{StatusLine_1} of the $i$-th interval
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between $x$-events.
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}
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\ccMethod{Curve_vertical_line_1 vertical_line_for_x(Algebraic_real_1 x,
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\ccMethod{Status_line_1 status_line_for_x(Algebraic_real_1 x,
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CGAL::Sign perturb = CGAL::ZERO);}{
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returns vertical\_line\_at\_event(i), if $x$ hits $i$-th event, otherwise
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returns vertical\_line\_of\_interval(i), where $i$ is the id of the interval
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returns status\_line\_at\_event(i), if $x$ hits $i$-th event, otherwise
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returns status\_line\_of\_interval(i), where $i$ is the id of the interval
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$x$ lies in. If $pertub$ is CGAL::NEGATIVE (CGAL::POSITIVE) and $x$ states
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an event, then vertical\_line\_of\_interval(i)
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(vertical\_line\_of\_interval(i+1)) is returned.
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an event, then status\_line\_of\_interval(i)
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(status\_line\_of\_interval(i+1)) is returned.
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\ccPrecond{$x$ is finite}
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}
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\ccMethod{Curve_vertical_line_1 vertical_line_at_exact_x(Algebraic_real_1 x);}{
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returns an instance of \ccc{CurveVerticalLine_1} at the given $x$.
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\ccMethod{Status_line_1 status_line_at_exact_x(Algebraic_real_1 x);}{
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returns an instance of \ccc{StatusLine_1} at the given $x$.
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\ccPrecond{$x$ is finite}
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}
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Note that the access methods to vertical lines are not redundant! The ones
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Note that the access methods to status lines are not redundant! The ones
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using an id-value are efficient for speed-ups (caching, avoids to search for
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some $x$, or the unique representative vertical line for an interval).
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The others enable a user to compute vertical lines for given $x$,
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some $x$, or the unique representative status line for an interval).
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The others enable a user to compute status lines for given $x$,
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i.e., also to access $y$-coordinates at given $x$.
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%\begin{ccAdvanced}
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%
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%\ccMethod{int find(Algebraic_real_2 s);}{
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% returns the index of the event at the vertical line defined by
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%\ccMethod{size_type find(Algebraic_real_2 s);}{
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% returns the index of the event at the status line defined by
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% $s$'s $x$-coordinate, or -1 if $s$ is does not lie on the curve.
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%}
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%
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@ -1,19 +1,23 @@
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\begin{ccRefConcept}{CurvePairAnalysis_2::CurvePairVerticalLine_1}
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\begin{ccRefConcept}{CurvePairAnalysis_2::StatusLine_1}
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\ccDefinition
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The \ccc{CurvePairVerticalLine_1} concept is meant to provide information
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about the intersections of a pair of curves with a (intended) vertical line
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(ignoring vertical lines of the curves themselves). Each intersection of a
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curve with the vertical line defined by some given $x$ induces an event.
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An event can be asked for its coordinates (\ccc{Algebraic_real_2})
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The \ccc{StatusLine_1} concept is meant to provide information
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about the intersections of a pair of curves with a vertical line $x = x_0$
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for some finite $x_0$,
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ignoring covered vertical lines of the curves themselves.
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Each intersection of a
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curve with the status line defined by some given $x$ induces an event.
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An event can be queried for its coordinates (\ccc{Algebraic_real_2})
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and the involved curve(s).
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Note that the involvement also holds for curve ends approaching the
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vertical asymptote. Again \ccc{CurvePairVerticalLine_1} at $x = \pm\infty$ are
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vertical asymptote. Again \ccc{StatusLine_1} at $x = \pm\infty$ are
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not allowed.
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\ccTypes
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\ccNestedType{size_type}{A instance of a size type, e.g., \ccc{int}}
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\ccNestedType{Algebraic_real_1}{Model of the concept
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\ccc{AlgebraicKernel_d_1::AlgebraicReal_1}.}
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@ -25,42 +29,44 @@ not allowed.
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\ccAccessFunctions
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\ccMethod{Algebraic_real_1 x();}{
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returns the $x$-coordinate of the vertical line (always a finite value).
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returns the $x$-coordinate of the status line (always a finite value).
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}
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\ccMethod{unsigned int number_of_events();}{
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\ccMethod{size_type number_of_events();}{
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returns number of distinct and finite intersections of a pair of
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curves with a
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(intended) vertical line ignoring a real vertical line component
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curves with a status line ignoring a real vertical line component
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of the curves at the given $x$-coordinate.
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}
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\ccMethod{unsigned int get_event_of_curve(int k, bool c);}{
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\ccMethod{size_type event_of_curve(size_type k, bool c);}{
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returns the $y$-position of the $k$-th event of the $c$-th
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(0 or 1) curve in the sequence of events. Note that each event
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is formed by the first, the second, or both curves.
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is formed by the first, the second, or both curves.
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\ccPrecond{$0 \leq k < \mbox{number of arcs defined for the curve at x()}$}
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The precondition can be checked by queried first the corresponding status
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line of the curve's analysis.
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}
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\ccMethod{unsigned int get_multiplicity_of_intersection(int j);}{
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\ccMethod{Multiplicity multiplicity_of_intersection(size_type j);}{
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returns the multiplicity of intersection defined at event with position $j$.
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May return $0$ in case multiplicity is unknown.
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\ccPrecond{There is an intersection of both curves at $j$-th event.}
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\ccPrecond{$0 \leq j < \mbox{num\_events()}$}
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}
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\ccMethod{std::pair< int, int > get_curves_at_event(int j);}{
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returns a pair of int indicating whether event $j$ is formed by
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\ccMethod{std::pair< size_type, size_type > curves_at_event(size_type j);}{
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returns a pair of \ccc{size_type} indicating whether event $j$ is formed by
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which arc numbers of the first and the second curve, or $-1$, if the
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corresponding curve is not involved.
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\ccPrecond{$0 \leq j < \mbox{num\_events()}$}
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}
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Note that this interface mainly rewrites $\{f,g,x\}^n$ in a different way -
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using ints. Actually the CPVL has to compute this sequence, but for
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using \ccc{size_type}. Actually the CPVL has to compute this sequence, but for
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the interface it is nicer to have it already here to avoid conversion objects
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(introducing additional constructor calls, cache-misses, lookup and so on) in
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the next layer on top (CK). Obviously, the ints can be computed in a generic
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the next layer on top (CK). Obviously, the \ccc{size_type}s
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can be computed in a generic
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way from a sequence, so that it makes sense to offer a default implementation
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providing such conversion. There is no need to document this fact on the
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conceptual view.
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@ -76,7 +82,7 @@ conceptual view.
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\end{ccRefConcept}
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\begin{ccRefConcept}{AlgebraicKernel_d_2::CurvePairAnalysis_2}
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\begin{ccRefConcept}{AlgebraicKernelWithAnalysis_d_2::CurvePairAnalysis_2}
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\ccDefinition
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@ -85,11 +91,11 @@ a pair of curves. An analysis is meant to describe the curve pair's
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interesting points and how they are connected.
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The analysis searches for {\it events}. Events only
|
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occur at a finite number of $x$-coordinate. Each such coordinate is
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covered by a \ccc{CurvePairVerticalLine_1},
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covered by a \ccc{StatusLine_1},
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originated by the events of a single curve
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and also the intersections of two curves.
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These coordinates also define open {\it intervals}
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on the $x$-axis. \ccc{CurvePairVerticalLine_1}
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on the $x$-axis. \ccc{StatusLine_1}
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at values in between one such interval
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differ only in the values of the \ccc{Algebraic_real_2} entries. Topological
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information are equal.
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|
@ -100,14 +106,16 @@ information are equal.
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\ccTypes
|
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\ccNestedType{size_type}{A instance of a size type, e.g., \ccc{int}}
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\ccNestedType{Algebraic_real_1}{Model of the concept
|
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\ccc{AlgebraicKernel_d_1::AlgebraicReal_1}.}
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\ccNestedType{Algebraic_real_2}{Model of the concept
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\ccc{AlgebraicKernel_d_2::AlgebraicReal_2}.}
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\ccNestedType{Curve_pair_vertical_line_1}{Model of the concept
|
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\ccc{CurvePairAnalysis_2::CurvePairVerticalLine_1}.}
|
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\ccNestedType{Status_line_1}{Model of the concept
|
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\ccc{CurvePairAnalysis_2::StatusLine_1}.}
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|
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\ccNestedType{Curve_analysis_2}{Model of the concept
|
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\ccc{CurvePairAnalysis::CurveAnalysis_2}.}
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|
|
@ -140,81 +148,82 @@ coprime.
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\ccAccessFunctions
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\ccMethod{Curve_analysis_2 get_curve_analysis(bool c);}{
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\ccMethod{Curve_analysis_2 curve_analysis(bool c);}{
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returns curve analysis for $c$-''th'' curve (0 or 1)
|
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}
|
||||
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\ccMethod{unsigned int number_of_vertical_lines_with_event();}{
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returns number of vertical lines that encode an event
|
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\ccMethod{size_type number_of_status_lines_with_event();}{
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returns number of status lines that encode an event
|
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}
|
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|
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\ccMethod{int event_of_curve_analysis(unsigned int i, bool c);}{
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\ccMethod{size_type event_of_curve_analysis(size_type i, bool c);}{
|
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Given the $i$-th event of the curve pair
|
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this method returns the id of the event of the corresponding curve
|
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analysis $c$ (0 or 1), or $-1$, if the curve has no event at this coordinate.
|
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}
|
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\ccMethod{Curve_pair_vertical_line vertical_line_at_event(int i);}{
|
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returns an instance of \ccc{CurvePairVerticalLine_1} at the $i$-th event
|
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\ccPrecond{$0 \leq i < \mbox{num\_vertical\_lines\_with\_event()}$}
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||||
\ccMethod{Status_line status_line_at_event(size_type i);}{
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returns an instance of \ccc{StatusLine_1} at the $i$-th event
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\ccPrecond{$0 \leq i < \mbox{num\_status\_lines\_with\_event()}$}
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}
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\ccMethod{Curve_pair_vertical_line vertical_line_of_interval(int i);}{
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returns an instance of \ccc{CurvePairVerticalLine_1} of the $i$-th interval
|
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\ccMethod{Status_line status_line_of_interval(size_type i);}{
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returns an instance of \ccc{StatusLine_1} of the $i$-th interval
|
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between $x$-events.
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\ccPrecond{$0 \leq i leq \mbox{num\_vertical\_lines\_with\_event()}$}
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\ccPrecond{$0 \leq i leq \mbox{num\_status\_lines\_with\_event()}$}
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}
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\ccMethod{Curve_pair_vertical_line vertical_line_for_x(Algebraic_real_1 x,
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\ccMethod{Status_line status_line_for_x(Algebraic_real_1 x,
|
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CGAL::Sign perturb = CGAL::ZERO);}{
|
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returns vertical\_line\_at\_event(i), if $x$ hits $i$-th event, otherwise
|
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returns vertical\_line\_of\_interval(i), where $i$ is the id of the interval
|
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returns status\_line\_at\_event(i), if $x$ hits $i$-th event, otherwise
|
||||
returns status\_line\_of\_interval(i), where $i$ is the id of the interval
|
||||
$x$ lies in.
|
||||
If $pertub$ is CGAL::NEGATIVE (CGAL::POSITIVE) and $x$ states
|
||||
an event, then vertical\_line\_of\_interval(i)
|
||||
(vertical\_line\_of\_interval(i+1)) is returned.
|
||||
an event, then status\_line\_of\_interval(i)
|
||||
(status\_line\_of\_interval(i+1)) is returned.
|
||||
\ccPrecond{$x$ is finite}
|
||||
}
|
||||
|
||||
\ccMethod{Curve_pair_vertical_line vertical_line_at_exact_x(Algebraic_real_1 x);}{
|
||||
returns an instance of \ccc{CurvePairVerticalLine_1} at the given $x$
|
||||
\ccMethod{Status_line status_line_at_exact_x(Algebraic_real_1 x);}{
|
||||
returns an instance of \ccc{StatusLine_1} at the given $x$
|
||||
\ccPrecond{$x$ is finite}
|
||||
}
|
||||
|
||||
Note that the access methods to vertical lines are not redundant! The ones
|
||||
Note that the access methods to status lines are not redundant! The ones
|
||||
using an id-value are efficient for speed-ups (caching, avoids to search some
|
||||
$x$, or the unique representative vertical line for an interval). The others
|
||||
enable a user to compute vertical lines for given $x$.
|
||||
$x$, or the unique representative status line for an interval). The others
|
||||
enable a user to compute status lines for given $x$.
|
||||
|
||||
\begin{ccAdvanced}
|
||||
%
|
||||
%\begin{ccAdvanced}
|
||||
%
|
||||
%\ccMethod{Algebraic_real_2_const_iterator solve_begin();}{
|
||||
% returns iterator running over all finite intersection of the two curves.
|
||||
%}
|
||||
%
|
||||
%\ccMethod{Algebraic_real_2_const_iterator solve_end();}{
|
||||
% returns past-end-value for all finite intersections of the two curves.
|
||||
%}
|
||||
|
||||
\ccMethod{Algebraic_real_2_const_iterator solve_begin();}{
|
||||
returns iterator running over all finite intersection of the two curves.
|
||||
}
|
||||
|
||||
\ccMethod{Algebraic_real_2_const_iterator solve_end();}{
|
||||
returns past-end-value for all finite intersections of the two curves.
|
||||
}
|
||||
|
||||
%\ccMethod{int find(Algebraic_real_2 s);}{
|
||||
% returns the index of the event at the vertical line defined by
|
||||
%\ccMethod{size_type find(Algebraic_real_2 s);}{
|
||||
% returns the index of the event at the status line defined by
|
||||
% $s$'s $x$-coordinate, or -1 if $s$ is does not lie on any curve.
|
||||
%}
|
||||
|
||||
\end{ccAdvanced}
|
||||
%\end{ccAdvanced}
|
||||
|
||||
|
||||
%Additionally note that we talk about 4 sequences of $x$-critical lines here.
|
||||
%
|
||||
%\begin{itemize}
|
||||
%\item The sequence of CurveVerticalLine\_1 of $p$ where each CVL has been
|
||||
%\item The sequence of StatusLine\_1 of $p$ where each CVL has been
|
||||
%converted and merged with $q$ to a CVPL.
|
||||
%\item The sequence of CurveVerticalLine\_1 of $q$ where each CVL has been
|
||||
%\item The sequence of StatusLine\_1 of $q$ where each CVL has been
|
||||
%converted and merged with $p$ to a CPVL.
|
||||
%\item The sequence of CurvePairVerticalLine\_1 of the intersections of
|
||||
%\item The sequence of StatusLine\_1 of the intersections of
|
||||
%$p$ and $q$
|
||||
%\item The merged sequence of CurvePairVerticalLine_1 of the former three
|
||||
%\item The merged sequence of StatusLine_1 of the former three
|
||||
%sequences. The method event\_id\_of\_x helps to find indexes in the first
|
||||
%three sequences starting from an index in this sequence!
|
||||
%\end{itemize}
|
||||
|
|
|
|||
Loading…
Reference in New Issue