CGAL 4.5.2 - 2D Envelopes
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This package consists of functions that compute the lower (or upper) envelope of a set of arbitrary curves in 2D. The output is represented as an envelope diagram, namely a subdivision of the \( x\)-axis into intervals, such that the identity of the curves that induce the envelope over each interval is unique.
CGAL::lower_envelope_2
CGAL::upper_envelope_2
CGAL::lower_envelope_x_monotone_2
CGAL::upper_envelope_x_monotone_2
CGAL::Envelope_diagram_1<Traits>
Modules | |
Concepts | |
Classes | |
class | CGAL::Envelope_diagram_1< Traits > |
This class is the default envelope-diagram class used by envelope functions to represent the minimization or the maximization diagram of a set of curves. More... | |
Functions | |
template<class InputIterator , class EnvelopeDiagram > | |
void | CGAL::lower_envelope_2 (InputIterator begin, InputIterator end, EnvelopeDiagram &diag) |
Computes the lower envelope of a set of curves in \( \mathbb{R}^2\), as given by the range [begin, end) . More... | |
template<class InputIterator , class EnvelopeDiagram > | |
void | CGAL::lower_envelope_x_monotone_2 (InputIterator begin, InputIterator end, EnvelopeDiagram &diag) |
Computes the lower envelope of a set of \( x\)-monotone curves in \( \mathbb{R}^2\), as given by the range [begin, end) . More... | |
template<class InputIterator , class EnvelopeDiagram > | |
void | CGAL::upper_envelope_2 (InputIterator begin, InputIterator end, EnvelopeDiagram &diag) |
Computes the upper envelope of a set of curves in \( \mathbb{R}^2\), as given by the range [begin, end) . More... | |
template<class InputIterator , class EnvelopeDiagram > | |
void | CGAL::upper_envelope_x_monotone_2 (InputIterator begin, InputIterator end, EnvelopeDiagram &diag) |
Computes the upper envelope of a set of \( x\)-monotone curves in \( \mathbb{R}^2\), as given by the range [begin, end) . More... | |
void CGAL::lower_envelope_2 | ( | InputIterator | begin, |
InputIterator | end, | ||
EnvelopeDiagram & | diag | ||
) |
Computes the lower envelope of a set of curves in \( \mathbb{R}^2\), as given by the range [begin, end)
.
The lower envelope is represented using the output minimization diagram diag
.
InputIterator | must be an input iterator with value type EnvelopeDiagram::Traits_2::Curve_2 . |
EnvelopeDiagram | must be a model of the concept EnvelopeDiagram_1 . |
#include <CGAL/envelope_2.h>
void CGAL::lower_envelope_x_monotone_2 | ( | InputIterator | begin, |
InputIterator | end, | ||
EnvelopeDiagram & | diag | ||
) |
Computes the lower envelope of a set of \( x\)-monotone curves in \( \mathbb{R}^2\), as given by the range [begin, end)
.
The lower envelope is represented using the output minimization diagram diag
.
InputIterator | must be an input iterator with value type EnvelopeDiagram::X_monotone_curve_2 . |
EnvelopeDiagram | must be a model of the concept EnvelopeDiagram_1 . |
#include <CGAL/envelope_2.h>
void CGAL::upper_envelope_2 | ( | InputIterator | begin, |
InputIterator | end, | ||
EnvelopeDiagram & | diag | ||
) |
Computes the upper envelope of a set of curves in \( \mathbb{R}^2\), as given by the range [begin, end)
.
The upper envelope is represented using the output maximization diagram diag
.
InputIterator | must be an input iterator with value type EnvelopeDiagram::Traits_2::Curve_2 . |
EnvelopeDiagram | must be a model of the concept EnvelopeDiagram_1 . |
#include <CGAL/envelope_2.h>
void CGAL::upper_envelope_x_monotone_2 | ( | InputIterator | begin, |
InputIterator | end, | ||
EnvelopeDiagram & | diag | ||
) |
Computes the upper envelope of a set of \( x\)-monotone curves in \( \mathbb{R}^2\), as given by the range [begin, end)
.
The upper envelope is represented using the output maximization diagram diag
.
InputIterator | must be an input iterator with value type EnvelopeDiagram::X_monotone_curve_2 . |
EnvelopeDiagram | must be a model of the concept EnvelopeDiagram_1 . |
#include <CGAL/envelope_2.h>