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Parma_Polyhedra_Library::C_Polyhedron Class Reference
C++ Language Interface

A closed convex polyhedron. More...

`#include <ppl.hh>`

Inheritance diagram for Parma_Polyhedra_Library::C_Polyhedron:
[legend]

## Public Member Functions
| C_Polyhedron (dimension_type num_dimensions=0, Degenerate_Element kind=UNIVERSE)
| Builds either the universe or the empty C polyhedron. More...
| C_Polyhedron (const Constraint_System &cs)
| Builds a C polyhedron from a system of constraints. More...
| C_Polyhedron (Constraint_System &cs, Recycle_Input dummy)
| Builds a C polyhedron recycling a system of constraints. More...
| C_Polyhedron (const Generator_System &gs)
| Builds a C polyhedron from a system of generators. More...
| C_Polyhedron (Generator_System &gs, Recycle_Input dummy)
| Builds a C polyhedron recycling a system of generators. More...
| C_Polyhedron (const Congruence_System &cgs)
| Builds a C polyhedron from a system of congruences. More...
| C_Polyhedron (Congruence_System &cgs, Recycle_Input dummy)
| Builds a C polyhedron recycling a system of congruences. More...
| C_Polyhedron (const NNC_Polyhedron &y, Complexity_Class complexity=ANY_COMPLEXITY)
| Builds a C polyhedron representing the topological closure of the NNC polyhedron `y`. More...
template<typename Interval >
| C_Polyhedron (const Box< Interval > &box, Complexity_Class complexity=ANY_COMPLEXITY)
| Builds a C polyhedron out of a box. More...
template<typename U >
| C_Polyhedron (const BD_Shape< U > &bd, Complexity_Class complexity=ANY_COMPLEXITY)
| Builds a C polyhedron out of a BD shape. More...
template<typename U >
| C_Polyhedron (const Octagonal_Shape< U > &os, Complexity_Class complexity=ANY_COMPLEXITY)
| Builds a C polyhedron out of an octagonal shape. More...
| C_Polyhedron (const Grid &grid, Complexity_Class complexity=ANY_COMPLEXITY)
| Builds a C polyhedron out of a grid. More...
| C_Polyhedron (const C_Polyhedron &y, Complexity_Class complexity=ANY_COMPLEXITY)
| Ordinary copy constructor. More...
C_Polyhedron & | operator= (const C_Polyhedron &y)
| The assignment operator. (`*this` and `y` can be dimension-incompatible.)
C_Polyhedron & | operator= (const NNC_Polyhedron &y)
| Assigns to `*this` the topological closure of the NNC polyhedron `y`.
| ~C_Polyhedron ()
| Destructor.
bool | poly_hull_assign_if_exact (const C_Polyhedron &y)
| If the poly-hull of `*this` and `y` is exact it is assigned to `*this` and `true` is returned, otherwise `false` is returned. More...
bool | upper_bound_assign_if_exact (const C_Polyhedron &y)
| Same as poly_hull_assign_if_exact(y).
void | positive_time_elapse_assign (const Polyhedron &y)
| Assigns to `*this` the smallest C polyhedron containing the result of computing the positive time-elapse between `*this` and `y`. More...
Public Member Functions inherited from Parma_Polyhedra_Library::Polyhedron
dimension_type | space_dimension () const
| Returns the dimension of the vector space enclosing `*this`.
dimension_type | affine_dimension () const
| Returns , if `*this` is empty; otherwise, returns the affine dimension of `*this`.
const Constraint_System & | constraints () const
| Returns the system of constraints.
const Constraint_System & | minimized_constraints () const
| Returns the system of constraints, with no redundant constraint.
const Generator_System & | generators () const
| Returns the system of generators.
const Generator_System & | minimized_generators () const
| Returns the system of generators, with no redundant generator.
Congruence_System | congruences () const
| Returns a system of (equality) congruences satisfied by `*this`.
Congruence_System | minimized_congruences () const
| Returns a system of (equality) congruences satisfied by `*this`, with no redundant congruences and having the same affine dimension as `*this`.
Poly_Con_Relation | relation_with (const Constraint &c) const
| Returns the relations holding between the polyhedron `*this` and the constraint `c`. More...
Poly_Gen_Relation | relation_with (const Generator &g) const
| Returns the relations holding between the polyhedron `*this` and the generator `g`. More...
Poly_Con_Relation | relation_with (const Congruence &cg) const
| Returns the relations holding between the polyhedron `*this` and the congruence `c`. More...
bool | is_empty () const
| Returns `true` if and only if `*this` is an empty polyhedron.
bool | is_universe () const
| Returns `true` if and only if `*this` is a universe polyhedron.
bool | is_topologically_closed () const
| Returns `true` if and only if `*this` is a topologically closed subset of the vector space.
bool | is_disjoint_from (const Polyhedron &y) const
| Returns `true` if and only if `*this` and `y` are disjoint. More...
bool | is_discrete () const
| Returns `true` if and only if `*this` is discrete.
bool | is_bounded () const
| Returns `true` if and only if `*this` is a bounded polyhedron.
bool | contains_integer_point () const
| Returns `true` if and only if `*this` contains at least one integer point.
bool | constrains (Variable var) const
| Returns `true` if and only if `var` is constrained in `*this`. More...
bool | bounds_from_above (const Linear_Expression &expr) const
| Returns `true` if and only if `expr` is bounded from above in `*this`. More...
bool | bounds_from_below (const Linear_Expression &expr) const
| Returns `true` if and only if `expr` is bounded from below in `*this`. More...
bool | maximize (const Linear_Expression &expr, Coefficient &sup_n, Coefficient &sup_d, bool &maximum) const
| Returns `true` if and only if `*this` is not empty and `expr` is bounded from above in `*this`, in which case the supremum value is computed. More...
bool | maximize (const Linear_Expression &expr, Coefficient &sup_n, Coefficient &sup_d, bool &maximum, Generator &g) const
| Returns `true` if and only if `*this` is not empty and `expr` is bounded from above in `*this`, in which case the supremum value and a point where `expr` reaches it are computed. More...
bool | minimize (const Linear_Expression &expr, Coefficient &inf_n, Coefficient &inf_d, bool &minimum) const
| Returns `true` if and only if `*this` is not empty and `expr` is bounded from below in `*this`, in which case the infimum value is computed. More...
bool | minimize (const Linear_Expression &expr, Coefficient &inf_n, Coefficient &inf_d, bool &minimum, Generator &g) const
| Returns `true` if and only if `*this` is not empty and `expr` is bounded from below in `*this`, in which case the infimum value and a point where `expr` reaches it are computed. More...
bool | frequency (const Linear_Expression &expr, Coefficient &freq_n, Coefficient &freq_d, Coefficient &val_n, Coefficient &val_d) const
| Returns `true` if and only if there exist a unique value `val` such that `*this` saturates the equality `expr = val`. More...
bool | contains (const Polyhedron &y) const
| Returns `true` if and only if `*this` contains `y`. More...
bool | strictly_contains (const Polyhedron &y) const
| Returns `true` if and only if `*this` strictly contains `y`. More...
bool | OK (bool check_not_empty=false) const
| Checks if all the invariants are satisfied. More...
void | add_constraint (const Constraint &c)
| Adds a copy of constraint `c` to the system of constraints of `*this` (without minimizing the result). More...
void | add_generator (const Generator &g)
| Adds a copy of generator `g` to the system of generators of `*this` (without minimizing the result). More...
void | add_congruence (const Congruence &cg)
| Adds a copy of congruence `cg` to `*this`, if `cg` can be exactly represented by a polyhedron. More...
void | add_constraints (const Constraint_System &cs)
| Adds a copy of the constraints in `cs` to the system of constraints of `*this` (without minimizing the result). More...
void | add_recycled_constraints (Constraint_System &cs)
| Adds the constraints in `cs` to the system of constraints of `*this` (without minimizing the result). More...
void | add_generators (const Generator_System &gs)
| Adds a copy of the generators in `gs` to the system of generators of `*this` (without minimizing the result). More...
void | add_recycled_generators (Generator_System &gs)
| Adds the generators in `gs` to the system of generators of `*this` (without minimizing the result). More...
void | add_congruences (const Congruence_System &cgs)
| Adds a copy of the congruences in `cgs` to `*this`, if all the congruences can be exactly represented by a polyhedron. More...
void | add_recycled_congruences (Congruence_System &cgs)
| Adds the congruences in `cgs` to `*this`, if all the congruences can be exactly represented by a polyhedron. More...
void | refine_with_constraint (const Constraint &c)
| Uses a copy of constraint `c` to refine `*this`. More...
void | refine_with_congruence (const Congruence &cg)
| Uses a copy of congruence `cg` to refine `*this`. More...
void | refine_with_constraints (const Constraint_System &cs)
| Uses a copy of the constraints in `cs` to refine `*this`. More...
void | refine_with_congruences (const Congruence_System &cgs)
| Uses a copy of the congruences in `cgs` to refine `*this`. More...
template<typename FP_Format , typename Interval_Info >
void | refine_with_linear_form_inequality (const Linear_Form< Interval< FP_Format, Interval_Info > > &left, const Linear_Form< Interval< FP_Format, Interval_Info > > &right, bool is_strict=false)
| Refines `*this` with the constraint expressed by `left` `right` if `is_strict` is set, with the constraint `left` `right` otherwise. More...
template<typename FP_Format , typename Interval_Info >
void | generalized_refine_with_linear_form_inequality (const Linear_Form< Interval< FP_Format, Interval_Info > > &left, const Linear_Form< Interval< FP_Format, Interval_Info > > &right, Relation_Symbol relsym)
| Refines `*this` with the constraint expressed by `left` `right`, where is the relation symbol specified by `relsym`.. More...
template<typename FP_Format , typename Interval_Info >
void | refine_fp_interval_abstract_store (Box< Interval< FP_Format, Interval_Info > > &store) const
| Refines `store` with the constraints defining `*this`. More...
void | unconstrain (Variable var)
| Computes the cylindrification of `*this` with respect to space dimension `var`, assigning the result to `*this`. More...
void | unconstrain (const Variables_Set &vars)
| Computes the cylindrification of `*this` with respect to the set of space dimensions `vars`, assigning the result to `*this`. More...
void | intersection_assign (const Polyhedron &y)
| Assigns to `*this` the intersection of `*this` and `y`. More...
void | poly_hull_assign (const Polyhedron &y)
| Assigns to `*this` the poly-hull of `*this` and `y`. More...
void | upper_bound_assign (const Polyhedron &y)
| Same as poly_hull_assign(y).
void | poly_difference_assign (const Polyhedron &y)
| Assigns to `*this` the poly-difference of `*this` and `y`. More...
void | difference_assign (const Polyhedron &y)
| Same as poly_difference_assign(y).
bool | simplify_using_context_assign (const Polyhedron &y)
| Assigns to `*this` a meet-preserving simplification of `*this` with respect to `y`. If `false` is returned, then the intersection is empty. More...
void | affine_image (Variable var, const Linear_Expression &expr, Coefficient_traits::const_reference denominator=Coefficient_one())
| Assigns to `*this` the affine image of `*this` under the function mapping variable `var` to the affine expression specified by `expr` and `denominator`. More...
template<typename FP_Format , typename Interval_Info >
void | affine_form_image (Variable var, const Linear_Form< Interval< FP_Format, Interval_Info > > &lf)
void | affine_preimage (Variable var, const Linear_Expression &expr, Coefficient_traits::const_reference denominator=Coefficient_one())
| Assigns to `*this` the affine preimage of `*this` under the function mapping variable `var` to the affine expression specified by `expr` and `denominator`. More...
void | generalized_affine_image (Variable var, Relation_Symbol relsym, const Linear_Expression &expr, Coefficient_traits::const_reference denominator=Coefficient_one())
| Assigns to `*this` the image of `*this` with respect to the generalized affine relation , where is the relation symbol encoded by `relsym`. More...
void | generalized_affine_preimage (Variable var, Relation_Symbol relsym, const Linear_Expression &expr, Coefficient_traits::const_reference denominator=Coefficient_one())
| Assigns to `*this` the preimage of `*this` with respect to the generalized affine relation , where is the relation symbol encoded by `relsym`. More...
void | generalized_affine_image (const Linear_Expression &lhs, Relation_Symbol relsym, const Linear_Expression &rhs)
| Assigns to `*this` the image of `*this` with respect to the generalized affine relation , where is the relation symbol encoded by `relsym`. More...
void | generalized_affine_preimage (const Linear_Expression &lhs, Relation_Symbol relsym, const Linear_Expression &rhs)
| Assigns to `*this` the preimage of `*this` with respect to the generalized affine relation , where is the relation symbol encoded by `relsym`. More...
void | bounded_affine_image (Variable var, const Linear_Expression &lb_expr, const Linear_Expression &ub_expr, Coefficient_traits::const_reference denominator=Coefficient_one())
| Assigns to `*this` the image of `*this` with respect to the bounded affine relation . More...
void | bounded_affine_preimage (Variable var, const Linear_Expression &lb_expr, const Linear_Expression &ub_expr, Coefficient_traits::const_reference denominator=Coefficient_one())
| Assigns to `*this` the preimage of `*this` with respect to the bounded affine relation . More...
void | time_elapse_assign (const Polyhedron &y)
| Assigns to `*this` the result of computing the time-elapse between `*this` and `y`. More...
void | positive_time_elapse_assign (const Polyhedron &y)
| Assigns to `*this` (the best approximation of) the result of computing the positive time-elapse between `*this` and `y`. More...
void | wrap_assign (const Variables_Set &vars, Bounded_Integer_Type_Width w, Bounded_Integer_Type_Representation r, Bounded_Integer_Type_Overflow o, const Constraint_System *cs_p=0, unsigned complexity_threshold=16, bool wrap_individually=true)
| Wraps the specified dimensions of the vector space. More...
void | drop_some_non_integer_points (Complexity_Class complexity=ANY_COMPLEXITY)
| Possibly tightens `*this` by dropping some points with non-integer coordinates. More...
void | drop_some_non_integer_points (const Variables_Set &vars, Complexity_Class complexity=ANY_COMPLEXITY)
| Possibly tightens `*this` by dropping some points with non-integer coordinates for the space dimensions corresponding to `vars`. More...
void | topological_closure_assign ()
| Assigns to `*this` its topological closure.
void | BHRZ03_widening_assign (const Polyhedron &y, unsigned *tp=0)
| Assigns to `*this` the result of computing the BHRZ03-widening between `*this` and `y`. More...
void | limited_BHRZ03_extrapolation_assign (const Polyhedron &y, const Constraint_System &cs, unsigned *tp=0)
| Assigns to `*this` the result of computing the limited extrapolation between `*this` and `y` using the BHRZ03-widening operator. More...
void | bounded_BHRZ03_extrapolation_assign (const Polyhedron &y, const Constraint_System &cs, unsigned *tp=0)
| Assigns to `*this` the result of computing the bounded extrapolation between `*this` and `y` using the BHRZ03-widening operator. More...
void | H79_widening_assign (const Polyhedron &y, unsigned *tp=0)
| Assigns to `*this` the result of computing the H79_widening between `*this` and `y`. More...
void | widening_assign (const Polyhedron &y, unsigned *tp=0)
| Same as H79_widening_assign(y, tp).
void | limited_H79_extrapolation_assign (const Polyhedron &y, const Constraint_System &cs, unsigned *tp=0)
| Assigns to `*this` the result of computing the limited extrapolation between `*this` and `y` using the H79-widening operator. More...
void | bounded_H79_extrapolation_assign (const Polyhedron &y, const Constraint_System &cs, unsigned *tp=0)
| Assigns to `*this` the result of computing the bounded extrapolation between `*this` and `y` using the H79-widening operator. More...
void | add_space_dimensions_and_embed (dimension_type m)
| Adds `m` new space dimensions and embeds the old polyhedron in the new vector space. More...
void | add_space_dimensions_and_project (dimension_type m)
| Adds `m` new space dimensions to the polyhedron and does not embed it in the new vector space. More...
void | concatenate_assign (const Polyhedron &y)
| Assigns to `*this` the concatenation of `*this` and `y`, taken in this order. More...
void | remove_space_dimensions (const Variables_Set &vars)
| Removes all the specified dimensions from the vector space. More...
void | remove_higher_space_dimensions (dimension_type new_dimension)
| Removes the higher dimensions of the vector space so that the resulting space will have dimension `new_dimension`. More...
template<typename Partial_Function >
void | map_space_dimensions (const Partial_Function &pfunc)
| Remaps the dimensions of the vector space according to a partial function. More...
void | expand_space_dimension (Variable var, dimension_type m)
| Creates `m` copies of the space dimension corresponding to `var`. More...
void | fold_space_dimensions (const Variables_Set &vars, Variable dest)
| Folds the space dimensions in `vars` into `dest`. More...
| ~Polyhedron ()
| Destructor.
void | m_swap (Polyhedron &y)
| Swaps `*this` with polyhedron `y`. (`*this` and `y` can be dimension-incompatible.) More...
void | ascii_dump () const
| Writes to `std::cerr` an ASCII representation of `*this`.
void | ascii_dump (std::ostream &s) const
| Writes to `s` an ASCII representation of `*this`.
void | print () const
| Prints `*this` to `std::cerr` using `operator<<`.
bool | ascii_load (std::istream &s)
| Loads from `s` an ASCII representation (as produced by ascii_dump(std::ostream&) const) and sets `*this` accordingly. Returns `true` if successful, `false` otherwise.
memory_size_type | total_memory_in_bytes () const
| Returns the total size in bytes of the memory occupied by `*this`.
memory_size_type | external_memory_in_bytes () const
| Returns the size in bytes of the memory managed by `*this`.
int32_t | hash_code () const
| Returns a 32-bit hash code for `*this`. More...

## Additional Inherited Members
Public Types inherited from Parma_Polyhedra_Library::Polyhedron
typedef Coefficient | coefficient_type
| The numeric type of coefficients.
Static Public Member Functions inherited from Parma_Polyhedra_Library::Polyhedron
static dimension_type | max_space_dimension ()
| Returns the maximum space dimension all kinds of Polyhedron can handle.
static bool | can_recycle_constraint_systems ()
| Returns `true` indicating that this domain has methods that can recycle constraints.
static void | initialize ()
| Initializes the class.
static void | finalize ()
| Finalizes the class.
static bool | can_recycle_congruence_systems ()
| Returns `false` indicating that this domain cannot recycle congruences.
Protected Member Functions inherited from Parma_Polyhedra_Library::Polyhedron
| Polyhedron (Topology topol, dimension_type num_dimensions, Degenerate_Element kind)
| Builds a polyhedron having the specified properties. More...
| Polyhedron (const Polyhedron &y, Complexity_Class complexity=ANY_COMPLEXITY)
| Ordinary copy constructor. More...
| Polyhedron (Topology topol, const Constraint_System &cs)
| Builds a polyhedron from a system of constraints. More...
| Polyhedron (Topology topol, Constraint_System &cs, Recycle_Input dummy)
| Builds a polyhedron recycling a system of constraints. More...
| Polyhedron (Topology topol, const Generator_System &gs)
| Builds a polyhedron from a system of generators. More...
| Polyhedron (Topology topol, Generator_System &gs, Recycle_Input dummy)
| Builds a polyhedron recycling a system of generators. More...
template<typename Interval >
| Polyhedron (Topology topol, const Box< Interval > &box, Complexity_Class complexity=ANY_COMPLEXITY)
| Builds a polyhedron from a box. More...
Polyhedron & | operator= (const Polyhedron &y)
| The assignment operator. (`*this` and `y` can be dimension-incompatible.)
void | drop_some_non_integer_points (const Variables_Set *vars_p, Complexity_Class complexity)
| Possibly tightens `*this` by dropping some points with non-integer coordinates for the space dimensions corresponding to `*vars_p`. More...
template<typename FP_Format , typename Interval_Info >
void | overapproximate_linear_form (const Linear_Form< Interval< FP_Format, Interval_Info > > &lf, const dimension_type lf_dimension, Linear_Form< Interval< FP_Format, Interval_Info > > &result)
| Helper function that overapproximates an interval linear form. More...
void | positive_time_elapse_assign_impl (const Polyhedron &y)
| Assuming `*this` is NNC, assigns to `*this` the result of the "positive time-elapse" between `*this` and `y`. More...
Static Protected Member Functions inherited from Parma_Polyhedra_Library::Polyhedron
template<typename FP_Format , typename Interval_Info >
static void | convert_to_integer_expression (const Linear_Form< Interval< FP_Format, Interval_Info > > &lf, const dimension_type lf_dimension, Linear_Expression &result)
| Helper function that makes `result` become a Linear_Expression obtained by normalizing the denominators in `lf`. More...
template<typename FP_Format , typename Interval_Info >
static void | convert_to_integer_expressions (const Linear_Form< Interval< FP_Format, Interval_Info > > &lf, const dimension_type lf_dimension, Linear_Expression &res, Coefficient &res_low_coeff, Coefficient &res_hi_coeff, Coefficient &denominator)
| Normalization helper function. More...
Related Functions inherited from Parma_Polyhedra_Library::Polyhedron
std::ostream & | operator<< (std::ostream &s, const Polyhedron &ph)
| Output operator. More...
void | swap (Polyhedron &x, Polyhedron &y)
| Swaps `x` with `y`. More...
bool | operator== (const Polyhedron &x, const Polyhedron &y)
| Returns `true` if and only if `x` and `y` are the same polyhedron. More...
bool | operator!= (const Polyhedron &x, const Polyhedron &y)
| Returns `true` if and only if `x` and `y` are different polyhedra. More...
void | swap (Polyhedron &x, Polyhedron &y)
bool | operator!= (const Polyhedron &x, const Polyhedron &y)

## Detailed Description

A closed convex polyhedron.

An object of the class C_Polyhedron represents a topologically closed convex polyhedron in the vector space .

When building a closed polyhedron starting from a system of constraints, an exception is thrown if the system contains a strict inequality constraint. Similarly, an exception is thrown when building a closed polyhedron starting from a system of generators containing a closure point.

Note
  Such an exception will be obtained even if the system of constraints (resp., generators) actually defines a topologically closed subset of the vector space, i.e., even if all the strict inequalities (resp., closure points) in the system happen to be redundant with respect to the system obtained by removing all the strict inequality constraints (resp., all the closure points). In contrast, when building a closed polyhedron starting from an object of the class NNC_Polyhedron, the precise topological closure test will be performed.

## Constructor & Destructor Documentation

Parma_Polyhedra_Library::C_Polyhedron::C_Polyhedron | ( | dimension_type | num_dimensions = `0`,
|  | Degenerate_Element | kind = `UNIVERSE`
| ) |  |
| inline explicit

Builds either the universe or the empty C polyhedron.

Parameters

  num_dimensions | The number of dimensions of the vector space enclosing the C polyhedron;
  kind | Specifies whether a universe or an empty C polyhedron should be built.

Exceptions

  std::length_error | Thrown if `num_dimensions` exceeds the maximum allowed space dimension.

Both parameters are optional: by default, a 0-dimension space universe C polyhedron is built.

Parma_Polyhedra_Library::C_Polyhedron::C_Polyhedron | ( | const Constraint_System & | cs | ) |
| inline explicit

Builds a C polyhedron from a system of constraints.

The polyhedron inherits the space dimension of the constraint system.

Parameters

  cs | The system of constraints defining the polyhedron.

Exceptions

  std::invalid_argument | Thrown if the system of constraints contains strict inequalities.

Parma_Polyhedra_Library::C_Polyhedron::C_Polyhedron | ( | Constraint_System & | cs,
|  | Recycle_Input | dummy
| ) |  |
| inline

Builds a C polyhedron recycling a system of constraints.

The polyhedron inherits the space dimension of the constraint system.

Parameters

  cs | The system of constraints defining the polyhedron. It is not declared `const` because its data-structures may be recycled to build the polyhedron.
  dummy | A dummy tag to syntactically differentiate this one from the other constructors.

Exceptions

  std::invalid_argument | Thrown if the system of constraints contains strict inequalities.

Parma_Polyhedra_Library::C_Polyhedron::C_Polyhedron | ( | const Generator_System & | gs | ) |
| inline explicit

Builds a C polyhedron from a system of generators.

The polyhedron inherits the space dimension of the generator system.

Parameters

  gs | The system of generators defining the polyhedron.

Exceptions

  std::invalid_argument | Thrown if the system of generators is not empty but has no points, or if it contains closure points.

Parma_Polyhedra_Library::C_Polyhedron::C_Polyhedron | ( | Generator_System & | gs,
|  | Recycle_Input | dummy
| ) |  |
| inline

Builds a C polyhedron recycling a system of generators.

The polyhedron inherits the space dimension of the generator system.

Parameters

  gs | The system of generators defining the polyhedron. It is not declared `const` because its data-structures may be recycled to build the polyhedron.
  dummy | A dummy tag to syntactically differentiate this one from the other constructors.

Exceptions

  std::invalid_argument | Thrown if the system of generators is not empty but has no points, or if it contains closure points.

Parma_Polyhedra_Library::C_Polyhedron::C_Polyhedron | ( | const Congruence_System & | cgs | ) |
| explicit

Builds a C polyhedron from a system of congruences.

The polyhedron inherits the space dimension of the congruence system.

Parameters

  cgs | The system of congruences defining the polyhedron.

Parma_Polyhedra_Library::C_Polyhedron::C_Polyhedron | ( | Congruence_System & | cgs,
|  | Recycle_Input | dummy
| ) |  |

Builds a C polyhedron recycling a system of congruences.

The polyhedron inherits the space dimension of the congruence system.

Parameters

  cgs | The system of congruences defining the polyhedron. It is not declared `const` because its data-structures may be recycled to build the polyhedron.
  dummy | A dummy tag to syntactically differentiate this one from the other constructors.

Parma_Polyhedra_Library::C_Polyhedron::C_Polyhedron | ( | const NNC_Polyhedron & | y,
|  | Complexity_Class | complexity = `ANY_COMPLEXITY`
| ) |  |
| explicit

Builds a C polyhedron representing the topological closure of the NNC polyhedron `y`.

Parameters

  y | The NNC polyhedron to be used;
  complexity | This argument is ignored.

template<typename Interval >

Parma_Polyhedra_Library::C_Polyhedron::C_Polyhedron | ( | const Box< Interval > & | box,
|  | Complexity_Class | complexity = `ANY_COMPLEXITY`
| ) |  |
| inline explicit

Builds a C polyhedron out of a box.

The polyhedron inherits the space dimension of the box and is the most precise that includes the box. The algorithm used has polynomial complexity.

Parameters

  box | The box representing the polyhedron to be approximated;
  complexity | This argument is ignored.

Exceptions

  std::length_error | Thrown if the space dimension of `box` exceeds the maximum allowed space dimension.

template<typename U >

Parma_Polyhedra_Library::C_Polyhedron::C_Polyhedron | ( | const BD_Shape< U > & | bd,
|  | Complexity_Class | complexity = `ANY_COMPLEXITY`
| ) |  |
| inline explicit

Builds a C polyhedron out of a BD shape.

The polyhedron inherits the space dimension of the BDS and is the most precise that includes the BDS.

Parameters

  bd | The BDS used to build the polyhedron.
  complexity | This argument is ignored as the algorithm used has polynomial complexity.

template<typename U >

Parma_Polyhedra_Library::C_Polyhedron::C_Polyhedron | ( | const Octagonal_Shape< U > & | os,
|  | Complexity_Class | complexity = `ANY_COMPLEXITY`
| ) |  |
| inline explicit

Builds a C polyhedron out of an octagonal shape.

The polyhedron inherits the space dimension of the octagonal shape and is the most precise that includes the octagonal shape.

Parameters

  os | The octagonal shape used to build the polyhedron.
  complexity | This argument is ignored as the algorithm used has polynomial complexity.

Parma_Polyhedra_Library::C_Polyhedron::C_Polyhedron | ( | const Grid & | grid,
|  | Complexity_Class | complexity = `ANY_COMPLEXITY`
| ) |  |
| explicit

Builds a C polyhedron out of a grid.

The polyhedron inherits the space dimension of the grid and is the most precise that includes the grid.

Parameters

  grid | The grid used to build the polyhedron.
  complexity | This argument is ignored as the algorithm used has polynomial complexity.

Parma_Polyhedra_Library::C_Polyhedron::C_Polyhedron | ( | const C_Polyhedron & | y,
|  | Complexity_Class | complexity = `ANY_COMPLEXITY`
| ) |  |
| inline

Ordinary copy constructor.

The complexity argument is ignored.

## Member Function Documentation

bool Parma_Polyhedra_Library::C_Polyhedron::poly_hull_assign_if_exact | ( | const C_Polyhedron & | y | ) |

If the poly-hull of `*this` and `y` is exact it is assigned to `*this` and `true` is returned, otherwise `false` is returned.

Exceptions

  std::invalid_argument | Thrown if `*this` and `y` are dimension-incompatible.

void Parma_Polyhedra_Library::C_Polyhedron::positive_time_elapse_assign | ( | const Polyhedron & | y | ) |

Assigns to `*this` the smallest C polyhedron containing the result of computing the positive time-elapse between `*this` and `y`.

Exceptions

  std::invalid_argument | Thrown if `*this` and `y` are dimension-incompatible.

The documentation for this class was generated from the following file:

- ppl.hh