Public Types | |
| enum | Type { LINE, RAY, POINT, CLOSURE_POINT } |
| The generator type. More... | |
Public Member Functions | |
| Generator (const Generator &g) | |
| Ordinary copy-constructor. | |
| ~Generator () | |
| Destructor. | |
| Generator & | operator= (const Generator &g) |
| Assignment operator. | |
| dimension_type | space_dimension () const |
Returns the dimension of the vector space enclosing *this. | |
| Type | type () const |
Returns the generator type of *this. | |
| bool | is_line () const |
Returns true if and only if *this is a line. | |
| bool | is_ray () const |
Returns true if and only if *this is a ray. | |
| bool | is_point () const |
Returns true if and only if *this is a point. | |
| bool | is_closure_point () const |
Returns true if and only if *this is a closure point. | |
| const Integer & | coefficient (Variable v) const |
Returns the coefficient of v in *this. | |
| const Integer & | divisor () const |
If *this is either a point or a closure point, returns its divisor. | |
| bool | OK () const |
| Checks if all the invariants are satisfied. | |
Static Public Member Functions | |
| Generator | line (const LinExpression &e) |
| Shorthand for Generator Generator::line(const LinExpression& e). | |
| Generator | ray (const LinExpression &e) |
| Shorthand for Generator Generator::ray(const LinExpression& e). | |
| Generator | point (const LinExpression &e=LinExpression::zero(), const Integer &d=Integer_one()) |
| Shorthand for Generator Generator::point(const LinExpression& e, const Integer& d). | |
| Generator | closure_point (const LinExpression &e=LinExpression::zero(), const Integer &d=Integer_one()) |
| Shorthand for Generator Generator::closure_point(const LinExpression& e, const Integer& d). | |
| const Generator & | zero_dim_point () |
Returns the origin of the zero-dimensional space . | |
| const Generator & | zero_dim_closure_point () |
Returns, as a closure point, the origin of the zero-dimensional space . | |
Related Functions | |
| (Note that these are not member functions.) | |
| std::ostream & | operator<< (std::ostream &s, const Generator &g) |
| Output operator. | |
| void | swap (Parma_Polyhedra_Library::Generator &x, Parma_Polyhedra_Library::Generator &y) |
Specializes std::swap. | |
An object of the class Generator is one of the following:
;
;
;
;
where
is the dimension of the space and, for points and closure points,
is the divisor.
using the generator system
, we need to include in the finite set
even points of
that are not vertices of
. This situation is even more frequent when working with NNC polyhedra and it is the reason why we prefer to use the word `point' where other libraries use the word `vertex'.line, ray, point or closure_point) to a linear expression, representing a direction in the space; the space-dimension of the generator is defined as the space-dimension of the corresponding linear expression. Linear expressions used to define a generator should be homogeneous (any constant term will be simply ignored). When defining points and closure points, an optional Integer argument can be used as a common divisor for all the coefficients occurring in the provided linear expression; the default value for this argument is 1.x, y and z are defined as follows: Variable x(0); Variable y(1); Variable z(2);
and having space-dimension
: As mentioned above, the constant term of the linear expression is not relevant. Thus, the following code has the same effect: By definition, the origin of the space is not a line, so that the following code throws an exception:
: The same effect can be obtained by using the following code: Similarly, the origin
can be defined using either one of the following lines of code: Note however that the following code would have defined a different point, namely
: The following two lines of code both define the only point having space-dimension zero, namely
. In the second case we exploit the fact that the first argument of the function point is optional.
specified in Example 3 above can also be obtained with the following code, where we provide a non-default value for the second argument of the function point (the divisor): Obviously, the divisor can be usefully exploited to specify points having some non-integer (but rational) coordinates. For instance, the point
can be specified by the following code: If a zero divisor is provided, an exception is thrown.
is defined by Generator c = closure_point(1*x + 0*y + 2*z);
Generator closure_origin0 = Generator::zero_dim_closure_point(); Generator closure_origin0_alt = closure_point();
g1 is a point having coordinates
, we construct the closure point g2 having coordinates
. if (g1.is_point()) { cout << "Point g1: " << g1 << endl; LinExpression e; for (int i = g1.space_dimension() - 1; i >= 0; i--) e += (i + 1) * g1.coefficient(Variable(i)) * Variable(i); Generator g2 = closure_point(e, g1.divisor()); cout << "Closure point g2: " << g2 << endl; } else cout << "Generator g1 is not a point." << endl;
Point g1: p((2*A - B + 3*C)/2) Closure point g2: cp((2*A - 2*B + 9*C)/2)
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The generator type.
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Shorthand for Generator Generator::line(const LinExpression& e).
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Shorthand for Generator Generator::ray(const LinExpression& e).
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Shorthand for Generator Generator::point(const LinExpression& e, const Integer& d).
Both
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Shorthand for Generator Generator::closure_point(const LinExpression& e, const Integer& d).
Both
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Returns the coefficient of
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If
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