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| template<class ForwardIterator > |
| Point_d< R > | center_of_sphere (ForwardIterator first, ForwardIterator last) |
| | returns the center of the sphere spanned by the points in A = tuple[first,last).
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Point_d< R > | lift_to_paraboloid (const Point_d< R > &p) |
| | returns the projection of \( p = (x_0,\ldots,x_{d-1})\) onto the paraboloid of revolution which is the point \( (p_0,
\ldots,p_{d-1},\sum_{0 \le i < d}p_i^2)\) in \( (d+1)\)-space.
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| template<class ForwardIterator , class OutputIterator > |
| OutputIterator | linear_base (ForwardIterator first, ForwardIterator last, OutputIterator result) |
| | computes a basis of the linear space spanned by the vectors in A = tuple [first,last) and returns it via an iterator range starting in result.
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| Point_d< R > | midpoint (const Point_d< R > &p, const Point_d< R > &q) |
| | computes the midpoint of the segment \( pq\).
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Point_d< R > | project_along_d_axis (const Point_d< R > &p) |
| | returns \( p\) projected along the \( d\)-axis onto the hyperspace spanned by the first \( d-1\) standard base vectors.
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| FT | squared_distance (Point_d< R > p, Point_d< R > q) |
| | computes the square of the Euclidean distance between the two points \( p\) and \( q\).
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| bool | do_intersect (Type1< R > obj1, Type2< R > obj2) |
| | checks whether obj1 and obj2 intersect.
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| decltype(auto) | intersection (Type1< R > f1, Type2< R > f2) |
| | returns the intersection between f1 and f2.
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| template<class ForwardIterator > |
| bool | affinely_independent (ForwardIterator first, ForwardIterator last) |
| | returns true iff the points in A = tuple [first,last) are affinely independent.
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| template<class ForwardIterator > |
| int | affine_rank (ForwardIterator first, ForwardIterator last) |
| | computes the affine rank of the points in A = tuple [first,last).
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| Comparison_result | compare_lexicographically (const Point_d< R > &p, const Point_d< R > &q) |
| | Compares the Cartesian coordinates of points p and q lexicographically in ascending order of its Cartesian components p[i] and q[i] for \( i = 0,\ldots,d-1\).
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| template<class ForwardIterator > |
| bool | contained_in_affine_hull (ForwardIterator first, ForwardIterator last, const Point_d< R > &p) |
| | determines whether \( p\) is contained in the affine hull of the points in A = tuple [first,last).
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| template<class ForwardIterator > |
| bool | contained_in_linear_hull (ForwardIterator first, ForwardIterator last, const Vector_d< R > &v) |
| | determines whether \( v\) is contained in the linear hull of the vectors in A = tuple [first,last).
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| template<class ForwardIterator > |
| bool | contained_in_simplex (ForwardIterator first, ForwardIterator last, const Point_d< R > &p) |
| | determines whether \( p\) is contained in the simplex of the points in A = tuple [first,last).
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| bool | lexicographically_smaller (const Point_d< R > &p, const Point_d< R > &q) |
| | returns true iff p is lexicographically smaller than q with respect to Cartesian lexicographic order of points.
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| bool | lexicographically_smaller_or_equal (const Point_d< R > &p, const Point_d< R > &q) |
| | returns true iff \( p\) is lexicographically smaller than \( q\) with respect to Cartesian lexicographic order of points or equal to \( q\).
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| template<class ForwardIterator > |
| bool | linearly_independent (ForwardIterator first, ForwardIterator last) |
| | decides whether the vectors in A = tuple [first,last) are linearly independent.
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| template<class ForwardIterator > |
| int | linear_rank (ForwardIterator first, ForwardIterator last) |
| | computes the linear rank of the vectors in A = tuple [first,last).
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| template<class ForwardIterator > |
| Orientation | orientation (ForwardIterator first, ForwardIterator last) |
| | determines the orientation of the points of the tuple A = tuple [first,last) where \( A\) consists of \( d+1\) points in \( d\)-space.
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| template<class ForwardIterator > |
| Bounded_side | side_of_bounded_sphere (ForwardIterator first, ForwardIterator last, const Point_d< R > &p) |
| | returns the relative position of point p to the sphere defined by A = tuple [first,last).
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| template<class ForwardIterator > |
| Oriented_side | side_of_oriented_sphere (ForwardIterator first, ForwardIterator last, const Point_d< R > &p) |
| | returns the relative position of point p to the oriented sphere defined by the points in A = tuple [first,last) The order of the points in \( A\) is important, since it determines the orientation of the implicitly constructed sphere.
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