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| template<typename T , typename U > |
| T | enum_cast (const U &u) |
| | converts between the various enums provided by the CGAL kernel.
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Oriented_side | opposite (const Oriented_side &o) |
| | returns the opposite side (for example CGAL::ON_POSITIVE_SIDE if o==CGAL::ON_NEGATIVE_SIDE), or CGAL::ON_ORIENTED_BOUNDARY if o==CGAL::ON_ORIENTED_BOUNDARY.
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Bounded_side | opposite (const Bounded_side &o) |
| | returns the opposite side (for example CGAL::ON_BOUNDED_SIDE if o==CGAL::ON_UNBOUNDED_SIDE), or returns CGAL::ON_BOUNDARY if o==CGAL::ON_BOUNDARY.
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| bool | do_intersect (Type1< Kernel > obj1, Type2< Kernel > obj2) |
| | checks whether obj1 and obj2 intersect.
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bool | do_intersect (Plane_3< Kernel > obj1, Plane_3< Kernel > obj2, Plane_3< Kernel > obj3) |
| | checks whether obj1, obj2 and obj3 intersect.
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| template<typename Kernel > |
| decltype(auto) | intersection (Type1< Kernel > obj1, Type2< Kernel > obj2) |
| | Two objects obj1 and obj2 intersect if there is a point p that is part of both obj1 and obj2.
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template<typename Kernel > |
| decltype(auto) | intersection (const Plane_3< Kernel > &pl1, const Plane_3< Kernel > &pl2, const Plane_3< Kernel > &pl3) |
| | returns the intersection of 3 planes, which can be a point, a line, a plane, or empty.
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template<typename Kernel > |
| Angle | angle (const CGAL::Vector_2< Kernel > &u, const CGAL::Vector_2< Kernel > &v) |
| | returns CGAL::OBTUSE, CGAL::RIGHT or CGAL::ACUTE depending on the angle formed by the two vectors u and v.
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| template<typename Kernel > |
| Angle | angle (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r) |
| | returns CGAL::OBTUSE, CGAL::RIGHT or CGAL::ACUTE depending on the angle formed by the three points p, q, r (q being the vertex of the angle).
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| template<typename Kernel > |
| Angle | angle (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r, const CGAL::Point_2< Kernel > &s) |
| | returns CGAL::OBTUSE, CGAL::RIGHT or CGAL::ACUTE depending on the angle formed by the two vectors pq, rs.
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template<typename Kernel > |
| Angle | angle (const CGAL::Vector_3< Kernel > &u, const CGAL::Vector_3< Kernel > &v) |
| | returns CGAL::OBTUSE, CGAL::RIGHT or CGAL::ACUTE depending on the angle formed by the two vectors u and v.
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template<typename Kernel > |
| Angle | angle (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r) |
| | returns CGAL::OBTUSE, CGAL::RIGHT or CGAL::ACUTE depending on the angle formed by the three points p, q, r (q being the vertex of the angle).
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| template<typename Kernel > |
| Angle | angle (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s) |
| | returns CGAL::OBTUSE, CGAL::RIGHT or CGAL::ACUTE depending on the angle formed by the two vectors pq, rs.
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template<typename Kernel > |
| Angle | angle (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Vector_3< Kernel > &v) |
| | returns CGAL::OBTUSE, CGAL::RIGHT or CGAL::ACUTE depending on the angle formed by the normal of the triangle pqr and the vector v.
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| template<typename Kernel > |
| Kernel::FT | approximate_angle (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r) |
| | returns an approximation of the angle between p-q and r-q.
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| template<typename Kernel > |
| Kernel::FT | approximate_angle (const CGAL::Vector_3< Kernel > &u, const CGAL::Vector_3< Kernel > &v) |
| | returns an approximation of the angle between u and v.
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| template<typename Kernel > |
| Kernel::FT | approximate_dihedral_angle (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s) |
| | returns an approximation of the signed dihedral angle in the tetrahedron pqrs of edge pq.
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template<typename Kernel > |
| Kernel::FT | area (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r) |
| | returns the signed area of the triangle defined by the points p, q and r.
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| template<typename Kernel > |
| bool | are_ordered_along_line (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r) |
| | returns true, iff the three points are collinear and q lies between p and r.
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| template<typename Kernel > |
| bool | are_ordered_along_line (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r) |
| | returns true, iff the three points are collinear and q lies between p and r.
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| template<typename Kernel > |
| bool | are_strictly_ordered_along_line (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r) |
| | returns true, iff the three points are collinear and q lies strictly between p and r.
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| template<typename Kernel > |
| bool | are_strictly_ordered_along_line (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r) |
| | returns true, iff the three points are collinear and q lies strictly between p and r.
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template<typename Kernel > |
| CGAL::Point_2< Kernel > | barycenter (const CGAL::Point_2< Kernel > &p1, const Kernel::FT &w1, const CGAL::Point_2< Kernel > &p2) |
| | compute the barycenter of the points p1 and p2 with corresponding weights w1 and 1-w1.
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| template<typename Kernel > |
| CGAL::Point_2< Kernel > | barycenter (const CGAL::Point_2< Kernel > &p1, const Kernel::FT &w1, const CGAL::Point_2< Kernel > &p2, const Kernel::FT &w2) |
| | compute the barycenter of the points p1 and p2 with corresponding weights w1 and w2.
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template<typename Kernel > |
| CGAL::Point_2< Kernel > | barycenter (const CGAL::Point_2< Kernel > &p1, const Kernel::FT &w1, const CGAL::Point_2< Kernel > &p2, const Kernel::FT &w2, const CGAL::Point_2< Kernel > &p3) |
| | compute the barycenter of the points p1, p2 and p3 with corresponding weights w1, w2 and 1-w1-w2.
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| template<typename Kernel > |
| CGAL::Point_2< Kernel > | barycenter (const CGAL::Point_2< Kernel > &p1, const Kernel::FT &w1, const CGAL::Point_2< Kernel > &p2, const Kernel::FT &w2, const CGAL::Point_2< Kernel > &p3, const Kernel::FT &w3) |
| | compute the barycenter of the points p1, p2 and p3 with corresponding weights w1, w2 and w3.
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template<typename Kernel > |
| CGAL::Point_2< Kernel > | barycenter (const CGAL::Point_2< Kernel > &p1, const Kernel::FT &w1, const CGAL::Point_2< Kernel > &p2, const Kernel::FT &w2, const CGAL::Point_2< Kernel > &p3, const Kernel::FT &w3, const CGAL::Point_2< Kernel > &p4) |
| | compute the barycenter of the points p1, p2, p3 and p4 with corresponding weights w1, w2, w3 and 1-w1-w2-w3.
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| template<typename Kernel > |
| CGAL::Point_2< Kernel > | barycenter (const CGAL::Point_2< Kernel > &p1, const Kernel::FT &w1, const CGAL::Point_2< Kernel > &p2, const Kernel::FT &w2, const CGAL::Point_2< Kernel > &p3, const Kernel::FT &w3, const CGAL::Point_2< Kernel > &p4, const Kernel::FT &w4) |
| | compute the barycenter of the points p1, p2, p3 and p4 with corresponding weights w1, w2, w3 and w4.
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template<typename Kernel > |
| CGAL::Point_3< Kernel > | barycenter (const CGAL::Point_3< Kernel > &p1, const Kernel::FT &w1, const CGAL::Point_3< Kernel > &p2) |
| | compute the barycenter of the points p1 and p2 with corresponding weights w1 and 1-w1.
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| template<typename Kernel > |
| CGAL::Point_3< Kernel > | barycenter (const CGAL::Point_3< Kernel > &p1, const Kernel::FT &w1, const CGAL::Point_3< Kernel > &p2, const Kernel::FT &w2) |
| | compute the barycenter of the points p1 and p2 with corresponding weights w1 and w2.
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template<typename Kernel > |
| CGAL::Point_3< Kernel > | barycenter (const CGAL::Point_3< Kernel > &p1, const Kernel::FT &w1, const CGAL::Point_3< Kernel > &p2, const Kernel::FT &w2, const CGAL::Point_3< Kernel > &p3) |
| | compute the barycenter of the points p1, p2 and p3 with corresponding weights w1, w2 and 1-w1-w2.
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| template<typename Kernel > |
| CGAL::Point_3< Kernel > | barycenter (const CGAL::Point_3< Kernel > &p1, const Kernel::FT &w1, const CGAL::Point_3< Kernel > &p2, const Kernel::FT &w2, const CGAL::Point_3< Kernel > &p3, const Kernel::FT &w3) |
| | compute the barycenter of the points p1, p2 and p3 with corresponding weights w1, w2 and w3.
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template<typename Kernel > |
| CGAL::Point_3< Kernel > | barycenter (const CGAL::Point_3< Kernel > &p1, const Kernel::FT &w1, const CGAL::Point_3< Kernel > &p2, const Kernel::FT &w2, const CGAL::Point_3< Kernel > &p3, const Kernel::FT &w3, const CGAL::Point_3< Kernel > &p4) |
| | compute the barycenter of the points p1, p2, p3 and p4 with corresponding weights w1, w2, w3 and 1-w1-w2-w3.
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| template<typename Kernel > |
| CGAL::Point_3< Kernel > | barycenter (const CGAL::Point_3< Kernel > &p1, const Kernel::FT &w1, const CGAL::Point_3< Kernel > &p2, const Kernel::FT &w2, const CGAL::Point_3< Kernel > &p3, const Kernel::FT &w3, const CGAL::Point_3< Kernel > &p4, const Kernel::FT &w4) |
| | compute the barycenter of the points p1, p2, p3 and p4 with corresponding weights w1, w2, w3 and w4.
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| template<typename Kernel > |
| CGAL::Line_2< Kernel > | bisector (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q) |
| | constructs the bisector line of the two points p and q.
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| template<typename Kernel > |
| CGAL::Line_2< Kernel > | bisector (const CGAL::Line_2< Kernel > &l1, const CGAL::Line_2< Kernel > &l2) |
| | constructs the bisector of the two lines l1 and l2.
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| template<typename Kernel > |
| CGAL::Plane_3< Kernel > | bisector (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q) |
| | constructs the bisector plane of the two points p and q.
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| template<typename Kernel > |
| CGAL::Plane_3< Kernel > | bisector (const CGAL::Plane_3< Kernel > &h1, const CGAL::Plane_3< Kernel > &h2) |
| | constructs the bisector of the two planes h1 and h2.
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template<typename Kernel > |
| CGAL::Point_2< Kernel > | centroid (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r) |
| | compute the centroid of the points p, q, and r.
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template<typename Kernel > |
| CGAL::Point_2< Kernel > | centroid (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r, const CGAL::Point_2< Kernel > &s) |
| | compute the centroid of the points p, q, r, and s.
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template<typename Kernel > |
| CGAL::Point_2< Kernel > | centroid (const CGAL::Triangle_2< Kernel > &t) |
| | compute the centroid of the triangle t.
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template<typename Kernel > |
| CGAL::Point_3< Kernel > | centroid (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r) |
| | compute the centroid of the points p, q, and r.
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template<typename Kernel > |
| CGAL::Point_3< Kernel > | centroid (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s) |
| | compute the centroid of the points p, q, r, and s.
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template<typename Kernel > |
| CGAL::Point_3< Kernel > | centroid (const CGAL::Triangle_3< Kernel > &t) |
| | compute the centroid of the triangle t.
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template<typename Kernel > |
| CGAL::Point_3< Kernel > | centroid (const CGAL::Tetrahedron_3< Kernel > &t) |
| | compute the centroid of the tetrahedron t.
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| template<typename Kernel > |
| CGAL::Point_2< Kernel > | circumcenter (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q) |
| | compute the center of the smallest circle passing through the points p and q.
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| template<typename Kernel > |
| CGAL::Point_2< Kernel > | circumcenter (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r) |
| | compute the center of the circle passing through the points p, q, and r.
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| template<typename Kernel > |
| CGAL::Point_2< Kernel > | circumcenter (const CGAL::Triangle_2< Kernel > &t) |
| | compute the center of the circle passing through the vertices of t.
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| template<typename Kernel > |
| CGAL::Point_3< Kernel > | circumcenter (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q) |
| | compute the center of the smallest sphere passing through the points p and q.
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| template<typename Kernel > |
| CGAL::Point_3< Kernel > | circumcenter (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r) |
| | compute the center of the circle passing through the points p, q, and r.
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| template<typename Kernel > |
| CGAL::Point_3< Kernel > | circumcenter (const CGAL::Triangle_3< Kernel > &t) |
| | compute the center of the circle passing through the vertices of t.
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| template<typename Kernel > |
| CGAL::Point_3< Kernel > | circumcenter (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s) |
| | compute the center of the sphere passing through the points p, q, r, and s.
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| template<typename Kernel > |
| CGAL::Point_3< Kernel > | circumcenter (const CGAL::Tetrahedron_3< Kernel > &t) |
| | compute the center of the sphere passing through the vertices of t.
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| template<typename Kernel > |
| bool | collinear_are_ordered_along_line (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r) |
| | returns true, iff q lies between p and r.
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| template<typename Kernel > |
| bool | collinear_are_ordered_along_line (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r) |
| | returns true, iff q lies between p and r.
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| template<typename Kernel > |
| bool | collinear_are_strictly_ordered_along_line (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r) |
| | returns true, iff q lies strictly between p and r.
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| template<typename Kernel > |
| bool | collinear_are_strictly_ordered_along_line (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r) |
| | returns true, iff q lies strictly between p and r.
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template<typename Kernel > |
| bool | collinear (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r) |
| | returns true, iff p, q, and r are collinear.
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template<typename Kernel > |
| bool | collinear (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r) |
| | returns true, iff p, q, and r are collinear.
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| template<typename Kernel > |
| Comparison_result | compare_angle (const CGAL::Point_3< Kernel > &a, const CGAL::Point_3< Kernel > &b, const CGAL::Point_3< Kernel > &c, const Kernel::FT &cosine) |
| | compares the angles \( \theta_1\) and \( \theta_2\), where \( \theta_1\) is the angle in \( [0, \pi]\) of the triangle \( (a, b, c)\) at the vertex b, and \( \theta_2\) is the angle in \( [0, \pi]\) such that \( cos(\theta_2) = cosine\).
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| template<typename Kernel > |
| Comparison_result | compare_dihedral_angle (const CGAL::Point_3< Kernel > &a1, const CGAL::Point_3< Kernel > &b1, const CGAL::Point_3< Kernel > &c1, const CGAL::Point_3< Kernel > &d1, const Kernel::FT &cosine) |
| | compares the dihedral angles \( \theta_1\) and \( \theta_2\), where \( \theta_1\) is the dihedral angle, in \( [0, \pi]\), of the tetrahedron (a1, b1, c1, d1) at the edge (a1, b1), and \( \theta_2\) is the angle in \( [0, \pi]\) such that \( cos(\theta_2) = cosine\).
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| template<typename Kernel > |
| Comparison_result | compare_dihedral_angle (const CGAL::Point_3< Kernel > &a1, const CGAL::Point_3< Kernel > &b1, const CGAL::Point_3< Kernel > &c1, const CGAL::Point_3< Kernel > &d1, const CGAL::Point_3< Kernel > &a2, const CGAL::Point_3< Kernel > &b2, const CGAL::Point_3< Kernel > &c2, const CGAL::Point_3< Kernel > &d2) |
| | compares the dihedral angles \( \theta_1\) and \( \theta_2\), where \( \theta_i\) is the dihedral angle in the tetrahedron (a_i, b_i, c_i, d_i) at the edge (a_i, b_i).
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| template<typename Kernel > |
| Comparison_result | compare_dihedral_angle (const CGAL::Vector_3< Kernel > &u1, const CGAL::Vector_3< Kernel > &v1, const CGAL::Vector_3< Kernel > &w1, const Kernel::FT &cosine) |
| | compares the dihedral angles \( \theta_1\) and \( \theta_2\), where \( \theta_1\) is the dihedral angle, in \( [0, \pi]\), between the vectorial planes defined by (u_1, v_1) and (u_1, w_1), and \( \theta_2\) is the angle in \( [0, \pi]\) such that \( cos(\theta_2) =
cosine\).
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| template<typename Kernel > |
| Comparison_result | compare_dihedral_angle (const CGAL::Vector_3< Kernel > &u1, const CGAL::Vector_3< Kernel > &v1, const CGAL::Vector_3< Kernel > &w1, const CGAL::Vector_3< Kernel > &u2, const CGAL::Vector_3< Kernel > &v2, const CGAL::Vector_3< Kernel > &w2) |
| | compares the dihedral angles \( \theta_1\) and \( \theta_2\), where \( \theta_i\) is the dihedral angle between the vectorial planes defined by (u_i, v_i) and (u_i, w_i).
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| template<typename Kernel > |
| Comparison_result | compare_distance_to_point (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r) |
| | compares the distances of points q and r to point p.
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| template<typename Kernel > |
| Comparison_result | compare_distance_to_point (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r) |
| | compares the distances of points q and r to point p.
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| template<typename Kernel > |
| Comparison_result | compare_lexicographically (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q) |
| | Compares the Cartesian coordinates of points p and q lexicographically in \( xy\) order: first \( x\)-coordinates are compared, if they are equal, \( y\)-coordinates are compared.
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| template<typename Kernel > |
| Comparison_result | compare_lexicographically (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q) |
| | Compares the Cartesian coordinates of points p and q lexicographically in \( xyz\) order: first \( x\)-coordinates are compared, if they are equal, \( y\)-coordinates are compared, and if both \( x\)- and \( y\)- coordinate are equal, \( z\)-coordinates are compared.
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template<typename Kernel > |
| Comparison_result | compare_signed_distance_to_line (const CGAL::Line_2< Kernel > &l, const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q) |
| | returns CGAL::LARGER iff the signed distance of p and l is larger than the signed distance of q and l, CGAL::SMALLER, iff it is smaller, and CGAL::EQUAL iff both are equal.
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template<typename Kernel > |
| Comparison_result | compare_signed_distance_to_line (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r, const CGAL::Point_2< Kernel > &s) |
| | returns CGAL::LARGER iff the signed distance of r and l is larger than the signed distance of s and l, CGAL::SMALLER, iff it is smaller, and CGAL::EQUAL iff both are equal, where l is the directed line through p and q.
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template<typename Kernel > |
| Comparison_result | compare_signed_distance_to_plane (const CGAL::Plane_3< Kernel > &h, const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q) |
| | returns CGAL::LARGER iff the signed distance of p and h is larger than the signed distance of q and h, CGAL::SMALLER, iff it is smaller, and CGAL::EQUAL iff both are equal.
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template<typename Kernel > |
| Comparison_result | compare_signed_distance_to_plane (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s, const CGAL::Point_3< Kernel > &t) |
| | returns CGAL::LARGER iff the signed distance of s and h is larger than the signed distance of t and h, CGAL::SMALLER, iff it is smaller, and CGAL::EQUAL iff both are equal, where h is the oriented plane through p, q and r.
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template<typename Kernel > |
| Comparison_result | compare_slope (const CGAL::Line_2< Kernel > &l1, const CGAL::Line_2< Kernel > &l2) |
| | compares the slopes of the lines l1 and l2
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template<typename Kernel > |
| Comparison_result | compare_slope (const CGAL::Segment_2< Kernel > &s1, const CGAL::Segment_2< Kernel > &s2) |
| | compares the slopes of the segments s1 and s2, where the slope is the variation of the y-coordinate from the left to the right endpoint of the segments.
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template<typename Kernel > |
| Comparison_result | compare_slope (const CGAL::Point_2< Kernel > &s1s, const CGAL::Point_2< Kernel > &s1t, const CGAL::Point_2< Kernel > &s2s, const CGAL::Point_2< Kernel > &s2t) |
| | compares the slopes of the segments (s1s,s1t) and (s2s,s2t), where the slope is the variation of the y-coordinate from the left to the right endpoint of the segments.
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template<typename Kernel > |
| Comparison_result | compare_slope (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s) |
| | compares the slopes of the segments (p,q) and (r,s), where the slope is the variation of the z-coordinate from the first to the second point of the segment divided by the length of the segment.
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| |
|
template<typename Kernel > |
| Comparison_result | compare_squared_distance (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const typename Kernel::FT &d2) |
| | compares the squared distance of points p and q to d2.
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| |
|
template<typename Kernel > |
| Comparison_result | compare_squared_distance (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const typename Kernel::FT &d2) |
| | compares the squared distance of points p and q to d2.
|
| |
| template<typename Kernel > |
| Comparison_result | compare_squared_radius (const CGAL::Point_3< Kernel > &p, const typename Kernel::FT &sr) |
| | compares the squared radius of the sphere of radius 0 centered at p to sr.
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| |
|
template<typename Kernel > |
| Comparison_result | compare_squared_radius (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const typename Kernel::FT &sr) |
| | compares the squared radius of the sphere defined by the points p and q to sr.
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| |
|
template<typename Kernel > |
| Comparison_result | compare_squared_radius (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const typename Kernel::FT &sr) |
| | compares the squared radius of the sphere defined by the points p, q, and r to sr.
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| |
|
template<typename Kernel > |
| Comparison_result | compare_squared_radius (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s, const typename Kernel::FT &sr) |
| | compares the squared radius of the sphere defined by the points p, q, r, and r to sr.
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| |
|
template<typename Kernel > |
| Comparison_result | compare_x (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q) |
| | compares the \( x\)-coordinates of p and q.
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| |
|
template<typename Kernel > |
| Comparison_result | compare_x (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q) |
| | compares the \( x\)-coordinates of p and q.
|
| |
| template<typename Kernel > |
| Comparison_result | compare_x (const CGAL::Point_2< Kernel > &p, const CGAL::Line_2< Kernel > &l1, const CGAL::Line_2< Kernel > &l2) |
| | compares the \( x\)-coordinates of p and the intersection of lines l1 and l2.
|
| |
| template<typename Kernel > |
| Comparison_result | compare_x (const CGAL::Line_2< Kernel > &l, const CGAL::Line_2< Kernel > &h1, const CGAL::Line_2< Kernel > &h2) |
| | compares the \( x\)-coordinates of the intersection of line l with line h1 and with line h2.
|
| |
| template<typename Kernel > |
| Comparison_result | compare_x (const CGAL::Line_2< Kernel > &l1, const CGAL::Line_2< Kernel > &l2, const CGAL::Line_2< Kernel > &h1, const CGAL::Line_2< Kernel > &h2) |
| | compares the \( x\)-coordinates of the intersection of lines l1 and l2 and the intersection of lines h1 and h2.
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| |
|
template<typename CircularKernel > |
| Comparison_result | compare_x (const CGAL::Circular_arc_point_2< CircularKernel > &p, const CGAL::Circular_arc_point_2< CircularKernel > &q) |
| | compares the \( x\)-coordinates of p and q.
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| |
|
template<typename CircularKernel > |
| Comparison_result | compare_x (const CGAL::Circular_arc_point_2< CircularKernel > &p, const CGAL::Point_2< CircularKernel > &q) |
| | compares the \( x\)-coordinates of p and q.
|
| |
|
template<typename SphericalKernel > |
| Comparison_result | compare_x (const CGAL::Circular_arc_point_3< SphericalKernel > &p, const CGAL::Circular_arc_point_3< SphericalKernel > &q) |
| | compares the \( x\)-coordinates of p and q.
|
| |
|
template<typename SphericalKernel > |
| Comparison_result | compare_x (const CGAL::Circular_arc_point_3< SphericalKernel > &p, const CGAL::Point_3< SphericalKernel > &q) |
| | compares the \( x\)-coordinates of p and q.
|
| |
|
template<typename Kernel > |
| Comparison_result | compare_xy (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q) |
| | Compares the Cartesian coordinates of points p and q lexicographically in \( xy\) order: first \( x\)-coordinates are compared, if they are equal, \( y\)-coordinates are compared.
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| |
|
template<typename Kernel > |
| Comparison_result | compare_xy (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q) |
| | Compares the Cartesian coordinates of points p and q lexicographically in \( xy\) order: first \( x\)-coordinates are compared, if they are equal, \( y\)-coordinates are compared.
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| |
|
template<typename CircularKernel > |
| Comparison_result | compare_xy (const CGAL::Circular_arc_point_2< CircularKernel > &p, const CGAL::Circular_arc_point_2< CircularKernel > &q) |
| | Compares the \( x\) and \( y\) Cartesian coordinates of points p and q lexicographically.
|
| |
|
template<typename CircularKernel > |
| Comparison_result | compare_xy (const CGAL::Circular_arc_point_2< CircularKernel > &p, const CGAL::Point_2< CircularKernel > &q) |
| | Compares the \( x\) and \( y\) Cartesian coordinates of points p and q lexicographically.
|
| |
|
template<typename SphericalKernel > |
| Comparison_result | compare_xy (const CGAL::Circular_arc_point_3< SphericalKernel > &p, const CGAL::Circular_arc_point_3< SphericalKernel > &q) |
| | Compares the \( x\) and \( y\) Cartesian coordinates of points p and q lexicographically.
|
| |
|
template<typename SphericalKernel > |
| Comparison_result | compare_xy (const CGAL::Circular_arc_point_3< SphericalKernel > &p, const CGAL::Point_3< SphericalKernel > &q) |
| | Compares the \( x\) and \( y\) Cartesian coordinates of points p and q lexicographically.
|
| |
| template<typename Kernel > |
| Comparison_result | compare_x_at_y (const CGAL::Point_2< Kernel > &p, const CGAL::Line_2< Kernel > &h) |
| | compares the \( x\)-coordinates of p and the horizontal projection of p on h.
|
| |
| template<typename Kernel > |
| Comparison_result | compare_x_at_y (const CGAL::Point_2< Kernel > &p, const CGAL::Line_2< Kernel > &h1, const CGAL::Line_2< Kernel > &h2) |
| | This function compares the \( x\)-coordinates of the horizontal projection of p on h1 and on h2.
|
| |
| template<typename Kernel > |
| Comparison_result | compare_x_at_y (const CGAL::Line_2< Kernel > &l1, const CGAL::Line_2< Kernel > &l2, const CGAL::Line_2< Kernel > &h) |
| | Let p be the intersection of lines l1 and l2.
|
| |
| template<typename Kernel > |
| Comparison_result | compare_x_at_y (const CGAL::Line_2< Kernel > &l1, const CGAL::Line_2< Kernel > &l2, const CGAL::Line_2< Kernel > &h1, const CGAL::Line_2< Kernel > &h2) |
| | Let p be the intersection of lines l1 and l2.
|
| |
| template<typename Kernel > |
| Comparison_result | compare_y_at_x (const CGAL::Point_2< Kernel > &p, const CGAL::Line_2< Kernel > &h) |
| | compares the \( y\)-coordinates of p and the vertical projection of p on h.
|
| |
| template<typename Kernel > |
| Comparison_result | compare_y_at_x (const CGAL::Point_2< Kernel > &p, const CGAL::Line_2< Kernel > &h1, const CGAL::Line_2< Kernel > &h2) |
| | compares the \( y\)-coordinates of the vertical projection of p on h1 and on h2.
|
| |
| template<typename Kernel > |
| Comparison_result | compare_y_at_x (const CGAL::Line_2< Kernel > &l1, const CGAL::Line_2< Kernel > &l2, const CGAL::Line_2< Kernel > &h) |
| | Let p be the intersection of lines l1 and l2.
|
| |
| template<typename Kernel > |
| Comparison_result | compare_y_at_x (const CGAL::Line_2< Kernel > &l1, const CGAL::Line_2< Kernel > &l2, const CGAL::Line_2< Kernel > &h1, const CGAL::Line_2< Kernel > &h2) |
| | Let p be the intersection of lines l1 and l2.
|
| |
| template<typename Kernel > |
| Comparison_result | compare_y_at_x (const CGAL::Point_2< Kernel > &p, const CGAL::Segment_2< Kernel > &s) |
| | compares the \( y\)-coordinates of p and the vertical projection of p on s.
|
| |
| template<typename Kernel > |
| Comparison_result | compare_y_at_x (const CGAL::Point_2< Kernel > &p, const CGAL::Segment_2< Kernel > &s1, const CGAL::Segment_2< Kernel > &s2) |
| | compares the \( y\)-coordinates of the vertical projection of p on s1 and on s2.
|
| |
|
template<typename Kernel > |
| Comparison_result | compare_y (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q) |
| | compares Cartesian \( y\)-coordinates of p and q.
|
| |
|
template<typename Kernel > |
| Comparison_result | compare_y (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q) |
| | compares Cartesian \( y\)-coordinates of p and q.
|
| |
| template<typename Kernel > |
| Comparison_result | compare_y (const CGAL::Point_2< Kernel > &p, const CGAL::Line_2< Kernel > &l1, const CGAL::Line_2< Kernel > &l2) |
| | compares the \( y\)-coordinates of p and the intersection of lines l1 and l2.
|
| |
| template<typename Kernel > |
| Comparison_result | compare_y (const CGAL::Line_2< Kernel > &l, const CGAL::Line_2< Kernel > &h1, const CGAL::Line_2< Kernel > &h2) |
| | compares the \( y\)-coordinates of the intersection of line l with line h1 and with line h2.
|
| |
| template<typename Kernel > |
| Comparison_result | compare_y (const CGAL::Line_2< Kernel > &l1, const CGAL::Line_2< Kernel > &l2, const CGAL::Line_2< Kernel > &h1, const CGAL::Line_2< Kernel > &h2) |
| | compares the \( y\)-coordinates of the intersection of lines l1 and l2 and the intersection of lines h1 and h2.
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| |
|
template<typename CircularKernel > |
| Comparison_result | compare_y (const CGAL::Circular_arc_point_2< CircularKernel > &p, const CGAL::Circular_arc_point_2< CircularKernel > &q) |
| | compares the \( y\)-coordinates of p and q.
|
| |
|
template<typename CircularKernel > |
| Comparison_result | compare_y (const CGAL::Circular_arc_point_2< CircularKernel > &p, const CGAL::Point_2< CircularKernel > &q) |
| | compares the \( y\)-coordinates of p and q.
|
| |
|
template<typename SphericalKernel > |
| Comparison_result | compare_y (const CGAL::Circular_arc_point_3< SphericalKernel > &p, const CGAL::Circular_arc_point_3< SphericalKernel > &q) |
| | compares the \( y\)-coordinates of p and q.
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| |
|
template<typename SphericalKernel > |
| Comparison_result | compare_y (const CGAL::Circular_arc_point_3< SphericalKernel > &p, const CGAL::Point_3< SphericalKernel > &q) |
| | compares the \( y\)-coordinates of p and q.
|
| |
|
template<typename Kernel > |
| Comparison_result | compare_xyz (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q) |
| | Compares the Cartesian coordinates of points p and q lexicographically in \( xyz\) order: first \( x\)-coordinates are compared, if they are equal, \( y\)-coordinates are compared, and if both \( x\)- and \( y\)- coordinate are equal, \( z\)-coordinates are compared.
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| |
|
template<typename SphericalKernel > |
| Comparison_result | compare_xyz (const CGAL::Circular_arc_point_3< SphericalKernel > &p, const CGAL::Circular_arc_point_3< SphericalKernel > &q) |
| | Compares the Cartesian coordinates of points p and q lexicographically.
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| |
|
template<typename SphericalKernel > |
| Comparison_result | compare_xyz (const CGAL::Circular_arc_point_3< SphericalKernel > &p, const CGAL::Point_3< SphericalKernel > &q) |
| | Compares the Cartesian coordinates of points p and q lexicographically.
|
| |
|
template<typename Kernel > |
| Comparison_result | compare_z (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q) |
| | compares the \( z\)-coordinates of p and q.
|
| |
|
template<typename SphericalKernel > |
| Comparison_result | compare_z (const CGAL::Circular_arc_point_3< SphericalKernel > &p, const CGAL::Circular_arc_point_3< SphericalKernel > &q) |
| | compares the \( z\)-coordinates of p and q.
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| |
|
template<typename SphericalKernel > |
| Comparison_result | compare_z (const CGAL::Circular_arc_point_3< SphericalKernel > &p, const CGAL::Point_3< SphericalKernel > &q) |
| | compares the \( z\)-coordinates of p and q.
|
| |
|
template<typename Kernel > |
| Comparison_result | compare_yx (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q) |
| | Compares the Cartesian coordinates of points p and q lexicographically in \( yx\) order: first \( y\)-coordinates are compared, if they are equal, \( x\)-coordinates are compared.
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| |
|
template<typename Kernel > |
| bool | coplanar (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s) |
| | returns true, if p, q, r, and s are coplanar.
|
| |
| template<typename Kernel > |
| Orientation | coplanar_orientation (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s) |
| | Let P be the plane defined by the points p, q, and r.
|
| |
| template<typename Kernel > |
| Orientation | coplanar_orientation (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r) |
| | If p,q,r are collinear, then CGAL::COLLINEAR is returned.
|
| |
| template<typename Kernel > |
| Bounded_side | coplanar_side_of_bounded_circle (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s) |
| | returns the bounded side of the circle defined by p, q, and r on which s lies.
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| |
|
template<typename Kernel > |
| CGAL::Vector_3< Kernel > | cross_product (const CGAL::Vector_3< Kernel > &u, const CGAL::Vector_3< Kernel > &v) |
| | returns the cross product of u and v.
|
| |
|
template<typename Kernel > |
| Kernel::FT | determinant (const CGAL::Vector_2< Kernel > &v, const CGAL::Vector_2< Kernel > &w) |
| | returns the determinant of v and w.
|
| |
|
template<typename Kernel > |
| Kernel::FT | determinant (const CGAL::Vector_3< Kernel > &u, const CGAL::Vector_3< Kernel > &v, const CGAL::Vector_3< Kernel > &w) |
| | returns the determinant of u, v and w.
|
| |
| template<typename Kernel > |
| CGAL::Line_3< Kernel > | equidistant_line (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r) |
| | constructs the line which is at the same distance from the three points p, q and r.
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| |
|
template<typename Kernel > |
| bool | has_larger_distance_to_point (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r) |
| | returns true iff the distance between q and p is larger than the distance between r and p.
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| |
|
template<typename Kernel > |
| bool | has_larger_distance_to_point (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r) |
| | returns true iff the distance between q and p is larger than the distance between r and p.
|
| |
|
template<typename Kernel > |
| bool | has_larger_signed_distance_to_line (const CGAL::Line_2< Kernel > &l, const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q) |
| | returns true iff the signed distance of p and l is larger than the signed distance of q and l.
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| |
|
template<typename Kernel > |
| bool | has_larger_signed_distance_to_line (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r, const CGAL::Point_2< Kernel > &s) |
| | returns true iff the signed distance of r and l is larger than the signed distance of s and l, where l is the directed line through points p and q.
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| |
|
template<typename Kernel > |
| bool | has_larger_signed_distance_to_plane (const CGAL::Plane_3< Kernel > &h, const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q) |
| | returns true iff the signed distance of p and h is larger than the signed distance of q and h.
|
| |
|
template<typename Kernel > |
| bool | has_larger_signed_distance_to_plane (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s, const CGAL::Point_3< Kernel > &t) |
| | returns true iff the signed distance of s and h is larger than the signed distance of t and h, where h is the oriented plane through p, q and r.
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| |
|
template<typename Kernel > |
| bool | has_smaller_distance_to_point (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r) |
| | returns true iff the distance between q and p is smaller than the distance between r and p.
|
| |
|
template<typename Kernel > |
| bool | has_smaller_distance_to_point (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r) |
| | returns true iff the distance between q and p is smaller than the distance between r and p.
|
| |
|
template<typename Kernel > |
| bool | has_smaller_signed_distance_to_line (const CGAL::Line_2< Kernel > &l, const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q) |
| | returns true iff the signed distance of p and l is smaller than the signed distance of q and l.
|
| |
|
template<typename Kernel > |
| bool | has_smaller_signed_distance_to_line (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r, const CGAL::Point_2< Kernel > &s) |
| | returns true iff the signed distance of r and l is smaller than the signed distance of s and l, where l is the oriented line through p and q.
|
| |
|
template<typename Kernel > |
| bool | has_smaller_signed_distance_to_plane (const CGAL::Plane_3< Kernel > &h, const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q) |
| | returns true iff the signed distance of p and h is smaller than the signed distance of q and h.
|
| |
|
template<typename Kernel > |
| bool | has_smaller_signed_distance_to_plane (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s, const CGAL::Point_3< Kernel > &t) |
| | returns true iff the signed distance of p and h is smaller than the signed distance of q and h, where h is the oriented plane through p, q and r.
|
| |
|
template<typename Kernel > |
| Kernel::FT | l_infinity_distance (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q) |
| | returns the distance between p and q in the L-infinity metric.
|
| |
|
template<typename Kernel > |
| Kernel::FT | l_infinity_distance (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q) |
| | returns the distance between p and q in the L-infinity metric.
|
| |
|
template<typename Kernel > |
| bool | left_turn (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r) |
| | returns true iff p, q, and r form a left turn.
|
| |
|
template<typename Kernel > |
| bool | lexicographically_xy_larger (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q) |
| | returns true iff p is lexicographically larger than q with respect to \( xy\) order.
|
| |
|
template<typename Kernel > |
| bool | lexicographically_xy_larger_or_equal (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q) |
| | returns true iff p is lexicographically not smaller than q with respect to \( xy\) order.
|
| |
|
template<typename Kernel > |
| bool | lexicographically_xy_smaller (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q) |
| | returns true iff p is lexicographically smaller than q with respect to \( xy\) order.
|
| |
|
template<typename Kernel > |
| bool | lexicographically_xy_smaller_or_equal (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q) |
| | returns true iff p is lexicographically not larger than q with respect to \( xy\) order.
|
| |
|
template<typename Kernel > |
| bool | lexicographically_xyz_smaller (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q) |
| | returns true iff p is lexicographically smaller than q with respect to \( xyz\) order.
|
| |
|
template<typename Kernel > |
| bool | lexicographically_xyz_smaller_or_equal (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q) |
| | returns true iff p is lexicographically not larger than q with respect to \( xyz\) order.
|
| |
| template<typename Kernel > |
| CGAL::Point_2< Kernel > | max_vertex (const CGAL::Iso_rectangle_2< Kernel > &ir) |
| | computes the vertex with the lexicographically largest coordinates of the iso rectangle ir.
|
| |
| template<typename Kernel > |
| CGAL::Point_3< Kernel > | max_vertex (const CGAL::Iso_cuboid_3< Kernel > &ic) |
| | computes the vertex with the lexicographically largest coordinates of the iso cuboid ic.
|
| |
|
template<typename Kernel > |
| CGAL::Point_2< Kernel > | midpoint (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q) |
| | computes the midpoint of the segment pq.
|
| |
|
template<typename Kernel > |
| CGAL::Point_2< Kernel > | midpoint (const CGAL::Segment_2< Kernel > &s) |
| | computes the midpoint of the segment s.
|
| |
|
template<typename Kernel > |
| CGAL::Point_3< Kernel > | midpoint (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q) |
| | computes the midpoint of the segment pq.
|
| |
|
template<typename Kernel > |
| CGAL::Point_3< Kernel > | midpoint (const CGAL::Segment_3< Kernel > &s) |
| | computes the midpoint of the segment s.
|
| |
| template<typename Kernel > |
| CGAL::Point_2< Kernel > | min_vertex (const CGAL::Iso_rectangle_2< Kernel > &ir) |
| | computes the vertex with the lexicographically smallest coordinates of the iso rectangle ir.
|
| |
| template<typename Kernel > |
| CGAL::Point_3< Kernel > | min_vertex (const CGAL::Iso_cuboid_3< Kernel > &ic) |
| | computes the vertex with the lexicographically smallest coordinates of the iso cuboid ic.
|
| |
| template<typename Kernel > |
| CGAL::Vector_3< Kernel > | normal (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r) |
| | computes the normal vector for the vectors q-p and r-p.
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template<typename Kernel > |
| Orientation | orientation (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r) |
| | returns CGAL::LEFT_TURN, if r lies to the left of the oriented line l defined by p and q, returns CGAL::RIGHT_TURN if r lies to the right of l, and returns CGAL::COLLINEAR if r lies on l.
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template<typename Kernel > |
| Orientation | orientation (const CGAL::Vector_2< Kernel > &u, const CGAL::Vector_2< Kernel > &v) |
| | returns CGAL::LEFT_TURN if u and v form a left turn, returns CGAL::RIGHT_TURN if u and v form a right turn, and returns CGAL::COLLINEAR if u and v are collinear.
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template<typename Kernel > |
| Orientation | orientation (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s) |
| | returns CGAL::POSITIVE, if s lies on the positive side of the oriented plane h defined by p, q, and r, returns CGAL::NEGATIVE if s lies on the negative side of h, and returns CGAL::COPLANAR if s lies on h.
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template<typename Kernel > |
| Orientation | orientation (const CGAL::Vector_3< Kernel > &u, const CGAL::Vector_3< Kernel > &v, const CGAL::Vector_3< Kernel > &w) |
| | returns CGAL::NEGATIVE if u, v and w are negatively oriented, CGAL::POSITIVE if u, v and w are positively oriented, and CGAL::COPLANAR if u, v and w are coplanar.
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template<typename Kernel > |
| CGAL::Vector_3< Kernel > | orthogonal_vector (const CGAL::Plane_3< Kernel > &p) |
| | computes an orthogonal vector of the plane p, which is directed to the positive side of this plane.
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template<typename Kernel > |
| CGAL::Vector_3< Kernel > | orthogonal_vector (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r) |
| | computes an orthogonal vector of the plane defined by p, q and r, which is directed to the positive side of this plane.
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template<typename Kernel > |
| bool | parallel (const CGAL::Line_2< Kernel > &l1, const CGAL::Line_2< Kernel > &l2) |
| | returns true, if l1 and l2 are parallel or if one of those (or both) is degenerate.
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template<typename Kernel > |
| bool | parallel (const CGAL::Ray_2< Kernel > &r1, const CGAL::Ray_2< Kernel > &r2) |
| | returns true, if r1 and r2 are parallel or if one of those (or both) is degenerate.
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template<typename Kernel > |
| bool | parallel (const CGAL::Segment_2< Kernel > &s1, const CGAL::Segment_2< Kernel > &s2) |
| | returns true, if s1 and s2 are parallel or if one of those (or both) is degenerate.
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template<typename Kernel > |
| bool | parallel (const CGAL::Line_3< Kernel > &l1, const CGAL::Line_3< Kernel > &l2) |
| | returns true, if l1 and l2 are parallel or if one of those (or both) is degenerate.
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template<typename Kernel > |
| bool | parallel (const CGAL::Plane_3< Kernel > &h1, const CGAL::Plane_3< Kernel > &h2) |
| | returns true, if h1 and h2 are parallel or if one of those (or both) is degenerate.
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template<typename Kernel > |
| bool | parallel (const CGAL::Ray_3< Kernel > &r1, const CGAL::Ray_3< Kernel > &r2) |
| | returns true, if r1 and r2 are parallel or if one of those (or both) is degenerate.
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template<typename Kernel > |
| bool | parallel (const CGAL::Segment_3< Kernel > &s1, const CGAL::Segment_3< Kernel > &s2) |
| | returns true, if s1 and s2 are parallel or if one of those (or both) is degenerate.
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| CGAL::Plane_3< Kernel > | radical_plane (const CGAL::Sphere_3< Kernel > &s1, const CGAL::Sphere_3< Kernel > &s2) |
| | returns the radical plane of the two spheres.
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| template<typename Kernel > |
| CGAL::Line_2< Kernel > | radical_line (const CGAL::Circle_2< Kernel > &c1, const CGAL::Circle_2< Kernel > &c2) |
| | returns the radical line of the two circles.
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template<typename Kernel > |
| bool | right_turn (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r) |
| | returns true iff p, q, and r form a right turn.
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template<typename Kernel > |
| Kernel::FT | scalar_product (const CGAL::Vector_2< Kernel > &u, const CGAL::Vector_2< Kernel > &v) |
| | returns the scalar product of u and v.
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template<typename Kernel > |
| Kernel::FT | scalar_product (const CGAL::Vector_3< Kernel > &u, const CGAL::Vector_3< Kernel > &v) |
| | returns the scalar product of u and v.
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| template<typename Kernel > |
| Bounded_side | side_of_bounded_circle (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r, const CGAL::Point_2< Kernel > &t) |
| | returns the relative position of point t to the circle defined by p, q and r.
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template<typename Kernel > |
| Bounded_side | side_of_bounded_circle (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &t) |
| | returns the position of the point t relative to the circle that has pq as its diameter.
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| template<typename Kernel > |
| Bounded_side | side_of_bounded_sphere (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s, const CGAL::Point_3< Kernel > &t) |
| | returns the relative position of point t to the sphere defined by p, q, r, and s.
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template<typename Kernel > |
| Bounded_side | side_of_bounded_sphere (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &t) |
| | returns the position of the point t relative to the sphere passing through p, q, and r and whose center is in the plane defined by these three points.
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template<typename Kernel > |
| Bounded_side | side_of_bounded_sphere (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &t) |
| | returns the position of the point t relative to the sphere that has pq as its diameter.
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| template<typename Kernel > |
| Oriented_side | side_of_oriented_circle (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r, const CGAL::Point_2< Kernel > &test) |
| | returns the relative position of point test to the oriented circle defined by p, q and r.
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| template<typename Kernel > |
| Oriented_side | side_of_oriented_sphere (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s, const CGAL::Point_3< Kernel > &test) |
| | returns the relative position of point test to the oriented sphere defined by p, q, r and s.
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template<typename Kernel > |
| Kernel::FT | squared_area (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r) |
| | returns the squared area of the triangle defined by the points p, q and r.
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template<typename Kernel > |
| FT | squared_length (const CGAL::Vector_2< Kernel > &v) |
| | compute the squared length of vector v.
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template<typename Kernel > |
| FT | squared_length (const CGAL::Segment_2< Kernel > &s) |
| | compute the squared length of segment s.
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template<typename Kernel > |
| FT | squared_length (const CGAL::Vector_3< Kernel > &v) |
| | compute the squared length of vector v.
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template<typename Kernel > |
| FT | squared_length (const CGAL::Segment_3< Kernel > &s) |
| | compute the squared length of segment s.
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| template<typename Kernel > |
| FT | squared_radius (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r) |
| | compute the squared radius of the circle passing through the points p, q, and r.
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template<typename Kernel > |
| FT | squared_radius (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q) |
| | compute the squared radius of the smallest circle passing through p, and q, i.e. one fourth of the squared distance between p and q.
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template<typename Kernel > |
| FT | squared_radius (const CGAL::Point_2< Kernel > &p) |
| | compute the squared radius of the smallest circle passing through p, i.e. \( 0\).
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| template<typename Kernel > |
| FT | squared_radius (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s) |
| | compute the squared radius of the sphere passing through the points p, q, r and s.
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template<typename Kernel > |
| FT | squared_radius (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r) |
| | compute the squared radius of the sphere passing through the points p, q, and r and whose center is in the same plane as those three points.
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template<typename Kernel > |
| FT | squared_radius (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q) |
| | compute the squared radius of the smallest circle passing through p, and q, i.e. one fourth of the squared distance between p and q.
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template<typename Kernel > |
| FT | squared_radius (const CGAL::Point_3< Kernel > &p) |
| | compute the squared radius of the smallest circle passing through p, i.e. \( 0\).
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| CGAL::Vector_3< Kernel > | unit_normal (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r) |
| | computes the unit normal vector for the vectors q-p and r-p.
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template<typename Kernel > |
| Kernel::FT | volume (const CGAL::Point_3< Kernel > &p0, const CGAL::Point_3< Kernel > &p1, const CGAL::Point_3< Kernel > &p2, const CGAL::Point_3< Kernel > &p3) |
| | Computes the signed volume of the tetrahedron defined by the four points p0, p1, p2 and p3.
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template<typename Kernel > |
| bool | x_equal (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q) |
| | returns true, iff p and q have the same x-coordinate.
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template<typename Kernel > |
| bool | x_equal (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q) |
| | returns true, iff p and q have the same x-coordinate.
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template<typename Kernel > |
| bool | y_equal (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q) |
| | returns true, iff p and q have the same y-coordinate.
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template<typename Kernel > |
| bool | y_equal (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q) |
| | returns true, iff p and q have the same y-coordinate.
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template<typename Kernel > |
| bool | z_equal (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q) |
| | returns true, iff p and q have the same z-coordinate.
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| template<RingNumberType > |
| void | rational_rotation_approximation (const RingNumberType &dirx, const RingNumberType &diry, RingNumberType &sin_num, RingNumberType &cos_num, RingNumberType &denom, const RingNumberType &eps_num, const RingNumberType &eps_den) |
| | computes integers sin_num, cos_num and denom, such that sin_num/denom approximates the sine of direction \( (\)dirx,diry \( )\).
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| template<typename Kernel > |
| Kernel::FT | squared_distance (Type1< Kernel > obj1, Type2< Kernel > obj2) |
| | computes the square of the Euclidean distance between two geometric objects.
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