CGAL 4.12 - 2D and 3D Linear Geometry Kernel
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AdaptableFunctor
(with two arguments)Operations | |
Kernel::FT | operator() (const Kernel::Weighted_point_2 &pw, const Kernel::Weighted_point_2 &qw) const |
returns the power product of pw and qw . More... | |
Kernel::FT Kernel::ComputePowerProduct_2::operator() | ( | const Kernel::Weighted_point_2 & | pw, |
const Kernel::Weighted_point_2 & | qw | ||
) | const |
returns the power product of pw
and qw
.
Let {p}^{(w)} = (p,w_p), p\in\mathbb{R}^2, w_p\in\mathbb{R} and {q}^{(w)}=(q,w_q), q\in\mathbb{R}^2, w_q\in\mathbb{R} be two weighted points.
The power product, also called power distance between {p}^{(w)} and {q}^{(w)} is defined as
\Pi({p}^{(w)},{q}^{(w)}) = {\|{p-q}\|^2-w_p-w_q}
where \|{p-q}\| is the Euclidean distance between p and q.
The weighted points {p}^{(w)} and {q}^{(w)} are said to be orthogonal iff \Pi{({p}^{(w)},{q}^{(w)})} = 0.
Three weighted points have, in 2D, a unique common orthogonal weighted point called the power circle. The power segment will denote the weighted point orthogonal to two weighted points on the line defined by these two points.