Version 5.0 The LEDA User Manual

16.5 Planes ( d3 plane )
1. Definition
An instance P of the data type d3 plane is an oriented plane in the three-dimensional
space R 3 . It can be defined by a tripel (a,b,c) of non-collinear points or a single point a
and a normal vector v.
#include < LEDA/geo/d3 plane.h >
2. Creation
d3 plane p;
introduces a variable p of type d3 plane initialized to the xy-plane.
d3 plane p(const d3 point& a, const d3 point& b, const d3 point& c);
introduces a variable p of type d3 plane initialized to the plane
through (a, b, c).
Precondition: a, b, and c are not collinear.
d3 plane p(const d3 point& a, const vector& v);
introduces a variable p of type d3 plane initialized to the plane that
contains a with normal vector v.
Precondition: v.dim( ) = 3 and v.length( ) > 0.
d3 plane p(const d3 point& a, const d3 point& b);
introduces a variable p of type d3 plane initialized to the plane that
contains a with normal vector b − a.
3. Operations
d3 point p.point1( ) returns the first point of p.
d3 point p.point2( ) returns the second point of p.
d3 point p.point3( ) returns the third point of p.
double p.A( ) returns the A parameter of the plane equation.
double p.B( ) returns the B parameter of the plane equation.
double p.C( ) returns the C parameter of the plane equation.
double p.D( ) returns the D parameter of the plane equation.
vector p.normal( ) returns a normal vector of p.