Version 5.0 The LEDA User Manual

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