Version 5.0 The LEDA User Manual

16.11 Rational Segments in 3D-Space (
d3 rat segment )
1. Definition
An instance s of the data type d3 rat segment is a directed straight line segment in
three-dimensional space, i.e., a line segment connecting two rational points p, q ∈ R 3 . p is
called the source or start point and q is called the target or end point of s. A segment is
called trivial if its source is equal to its target. If s is not trivial, we use line(s) to denote
the straight line containing s.
#include < LEDA/geo/d3 rat segment.h >
2. Creation
d3 rat segment s(const d3 rat point& p1 , const d3 rat point& p2 );
introduces a variable S of type d3 rat segment. S is initialized to
the segment through points p1 , p2 .
d3 rat segment s;
introduces a variable S of type d3 rat segment. S is initialized to
the segment through points (0, 0, 0, 1) and (1, 0, 0, 1).
3. Operations
d3 segment s.to float( ) returns a floating point approximation of s.
bool s.contains(const d3 rat point& p)
decides whether s contains p.
d3 rat point s.source( ) returns the source point of segment s.
d3 rat point s.target( ) returns the target point of segment s.
rational s.xcoord1( ) returns the x-coordinate of s.source().
rational s.xcoord2( ) returns the x-coordinate of s.target().
rational s.ycoord1( ) returns the y-coordinate of s.source().
rational s.ycoord2( ) returns the y-coordinate of s.target().
rational s.zcoord1( ) returns the z-coordinate of s.source().
rational s.zcoord2( ) returns the z-coordinate of s.target().
rational s.dx( ) returns xcoord2( ) − xcoord1( ).