Version 5.0 The LEDA User Manual

16.3 Segments in 3D-Space ( d3 segment )
1. Definition
An instance s of the data type d3 segment is a directed straight line segment in threedimensional
space, i.e., a straight line segment [p, q] connecting two points p, q ∈ R 3 . p
is called the source or start point and q is called the target or end point of s. The length
of s is the Euclidean distance between p and q. 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 segment.h >
2. Creation
d3 segment s(const d3 point& p1 , const d3 point& p2 );
introduces a variable s of type d3 segment. s is initialized to the
segment from p1 to p2 .
d3 segment s;
introduces a variable s of type d3 segment. s is initialized to the
segment from (0, 0, 0) to (1, 0, 0).
3. Operations
bool s.contains(const d3 point& p)
decides whether s contains p.
d3 point s.source( ) returns the source point of segment s.
d3 point s.target( ) returns the target point of segment s.
double s.xcoord1( ) returns the x-coordinate of s.source().
double s.xcoord2( ) returns the x-coordinate of s.target().
double s.ycoord1( ) returns the y-coordinate of s.source().
double s.ycoord2( ) returns the y-coordinate of s.target().
double s.zcoord1( ) returns the z-coordinate of s.source().
double s.zcoord2( ) returns the z-coordinate of s.target().
double s.dx( ) returns xcoord2( ) − xcoord1( ).
double s.dy( ) returns ycoord2 ( ) − ycoord1 ( ).
double s.dz( ) returns zcoord2( ) − zcoord1( ).