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Segments in 3D-Space ( d3_segment )

Definition

An instance s of the data type d3$ \_$segment is a directed straight line segment in three-dimensional space, i.e., a straight line segment [p, q] connecting two points p, q $ \in$ R3. 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 >

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).

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().

segment s.project_xy() returns the projection into the xy plane.

segment s.project_xz() returns the projection into the xz plane.

segment s.project_yz() returns the projection into the yz plane.

d3_segment s.project(const d3_point& p, const d3_point& q, const d3_point& v)
    returns s projected into the plane through (p,q,v).

d3_segment s.reflect(const d3_point& p, const d3_point& q, const d3_point& v)
    returns s reflected across the plane through (p,q,v).

d3_segment s.reflect(const d3_point& p)
    returns s reflected across point p.

d3_segment s.reverse() returns s reversed.

vector s.to_vector() returns s.target()-s.source().

bool s.intersection(const d3_segment& t)
    decides, whether s and t intersect in a single point.

bool s.intersection(const d3_segment& t, d3_point& p)
    decides, whether s and t intersect in a single point. If they intersect in a single point, the point is assigned to p and the result is true, otherwise the result is false

bool s.intersection_of_lines(const d3_segment& t, d3_point& p)
    If line(s) and line(t) intersect in a single point this point is assigned to p and the result is true, otherwise the result is false.

bool s.is_trivial() returns true if s is trivial.

double s.sqr_length() returns the square of the length of s.

double s.length() returns the length of s.

d3_segment s.translate(const vector& v)
    returns s translated by vector v.
Precond.: v.dim()=3.

d3_segment s.translate(double dx, double dy, double dz)
    returns s translated by vector (dx,dy,dz).

d3_segment s + const vector& v returns s translated by vector v.

d3_segment s - const vector& v returns s translated by vector - v.


next up previous contents index
Next: Straight Lines in 3D-Space Up: Basic Data Types for Previous: Straight Rays in 3D-Space   Contents   Index
root 2008-01-09