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# Rational Segments in 3D-Space ( d3_rat_segment )

Definition

An instance s of the data type d3ratsegment is a directed straight line segment in three-dimensional space, i.e., a line segment connecting two rational points p, q R3 . 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 >

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).

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(). rational s.dy() returns ycoord2()-ycoord1(). rational s.dz() returns zcoord2()-zcoord1(). rat_segment s.project_xy() returns the projection into the xy plane. rat_segment s.project_xz() returns the projection into the xz plane. rat_segment s.project_yz() returns the projection into the yz plane. d3_rat_segment s.project(const d3_rat_point& p, const d3_rat_point& q, const d3_rat_point& v) returns s projected into the plane through (p,q,v). d3_rat_segment s.reflect(const d3_rat_point& p, const d3_rat_point& q, const d3_rat_point& v) returns s reflected across the plane through (p,q,v). d3_rat_segment s.reflect(const d3_rat_point& p) returns s reflected across point p. d3_rat_segment s.reverse() returns s reversed. rat_vector s.to_vector() returns S.target()-S.source(). bool s.intersection(const d3_rat_segment& t) decides, whether s and t intersect in a single point. bool s.intersection(const d3_rat_segment& t, d3_rat_point& p) decides, whether s and t intersect. If they intersect in a single point, the point is assigned to p bool s.intersection_of_lines(const d3_rat_segment& t, d3_rat_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. rational s.sqr_length() returns the square of the length of s. d3_rat_segment s.translate(const rat_vector& v) returns s translated by vector v. Precond.: v.dim()=3. d3_rat_segment s.translate(rational dx, rational dy, rational dz) returns s translated by vector (dx,dy,dz). d3_rat_segment s.translate(integer dx, integer dy, integer dz, integer dw) returns s translated by vector (dx/dw,dy/dw,dz/w). d3_rat_segment s + const rat_vector& v returns s translated by vector v . d3_rat_segment s - const rat_vector& v returns s translated by vector - v .

Next: Rational Planes ( d3_rat_plane Up: Basic Data Types for Previous: Rational Lines in 3D-Space   Contents   Index
Christian Uhrig 2017-04-07