gp_Ax3

Open CASCADE Technology »  Module FoundationClasses »  Toolkit TKMath  »   Package gp

gp_Ax3 Class Reference

Describes a coordinate system in 3D space. Unlike a 
gp_Ax2 coordinate system, a gp_Ax3 can be 
right-handed ("direct sense") or left-handed ("indirect sense"). 
A coordinate system is defined by: 

• its origin (also referred to as its "Location point"), and 
  
• three orthogonal unit vectors, termed the "X <br> Direction", the "Y Direction" and the "Direction" (also 
  referred to as the "main Direction"). 
  The "Direction" of the coordinate system is called its 
  "main Direction" because whenever this unit vector is 
  modified, the "X Direction" and the "Y Direction" are 
  recomputed. However, when we modify either the "X <br> Direction" or the "Y Direction", "Direction" is not modified. 
  "Direction" is also the "Z Direction". 
  The "main Direction" is always parallel to the cross 
  product of its "X Direction" and "Y Direction". 
  If the coordinate system is right-handed, it satisfies the equation: 
  "main Direction" = "X Direction" ^ "Y Direction" 
  and if it is left-handed, it satisfies the equation: 
  "main Direction" = -"X Direction" ^ "Y Direction" 
  A coordinate system is used: 
  
• to describe geometric entities, in particular to position 
  them. The local coordinate system of a geometric 
  entity serves the same purpose as the STEP function 
  "axis placement three axes", or 
  
• to define geometric transformations. 
  Note: 
  
• We refer to the "X Axis", "Y Axis" and "Z Axis", 
  respectively, as the axes having: 
  
• the origin of the coordinate system as their origin, and 
  
• the unit vectors "X Direction", "Y Direction" and 
  "main Direction", respectively, as their unit vectors. 
  
• The "Z Axis" is also the "main Axis". 
  
• gp_Ax2 is used to define a coordinate system that must be always right-handed. 
  

#include <gp_Ax3.hxx>