FreeCAD vector math library/it

Questo è un file python che contiene un paio di funzioni utili per manipolare i vettori di FreeCAD. Per usarle, basta incollare il seguente codice in un file di python, e importare il file nel vostro script python. Questa libreria è inclusa nel Modulo Draft e vi si può accedere tramite l'interprete python in questo modo:

from draftlibs import DraftVecUtils

I vettori sono i mattoni costitutivi di quasi tutte le operazioni geometriche 3D, quindi è utile conoscerli un po' per capire come queste funzioni possono essere utili. Ecco alcune valide pagine per imparare le basi della matematica vettoriale:

• http://en.wikipedia.org/wiki/Vector_space
• http://maths-wiki.wikispaces.com/Vectors
• http://darksleep.com/player/opengl_coordinate_system_and_matrix_math.html

 "Vector math library for FreeCAD"

 import math,FreeCAD
 
 def add(first, other):
 "add(Vector,Vector) - adds two vectors"
 if isinstance(first,FreeCAD.Vector) and isinstance(other,FreeCAD.Vector):
 return FreeCAD.Vector(first.x+other.x, first.y+other.y, first.z+other.z)
 
 def sub(first, other): 
 "sub(Vector,Vector) - subtracts second vector from first one"
 if isinstance(first,FreeCAD.Vector) and isinstance(other,FreeCAD.Vector):
 return FreeCAD.Vector(first.x-other.x, first.y-other.y, first.z-other.z)
 
 def scale(first,scalar):
 "scale(Vector,Float) - scales (multiplies) a vector by a factor"
 if isinstance(first,FreeCAD.Vector):
 return FreeCAD.Vector(first.x*scalar, first.y*scalar, first.z*scalar)
 
 def length(first):
 "lengh(Vector) - gives vector length"
 if isinstance(first,FreeCAD.Vector):
 return math.sqrt(first.x*first.x + first.y*first.y + first.z*first.z)
 
 def dist(first, other):
 "dist(Vector,Vector) - returns the distance between both points/vectors"
 if isinstance(first,FreeCAD.Vector) and isinstance(other,FreeCAD.Vector):
 return length(sub(first,other))
 
 def normalized(first):
 "normalized(Vector) - returns a unit vector"
 if isinstance(first,FreeCAD.Vector):
 l=length(first)
 return FreeCAD.Vector(first.x/l, first.y/l, first.z/l)
 
 def dotproduct(first, other):
 "dotproduct(Vector,Vector) - returns the dot product of both vectors"
 if isinstance(first,FreeCAD.Vector) and isinstance(other,FreeCAD.Vector):
 return (first.x*other.x + first.y*other.y + first.z*other.z)
 
 def crossproduct(first, other=FreeCAD.Vector(0,0,1)):
 "crossproduct(Vector,Vector) - returns the cross product of both vectors. 
 If only one is specified, cross product is made with vertical axis, thus returning its perpendicular in XY plane"
 if isinstance(first,FreeCAD.Vector) and isinstance(other,FreeCAD.Vector):
 return FreeCAD.Vector(first.y*other.z - first.z*other.y, first.z*other.x - first.x*other.z, first.x*other.y - first.y*other.x)
 
 def angle(first, other=FreeCAD.Vector(1,0,0)):
 "angle(Vector,Vector) - returns the angle in radians between the two vectors. 
 If only one is given, angle is between the vector and the horizontal East direction"
 if isinstance(first,FreeCAD.Vector) and isinstance(other,FreeCAD.Vector):
 return math.acos(dotproduct(normalized(first),normalized(other)))
 
 def project(first, other):
 "project(Vector,Vector): projects the first vector onto the second one"
 if isinstance(first,FreeCAD.Vector) and isinstance(other,FreeCAD.Vector):
 return scale(other, dotproduct(first,other)/dotproduct(other,other))