FreeCAD vector math library/it

=Libreria di matematica vettoriale di FreeCAD=

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 fcvec

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))