# Difference between revisions of "FreeCAD vector math library/de"

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Dies ist eine Python-Datei mit einigen nützlichen Funktionen zur Manipulation von Freecad-Vektoren. Füge einfach den folgenden Code in eine Python-Datei ein und importiere diese Datei in dein Python-Skript, um sie zu verwenden. Diese Bibliothek ist im Draft Module enthalten und kann so vom Python-Interpreter aus aufgerufen werden:

```import DraftVecUtils
```

Vectors are the building bricks of almost all 3D geometric operations, so it is useful to know a bit about them to understand how these functions can be useful to you. A couple of good pages to learn the basics of vector math:

``` "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))
```