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

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This is a python file containing a couple of useful functions to manipulate freecad vectors. Just paste the following code in a python file, and import that file in your python script in order to use them. This library is included in the Draft Module and can be accessed like this from the python interpreter:

```from draftlibs import fcvec
```

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))
```
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