# FreeCAD vector math library

## Introduction

This is a Python module containing a couple of useful functions to manipulate vectors. This library is included in the Draft_Workbench and can be accessed like this from the Python interpreter:

```
import DraftVecUtils
```

Please note that this module was created a long time ago, when the `Vector`

class didn't have many of its methods. Now these operations can be done by the Vector class itself.

Although the `DraftVecUtils`

module still exists, and it is still used inside the Draft Workbench, it is probably better to use the `Vector`

methods directly for new developments.

## Functions

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:

- 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
import 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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