FreeCAD Vektor Mathematische Bibliothek

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Einführung

Dies ist eine Python-Modul mit einigen nützlichen Funktionen zur Manipulation von Vektoren. Diese Bibliothek ist im Draft-Modul enthalten und kann so vom Python-Interpreter aus aufgerufen werden:

import DraftVecUtils

Bitte beachte, dass dieses Modul vor langer Zeit erstellt wurde, als die Vector-Klasse viele ihrer Methoden noch nicht hatte. Nun können diese Operationen von der Vector-Klasse selbst erledigt werden.

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

Vektoren sind die Bausteine fast aller geometrischen 3D-Operationen, daher ist es nützlich, ein wenig über sie zu wissen, um zu verstehen, wie diese Funktionen für Dich nützlich sein können. Ein paar gute Seiten, um die Grundlagen der Vektor-Mathematik zu lernen:

"""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))