import Draft, Part, FreeCADGui
import FreeCAD as App
import os
from pathlib import Path
from math import pi, sin,cos

origin=App.Vector(0,0,0)

x=3*cos(pi/4)
y=3*sin(pi/4)

v3=App.Vector(x,y,0)

lv3 = Draft.makeWire([ origin, v3], closed=False, face=False, support=None)
lv3.Label='PointAsVector'

vt3= Part.Vertex(v3)
vt=Part.show(vt3)
vt.Label = 'point'

v1=App.Vector(0,10,10)
v2=App.Vector(10,5,15)

line = Draft.makeWire([ v1, v2], closed=False, face=False, support=None)
line.Label='path vector'


z=App.Vector(0,0,1)

circ = Part.makeCircle(3,origin,z,0,360)
c=Part.show(circ)
c.Label='Circle1'

normal = Draft.makeWire([ origin, z*5], closed=False, face=False, support=None)
normal.Label='Normal'

axis = v2-v1
axis.normalize()
y=axis.cross(z)
y.normalize()
x=axis.cross(y)
x.normalize()

m=App.Matrix(x,y,axis)

NewNormal = Draft.makeWire([ origin, axis*5], closed=False, face=False, support=None)
NewNormal.Label='NewNormal'

Hingex = Draft.makeWire([ origin, x*5], closed=False, face=False, support=None)
Hingex.Label="HingeX"

Hingey = Draft.makeWire([ origin, y*5], closed=False, face=False, support=None)
Hingey.Label="HingeY"

vm = m*v3

lv4 = Draft.makeWire([ origin, vm], closed=False, face=False, support=None)
lv4.Label='RotatedPointAsVector'

circ2 = Part.makeCircle(3,origin,axis,0,360)
c2=Part.show(circ2)
c2.Label='RotatedCircle'


vt=vm+v1

lv5 = Draft.makeWire([ v1, vt], closed=False, face=False, support=None)
lv5.Label='TranslatedPointAsVector'