def schnittgerade(self, plane1: Plane, plane2: Plane):
"""Calculates and Returns the schnittgerade of two Planes.
Returns a Line instance."""
pla1 = plane1.convertToHessianNormalForm()
pla2 = plane2.convertToHessianNormalForm()
normvec1 = pla1.normVec
normvec2 = pla2.normVec
posnum1 = pla1.posVec.scalarProduct(normvec1)
posnum2 = pla2.posVec.scalarProduct(normvec2)
schnittgerade = not Solvers.checkLinearAbhaengig(
normvec1, normvec2) # Testing if the Planes are not Parallel
if schnittgerade:
dirVec = normvec1.vectorProduct(normvec2)
posVecScalar1 = ((posnum1 * normvec2.square()) -
(posnum2 * normvec1.scalarProduct(normvec2))) / (
(normvec1.square() * normvec2.square()) -
normvec1.scalarProduct(normvec2)**2)
posVecScalar2 = ((posnum2 * normvec1.square()) -
(posnum1 * normvec1.scalarProduct(normvec2))) / (
(normvec1.square() * normvec2.square()) -
normvec1.scalarProduct(normvec2)**2)
normvec1 = normvec1.scalarMultiplication(posVecScalar1)
normvec2 = normvec2.scalarMultiplication(posVecScalar2)
posVec = normvec1.add(normvec2)
schnittgerade = Line(posVec,
dirVec,
name=("Schnittgerade von " + pla1.name +
" und " + pla2.name))
return schnittgerade
def solveForPointPlane(self, line: Line, plane: Plane):
if plane.getType() == "normal":
normVec = plane.getNormalVector()
posVecP = plane.getPositionVector()
scalarParam = posVecP.scalarProduct(normVec)
posVec = line.getPositionVector()
dirVec = line.getDirectionVector()
xValNoVar = normVec.getX() * posVec.getX()
yValNoVar = normVec.getY() * posVec.getY()
zValNoVar = normVec.getZ() * posVec.getZ()
xValVar = normVec.getX() * dirVec.getX()
yValVar = normVec.getY() * dirVec.getY()
zValVar = normVec.getZ() * dirVec.getZ()
ValVar = xValVar + yValVar + zValVar
ValNoVar = scalarParam - xValNoVar - yValNoVar - zValNoVar
Var = ValNoVar / ValVar
SchnittPoint = Point(posVec.getX() + Var * dirVec.getX(),
posVec.getY() + Var * dirVec.getY(),
posVec.getZ() + Var * dirVec.getZ())
return SchnittPoint
elif plane.getType() == "coordinate":
normVec = plane.getNormalVector()
scalarParam = plane.getScalarParameter()
posVec = line.getPositionVector()
dirVec = line.getDirectionVector()
xValNoVar = normVec.getX() * posVec.getX()
yValNoVar = normVec.getY() * posVec.getY()
zValNoVar = normVec.getZ() * posVec.getZ()
xValVar = normVec.getX() * dirVec.getX()
yValVar = normVec.getY() * dirVec.getY()
zValVar = normVec.getZ() * dirVec.getZ()
ValVar = xValVar + yValVar + zValVar
ValNoVar = scalarParam - xValNoVar - yValNoVar - zValNoVar
Var = ValNoVar / ValVar
SchnittPoint = Point(posVec.getX() + Var * dirVec.getX(),
posVec.getY() + Var * dirVec.getY(),
posVec.getZ() + Var * dirVec.getZ())
return SchnittPoint
elif plane.getType() == "parameter":
normVec = plane.getDirectionVectorOne().vectorProduct(
plane.getDirectionVectorTwo())
posVecP = plane.getPositionVector()
scalarParam = posVecP.scalarProduct(normVec)
posVec = line.getPositionVector()
dirVec = line.getDirectionVector()
xValNoVar = normVec.getX() * posVec.getX()
yValNoVar = normVec.getY() * posVec.getY()
zValNoVar = normVec.getZ() * posVec.getZ()
xValVar = normVec.getX() * dirVec.getX()
yValVar = normVec.getY() * dirVec.getY()
zValVar = normVec.getZ() * dirVec.getZ()
ValVar = xValVar + yValVar + zValVar
ValNoVar = scalarParam - xValNoVar - yValNoVar - zValNoVar
Var = ValNoVar / ValVar
SchnittPoint = Point(posVec.getX() + Var * dirVec.getX(),
posVec.getY() + Var * dirVec.getY(),
posVec.getZ() + Var * dirVec.getZ())
return SchnittPoint
def checkPointInPlane(self, plane: Plane, point: Point):
vector = Vector3D(point.getX(), point.getY(), point.getZ())
typeOfPlane = plane.getType()
pointInPlane = False
if typeOfPlane == "normal":
result = vector.subtract(plane.getPositionVector())
answer = result.scalarProduct(plane.getNormalVector())
if answer == 0:
pointInPlane = True
else:
pointInPlane = False
elif typeOfPlane == "parameter":
dirVec1 = plane.getDirectionVectorOne()
dirVec2 = plane.getDirectionVectorTwo()
result = vector.subtract(plane.getPositionVector())
arrayOne = np.array([[dirVec1.getX(),
dirVec1.getY()],
[dirVec2.getX(),
dirVec2.getY()]])
arrayTwo = np.array([result.getX(), result.getY()])
solution = np.linalg.solve(arrayOne, arrayTwo)
if solution[0] * dirVec1.getZ() + solution[1] * dirVec2.getZ(
) == result.getZ():
pointInPlane = True
else:
pointInPlane = False
elif typeOfPlane == "coordinate":
normVec = plane.getNormalVector()
if point.getX() * normVec.getX() + point.getY() * normVec.getY(
) + point.getZ() * normVec.getZ() == plane.getScalarParameter():
pointInPlane = True
else:
pointInPlane = False
return pointInPlane
def distancePlanePoint(self, point: Point, plane: Plane):
if Solvers.checkPointInPlane(plane, point) == False:
if plane.getType() == "coordinate":
hess = plane.convertToHessianNormalForm()
normVec = hess.getNormalVector()
scalarParam = hess.getScalarParameter()
distance = normVec.getX() * point.getX() + normVec.getY(
) * point.getY() + normVec.getZ() * point.getZ() - scalarParam
else:
hess = plane.convertToHessianNormalForm()
pointVec = Vector3D(point.getX(), point.getY(), point.getZ())
subtract = pointVec.subtract(hess.getPositionVector())
distance = subtract.scalarProduct(hess.getNormalVector())
distance = abs(distance)
else:
distance = 0
return distance
def distancePointLine(self, point: Point, line: Line):
helpPlane = Plane.normalForm(
Vector3D(point.getX(), point.getY(), point.getZ()),
line.getDirectionVector())
pointSchnitt = Solvers.solveForPointPlane(line, helpPlane)
schnittPoint = Point(pointSchnitt.getX(), pointSchnitt.getY(),
pointSchnitt.getZ())
distance = Solvers.distancePointPoint(schnittPoint, point)
return distance
def distanceLinePlane(self, line: Line, plane: Plane):
if plane.getType() == "normal" or plane.getType() == "coordinate":
normVec = plane.getNormalVector()
if normVec.scalarProduct(line.getDirectionVector()) == 0:
distance = Solvers.distancePlanePoint(line.getPositionVector(),
plane)
else:
distance = 0
return distance
else:
normVec = plane.getDirectionVectorOne().vectorProduct(
plane.getDirectionVectorTwo())
if normVec.scalarProduct(line.getDirectionVector()) == 0:
distance = Solvers.distancePlanePoint(line.getPositionVector(),
plane)
else:
distance = 0
return distance
def distanceLineLine(self, line1: Line, line2: Line):
if Solvers.checkLinearAbhaengig(line1.getDirectionVector(),
line2.getDirectionVector()) == True:
if Solvers.checkPointInLine(line1,
line2.getPositionVector()) == True:
print("Identisch")
else:
distance = Solvers.distancePointLine(line2.getPositionVector(),
line1)
elif Solvers.schnittpunkt(line1, line2) is not None:
distance = 0
else:
normVec = line1.getDirectionVector().vectorProduct(
line2.getDirectionVector())
scalarParam = normVec.scalarProduct(line1.getPositionVector())
helpPlane = Plane.coordinateForm(normVec, scalarParam)
distance = Solvers.distancePlanePoint(line2.getPositionVector(),
helpPlane)
return distance
import tkinter as tk
from tkinter import Canvas, ttk
from tkinter.constants import RIDGE
from listclass import ObjectLists
from vector3Dclass import Vector3D
from pointclass import Point
from lineclass import Line
from planeclass import Plane
from nameAssignclass import NameAssign
from colorAssignclass import ColorAssign
x = Vector3D(3, 4, 5)
y = Plane.normalForm(Vector3D(1, 1, 1), Vector3D(2, 2, 2))
z = Plane.parameterForm(Vector3D(3, 4, 5), Vector3D(2, 2, 2),
Vector3D(2, 2, 2))
class MainGUI(tk.Frame):
width = 1200
height = 700
size = str(width) + "x" + str(height)
def __init__(self):
self.root = tk.Tk()
self.root.title("Vektorplotter")
self.root.geometry(self.size)
#self.root.resizable(0, 0)
self.makeMainframe()
self.makeListFrame()
self.makeMenuFrame()
print("Position Vector: ")
Vec1 = Vector3D(input("x = "),input("y = "),input("z = "),input("Name = "))
print("Direction Vector: ")
Vec2 = Vector3D(input("x = "),input("y = "),input("z = "),input("Name = "))
name = input("Name: ")
LinList.append(Line(Vec1, Vec2, name, (0, 0, 0)))
print(str(LinList[-1]))
elif UserInput == "NewPla":
print("Position Vector: ")
Vec1 = Vector3D(input("x = "),input("y = "),input("z = "),input("Name = "))
print("Direction Vector One: ")
Vec2 = Vector3D(input("x = "),input("y = "),input("z = "),input("Name = "))
print("Direction Vector Two: ")
Vec3 = Vector3D(input("x = "),input("y = "),input("z = "),input("Name = "))
name = input("Name: ")
PlaList.append(Plane.parameterForm(Vec1, Vec2, Vec3, name, (0, 0, 0)))
print(str(PlaList[-1]))
elif UserInput == "ConvertPlaToHess":
print("Position Vector: ")
Vec1 = Vector3D(input("x = "),input("y = "),input("z = "),input("Name = "))
print("Direction Vector One: ")
Vec2 = Vector3D(input("x = "),input("y = "),input("z = "),input("Name = "))
print("Direction Vector Two: ")
Vec3 = Vector3D(input("x = "),input("y = "),input("z = "),input("Name = "))
name = input("Name: ")
PlaList.append(Plane.parameterForm(Vec1, Vec2, Vec3, name, (0, 0, 0)))
print(str(PlaList[-1].convertToHessianNormalForm()))
elif UserInput == "X":
running = False
else:
print("Uberprüfen Sie bitte ihre Eingabe!")