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 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 schnittpunkt(self, line1: Line, line2: Line):
"""Returns the Schnittpunkt between two Lines.
Uses Solvers.solveForSchnittstelle.
Returns a Point instance."""
posVec1 = line1.getPositionVector()
posVec2 = line2.getPositionVector()
dirVec1 = line1.getDirectionVector()
dirVec2 = line2.getDirectionVector()
schnittstelle = self.solveForSchnittstelle(line1, line2)
ValOne = posVec1.add(dirVec1.scalarMultiplication(schnittstelle[0]))
ValTwo = posVec2.add(dirVec2.scalarMultiplication(schnittstelle[0]))
if ValOne.getX() == ValTwo.getX() and ValOne.getY() == ValTwo.getY(
) and ValOne.getZ() == ValTwo.getZ():
schnittpunkt = ValOne
else:
schnittpunkt = None
return schnittpunkt
def main():
pygame.init()
screen = pygame.display.set_mode((640,480))
pygame.display.set_caption("Animated Line")
line = Line(screen)
clock = pygame.time.Clock()
while 1:
clock.tick(30)
screen.fill((50, 50, 100))
line.update()
line.draw()
pygame.display.flip()
for event in pygame.event.get():
if event.type == QUIT:
pygame.quit()
return
elif event.type == KEYDOWN and event.key == K_ESCAPE:
pygame.quit()
return
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 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
def main():
pygame.init()
screen = pygame.display.set_mode((640,480))
pygame.display.set_caption("Animated Line")
lines = [Line(screen) for x in range(20)]
clock = pygame.time.Clock()
while 1:
clock.tick(30)
screen.fill((50, 50, 100))
for line in lines:
line.update()
line.draw()
pygame.display.flip()
for event in pygame.event.get():
if event.type == QUIT:
pygame.quit()
return
elif event.type == KEYDOWN and event.key == K_ESCAPE:
pygame.quit()
return
Vec2 = Vector3D(input("x = "),input("y = "),input("z = "),input("Name = "))
print("Ergebnis: " + str(Vec1.scalarProduct(Vec2)))
elif UserInput == "VecMultVecCro":
Vec1 = Vector3D(input("x = "),input("y = "),input("z = "),input("Name = "))
Vec2 = Vector3D(input("x = "),input("y = "),input("z = "),input("Name = "))
print("Ergebnis: " + str(Vec1.vectorProduct(Vec2)))
elif UserInput == "NewPoi":
PoiList.append(Point(input("x = "),input("y = "),input("z = "),input("Name = ")))
print(str(PoiList[-1]))
elif UserInput == "NewLin":
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: ")