def limitizeLogSpiral(center, n):
'''Calculates limit of spiral constants "a" and "k"'''
spiral = Spiral()
I0 = center
for i in range(n):
r1 = points[i].distance(I0)
r2 = points[i + 1].distance(I0)
theta1 = angle(i, Line(I0, points[i]).slope)
theta2 = angle(i + 1, Line(I0, points[i + 1]).slope)
k = math.log(r1 / r2) / (theta1 - theta2)
t = r1 * math.exp(-1 * k * theta1)
if abs(t - spiral.t) < epsilon and abs(k - spiral.k) < epsilon:
return ("logarithmicSpiral", {
"comment": "Converged at expected values",
"t": t,
"k": k,
"iteration": i
})
else:
return ("logarithmicSpiral", {
"comment": "Did not converge at expected values of 't' and 'k'",
"t": {
"expected": spiral.t,
"limitized": t,
"error": spiral.t - t,
},
"k": {
"expected": spiral.k,
"limitized": k,
"error": spiral.k - k
}
})
def testValidateLine(self):
l1 = ShapeFactory.build("line", Point(1, 1), Point(-1, -5))
Line.validateLine(l1, "Line unexpectedly invalid")
self.assertRaises(ShapeException, Line.validateLine, "(1, 1, -1, -5)",
"String \'(1, 1, -1, -5)\' is not a valid line")
self.assertRaises(ShapeException, Line.validateLine, Point(1, 1), "Point is not a valid line")
def testValidConstruction(self):
p1 = Point(1, 2)
p2 = Point(1, 1)
p3 = Point(2, 1)
t1 = ShapeFactory.build("triangle", p1, p2, p3)
self.assertEqual(p1, t1.point1)
self.assertEqual(p2, t1.point2)
self.assertEqual(p3, t1.point3)
l1 = Line(Point(4.33, 8), Point(-4, 3.67))
l2 = Line(Point(-4, 3.67), Point(2.19, -5))
l3 = Line(Point(2.19, -5), Point(4.33, 8))
t2 = ShapeFactory.build("triangle", l1.point1, l2.point1, l3.point1)
self.assertEqual(l1, t2.line1)
self.assertEqual(l2, t2.line2)
self.assertEqual(l3, t2.line3)
t3 = ShapeFactory.build("triangle", Point(1, 2), Point(5, 1), Point(3, 3))
self.assertEqual(1, t3.point1.x)
self.assertEqual(2, t3.point1.y)
self.assertEqual(5, t3.point2.x)
self.assertEqual(1, t3.point2.y)
self.assertEqual(3, t3.point3.x)
self.assertEqual(3, t3.point3.y)
def testValidConstruction(self):
p1 = Point(1, 3)
p2 = Point(5, 3)
p3 = Point(5, 1)
p4 = Point(1, 1)
r1 = Rectangle(p1, p2, p3, p4)
self.assertEqual(p1, r1.point1)
self.assertEqual(p2, r1.point2)
self.assertEqual(p3, r1.point3)
self.assertEqual(p4, r1.point4)
l1 = Line(-3, 1, 1, 1)
l2 = Line(1, 1, 1, -5)
l3 = Line(1, -5, -3, -5)
l4 = Line(-3, -5, -3, 1)
r2 = Rectangle(l1, l2, l3, l4)
self.assertEqual(l1, r2.line1)
self.assertEqual(l2, r2.line2)
self.assertEqual(l3, r2.line3)
self.assertEqual(l4, r2.line4)
r3 = Rectangle(-.8, .4, 0, 2, .8, 1.6, 0, 0)
self.assertEqual(-.8, r3.point1.x)
self.assertEqual(.4, r3.point1.y)
self.assertEqual(0, r3.point2.x)
self.assertEqual(2, r3.point2.y)
self.assertEqual(.8, r3.point3.x)
self.assertEqual(1.6, r3.point3.y)
self.assertEqual(0, r3.point4.x)
self.assertEqual(0, r3.point4.y)
def testValidConstruction(self):
p1 = Point(1, 2)
p2 = Point(1, 1)
p3 = Point(2, 1)
t1 = Triangle(p1, p2, p3)
self.assertEqual(p1, t1.point1)
self.assertEqual(p2, t1.point2)
self.assertEqual(p3, t1.point3)
l1 = Line(4.33, 8, -4, 3.67)
l2 = Line(-4, 3.67, 2.19, -5)
l3 = Line(2.19, -5, 4.33, 8)
t2 = Triangle(l1, l2, l3)
self.assertEqual(l1, t2.line1)
self.assertEqual(l2, t2.line2)
self.assertEqual(l3, t2.line3)
t3 = Triangle(1, 2, 5, 1, 3, 3)
self.assertEqual(1, t3.point1.x)
self.assertEqual(2, t3.point1.y)
self.assertEqual(5, t3.point2.x)
self.assertEqual(1, t3.point2.y)
self.assertEqual(3, t3.point3.x)
self.assertEqual(3, t3.point3.y)
def testValidConstruction(self):
p1 = Point(1, 3)
p2 = Point(5, 3)
p3 = Point(5, 1)
p4 = Point(1, 1)
r1 = ShapeFactory.build("rectangle", p1, p2, p3, p4)
self.assertEqual(p1, r1.point1)
self.assertEqual(p2, r1.point2)
self.assertEqual(p3, r1.point3)
self.assertEqual(p4, r1.point4)
l1 = Line(Point(-3, 1), Point(1, 1))
l2 = Line(Point(1, 1), Point(1, -5))
l3 = Line(Point(1, -5), Point(-3, -5))
l4 = Line(Point(-3, -5), Point(-3, 1))
r2 = ShapeFactory.build("rectangle", l1.point1, l2.point1, l3.point1,
l4.point1)
self.assertEqual(l1, r2.line1)
self.assertEqual(l2, r2.line2)
self.assertEqual(l3, r2.line3)
self.assertEqual(l4, r2.line4)
r3 = ShapeFactory.build("rectangle", Point(-.8, .4), Point(0, 2),
Point(.8, 1.6), Point(0, 0))
self.assertEqual(-.8, r3.point1.x)
self.assertEqual(.4, r3.point1.y)
self.assertEqual(0, r3.point2.x)
self.assertEqual(2, r3.point2.y)
self.assertEqual(.8, r3.point3.x)
self.assertEqual(1.6, r3.point3.y)
self.assertEqual(0, r3.point4.x)
self.assertEqual(0, r3.point4.y)
def testInvalidConstruction(self):
p1 = Point(1, 2)
p2 = Point(1, 1)
p3 = Point(1, 3)
self.assertRaises(ShapeException, ShapeFactory.build, "triangle", p1, p2, p3)
l4 = Line(Point(1, 1), Point(1, 4))
l5 = Line(Point(2, 1), Point(2, 5))
l6 = Line(Point(3, 1), Point(3, 6))
self.assertRaises(ShapeException, ShapeFactory.build, "triangle", l4.point1, l5.point1, l6.point1)
def __init__(self, *args, **kwargs):
if len(list(args)) == 4:
center = Point.getCenterPoint(args[0], args[2])
super().__init__(center, *args, **kwargs)
else:
super().__init__(*args, **kwargs)
self.lines.append(Line(self.point1, self.point2))
self.lines.append(Line(self.point2, self.point3))
self.lines.append(Line(self.point3, self.point4))
self.lines.append(Line(self.point4, self.point1))
Rectangle.validateRectangle(self, "Rectangle is invalid")
def validateEllipse(value, errorMessage):
if not isinstance(value, Ellipse):
raise ShapeException(errorMessage)
Line.validateLine(value.axis1, "Axis1 is not a valid line")
Line.validateLine(value.axis2, "Axis2 is not a valid line")
if value.computeArea() <= 0:
raise ShapeException(errorMessage)
Validator.validateLinesFormRightAngles([value.axis1, value.axis2],
"Axis are not perpendicular")
def testComputeLength(self):
l1 = Line(1, 2, 4, 10)
self.assertAlmostEqual(8.544, l1.computeLength(), places=3)
l2 = Line(1, 2, 1, 3)
self.assertAlmostEqual(1, l2.computeLength(), places=3)
l3 = Line(3, -2, -4, 10)
self.assertAlmostEqual(13.892, l3.computeLength(), places=3)
def testInvalidConstruction(self):
p1 = Point(1, 3)
p2 = Point(5, 3)
p3 = Point(5, 1)
p4 = Point(1, -1)
self.assertRaises(ShapeException, Rectangle, p1, p2, p3, p4)
l1 = Line(-3, 1, 4, 1)
l2 = Line(1, 1, 1, -5)
l3 = Line(1, -5, -3, -5)
l4 = Line(-3, -5, -3, 1)
self.assertRaises(ShapeException, Rectangle, l1, l2, l3, l4)
self.assertRaises(ShapeException, Rectangle, -1, 0, 0, 2, 1, 1, 0, -1)
def onAddLine(self, button):
self.printToLog("onAddLine")
name_entry = self.builder.get_object("EntryNameNewLine")
x1_entry = self.builder.get_object("EntryX1Line")
y1_entry = self.builder.get_object("EntryY1Line")
x2_entry = self.builder.get_object("EntryX2Line")
y2_entry = self.builder.get_object("EntryY2Line")
l1 = Line(name_entry.get_text())
l1.addCoords(float(x1_entry.get_text()), float(y1_entry.get_text()))
l1.addCoords(float(x2_entry.get_text()), float(y2_entry.get_text()))
self.display_file.addObject(l1)
self.add_object_window.hide()
def importFile(self, path):
self.display_file.wipeOut()
#print("{}".format(path))
vertices = dict()
vertice_counter = 0
name = ""
self.file = open(path, "r+") # read and write
for line in self.file:
if (line[0] == "v"): # store vertices in a dictionary
vertice_counter += 1
vertices[vertice_counter] = line
elif (line[0] == "o"
): # store temporarily the name of the object to come
match = re.findall(r"\S+", line)
name = match[1]
elif (line[0] == "p"): # TODO: FINISH THIS
match = re.findall(r"\S+", line)
vertice_for_point = vertices[float(match[1])]
match = re.findall(r"\S+", vertice_for_point)
coord = {"x": float(match[1]), "y": float(match[2])}
p1 = Point(name)
p1.addCoords(coord["x"], coord["y"])
self.display_file.addObject(p1)
elif (line[0] == "l"):
match = re.findall(r"\S+", line)
if (len(match) == 3): # line
l = Line(name)
else: # polygon
l = None
if (match[1] == match[-1]):
l = Polygon(name)
else:
l = Curve(name)
for item in match:
if (
item != "l"
): # ignore the first character, only compute coordinates
vertice_for_point = vertices[float(item)]
match_vertice = re.findall(r"\S+", vertice_for_point)
coord = {
"x": float(match_vertice[1]),
"y": float(match_vertice[2])
}
l.addCoords(coord["x"], coord["y"])
if (match[1] == match[-1]
): # if polygon (last coords == first coords)
l.popCoords() # remove repeated coords
self.display_file.addObject(l)
def __constructWithPoints(self, point1, point2, point3, point4, point5):
try:
self.__center = point1
focus1 = point2
focus2 = point3
mirror1 = self.__getMirrorFocus(self.__center, focus1)
mirror2 = self.__getMirrorFocus(self.__center, focus2)
self.__foci1 = [focus1, mirror1]
self.__foci2 = [focus2, mirror2]
self.__axis1 = Line(self.__center.copy(), point4)
self.__axis2 = Line(self.__center.copy(), point5)
Validator.validateEllipse(value=self,
errorMessage="Ellipse is invalid")
return True
except ShapeException:
return False
def __constructWithCoords(self, x1, y1, x2, y2, x3, y3, x4, y4, x5, y5):
try:
self.__center = Point(x1, y1)
focus1 = Point(x2, y2)
focus2 = Point(x3, y3)
mirror1 = self.__getMirrorFocus(self.__center, focus1)
mirror2 = self.__getMirrorFocus(self.__center, focus2)
self.__foci1 = [focus1, mirror1]
self.__foci2 = [focus2, mirror2]
self.__axis1 = Line(self.__center.copy(), Point(x4, y4))
self.__axis2 = Line(self.__center.copy(), Point(x5, y5))
Validator.validateEllipse(value=self,
errorMessage="Ellipse is invalid")
return True
except ShapeException:
return False
def testValidateLine(self):
l1 = Line(1, 1, -1, -5)
Validator.validateLine(l1, "Line unexpectedly invalid")
self.assertRaises(ShapeException, Validator.validateLine,
"(1, 1, -1, -5)",
"String \'(1, 1, -1, -5)\' is not a valid line")
self.assertRaises(ShapeException, Validator.validateLine, Point(1, 1),
"Point is not a valid line")
def __constructWithPoints(self, point1, point2, point3, point4):
try:
self.__line1 = Line(point1, point2)
self.__line2 = Line(point2, point3)
self.__line3 = Line(point3, point4)
self.__line4 = Line(point4, point1)
Validator.validateRectangle(value=self,
errorMessage="Invalid Rectangle")
return True
except ShapeException:
return False
def __constructWithCoords(self, x1, y1, x2, y2, x3, y3, x4, y4):
try:
self.__line1 = Line(x1, y1, x2, y2)
self.__line2 = Line(x2, y2, x3, y3)
self.__line3 = Line(x3, y3, x4, y4)
self.__line4 = Line(x4, y4, x1, y1)
Validator.validateRectangle(value=self,
errorMessage="Invalid Rectangle")
return True
except ShapeException:
return False
def validateRectangle(value, errorMessage):
if not isinstance(value, Rectangle):
raise ShapeException(errorMessage)
Line.validateLine(value.line1, "Line 1 is not a valid line.")
Line.validateLine(value.line2, "Line 2 is not a valid line.")
Line.validateLine(value.line3, "Line 3 is not a valid line.")
Line.validateLine(value.line4, "Line 4 is not a valid line.")
Validator.validateLinesFormLoop([value.line1, value.line2, value.line3, value.line4], "Lines do not form an enclosed rectangle.")
Validator.validateLinesFormRightAngles([value.line1, value.line2, value.line3, value.line4], "Lines do not form 90 degree angles.")
def testValidConstruction(self):
p1 = Point(1, 2)
p2 = Point(4, 10)
l1 = Line(p1, p2)
self.assertEqual(p1, l1.point1)
self.assertEqual(p2, l1.point2)
p3 = Point(1.4, 2.5)
p4 = Point(4.6, 10.7)
l2 = Line(p3, p4)
self.assertEqual(p3, l2.point1)
self.assertEqual(p4, l2.point2)
l3 = Line(1, 3.33, 4.444, 5.5555)
self.assertEqual(1, l3.point1.x)
self.assertEqual(3.33, l3.point1.y)
self.assertEqual(4.444, l3.point2.x)
self.assertEqual(5.5555, l3.point2.y)
def testValidConstruction(self):
p1 = Point(1, 3)
p2 = Point(5, 3)
p3 = Point(5, -1)
p4 = Point(1, -1)
s1 = ShapeFactory.build("square", p1, p2, p3, p4)
self.assertEqual(p1, s1.point1)
self.assertEqual(p2, s1.point2)
self.assertEqual(p3, s1.point3)
self.assertEqual(p4, s1.point4)
self.assertTrue(s1.line1.computeLength() == s1.line2.computeLength() ==
s1.line3.computeLength() == s1.line4.computeLength())
l1 = Line(Point(-3, 1), Point(1, 1))
l2 = Line(Point(1, 1), Point(1, -3))
l3 = Line(Point(1, -3), Point(-3, -3))
l4 = Line(Point(-3, -3), Point(-3, 1))
s2 = ShapeFactory.build("square", l1.point1, l2.point1, l3.point1,
l4.point1)
self.assertEqual(l1, s2.line1)
self.assertEqual(l2, s2.line2)
self.assertEqual(l3, s2.line3)
self.assertEqual(l4, s2.line4)
self.assertTrue(s2.line1.computeLength() == s2.line2.computeLength() ==
s2.line3.computeLength() == s2.line4.computeLength())
s3 = ShapeFactory.build("square", Point(-.8, .4), Point(1.2, 2.4),
Point(3.2, .4), Point(1.2, -1.6))
self.assertEqual(-.8, s3.point1.x)
self.assertEqual(.4, s3.point1.y)
self.assertEqual(1.2, s3.point2.x)
self.assertEqual(2.4, s3.point2.y)
self.assertEqual(3.2, s3.point3.x)
self.assertEqual(.4, s3.point3.y)
self.assertEqual(1.2, s3.point4.x)
self.assertEqual(-1.6, s3.point4.y)
self.assertTrue(s3.line1.computeLength() == s3.line2.computeLength() ==
s3.line3.computeLength() == s3.line4.computeLength())
def testValidConstruction(self):
p1 = Point(1, 3)
p2 = Point(5, 3)
p3 = Point(5, -1)
p4 = Point(1, -1)
s1 = Square(p1, p2, p3, p4)
self.assertEqual(p1, s1.point1)
self.assertEqual(p2, s1.point2)
self.assertEqual(p3, s1.point3)
self.assertEqual(p4, s1.point4)
self.assertTrue(s1.line1.computeLength() == s1.line2.computeLength() ==
s1.line3.computeLength() == s1.line4.computeLength())
l1 = Line(-3, 1, 1, 1)
l2 = Line(1, 1, 1, -3)
l3 = Line(1, -3, -3, -3)
l4 = Line(-3, -3, -3, 1)
s2 = Square(l1, l2, l3, l4)
self.assertEqual(l1, s2.line1)
self.assertEqual(l2, s2.line2)
self.assertEqual(l3, s2.line3)
self.assertEqual(l4, s2.line4)
self.assertTrue(s2.line1.computeLength() == s2.line2.computeLength() ==
s2.line3.computeLength() == s2.line4.computeLength())
s3 = Square(-.8, .4, 1.2, 2.4, 3.2, .4, 1.2, -1.6)
self.assertEqual(-.8, s3.point1.x)
self.assertEqual(.4, s3.point1.y)
self.assertEqual(1.2, s3.point2.x)
self.assertEqual(2.4, s3.point2.y)
self.assertEqual(3.2, s3.point3.x)
self.assertEqual(.4, s3.point3.y)
self.assertEqual(1.2, s3.point4.x)
self.assertEqual(-1.6, s3.point4.y)
self.assertTrue(s3.line1.computeLength() == s3.line2.computeLength() ==
s3.line3.computeLength() == s3.line4.computeLength())
def testMove(self):
l1 = Line(1, 2, 4, 10)
l1.move(3, 4)
self.assertEqual(4, l1.point1.x)
self.assertEqual(6, l1.point1.y)
self.assertEqual(7, l1.point2.x)
self.assertEqual(14, l1.point2.y)
l1.move(.4321, .7654)
self.assertEqual(4.4321, l1.point1.x)
self.assertEqual(6.7654, l1.point1.y)
self.assertEqual(7.4321, l1.point2.x)
self.assertEqual(14.7654, l1.point2.y)
l1.move(-.4321, -.7654)
self.assertEqual(4, l1.point1.x)
self.assertEqual(6, l1.point1.y)
self.assertEqual(7, l1.point2.x)
self.assertEqual(14, l1.point2.y)
def testInvalidConstruction(self):
p1 = Point(1, 2)
p2 = Point(1, 1)
p3 = Point(1, 3)
self.assertRaises(ShapeException, Triangle, p1, p2, p3)
l1 = Line(4.33, 8, -4, 3.67)
l2 = Line(-4, 3.67, 2.19, -5)
l3 = Line(2.19, -5, 4.33, 7)
self.assertRaises(ShapeException, Triangle, l1, l2, l3)
l4 = Line(1, 1, 1, 4)
l5 = Line(2, 1, 2, 5)
l6 = Line(3, 1, 3, 6)
self.assertRaises(ShapeException, Triangle, l4, l5, l6)
def validateTriangle(value, errorMessage):
if not isinstance(value, Triangle):
raise ShapeException(errorMessage)
Line.validateLine(value.line1, "Line 1 has is not a valid line.")
Line.validateLine(value.line2, "Line 2 has is not a valid line.")
Line.validateLine(value.line3, "Line 3 has is not a valid line.")
Validator.validateSlopesAreDifferent(
[value.line1, value.line2, value.line3],
"Angles of lines form an invalid triangle")
Validator.validateLinesFormLoop(
[value.line1, value.line2, value.line3],
"Lines do not form an enclosed triangle")
def paint(canvas):
text = read_file()
for line in text:
if "rcl" in line or "va" in line:
prop = line.split(", ")
Oval(canvas, prop[1], prop[2], prop[3], prop[4], prop[5], prop[6],
prop[7])
elif "ua" in line or "rect" in line:
prop = line.split(", ")
Rectangle(canvas, prop[1], prop[2], prop[3], prop[4], prop[5],
prop[6], prop[7])
elif "tri" in line:
prop = line.split(", ")
Triangle(canvas, prop[1], prop[2], prop[3], prop[4], prop[5],
prop[6], prop[7], prop[8], prop[9])
elif "in" in line:
prop = line.split(", ")
Line(canvas, prop[1], prop[2], prop[3], prop[4], prop[5], prop[6])
elif "arc" in line:
prop = line.split(", ")
Arc(canvas, prop[1], prop[2], prop[3], prop[4], prop[5], prop[6],
prop[7], prop[8], prop[9])
def __init__(self, *args, **kwargs):
super().__init__(*args, **kwargs)
self.lines.append(Line(self.center, self.point1))
self.lines.append(Line(self.center, self.point2))
Ellipse.validateEllipse(self, "Ellipse is invalid")
class Triangle:
def __init__(self, *args, **kwargs):
try:
if not self.__constructWithPoints(args[0], args[1], args[2]):
if not self.__constructWithLines(args[0], args[1], args[2]):
if not self.__constructWithCoords(
args[0], args[1], args[2], args[3], args[4],
args[5]):
raise ShapeException("Triangle construction failed")
except IndexError:
raise ShapeException("Invalid arguments for triangle construction")
def __constructWithCoords(self, x1, y1, x2, y2, x3, y3):
try:
self.__line1 = Line(x1, y1, x2, y2)
self.__line2 = Line(x2, y2, x3, y3)
self.__line3 = Line(x3, y3, x1, y1)
Validator.validateTriangle(value=self,
errorMessage="Triangle invalid")
return True
except ShapeException:
return False
def __constructWithPoints(self, point1, point2, point3):
try:
self.__line1 = Line(point1, point2)
self.__line2 = Line(point2, point3)
self.__line3 = Line(point3, point1)
Validator.validateTriangle(value=self,
errorMessage="Triangle invalid")
return True
except ShapeException:
return False
def __constructWithLines(self, line1, line2, line3):
try:
self.__line1 = line1
self.__line2 = line2
self.__line3 = line3
Validator.validateTriangle(value=self,
errorMessage="Triangle invalid")
return True
except ShapeException:
return False
@property
def point1(self):
return self.__line1.point1
@property
def point2(self):
return self.__line2.point1
@property
def point3(self):
return self.__line3.point1
@property
def line1(self):
return self.__line1
@property
def line2(self):
return self.__line2
@property
def line3(self):
return self.__line3
def move(self, deltaX, deltaY):
self.__line1.move(deltaX, deltaY)
self.__line2.move(deltaX, deltaY)
self.__line3.move(deltaX, deltaY)
def computeArea(self):
"""Compute area using Heron's formula"""
a = self.__line1.computeLength()
b = self.__line2.computeLength()
c = self.__line3.computeLength()
s = (a + b + c) / 2
return math.sqrt(s * (s - a) * (s - b) * (s - c))
def testComputeSlope(self):
l1 = Line(2, 2, 4, 10)
self.assertAlmostEqual(4, l1.computeSlope(), places=3)
l2 = Line(2, 2, 10, 4)
self.assertAlmostEqual(.25, l2.computeSlope(), places=3)
l3 = Line(2, 2, 4, 2)
self.assertAlmostEqual(0, l3.computeSlope(), places=3)
l4 = Line(2, 2, 2, 4)
self.assertAlmostEqual(float('inf'), l4.computeSlope(), places=3)
l5 = Line(2, 4, 2, 2)
self.assertAlmostEqual(float('-inf'), l5.computeSlope(), places=3)
def makeTriangles(n):
for i in range(1, n):
triangles.append(
Triangle(triangles[i - 1].line2, Line(points[i - 1], points[i]),
lines[i]))