import random
import math
import numpy as np
from matplotlib import pyplot as plt
class Point:
def __init__(self, x: float, y: float):
self.x = x
self.y = y
def rotate(self, angle: int):
X = round(self.x*math.cos(angle*math.pi/180) -
self.y*math.sin(angle*math.pi/180), 2)
Y = round(self.y*math.cos(angle*math.pi/180) -
self.x*math.sin(angle*math.pi/180), 2)
self.x = X
self.y = Y
def reflection_OX(self):
self.y *= -1 # reflection about the axis X
def reflection_OY(self):
self.x *= -1 # reflection about the axis Y
def print(self, color: str, text: str | None = ''):
plt.scatter(self.x, self.y, color=color) # plotting single point
plt.text(self.x, self.y, " "+text)
class Line:
def __init__(self, head: Point, tail: Point):
self.head = head
self.tail = tail
self.calculateFunction()
def fEquation(self) -> str:
if self.b > 0:
return ("y = {}x + {}".format(self.a, self.b))
elif self.b == 0:
return ("y = {}x ".format(self.a))
elif self.b < 0:
return ("y = {}x - {}".format(self.a, self.b*(-1)))
def print(self):
x = np.arange(self.head.x, self.tail.x+1)
plt.plot(x, self.a*x+self.b)
plt.text(self.tail.x, self.tail.y, " "+self.fEquation())
def calculateFunction(self):
self.a = (self.head.y - self.tail.y)/(self.head.x-self.tail.x)
self.b = self.head.y - self.a * self.head.x
self.A = self.a
self.B = -1
self.C = self.b
def vectorTranslation(self, vector: list):
self.head.x += vector[0]
self.head.y += vector[1]
self.tail.x += vector[0]
self.tail.y += vector[1]
self.calculateFunction()
def pointContainsion(self, point: Point):
if self.a * point.x + self.b - point.y == 0:
if point.x >= self.head.x and point.x <= self.tail.x:
plt.text(point.x, point.y, "Point belongs to the line segment")
else:
plt.text(point.x, point.y,
"Point belongs to the line" + self.fEquation())
else:
plt.text(point.x, point.y, "("+str(point.x)+","+str(point.y) +
") Point is not on the line " + self.fEquation())
def whichSide(self, point: Point) -> int:
side = self.a*point.x-point.y+self.b
if side < 0:
print("Lewa")
return -1
elif side == 0:
return 0
elif side > 0:
print("Prawa")
return 1
def crossingPointCramer(l1: Line, l2: Line) -> Point:
W = (l1.A*l2.B)-(l2.A*l1.B)
Wx = ((-l1.C)*l2.B)-((-l2.C)*l1.B)
Wy = (l1.A*(-l2.C))-(l2.A*(-l1.C))
if W != 0:
x = Wx/W
y = Wy/W
return Point(x, y)
return Point(None, None)
def crossingPointCramerLineSegment(l1: Line, l2: Line) -> Point:
W = (l1.A*l2.B)-(l2.A*l1.B)
Wx = ((-l1.C)*l2.B)-((-l2.C)*l1.B)
Wy = (l1.A*(-l2.C))-(l2.A*(-l1.C))
if W != 0:
x = Wx/W
y = Wy/W
if ((x >= l1.head.x and x <= l1.tail.x) or (x <= l1.head.x and x >= l1.tail.x)):
return Point(x, y)
return Point(None, None)
def triangleArea(P1: Point, P2: Point, P3: Point) -> int:
a = (P2.x-P1.x, P2.y-P1.y)
b = (P3.x-P1.x, P3.y-P1.y)
P = 1/2*((a[0]*b[1])-(a[1]*b[0]))
return P
if __name__ == '__main__':
p1 = Point(4, 2)
p2 = Point(8, 10)
l1 = Line(p1, p2)
l1.print()
p3 = Point(2, 2)
p4 = Point(8, 8)
l2 = Line(p3, p4)
l2.print()
l1.whichSide(p3)
p5 = crossingPointCramer(l1, l2)
p5.print("yellow", "({},{})".format(p5.x, p5.y))
t1 = Point(0, 0)
t1.print("black", "A")
t2 = Point(2, 1)
t2.print("black", "B")
t3 = Point(1, 1)
t3.print("black", "C")
print("Pole trójkąta t1, t2, t3: ", triangleArea(t1, t2, t3))
plt.title("Jakub Litewka GO lab_02")
plt.xlabel("x axis caption")
plt.ylabel("y axis caption")
plt.axhline(0, alpha=0.3) # x-axis line
plt.axvline(0, alpha=0.3) # y-axis line
plt.xlim(-4, 12)
plt.ylim(-4, 12)
plt.show()
