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from math import sin, cos, atan2, hypot
################################################################################
### Point (x,y) operations
################################################################################
class P:
def __init__(self, x, y=None):
if not y==None:
self.x, self.y = float(x), float(y)
elif x.__class__ == P :
self.x, self.y = float(x.x), float(x.y)
else:
self.x, self.y = float(x[0]), float(x[1])
def __add__(self, other): return P(self.x + other.x, self.y + other.y)
def __sub__(self, other): return P(self.x - other.x, self.y - other.y)
def __neg__(self): return P(-self.x, -self.y)
def __mul__(self, other):
if isinstance(other, P):
return self.x * other.x + self.y * other.y
return P(self.x * other, self.y * other)
__rmul__ = __mul__
def __div__(self, other): return P(self.x / other, self.y / other)
def mag(self): return hypot(self.x, self.y)
def unit(self):
h = self.mag()
if h: return self / h
else: return P(0,0)
def dot(self, other): return self.x * other.x + self.y * other.y
def cross(self, other): return self.x * other.y - self.y * other.x
def rot(self, theta):
c = cos(theta)
s = sin(theta)
return P(self.x * c - self.y * s, self.x * s + self.y * c)
def rotate(self, theta):
c = cos(theta)
s = sin(theta)
return P(self.x * c - self.y * s, self.x * s + self.y * c)
def angle(self): return atan2(self.y, self.x)
def __repr__(self): return '%.2f,%.2f' % (self.x, self.y)
def pr(self): return "%.2f,%.2f" % (self.x, self.y)
def to_list(self): return [self.x, self.y]
def ccw(self): return P(-self.y,self.x)
def l2(self): return self.x*self.x + self.y*self.y
def transform(self, matrix) :
x = self.x
self.x = x*matrix[0][0] + self.y*matrix[0][1] + matrix[0][2]
self.y = x*matrix[1][0] + self.y*matrix[1][1] + matrix[1][2]
def near(self, b, tolerance=None ) :
if tolerance==None : tolerance = 1e-7
return (self-b).l2() < tolerance
def copy(self) : return P(self.x,self.y)
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