def _circle_tangents(self, other, invert_second_radius):
"compute tangents as explained in \
https://en.wikipedia.org/wiki/Tangent_lines_to_circles#Analytic_geometry"
dx = other.pos.pos_x - self.pos.pos_x
dy = other.pos.pos_y - self.pos.pos_y
if not invert_second_radius:
dr = other.radius - self.radius
else:
dr = -other.radius - self.radius
d = sqrt(dx * dx + dy * dy)
x = dx / d
y = dy / d
r = dr / d
a1 = r * x - y * sqrt(1 - r * r)
b1 = r * y + x * sqrt(1 - r * r)
c1 = self.radius - (a1 * self.pos.pos_x + b1 * self.pos.pos_y)
a2 = r * x + y * sqrt(1 - r * r)
b2 = r * y - x * sqrt(1 - r * r)
c2 = self.radius - (a2 * self.pos.pos_x + b2 * self.pos.pos_y)
x11 = (b1 * (b1 * self.pos.pos_x - a1 * self.pos.pos_y) - a1 * c1)
y11 = (a1 * (-b1 * self.pos.pos_x + a1 * self.pos.pos_y) - b1 * c1)
x12 = (b1 * (b1 * other.pos.pos_x - a1 * other.pos.pos_y) - a1 * c1)
y12 = (a1 * (-b1 * other.pos.pos_x + a1 * other.pos.pos_y) - b1 * c1)
x21 = (b2 * (b2 * self.pos.pos_x - a2 * self.pos.pos_y) - a2 * c2)
y21 = (a2 * (-b2 * self.pos.pos_x + a2 * self.pos.pos_y) - b2 * c2)
x22 = (b2 * (b2 * other.pos.pos_x - a2 * other.pos.pos_y) - a2 * c2)
y22 = (a2 * (-b2 * other.pos.pos_x + a2 * other.pos.pos_y) - b2 * c2)
start1 = Vec2D(x11, y11)
end1 = Vec2D(x12, y12)
orient11 = Vec2D.orientation(end1, start1, self.pos)
orient12 = Vec2D.orientation(start1, end1, other.pos)
start2 = Vec2D(x21, y21)
end2 = Vec2D(x22, y22)
orient21 = Vec2D.orientation(end2, start2, self.pos)
orient22 = Vec2D.orientation(start2, end2, other.pos)
tan1 = Tangent(start1, self, orient11, end1, other, orient12)
tan2 = Tangent(start2, self, orient21, end2, other, orient22)
return [tan1, tan2]
def _circle_tangents(self, other, invert_second_radius):
"compute tangents as explained in \
https://en.wikipedia.org/wiki/Tangent_lines_to_circles#Analytic_geometry"
dx = other.pos.pos_x - self.pos.pos_x
dy = other.pos.pos_y - self.pos.pos_y
if not invert_second_radius:
dr = other.radius - self.radius
else:
dr = - other.radius - self.radius
d = sqrt(dx*dx + dy*dy)
x = dx/d
y = dy/d
r = dr/d
a1 = r*x - y*sqrt(1 - r*r)
b1 = r*y + x*sqrt(1 - r*r)
c1 = self.radius - (a1*self.pos.pos_x + b1*self.pos.pos_y)
a2 = r*x + y*sqrt(1 - r*r)
b2 = r*y - x*sqrt(1 - r*r)
c2 = self.radius - (a2*self.pos.pos_x + b2*self.pos.pos_y)
x11 = (b1*(b1*self.pos.pos_x - a1*self.pos.pos_y) - a1*c1)
y11 = (a1*(-b1*self.pos.pos_x + a1*self.pos.pos_y) - b1*c1)
x12 = (b1*(b1*other.pos.pos_x - a1*other.pos.pos_y) - a1*c1)
y12 = (a1*(-b1*other.pos.pos_x + a1*other.pos.pos_y) - b1*c1)
x21 = (b2*(b2*self.pos.pos_x - a2*self.pos.pos_y) - a2*c2)
y21 = (a2*(-b2*self.pos.pos_x + a2*self.pos.pos_y) - b2*c2)
x22 = (b2*(b2*other.pos.pos_x - a2*other.pos.pos_y) - a2*c2)
y22 = (a2*(-b2*other.pos.pos_x + a2*other.pos.pos_y) - b2*c2)
start1 = Vec2D(x11, y11)
end1 = Vec2D(x12, y12)
orient11 = Vec2D.orientation(end1, start1, self.pos)
orient12 = Vec2D.orientation(start1, end1, other.pos)
start2 = Vec2D(x21, y21)
end2 = Vec2D(x22, y22)
orient21 = Vec2D.orientation(end2, start2, self.pos)
orient22 = Vec2D.orientation(start2, end2, other.pos)
tan1 = Tangent(start1, self, orient11, end1, other, orient12)
tan2 = Tangent(start2, self, orient21, end2, other, orient22)
return [tan1, tan2]
def test_orientation_colinear(self):
"test that orientation returns (almost) zero for colinear points"
vec1 = Vec2D(0, 0)
vec2 = Vec2D(1, 0)
vec3 = Vec2D(2, 0)
self.assertAlmostEqual(0, Vec2D.orientation(vec1, vec2, vec3))
def test_negative_orientation(self):
"test that orientation returns postive value for positively oriented \
points"
vec1 = Vec2D(0, 0)
vec2 = Vec2D(0, 1)
vec3 = Vec2D(1, 0)
self.assertTrue(Vec2D.orientation(vec1, vec2, vec3) < 0)
def test_orientation_colinear(self):
"test that orientation returns (almost) zero for colinear points"
vec1 = Vec2D(0, 0)
vec2 = Vec2D(1, 0)
vec3 = Vec2D(2, 0)
self.assertAlmostEqual(0, Vec2D.orientation(vec1, vec2, vec3))
def test_negative_orientation(self):
"test that orientation returns postive value for positively oriented \
points"
vec1 = Vec2D(0, 0)
vec2 = Vec2D(0, 1)
vec3 = Vec2D(1, 0)
self.assertTrue(Vec2D.orientation(vec1, vec2, vec3) < 0)
def sort_points_on_circle(points, circle):
"sort points by their angle on the circle"
if not points:
return []
reference = points[0]
rest = points[1:len(points)]
sorted_points = sorted(
rest, key=lambda p: Vec2D.orientation(reference, circle.pos, p))
return [reference] + sorted_points
def sort_points_on_circle(points, circle):
"sort points by their angle on the circle"
if not points:
return []
reference = points[0]
rest = points[1: len(points)]
sorted_points = sorted(rest,
key=lambda p:
Vec2D.orientation(reference, circle.pos, p))
return [reference] + sorted_points
