def quadratic(a, b, c):
# Returns the two roots of a quadratic
inside = math.sqrt((b*b) - (4*a*c))
if a != 0:
return (-b + inside)/(2*a), (-b - inside)/(2*a)
return -1, -1
def quadratic(a, b, c):
# Returns the two roots of a quadratic
inside = (b*b) - (4*a*c)
try:
inside = math.sqrt(inside)
except ValueError:
return -1, -1
if a == 0:
return -1, -1
return (-b + inside)/(2*a), (-b - inside)/(2*a)
def ray_intersects_with_circle(origin, direction, center, radius):
L = center - origin
tca = L.dot(direction)
if tca < 0:
return False
d2 = L.dot(L) - tca * tca
if d2 > radius:
return False
thc = math.sqrt(radius * radius - d2)
t0 = tca - thc
t1 = tca + thc
return t0 > 0 or t1 > 0
def quadratic(a, b, c):
# Returns the two roots of a quadratic
inside = (b*b) - (4*a*c)
try:
inside = math.sqrt(inside)
except ValueError:
return ()
if inside < 0:
return ()
b = -b
a = 2*a
if inside == 0:
return (b/a,)
return ((b + inside)/a, (b - inside)/a)
def vertex_quadratic_solve_for_x_min_non_neg(a, h, k, y):
try:
v_sqrt = math.sqrt((y - k) / a)
except ValueError:
return 0
return min_non_neg(v_sqrt + h, -v_sqrt + h)
def perimeter_of_ellipse(a,b):
return math.pi * (3*(a+b) - math.sqrt((3*a + b) * (a + 3*b)))
