def calculateQuadraticBounds(pt1, pt2, pt3):
"""
Return the bounding rectangle for a qudratic bezier segment.
pt1 and pt3 are the "anchor" points, pt2 is the "handle".
>>> calculateQuadraticBounds((0, 0), (50, 100), (100, 0))
(0.0, 0.0, 100.0, 50.0)
>>> calculateQuadraticBounds((0, 0), (100, 0), (100, 100))
(0.0, 0.0, 100.0, 100.0)
"""
a, b, c = calculateQuadraticParameters(pt1, pt2, pt3)
## calc first derivative
ax, ay = a * 2
bx, by = b
roots = []
if ax != 0:
roots.append(-bx/ax)
if ay != 0:
roots.append(-by/ay)
points = [a*t*t + b*t + c for t in roots if 0 <= t < 1] + [pt1, pt3]
return array.calculateBounds(points)
def calculateCubicBounds(pt1, pt2, pt3, pt4):
"""
Return the bounding rectangle for a cubic bezier segment.
pt1 and pt4 are the "anchor" points, pt2 and pt3 are the "handles".
>>> calculateCubicBounds((0, 0), (25, 100), (75, 100), (100, 0))
(0.0, 0.0, 100.0, 75.0)
>>> calculateCubicBounds((0, 0), (50, 0), (100, 50), (100, 100))
(0.0, 0.0, 100.0, 100.0)
>>> calculateCubicBounds((50, 0), (0, 100), (100, 100), (50, 0))
(35.5662432703, 0.0, 64.4337567297, 75.0)
"""
a, b, c, d = calculateCubicParameters(pt1, pt2, pt3, pt4)
# calc first derivative
ax, ay = a * 3.0
bx, by = b * 2.0
cx, cy = c
xRoots = [t for t in solveQuadratic(ax, bx, cx) if 0 <= t < 1]
yRoots = [t for t in solveQuadratic(ay, by, cy) if 0 <= t < 1]
roots = xRoots + yRoots
points = [(a*t*t*t + b*t*t + c * t + d) for t in roots] + [pt1, pt4]
return array.calculateBounds(points)
