def calcCubicBounds(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".
>>> calcCubicBounds((0, 0), (25, 100), (75, 100), (100, 0))
(0, 0, 100, 75.0)
>>> calcCubicBounds((0, 0), (50, 0), (100, 50), (100, 100))
(0.0, 0.0, 100, 100)
>>> calcCubicBounds((50, 0), (0, 100), (100, 100), (50, 0))
(35.566243270259356, 0, 64.43375672974068, 75.0)
"""
(ax, ay), (bx, by), (cx,
cy), (dx,
dy) = calcCubicParameters(pt1, pt2, pt3, pt4)
# calc first derivative
ax3 = ax * 3.0
ay3 = ay * 3.0
bx2 = bx * 2.0
by2 = by * 2.0
xRoots = [t for t in solveQuadratic(ax3, bx2, cx) if 0 <= t < 1]
yRoots = [t for t in solveQuadratic(ay3, by2, cy) if 0 <= t < 1]
roots = xRoots + yRoots
points = [(ax * t * t * t + bx * t * t + cx * t + dx,
ay * t * t * t + by * t * t + cy * t + dy)
for t in roots] + [pt1, pt4]
return calcBounds(points)
def calcQuadraticBounds(pt1, pt2, pt3):
"""Return the bounding rectangle for a qudratic bezier segment.
pt1 and pt3 are the "anchor" points, pt2 is the "handle".
>>> calcQuadraticBounds((0, 0), (50, 100), (100, 0))
(0, 0, 100, 50.0)
>>> calcQuadraticBounds((0, 0), (100, 0), (100, 100))
(0.0, 0.0, 100, 100)
"""
(ax, ay), (bx, by), (cx, cy) = calcQuadraticParameters(pt1, pt2, pt3)
ax2 = ax*2.0
ay2 = ay*2.0
roots = []
if ax2 != 0:
roots.append(-bx/ax2)
if ay2 != 0:
roots.append(-by/ay2)
points = [(ax*t*t + bx*t + cx, ay*t*t + by*t + cy) for t in roots if 0 <= t < 1] + [pt1, pt3]
return calcBounds(points)
def calcQuadraticBounds(pt1, pt2, pt3):
"""Return the bounding rectangle for a qudratic bezier segment.
pt1 and pt3 are the "anchor" points, pt2 is the "handle".
>>> calcQuadraticBounds((0, 0), (50, 100), (100, 0))
(0, 0, 100, 50.0)
>>> calcQuadraticBounds((0, 0), (100, 0), (100, 100))
(0.0, 0.0, 100, 100)
"""
(ax, ay), (bx, by), (cx, cy) = calcQuadraticParameters(pt1, pt2, pt3)
ax2 = ax * 2.0
ay2 = ay * 2.0
roots = []
if ax2 != 0:
roots.append(-bx / ax2)
if ay2 != 0:
roots.append(-by / ay2)
points = [(ax * t * t + bx * t + cx, ay * t * t + by * t + cy)
for t in roots if 0 <= t < 1] + [pt1, pt3]
return calcBounds(points)
def calcCubicBounds(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".
>>> calcCubicBounds((0, 0), (25, 100), (75, 100), (100, 0))
(0, 0, 100, 75.0)
>>> calcCubicBounds((0, 0), (50, 0), (100, 50), (100, 100))
(0.0, 0.0, 100, 100)
>>> calcCubicBounds((50, 0), (0, 100), (100, 100), (50, 0))
(35.566243270259356, 0, 64.43375672974068, 75.0)
"""
(ax, ay), (bx, by), (cx, cy), (dx, dy) = calcCubicParameters(pt1, pt2, pt3, pt4)
# calc first derivative
ax3 = ax * 3.0
ay3 = ay * 3.0
bx2 = bx * 2.0
by2 = by * 2.0
xRoots = [t for t in solveQuadratic(ax3, bx2, cx) if 0 <= t < 1]
yRoots = [t for t in solveQuadratic(ay3, by2, cy) if 0 <= t < 1]
roots = xRoots + yRoots
points = [(ax*t*t*t + bx*t*t + cx * t + dx, ay*t*t*t + by*t*t + cy * t + dy) for t in roots] + [pt1, pt4]
return calcBounds(points)
print time.time() - n
print
##############
print "no-numpy"
print "calcQuadraticParameters\t\t",
n = time.time()
for i in range(c):
noNumpyBezierTools.calcQuadraticParameters(pt1, pt2, pt3)
print time.time() - n
print "calcBounds\t\t\t",
n = time.time()
for i in range(c):
noNumpyArrayTools.calcBounds(
[pt1, pt2, pt3, pt1, pt2, pt3, pt1, pt2, pt3, pt1, pt2, pt3])
print time.time() - n
print "pointsInRect\t\t\t",
n = time.time()
for i in range(c):
noNumpyArrayTools.pointsInRect(
[pt1, pt2, pt3, pt1, pt2, pt3, pt1, pt2, pt3, pt1, pt2, pt3, pt4],
rect)
print time.time() - n
print "calcQuadraticBounds\t\t",
n = time.time()
for i in range(c):
noNumpyBezierTools.calcQuadraticBounds(pt1, pt2, pt3)
print time.time() - n
print time.time() - n
print
##############
print "no-numpy"
print "calcQuadraticParameters\t\t",
n = time.time()
for i in range(c):
noNumpyBezierTools.calcQuadraticParameters(pt1, pt2, pt3)
print time.time() - n
print "calcBounds\t\t\t",
n = time.time()
for i in range(c):
noNumpyArrayTools.calcBounds([pt1, pt2, pt3, pt1, pt2, pt3, pt1, pt2, pt3, pt1, pt2, pt3])
print time.time() - n
print "pointsInRect\t\t\t",
n = time.time()
for i in range(c):
noNumpyArrayTools.pointsInRect([pt1, pt2, pt3, pt1, pt2, pt3, pt1, pt2, pt3, pt1, pt2, pt3, pt4], rect)
print time.time() - n
print "calcQuadraticBounds\t\t",
n = time.time()
for i in range(c):
noNumpyBezierTools.calcQuadraticBounds(pt1, pt2, pt3)
print time.time() - n
print "calcCubicBounds\t\t\t",
