def impulse00_y(self, i):
eps = 1e-8
def helper(t):
if self.Yp(t) >= -eps: # >= 0
return cpsi_1d(self.X(t)) * dF_dp(i, t)
else: # < 0
return -cpsi_1d(self.X(t)) * dF_dp(i, t)
result = 0
a, b, c, d = cubicCoefficients(self.yPara)
# t0
roots = cubic(a, b, c, d)
for root in roots:
if -eps <= root <= 1 + eps:
result += helper(root)
# t1
roots = cubic(a, b, c, d - 1.0)
for root in roots:
if -eps <= root <= 1 + eps:
result -= helper(root)
return result
def impulse11_y(self, i, j, kx, ky):
eps = 1e-8
def helper(t):
if self.Yp(t) >= -eps: # >= 0
return cpsi_1d_jk(self.X(t), j, kx) * dF_dp(i, t)
else: # < 0
return -cpsi_1d_jk(self.X(t), j, kx) * dF_dp(i, t)
result = 0
a, b, c, d = cubicCoefficients(self.yPara)
# t0
roots = cubic(a, b, c, d - float(ky) / 2**j)
for root in roots:
if -eps <= root <= 1 + eps:
result += helper(root) * 2**j
# t1
roots = cubic(a, b, c, d - (0.5 + ky) / 2**j)
for root in roots:
if -eps <= root <= 1 + eps:
result -= helper(root) * 2**(j + 1)
# t2
roots = cubic(a, b, c, d - (1.0 + ky) / 2**j)
for root in roots:
if -eps <= root <= 1 + eps:
result += helper(root) * 2**j
return result
def impulse11_y(self, i, j, kx, ky):
eps = 1e-8
def helper(t):
if self.Yp(t) >= -eps: # >= 0
return cpsi_1d_jk(self.X(t), j, kx) * dF_dp(i, t)
else: # < 0
return -cpsi_1d_jk(self.X(t), j, kx) * dF_dp(i, t)
result = 0
a, b, c, d = cubicCoefficients(self.yPara)
# t0
roots = cubic(a, b, c, d - float(ky) / 2 ** j)
for root in roots:
if -eps <= root <= 1 + eps:
result += helper(root) * 2 ** j
# t1
roots = cubic(a, b, c, d - (0.5 + ky) / 2 ** j)
for root in roots:
if -eps <= root <= 1 + eps:
result -= helper(root) * 2 ** (j + 1)
# t2
roots = cubic(a, b, c, d - (1.0 + ky) / 2 ** j)
for root in roots:
if -eps <= root <= 1 + eps:
result += helper(root) * 2 ** j
return result
def impulse00_y(self, i):
eps = 1e-8
def helper(t):
if self.Yp(t) >= -eps: # >= 0
return cpsi_1d(self.X(t)) * dF_dp(i, t)
else: # < 0
return -cpsi_1d(self.X(t)) * dF_dp(i, t)
result = 0
a, b, c, d = cubicCoefficients(self.yPara)
# t0
roots = cubic(a, b, c, d)
for root in roots:
if -eps <= root <= 1 + eps:
result += helper(root)
# t1
roots = cubic(a, b, c, d - 1.0)
for root in roots:
if -eps <= root <= 1 + eps:
result -= helper(root)
return result
def impulse10_y(self, i, j, k):
eps = 1e-8
kx, ky = k
def helper(t):
if self.Yp(t) >= -eps: # >= 0
return CubicBezier.cpsi_1d_jk(self.X(t), j, kx) * CubicBezier.dF_dp(i, t)
else: # < 0
return -CubicBezier.cpsi_1d_jk(self.X(t), j, kx) * CubicBezier.dF_dp(i, t)
result = 0
a, b, c, d = CubicBezier.cubicCoefficients(self.y0, self.y1, self.y2, self.y3)
# t0
roots = cubic(a, b, c, d - float(ky) / 2 ** j)
for root in roots:
if -eps <= root <= 1 + eps:
result += helper(root) * 2 ** j
# t1
roots = cubic(a, b, c, d - (1.0 + ky) / 2 ** j)
for root in roots:
if -eps <= root <= 1 + eps:
result -= helper(root) * 2 ** j
return result
def clip(self, left, right, bottom, top, return_t = False):
def is_t_in(t, eps = 1e-5):
pt = self.evaluate(t)
return left-eps<=pt[0]<=right+eps and top-eps<=pt[1]<=bottom+eps
def is_subsection_valid(sec, eps = 1e-5):
return abs(sec.x0 - right) < eps and abs(sec.x1 - right) < eps \
and abs(sec.x2 - right) < eps and abs(sec.x3 - right) < eps \
or abs(sec.y0 -bottom) < eps and abs(sec.y1 -bottom) < eps \
and abs(sec.y2 -bottom) < eps and abs(sec.y3 -bottom) < eps
ax = -self.x0 + 3*self.x1 - 3*self.x2 + self.x3
bx = 3*self.x0 - 6*self.x1 + 3*self.x2
cx, _dx = 3*self.x1 - 3*self.x0, self.x0
ay = -self.y0 + 3*self.y1 - 3*self.y2 + self.y3
by = 3*self.y0 - 6*self.y1 + 3*self.y2
cy, _dy = 3*self.y1 - 3*self.y0, self.y0
ts = [0]
ts += cubic(ax, bx, cx, _dx-left)
ts += cubic(ax, bx, cx, _dx-right)
ts += cubic(ay, by, cy, _dy-bottom)
ts += cubic(ay, by, cy, _dy-top)
ts.append(1)
ts = [t for t in ts if 0 <= t <= 1 and is_t_in(t)]
ts = sorted(ts)
ts = [t for i, t in enumerate(ts) if t != ts[i-1]]
pairs = [(ts[i-1], t) for i, t in enumerate(ts) \
if i > 0 and is_t_in((t + ts[i-1]) * 0.5)]
sections = []
for a, b in pairs:
sec = self.subsection(a, b)
if not is_subsection_valid(sec):
sections.append((a, b) if return_t else sec)
return sections
def impulse00_y(self, i):
eps = 1e-8
def helper(t):
if self.Yp(t) >= -eps: # >= 0
return CubicBezier.cphi_1d(self.X(t)) * CubicBezier.dF_dp(i, t)
else: # < 0
return -CubicBezier.cphi_1d(self.X(t)) * CubicBezier.dF_dp(i, t)
result = 0
a, b, c, d = CubicBezier.cubicCoefficients(self.y0, self.y1, self.y2, self.y3)
# t0
roots = cubic(a, b, c, d)
for root in roots:
if -eps <= root <= 1 + eps:
result += helper(root)
# t1
roots = cubic(a, b, c, d - 1.0)
for root in roots:
if -eps <= root <= 1 + eps:
result -= helper(root)
return result
def clip(self, left, right, bottom, top):
def is_t_in(t, eps=1e-5):
pt = self.evaluate(t)
return left - eps <= pt[0] <= right + eps and top - eps <= pt[
1] <= bottom + eps
ax = -self.x0 + 3 * self.x1 - 3 * self.x2 + self.x3
bx = 3 * self.x0 - 6 * self.x1 + 3 * self.x2
cx, _dx = 3 * self.x1 - 3 * self.x0, self.x0
ay = -self.y0 + 3 * self.y1 - 3 * self.y2 + self.y3
by = 3 * self.y0 - 6 * self.y1 + 3 * self.y2
cy, _dy = 3 * self.y1 - 3 * self.y0, self.y0
ts = [0]
ts += cubic(ax, bx, cx, _dx - left)
ts += cubic(ax, bx, cx, _dx - right)
ts += cubic(ay, by, cy, _dy - bottom)
ts += cubic(ay, by, cy, _dy - top)
ts.append(1)
ts = [t for t in ts if 0 <= t <= 1 and is_t_in(t)]
ts = sorted(ts)
ts = [t for i, t in enumerate(ts) if t != ts[i - 1]]
pairs = [(ts[i-1], t) for i, t in enumerate(ts) \
if i > 0 and is_t_in((t + ts[i-1]) * 0.5)]
sections = [self.subsection(a, b) for a, b in pairs]
return sections
def clip(self, left, right, bottom, top):
def is_t_in(t, eps = 1e-5):
pt = self.evaluate(t)
return left-eps<=pt[0]<=right+eps and top-eps<=pt[1]<=bottom+eps
ax = -self.x0 + 3*self.x1 - 3*self.x2 + self.x3
bx = 3*self.x0 - 6*self.x1 + 3*self.x2
cx, _dx = 3*self.x1 - 3*self.x0, self.x0
ay = -self.y0 + 3*self.y1 - 3*self.y2 + self.y3
by = 3*self.y0 - 6*self.y1 + 3*self.y2
cy, _dy = 3*self.y1 - 3*self.y0, self.y0
ts = [0]
ts += cubic(ax, bx, cx, _dx-left)
ts += cubic(ax, bx, cx, _dx-right)
ts += cubic(ay, by, cy, _dy-bottom)
ts += cubic(ay, by, cy, _dy-top)
ts.append(1)
ts = [t for t in ts if 0 <= t <= 1 and is_t_in(t)]
ts = sorted(ts)
ts = [t for i, t in enumerate(ts) if t != ts[i-1]]
pairs = [(ts[i-1], t) for i, t in enumerate(ts) \
if i > 0 and is_t_in((t + ts[i-1]) * 0.5)]
sections = [self.subsection(a, b) for a, b in pairs]
return sections