def s(self, *xy):
"""
Add smooth cubic Bezier curves to the curve.
Parameters
----------
xy : numbers
Coordinate pairs. Each set of 2 pairs are interpreted as
the control point at the end of the curve and the endpoint
of the curve. The control point at the beginning of the
curve is assumed to be the reflection of the control point
at the end of the last curve relative to the starting point
of the curve. If the previous curve is not a cubic Bezier,
the control point is coincident with the starting point.
All coordinates are relative to the current end point.
Returns
-------
out : `Curve`
This curve.
"""
self.last_q = None
if self.last_c is None:
self.last_c = self.points[-1]
x0, y0 = self.points[-1]
i = 0
while i < len(xy):
ctrl = numpy.empty((4, 2))
ctrl[0, 0] = x0
ctrl[0, 1] = y0
ctrl[1] = 2 * ctrl[0] - self.last_c
for j in range(2, 4):
if isinstance(xy[i], complex):
ctrl[j, 0] = x0 + xy[i].real
ctrl[j, 1] = y0 + xy[i].imag
i += 1
else:
ctrl[j, 0] = x0 + xy[i]
ctrl[j, 1] = y0 + xy[i + 1]
i += 2
f = _func_bezier(ctrl)
uu = [0, 0.2, 0.5, 0.8, 1]
fu = [f(u) for u in uu]
iu = 1
while iu < len(fu):
test_u = 0.5 * (uu[iu - 1] + uu[iu])
test_pt = f(test_u)
test_err = 0.5 * (fu[iu - 1] + fu[iu]) - test_pt
if test_err[0]**2 + test_err[1]**2 > self.tol:
uu.insert(iu, test_u)
fu.insert(iu, test_pt)
else:
iu += 1
self.points.extend(xy for xy in fu[1:])
self.last_c = ctrl[2]
return self
def T(self, *xy):
"""
Add smooth quadratic Bezier curves to the curve.
Parameters
----------
xy : numbers
Coordinates of the endpoints of the curves. The control
point is assumed to be the reflection of the control point
of the last curve relative to the starting point of the
curve. If the previous curve is not a quadratic Bezier,
the control point is coincident with the starting point.
Returns
-------
out : `Curve`
This curve.
"""
self.last_c = None
if self.last_q is None:
self.last_q = self.points[-1]
i = 0
while i < len(xy):
ctrl = numpy.empty((3, 2))
ctrl[0] = self.points[-1]
ctrl[1] = 2 * ctrl[0] - self.last_q
if isinstance(xy[i], complex):
ctrl[2, 0] = xy[i].real
ctrl[2, 1] = xy[i].imag
i += 1
else:
ctrl[2, 0] = xy[i]
ctrl[2, 1] = xy[i + 1]
i += 2
f = _func_bezier(ctrl)
uu = [0, 0.2, 0.5, 0.8, 1]
fu = [f(u) for u in uu]
iu = 1
while iu < len(fu):
test_u = 0.5 * (uu[iu - 1] + uu[iu])
test_pt = f(test_u)
test_err = 0.5 * (fu[iu - 1] + fu[iu]) - test_pt
if test_err[0]**2 + test_err[1]**2 > self.tol:
uu.insert(iu, test_u)
fu.insert(iu, test_pt)
else:
iu += 1
self.points.extend(xy for xy in fu[1:])
self.last_q = ctrl[1]
return self
def c(self, *xy):
"""
Add cubic Bezier curves to the curve.
Parameters
----------
xy : numbers
Coordinate pairs. Each set of 3 pairs are interpreted as
the control point at the beginning of the curve, the control
point at the end of the curve and the endpoint of the curve.
All coordinates are relative to the current end point.
Returns
-------
out : `Curve`
This curve.
"""
self.last_q = None
x0, y0 = self.points[-1]
i = 0
while i < len(xy):
ctrl = numpy.empty((4, 2))
ctrl[0, 0] = x0
ctrl[0, 1] = y0
for j in range(1, 4):
if isinstance(xy[i], complex):
ctrl[j, 0] = x0 + xy[i].real
ctrl[j, 1] = y0 + xy[i].imag
i += 1
else:
ctrl[j, 0] = x0 + xy[i]
ctrl[j, 1] = y0 + xy[i + 1]
i += 2
f = _func_bezier(ctrl)
uu = [0, 0.2, 0.5, 0.8, 1]
fu = [f(u) for u in uu]
iu = 1
while iu < len(fu):
test_u = 0.5 * (uu[iu - 1] + uu[iu])
test_pt = f(test_u)
test_err = 0.5 * (fu[iu - 1] + fu[iu]) - test_pt
if test_err[0]**2 + test_err[1]**2 > self.tol:
uu.insert(iu, test_u)
fu.insert(iu, test_pt)
else:
iu += 1
self.points.extend(xy for xy in fu[1:])
self.last_c = ctrl[2]
return self
def b(self, *xy):
"""
Add a general degree Bezier curve.
Parameters
----------
xy : numbers
Coordinate pairs. The last coordinate is the endpoint of
curve and all other are control points. All coordinates are
relative to the current end point.
Returns
-------
out : `Curve`
This curve.
"""
self.last_c = self.last_q = None
x0, y0 = self.points[-1]
i = 0
ctrl = [self.points[-1]]
while i < len(xy):
if isinstance(xy[i], complex):
ctrl.append((x0 + xy[i].real, y0 + xy[i].imag))
i += 1
else:
ctrl.append((x0 + xy[i], y0 + xy[i + 1]))
i += 2
ctrl = numpy.array(ctrl)
f = _func_bezier(ctrl)
uu = numpy.linspace(-1, 1, ctrl.shape[0] + 1)
uu = list(0.5 * (1 + numpy.sign(uu) * numpy.abs(uu)**0.8))
fu = [f(u) for u in uu]
iu = 1
while iu < len(fu):
test_u = 0.5 * (uu[iu - 1] + uu[iu])
test_pt = f(test_u)
test_err = 0.5 * (fu[iu - 1] + fu[iu]) - test_pt
if test_err[0]**2 + test_err[1]**2 > self.tol:
uu.insert(iu, test_u)
fu.insert(iu, test_pt)
else:
iu += 1
self.points.extend(xy for xy in fu[1:])
return self
