3 from ..nvector
import NVector, PolarVector
4 from ..objects.bezier
import BezierPoint, Bezier
11 @param center 2D vector, center of the ellipse
12 @param radii 2D vector, x/y radius of the ellipse
13 @param xrot Angle between the main axis of the ellipse and the x axis (in radians)
22 + self.
radiiradii[0] * math.cos(self.
xrotxrot) * math.cos(t)
23 - self.
radiiradii[1] * math.sin(self.
xrotxrot) * math.sin(t),
26 + self.
radiiradii[0] * math.sin(self.
xrotxrot) * math.cos(t)
27 + self.
radiiradii[1] * math.cos(self.
xrotxrot) * math.sin(t)
32 - self.
radiiradii[0] * math.cos(self.
xrotxrot) * math.sin(t)
33 - self.
radiiradii[1] * math.sin(self.
xrotxrot) * math.cos(t),
35 - self.
radiiradii[0] * math.sin(self.
xrotxrot) * math.sin(t)
36 + self.
radiiradii[1] * math.cos(self.
xrotxrot) * math.cos(t)
42 angle_left = abs(angle_delta)
43 sign = -1
if anglestart+angle_delta < angle1
else 1
44 tolerance = math.pi / 100
45 if angle_left % step > tolerance:
46 step = angle_left / max(1, round(angle_left / step))
49 firststep = min(angle_left, step) * sign
50 alpha = self.
_alpha_alpha(firststep)
57 if angle_left < half_step:
60 lstep = min(angle_left, step)
61 step_sign = lstep * sign
62 angle2 = angle1 + step_sign
63 angle_left -= abs(lstep)
65 alpha = self.
_alpha_alpha(step_sign)
66 p2 = self.
pointpoint(angle2)
74 def to_bezier(self, angle_start, angle_delta, step=math.pi / 2):
76 points = self.
to_bezier_pointsto_bezier_points(angle_start, angle_delta, step)
78 if angle_delta == math.pi * 2:
83 bezier.add_point(point.vertex, point.in_tangent, point.out_tangent)
86 def _alpha(self, step):
87 return math.sin(step) * (math.sqrt(4+3*math.tan(step/2)**2) - 1) / 3
98 phi = math.pi * xrot / 180
100 x1p, y1p = _matrix_mul(phi, (start-dest)/2, -1)
102 cr = x1p ** 2 / rx**2 + y1p**2 / ry**2
108 dq = rx**2 * y1p**2 + ry**2 * x1p**2
109 pq = (rx**2 * ry**2 - dq) / dq
110 cpm = math.sqrt(max(0, pq))
113 cp =
NVector(cpm * rx * y1p / ry, -cpm * ry * x1p / rx)
114 c = _matrix_mul(phi, cp) +
NVector((x1+x2)/2, (y1+y2)/2)
115 theta1 = _angle(
NVector(1, 0),
NVector((x1p - cp[0]) / rx, (y1p - cp[1]) / ry))
117 NVector((x1p - cp[0]) / rx, (y1p - cp[1]) / ry),
118 NVector((-x1p - cp[0]) / rx, (-y1p - cp[1]) / ry)
121 if not sweep
and deltatheta > 0:
122 deltatheta -= 2*math.pi
123 elif sweep
and deltatheta < 0:
124 deltatheta += 2*math.pi
126 return cls(c,
NVector(rx, ry), phi), theta1, deltatheta
129 def _matrix_mul(phi, p, sin_mul=1):
131 s = math.sin(phi) * sin_mul
133 xr = c * p.x - s * p.y
134 yr = s * p.x + c * p.y
139 arg = math.acos(max(-1, min(1, u.dot(v) / (u.length * v.length))))
140 if u[0] * v[1] - u[1] * v[0] < 0:
def from_svg_arc(cls, start, rx, ry, xrot, large, sweep, dest)
def to_bezier_points(self, anglestart, angle_delta, step=math.pi/2)
def __init__(self, center, radii, xrot)
def to_bezier(self, angle_start, angle_delta, step=math.pi/2)