126 lines
4.5 KiB
Python
126 lines
4.5 KiB
Python
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from inkscape_helper.PathSegment import *
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from inkscape_helper.Coordinate import Coordinate
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from inkscape_helper.Ellipse import Ellipse
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from math import sqrt, pi
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import copy
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class EllipticArc(PathSegment):
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ell_dict = {}
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def __init__(self, start, end, rx, ry, axis_rot, pos_dir=True, large_arc=False):
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self.rx = rx
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self.ry = ry
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# calculate ellipse center
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# the center is on two ellipses one with its center at the start point, the other at the end point
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# for simplicity take the one ellipse at the origin and the other with offset (tx, ty),
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# find the center and translate back to the original offset at the end
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axis_rot *= pi / 180 # convert to radians
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# start and end are mutable objects, copy to avoid modifying them
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r_start = copy.copy(start)
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r_end = copy.copy(end)
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r_start.t -= axis_rot
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r_end.t -= axis_rot
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end_o = r_end - r_start # offset end vector
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tx = end_o.x
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ty = end_o.y
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# some helper variables for the intersection points
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# used sympy to come up with the equations
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ff = (rx**2*ty**2 + ry**2*tx**2)
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cx = rx**2*ry*tx*ty**2 + ry**3*tx**3
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cy = rx*ty*ff
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sx = rx*ty*sqrt(4*rx**4*ry**2*ty**2 - rx**4*ty**4 + 4*rx**2*ry**4*tx**2 - 2*rx**2*ry**2*tx**2*ty**2 - ry**4*tx**4)
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sy = ry*tx*sqrt(-ff*(-4*rx**2*ry**2 + rx**2*ty**2 + ry**2*tx**2))
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# intersection points
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c1 = Coordinate((cx - sx) / (2*ry*ff), (cy + sy) / (2*rx*ff))
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c2 = Coordinate((cx + sx) / (2*ry*ff), (cy - sy) / (2*rx*ff))
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if end_o.cross_norm(c1 - r_start) < 0: # c1 is to the left of end_o
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left = c1
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right = c2
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else:
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left = c2
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right = c1
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if pos_dir != large_arc: #center should be on the left of end_o
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center_o = left
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else: #center should be on the right of end_o
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center_o = right
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#re-use ellipses with same rx, ry to save some memory
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if (rx, ry) in self.ell_dict:
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self.ellipse = self.ell_dict[(rx, ry)]
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else:
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self.ellipse = Ellipse(rx, ry)
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self.ell_dict[(rx, ry)] = self.ellipse
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self.start = start
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self.end = end
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self.axis_rot = axis_rot
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self.pos_dir = pos_dir
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self.large_arc = large_arc
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self.start_theta = self.ellipse.theta_at_angle((-center_o).t)
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self.end_theta = self.ellipse.theta_at_angle((end_o - center_o).t)
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# translate center back to original offset
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center_o.t += axis_rot
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self.center = center_o + start
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@property
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def length(self):
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return self.ellipse.dist_from_theta(self.start_theta, self.end_theta)
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def t_to_theta(self, t):
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"""convert t (always between 0 and 1) to angle theta"""
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start = self.start_theta
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end = self.end_theta
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if self.pos_dir and end < start:
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end += 2 * pi
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if not self.pos_dir and start < end:
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end -= 2 * pi
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arc_size = end - start
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return (start + (end - start) * t) % (2 * pi)
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def theta_to_t(self, theta):
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full_arc_size = (self.end_theta - self.start_theta + 2 * pi) % (2 * pi)
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theta_arc_size = (theta - self.start_theta + 2 * pi) % (2 * pi)
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return theta_arc_size / full_arc_size
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def curvature(self, t):
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theta = self.t_to_theta(t)
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return self.ellipse.curvature(theta)
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def tangent(self, t):
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theta = self.t_to_theta(t)
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return self.ellipse.tangent(theta)
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def t_at_length(self, length):
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"""interpolated t where the curve is at the given length"""
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theta = self.ellipse.theta_from_dist(length, self.start_theta)
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return self.theta_to_t(theta)
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def length_at_t(self, t):
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return self.ellipse.dist_from_theta(self.start_theta, self.t_to_theta(t))
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def pathpoint_at_t(self, t):
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"""pathpoint on the curve from t=0 to point at t."""
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centered = self.ellipse.coordinate_at_theta(self.t_to_theta(t))
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centered.t += self.axis_rot
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return PathPoint(t, centered + self.center, self.tangent(t), self.curvature(t), self.length_at_t(t))
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# identical to Bezier code
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def subdivide(self, part_length, start_offset=0):
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nr_parts = int((self.length - start_offset) // part_length)
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k_o = start_offset / self.length
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k2t = lambda k : k_o + k * part_length / self.length
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points = [self.pathpoint_at_t(k2t(k)) for k in range(nr_parts + 1)]
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return(points, self.length - points[-1].c_dist)
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