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from numpy import sqrt, dot, sin, dot, array, pi
from math import atan2, acos
def two_point_arc_to_kiva_arc(p1, p2, theta):
"""
Converts an arc in two point and subtended angle format (startpoint,
endpoint, theta (positive for ccw, negative for cw)) into kiva format
(x, y, radius, start_angle, end_angle, cw)
"""
chord = p2-p1
chordlen = sqrt(dot(chord, chord))
radius = abs(chordlen/(2*sin(theta/2)))
altitude = sqrt(pow(radius, 2)-pow(chordlen/2, 2))
if theta>pi or theta<0:
altitude = -altitude
chordmidpoint = (p1+p2)/2
rotate90 = array(((0.0,-1.0),
(1.0, 0.0)))
centerpoint = dot(rotate90, (chord/chordlen))*altitude + chordmidpoint
start_angle = atan2(*(p1-centerpoint)[::-1])
end_angle = start_angle+theta
if theta<0:
start_angle, end_angle, = end_angle, start_angle
cw = False
radius = abs(radius)
return (centerpoint[0], centerpoint[1], radius, start_angle, end_angle, cw)
def arc_to_tangent_points(start, p1, p2, radius):
""" Given a starting point, two endpoints of a line segment, and a radius,
calculate the tangent points for arc_to().
"""
def normalize_vector(x, y):
""" Given a vector, return its unit length representation.
"""
length = sqrt(x**2+y**2)
if length <= 1e-6:
return (0.0, 0.0)
return (x/length, y/length)
# calculate the angle between the two line segments
v1 = normalize_vector(start[0]-p1[0], start[1]-p1[1])
v2 = normalize_vector(p2[0]-p1[0], p2[1]-p1[1])
angle = acos(v1[0]*v2[0]+v1[1]*v2[1])
# punt if the half angle is zero or a multiple of pi
sin_half_angle = sin(angle/2.0)
if sin_half_angle == 0.0:
return (p1, p2)
# calculate the distance from p1 to the center of the arc
dist_to_center = radius / sin_half_angle
# calculate the distance from p1 to each tangent point
dist_to_tangent = sqrt(dist_to_center**2-radius**2)
# calculate the tangent points
t1 = (p1[0]+v1[0]*dist_to_tangent, p1[1]+v1[1]*dist_to_tangent)
t2 = (p1[0]+v2[0]*dist_to_tangent, p1[1]+v2[1]*dist_to_tangent)
return (t1, t2)
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