def test_circum_center_radius():
'''
circum_center_radius(): boundary, near lon=0, big triangle
'''
from numpy import pi
from circumcircle import circum_center_radius
from sphere import angle
from convert_coord.cart_ll import latlon2xyz
# boundary
ll1, ll2, ll3 = (0,pi/3), (0,2/3*pi), (pi/6,pi/2)
xyz1, xyz2, xyz3 = [latlon2xyz(*ll) for ll in [ll1,ll2,ll3]]
center, radius = circum_center_radius(xyz1, xyz2, xyz3)
equal(center, (0,1,0))
# near lon=0
ll1, ll2, ll3 = (pi/5, 2*pi-pi/6), (0,pi/7), (pi/7,pi/6)
xyz1, xyz2, xyz3 = [latlon2xyz(*ll) for ll in [ll1,ll2,ll3]]
center, radius = circum_center_radius(xyz1, xyz2, xyz3)
d1 = angle(center, xyz1)
d2 = angle(center, xyz2)
d3 = angle(center, xyz3)
aa_equal(d1, radius, 15)
aa_equal(d2, radius, 15)
aa_equal(d3, radius, 15)
# big triangle
ll1, ll2, ll3 = (pi/2,0), (0,0), (0,pi/2)
xyz1, xyz2, xyz3 = [latlon2xyz(*ll) for ll in [ll1,ll2,ll3]]
center, radius = circum_center_radius(xyz1, xyz2, xyz3)
aa_equal(center, latlon2xyz(0.61547970867038737,pi/4), 15)
def circum_center_radius(xyz1, xyz2, xyz3):
x1, y1, z1 = xyz1
x2, y2, z2 = xyz2
x3, y3, z3 = xyz3
# bisector plane of p1 and p2
mx, my, mz = (x1+x2)/2, (y1+y2)/2, (z1+z2)/2
cx, cy, cz = y1*z2-z1*y2, z1*x2-x1*z2, x1*y2-y1*x2
a1, b1, c1 = my*cz-mz*cy, mz*cx-mx*cz, mx*cy-my*cx # plane parameters
# bisector plane of p2 and p3
mx, my, mz = (x2+x3)/2, (y2+y3)/2, (z2+z3)/2
cx, cy, cz = y2*z3-z2*y3, z2*x3-x2*z3, x2*y3-y2*x3
a2, b2, c2 = my*cz-mz*cy, mz*cx-mx*cz, mx*cy-my*cx # plane parameters
# intersection points
cc1, cc2 = intersect_two_greatcircles((a1,b1,c1), (a2,b2,c2))
# circumcircle point
mxyz = (x1+x2+x3)/2, (x2+y2+y3)/2, (x3+z2+z3)/2
d1 = angle(cc1, mxyz)
d2 = angle(cc2, mxyz)
cc = cc1 if d1 < d2 else cc2
dist = angle(cc,xyz1)
return cc, dist
def __init__(self, latlon1, latlon2):
self.latlon1 = latlon1
self.latlon2 = latlon2
self.xyz1 = latlon2xyz(*latlon1)
self.xyz2 = latlon2xyz(*latlon2)
self.max_angle = angle(self.xyz1, self.xyz2)
# pt3 which is perpendicular with pt1 on the great circle pt1_pt2
self.xyz3 = self.get_xyz3()
self.latlon3 = xyz2latlon(*self.xyz3)
def test_angle():
'''
angle(): yz plane circle, oblique circle
'''
from sphere import angle
from convert_coord.cart_ll import latlon2xyz
ret = angle(latlon2xyz(pi/4,0), latlon2xyz(0,0))
equal(ret, pi/4)
ret = angle(latlon2xyz(pi/2,0), latlon2xyz(0,0))
equal(ret, pi/2)
ret = angle(latlon2xyz(0,0), latlon2xyz(0,0))
equal(ret, 0)
ret = angle(latlon2xyz(pi/4,0), latlon2xyz(-pi/4,0))
aa_equal(ret, pi/2, 15)
ret = angle(latlon2xyz(pi/2,0), latlon2xyz(-pi/4,0))
aa_equal(ret, 3*pi/4, 15)
ret = angle(latlon2xyz(pi/2,0), latlon2xyz(-pi/2,0))
aa_equal(ret, pi, 15)
def circum_center_radius(latlon1, latlon2, latlon3, return_xyz=False):
xyz1 = x1,y1,z1 = latlon2xyz(*latlon1)
xyz2 = x2,y2,z2 = latlon2xyz(*latlon2)
xyz3 = x3,y3,z3 = latlon2xyz(*latlon3)
# bisector plane of p1 and p2
mx, my, mz = (x1+x2)/2, (y1+y2)/2, (z1+z2)/2
cx, cy, cz = y1*z2-z1*y2, z1*x2-x1*z2, x1*y2-y1*x2
a1, b1, c1 = my*cz-mz*cy, mz*cx-mx*cz, mx*cy-my*cx # plane parameters
# bisector plane of p2 and p3
mx, my, mz = (x2+x3)/2, (y2+y3)/2, (z2+z3)/2
cx, cy, cz = y2*z3-z2*y3, z2*x3-x2*z3, x2*y3-y2*x3
a2, b2, c2 = my*cz-mz*cy, mz*cx-mx*cz, mx*cy-my*cx # plane parameters
# intersection points
cc1, cc2 = intersect_two_greatcircles((a1,b1,c1), (a2,b2,c2))
# circumcircle point
mxyz = (x1+x2+x3)/2, (x2+y2+y3)/2, (x3+z2+z3)/2
d1 = angle(cc1, mxyz)
d2 = angle(cc2, mxyz)
#d1 = distance(cc1, mxyz)
#d2 = distance(cc2, mxyz)
cc = cc1 if d1 < d2 else cc2
dist = angle(cc,xyz1)
if return_xyz:
return cc, dist
else:
return xyz2latlon(*cc), dist
