def inCenter4(vs):
vs = [Vec(v) for v in vs]
n = len(vs)
assert n == 4
inwardNormals = [(vs[(i+1)%n]-vs[i]).perpDot().normalized() for i in xrange(n)]
offsets = [inwardNormals[i].dot(vs[i]) for i in xrange(n)]
if use_numpy:
M = numpy.matrix([
list(inwardNormals[0])+[1,0],
list(inwardNormals[1])+[0,1],
list(inwardNormals[2])+[1,0],
list(inwardNormals[3])+[0,1],
])
xyrr = numpy.linalg.solve(M,offsets)
else:
M = Mat([
list(inwardNormals[0])+[1,0],
list(inwardNormals[1])+[0,1],
list(inwardNormals[2])+[1,0],
list(inwardNormals[3])+[0,1],
])
xyrr = M.inverse() * Vec(offsets)
x,y,r,R = xyrr
return Vec(x,y)
def inCenter(vs):
if False:
do('vs')
vs = [Vec(v) for v in vs]
n = len(vs)
inwardNormals = [(vs[(i+1)%n]-vs[i]).perpDot().normalized() for i in xrange(n)]
offsets = [inwardNormals[i].dot(vs[i]) for i in xrange(n)]
# compute n-2 tri-side in-centers...
centers = []
radii = []
for i in xrange(n-2):
if use_numpy:
M = numpy.matrix([
list(inwardNormals[ 0 ])+[-1],
list(inwardNormals[i+1])+[-1],
list(inwardNormals[i+2])+[-1],
])
o = numpy.matrix([
[offsets[ 0 ]],
[offsets[i+1]],
[offsets[i+2]],
])
#x,y,r = numpy.linalg.solve(M,o)
x,y,r = [float(x) for x in numpy.linalg.solve(M,o)]
else:
M = Mat([
list(inwardNormals[ 0 ])+[-1],
list(inwardNormals[i+1])+[-1],
list(inwardNormals[i+2])+[-1],
])
o = Vec([
offsets[ 0 ],
offsets[i+1],
offsets[i+2],
])
x,y,r = M.inverse() * o
if False:
# FUDGE
r = abs(r)
centers.append(Vec(x,y))
radii.append(r)
if False:
#do('x')
#do('y')
do('r')
if n == 3:
# single weight will be zero in this case... no point in doing the undefined arithmetic
return centers[0]
if n == 4:
# Either way works, but neither way is robust when cocircular
if False:
weights = [
1./(inwardNormals[3].dot(centers[0]) - offsets[3] - radii[0]),
1./(inwardNormals[n-3].dot(centers[n-2-1])-offsets[n-3] - radii[n-2-1])
]
else:
weights = [
inwardNormals[1].dot(centers[1])-offsets[1] - radii[1],
inwardNormals[3].dot(centers[0])-offsets[3] - radii[0],
]
# fudge-- this shouldn't be needed, if I get a more robust formula to begin with
if weights[0] == 0. and weights[1] == 0.:
weights = [1.,1.]
if n == 5:
# I fear this doesn't really work
weights = [
(inwardNormals[1].dot(centers[1])-offsets[1] - radii[1])*(inwardNormals[2].dot(centers[2])-offsets[2] - radii[2]),
(inwardNormals[2].dot(centers[2])-offsets[2] - radii[2])*(inwardNormals[3].dot(centers[0])-offsets[3] - radii[0]),
(inwardNormals[3].dot(centers[0])-offsets[3] - radii[0])*(inwardNormals[4].dot(centers[1])-offsets[4] - radii[1]),
]
if False: # XXX GET RID
# weights other than first and last are
# 1 / (distance from last side not involving that circle) / (distance from first side not involving that circle)
for i in xrange(n-4):
weights.append(1./((inwardNormals[1+i].dot(centers[1+i]) - offsets[1+i] - radii[1+i])
* (inwardNormals[4+i].dot(centers[1+i]) - offsets[4+i] - radii[1+i]) ))
weightsSum = sum(weights)
if weightsSum == 0.:
return centers[0] # hack
if False:
do('[float(weight) for weight in weights]')
do('weightsSum')
do('[float(weight/weightsSum) for weight in weights]')
return sum([center*(weight/weightsSum) for center,weight in zip(centers,weights)])