def curve_normal(xy1, xy2, xy3=None):
if xy3 == None:
xy3 = xy2
xy2 = vec.scale(vec.add(xy1, xy2), 0.5)
if vec.colinear(vec.sub(xy2, xy1), vec.sub(xy3, xy2)):
xy2 = (xy2[0] + gauss(0, 0.001), xy2[1] + gauss(0, 0.001))
vec12 = vec.norm((xy2[0] - xy1[0], xy2[1] - xy1[1]))
vec32 = vec.norm((xy2[0] - xy3[0], xy2[1] - xy3[1]))
return vec.norm(vec.add(vec12, vec32))
def curve_normal(xy1, xy2, xy3=None):
if xy3 == None:
xy3 = xy2
xy2 = vec.scale(vec.add(xy1, xy2), 0.5)
if vec.colinear(vec.sub(xy2, xy1), vec.sub(xy3, xy2)):
xy2 = (xy2[0] + gauss(0, 0.001), xy2[1] + gauss(0, 0.001))
vec12 = vec.norm((xy2[0] - xy1[0], xy2[1] - xy1[1]))
vec32 = vec.norm((xy2[0] - xy3[0], xy2[1] - xy3[1]))
return vec.norm(vec.add(vec12, vec32))
def leapfrog(gradient_fx, x, u, epsilon):
dU = gradient_fx(x)
u_new = dict(map(lambda (k, v): (k, vec.sub(v, vec.scale(dU[k], epsilon*0.5))), u.items()))
x = dict(map(lambda (k, v): (k, vec.add(x[k], vec.scale(v, epsilon))), u_new.items()))
dU = gradient_fx(x)
u_new = dict(map(lambda (k, v): (k, vec.sub(v, vec.scale(dU[k], epsilon*0.5))), u.items()))
return x, u_new
def gradient_fromfactors(factors, x):
dUdx = {}
def setdU(k, v):
dUdx[k] = v
bound = map(lambda f: (f, map(lambda v: x[v], f.variables)), factors)
gradient_results = map(lambda (f, a): (f, f.grad(*a)), bound) #(f, {f.variables[0]:(...)})
map(lambda (f, grad): (f, map(lambda (var, g): setdU(var, vec.add(dUdx.get(var, (0, 0)), g)), grad.items())), gradient_results) #FIXME
return dUdx
def signed_straightness(xy1, xy2, xy3):
vec12 = (xy2[0] - xy1[0], xy2[1] - xy1[1], 0)
vec32 = (xy2[0] - xy3[0], xy2[1] - xy3[1], 0)
if vec.length(vec12) > 0 and vec.length(vec32) > 0:
vec12 = vec.norm(vec12)
vec32 = vec.norm(vec32)
sign = 1 if vec.cross(vec12, vec32)[2] > 0 else -1
return sign * vec.length(vec.add(vec12, vec32))
else:
return 0
def signed_straightness(xy1, xy2, xy3):
vec12 = (xy2[0] - xy1[0], xy2[1] - xy1[1], 0)
vec32 = (xy2[0] - xy3[0], xy2[1] - xy3[1], 0)
if vec.length(vec12) > 0 and vec.length(vec32) > 0:
vec12 = vec.norm(vec12)
vec32 = vec.norm(vec32)
sign = 1 if vec.cross(vec12, vec32)[2] > 0 else -1
return sign * vec.length(vec.add(vec12, vec32))
else:
return 0
def leapfrog(gradient_fx, x, u, epsilon):
dU = gradient_fx(x)
u_new = dict(
map(lambda (k, v): (k, vec.sub(v, vec.scale(dU[k], epsilon * 0.5))),
u.items()))
x = dict(
map(lambda (k, v): (k, vec.add(x[k], vec.scale(v, epsilon))),
u_new.items()))
dU = gradient_fx(x)
u_new = dict(
map(lambda (k, v): (k, vec.sub(v, vec.scale(dU[k], epsilon * 0.5))),
u.items()))
return x, u_new
def gradient_fromfactors(factors, x):
dUdx = {}
def setdU(k, v):
dUdx[k] = v
bound = map(lambda f: (f, map(lambda v: x[v], f.variables)), factors)
gradient_results = map(lambda (f, a): (f, f.grad(*a)),
bound) #(f, {f.variables[0]:(...)})
map(lambda (f, grad):
(f,
map(lambda (var, g): setdU(var, vec.add(dUdx.get(var, (0, 0)), g)),
grad.items())), gradient_results) #FIXME
return dUdx
def straightness(xy1, xy2, xy3):
vec12 = vec.norm((xy2[0] - xy1[0], xy2[1] - xy1[1]))
vec32 = vec.norm((xy2[0] - xy3[0], xy2[1] - xy3[1]))
return vec.length(vec.add(vec12, vec32))
def straightness(xy1, xy2, xy3):
vec12 = vec.norm((xy2[0] - xy1[0], xy2[1] - xy1[1]))
vec32 = vec.norm((xy2[0] - xy3[0], xy2[1] - xy3[1]))
return vec.length(vec.add(vec12, vec32))
