def selection_problem():
"""The double tetrahedron problem with selection constraints"""
problem = GeometricProblem(dimension=3, use_prototype=False) # no prototype based selection
problem.add_point('v1', vector([0.0, 0.0, 0.0]))
problem.add_point('v2', vector([1.0, 0.0, 0.0]))
problem.add_point('v3', vector([0.0, 1.0, 0.0]))
problem.add_point('v4', vector([0.5, 0.5, 1.0]))
problem.add_point('v5', vector([0.5, 0.5,-1.0]))
problem.add_constraint(DistanceConstraint('v1', 'v2', 10.0))
problem.add_constraint(DistanceConstraint('v1', 'v3', 10.0))
problem.add_constraint(DistanceConstraint('v2', 'v3', 10.0))
problem.add_constraint(DistanceConstraint('v1', 'v4', 10.0))
problem.add_constraint(DistanceConstraint('v2', 'v4', 10.0))
problem.add_constraint(DistanceConstraint('v3', 'v4', 10.0))
problem.add_constraint(DistanceConstraint('v1', 'v5', 10.0))
problem.add_constraint(DistanceConstraint('v2', 'v5', 10.0))
problem.add_constraint(DistanceConstraint('v3', 'v5', 10.0))
#problem.add_constraint(SelectionConstraint(is_right_handed, ['v1','v2','v4','v5']))
problem.add_constraint(RightHandedConstraint('v1','v2','v4','v5'))
return problem
def balloon_problem():
"""test angle propagation via balloon"""
problem = GeometricProblem(dimension=2)
problem.add_point('A', vector([0.0, 0.0]))
problem.add_point('B', vector([1.0, -1.0]))
problem.add_point('C', vector([1.0, +1.0]))
problem.add_point('D', vector([2.0, 0.0]))
problem.add_constraint(
AngleConstraint(
'B', 'A', 'C',
angle_3p(problem.get_point('B'), problem.get_point('A'),
problem.get_point('C'))))
problem.add_constraint(
AngleConstraint(
'A', 'B', 'C',
angle_3p(problem.get_point('A'), problem.get_point('B'),
problem.get_point('C'))))
problem.add_constraint(
AngleConstraint(
'B', 'C', 'D',
angle_3p(problem.get_point('B'), problem.get_point('C'),
problem.get_point('D'))))
problem.add_constraint(
AngleConstraint(
'C', 'D', 'B',
angle_3p(problem.get_point('C'), problem.get_point('D'),
problem.get_point('B'))))
problem.add_constraint(DistanceConstraint('A', 'D', 6.0))
return problem
def solve_ada_3D(a, b, c, a_cab, d_ab, a_abc):
"""returns a list of Configurations of v1,v2,v3 such that distance v1-v2=d12 etc.
v<x>: name of point variables
d<xy>: numeric distance values
a<xyz>: numeric angle in radians
"""
diag_print("solve_ada: %s %s %s %f %f %f" % (a, b, c, a_cab, d_ab, a_abc),
"clmethods")
p_a = vector([0.0, 0.0])
p_b = vector([d_ab, 0.0])
dir_ac = vector([math.cos(-a_cab), math.sin(-a_cab)])
dir_bc = vector([math.cos(math.pi - a_abc), math.sin(math.pi - a_abc)])
dir_ac[1] = math.fabs(dir_ac[1])
dir_bc[1] = math.fabs(dir_bc[1])
if tol_eq(math.sin(a_cab), 0.0) and tol_eq(math.sin(a_abc), 0.0):
m = d_ab / 2 + math.cos(-a_cab) * d_ab - math.cos(-a_abc) * d_ab
p_c = vector([m, 0.0])
# p_c = (p_a + p_b) / 2
p_a.append(0.0)
p_b.append(0.0)
p_c.append(0.0)
map = {a: p_a, b: p_b, c: p_c}
cluster = _Configuration(map)
cluster.underconstrained = True
rval = [cluster]
else:
solutions = rr_int(p_a, dir_ac, p_b, dir_bc)
p_a.append(0.0)
p_b.append(0.0)
rval = []
for p_c in solutions:
p_c.append(0.0)
map = {a: p_a, b: p_b, c: p_c}
rval.append(Configuration(map))
return rval
def line_problem_2d_1():
"""A problem with a Line and 1 CoincicentConstraint"""
problem = GeometricProblem(dimension=2)
problem.add_variable(Point('p1'),vector([3.0, 2.0]))
problem.add_variable(Line('l1'),vector([0.0, 0.0, 1.0, 1.0]))
problem.add_constraint(CoincidenceConstraint(Point('p1'), Line('l1')))
return problem
def solve_ddd_3D(v1, v2, v3, d12, d23, d31):
"""returns a list of Configurations of v1,v2,v3 such that distance v1-v2=d12 etc.
v<x>: name of point variables
d<xy>: numeric distance values
a<xyz>: numeric angle in radians
"""
diag_print("solve_ddd: %s %s %s %f %f %f" % (v1, v2, v3, d12, d23, d31),
"clmethods")
# solve in 2D
p1 = vector([0.0, 0.0])
p2 = vector([d12, 0.0])
p3s = cc_int(p1, d31, p2, d23)
solutions = []
# extend coords to 3D!
p1.append(0.0)
p2.append(0.0)
for p3 in p3s:
p3.append(0.0)
solution = Configuration({v1: p1, v2: p2, v3: p3})
solutions.append(solution)
# return only one solution (if any)
if len(solutions) > 0:
solutions = [solutions[0]]
diag_print("solve_ddd solutions" + str(solutions), "clmethods")
return solutions
def add_layers(self, layers):
#
# for l in layers:
#Todo: check that shape actually needs constraints before defining
# l = self.define_shape(l)
for l in layers:
straight_pairs = []
[
straight_pairs.append(x) for x in l.straight_pairs
if x not in straight_pairs
]
#Need at least 3 points to calculate plane
if straight_pairs < 3:
pass
conf = {}
i = 0
for p in straight_pairs:
# print(p)
#path4581_p1
layername = l.name + '_p' + str(i)
#rigid objects
print('df', layername)
self.solver.add_point(layername, vector(p + [0.0]))
conf[layername] = vector([0, 0, 0])
i += 1
self.solver.add_constraint(RigidConstraint(Configuration(conf)))
def ddd_problem():
problem = GeometricProblem(dimension=2)
problem.add_point('v1', vector([random.random() for i in [1,2]]))
problem.add_point('v2', vector([random.random() for i in [1,2]]))
problem.add_point('v3', vector([random.random() for i in [1,2]]))
problem.add_constraint(DistanceConstraint('v1','v2',distance_2p(problem.get_point('v1'), problem.get_point('v2'))))
problem.add_constraint(DistanceConstraint('v1','v3',distance_2p(problem.get_point('v1'), problem.get_point('v3'))))
problem.add_constraint(DistanceConstraint('v2','v3',distance_2p(problem.get_point('v2'), problem.get_point('v3'))))
return problem
def line_problem_3d_2():
"""A problem with a Line and 2 CoincicentConstraints"""
problem = GeometricProblem(dimension=3)
problem.add_variable(Point('p1'),vector([3.0, 2.0, 1.0]))
problem.add_variable(Point('p2'),vector([1.0, 1.0, 1.0]))
problem.add_variable(Line('l1'),vector([0.0, 0.0, 0.0, 1.0, 1.0, 1.0]))
problem.add_constraint(CoincidenceConstraint(Point('p1'), Line('l1')))
problem.add_constraint(CoincidenceConstraint(Point('p2'), Line('l1')))
problem.add_constraint(DistanceConstraint(Point('p1'), Point('p2'), 5.0))
return problem
def triple_double_triangle():
problem = GeometricProblem(dimension=2)
problem.add_point('QX', vector([0.0, 0.0]))
problem.add_point('QA2', vector([1.0, 0.0]))
problem.add_point('QA3', vector([0.0, 1.0]))
problem.add_point('QY', vector([1.0, 1.0]))
problem.add_constraint(DistanceConstraint('QX', 'QA2', 10.0))
problem.add_constraint(DistanceConstraint('QX', 'QA3', 10.0))
problem.add_constraint(DistanceConstraint('QA2', 'QA3', 10.0))
problem.add_constraint(DistanceConstraint('QA2', 'QY', 10.0))
problem.add_constraint(DistanceConstraint('QA3', 'QY', 10.0))
#problem.add_point('QX', vector([0.0, 0.0]))
problem.add_point('QB2', vector([1.0, 0.0]))
problem.add_point('QZ', vector([0.0, 1.0]))
problem.add_point('QB4', vector([1.0, 1.0]))
problem.add_constraint(DistanceConstraint('QX', 'QB2', 10.0))
problem.add_constraint(DistanceConstraint('QX', 'QZ', 10.0))
problem.add_constraint(DistanceConstraint('QB2', 'QZ', 10.0))
problem.add_constraint(DistanceConstraint('QB2', 'QB4', 10.0))
problem.add_constraint(DistanceConstraint('QZ', 'QB4', 10.0))
#problem.add_point('QY', vector([0.0, 0.0]))
problem.add_point('QC2', vector([1.0, 0.0]))
#problem.add_point('QZ', vector([0.0, 1.0]))
problem.add_point('QC4', vector([1.0, 1.0]))
problem.add_constraint(DistanceConstraint('QY', 'QC2', 10.0))
problem.add_constraint(DistanceConstraint('QY', 'QZ', 10.0))
problem.add_constraint(DistanceConstraint('QC2', 'QZ', 10.0))
problem.add_constraint(DistanceConstraint('QC2', 'QC4', 10.0))
problem.add_constraint(DistanceConstraint('QZ', 'QC4', 10.0))
return problem
def triple_double_triangle():
problem = GeometricProblem(dimension=2)
problem.add_point('QX', vector([0.0, 0.0]))
problem.add_point('QA2', vector([1.0, 0.0]))
problem.add_point('QA3', vector([0.0, 1.0]))
problem.add_point('QY', vector([1.0, 1.0]))
problem.add_constraint(DistanceConstraint('QX', 'QA2', 10.0))
problem.add_constraint(DistanceConstraint('QX', 'QA3', 10.0))
problem.add_constraint(DistanceConstraint('QA2', 'QA3', 10.0))
problem.add_constraint(DistanceConstraint('QA2', 'QY', 10.0))
problem.add_constraint(DistanceConstraint('QA3', 'QY', 10.0))
#problem.add_point('QX', vector([0.0, 0.0]))
problem.add_point('QB2', vector([1.0, 0.0]))
problem.add_point('QZ', vector([0.0, 1.0]))
problem.add_point('QB4', vector([1.0, 1.0]))
problem.add_constraint(DistanceConstraint('QX', 'QB2', 10.0))
problem.add_constraint(DistanceConstraint('QX', 'QZ', 10.0))
problem.add_constraint(DistanceConstraint('QB2', 'QZ', 10.0))
problem.add_constraint(DistanceConstraint('QB2', 'QB4', 10.0))
problem.add_constraint(DistanceConstraint('QZ', 'QB4', 10.0))
#problem.add_point('QY', vector([0.0, 0.0]))
problem.add_point('QC2', vector([1.0, 0.0]))
#problem.add_point('QZ', vector([0.0, 1.0]))
problem.add_point('QC4', vector([1.0, 1.0]))
problem.add_constraint(DistanceConstraint('QY', 'QC2', 10.0))
problem.add_constraint(DistanceConstraint('QY', 'QZ', 10.0))
problem.add_constraint(DistanceConstraint('QC2', 'QZ', 10.0))
problem.add_constraint(DistanceConstraint('QC2', 'QC4', 10.0))
problem.add_constraint(DistanceConstraint('QZ', 'QC4', 10.0))
return problem
def double_triangle():
problem = GeometricProblem(dimension=2)
problem.add_point('v1', vector([0.0, 0.0]))
problem.add_point('v2', vector([1.0, 0.0]))
problem.add_point('v3', vector([0.0, 1.0]))
problem.add_point('v4', vector([1.0, 1.0]))
problem.add_constraint(DistanceConstraint('v1', 'v2', 10.0))
problem.add_constraint(DistanceConstraint('v1', 'v3', 10.0))
problem.add_constraint(DistanceConstraint('v2', 'v3', 10.0))
problem.add_constraint(DistanceConstraint('v2', 'v4', 10.0))
problem.add_constraint(DistanceConstraint('v3', 'v4', 10.0))
return problem
def double_triangle():
problem = GeometricProblem(dimension=2)
problem.add_point('v1', vector([0.0, 0.0]))
problem.add_point('v2', vector([1.0, 0.0]))
problem.add_point('v3', vector([0.0, 1.0]))
problem.add_point('v4', vector([1.0, 1.0]))
problem.add_constraint(DistanceConstraint('v1', 'v2', 10.0))
problem.add_constraint(DistanceConstraint('v1', 'v3', 10.0))
problem.add_constraint(DistanceConstraint('v2', 'v3', 10.0))
problem.add_constraint(DistanceConstraint('v2', 'v4', 10.0))
problem.add_constraint(DistanceConstraint('v3', 'v4', 10.0))
return problem
def hog1():
# double triangle with inter-angle (needs angle propagation)
problem = GeometricProblem(dimension=2)
problem.add_point('A', vector([0.0, 0.0]))
problem.add_point('B', vector([1.0, 0.0]))
problem.add_point('C', vector([1.0, 1.0]))
problem.add_point('D', vector([0.0, 1.0]))
problem.add_constraint(DistanceConstraint('A', 'B', 10.0))
problem.add_constraint(DistanceConstraint('B', 'C', 10.0))
problem.add_constraint(DistanceConstraint('C', 'D', 10.0))
problem.add_constraint(AngleConstraint('B','A','C', math.pi / 8))
problem.add_constraint(AngleConstraint('B','A','D', math.pi / 4))
return problem
def balloons():
# for testing angle propagation via balloon
problem = GeometricProblem(dimension=2)
problem.add_point('A', vector([0.0, 0.0]))
problem.add_point('B', vector([0.0, 1.0]))
problem.add_point('C', vector([1.0, 1.0]))
problem.add_point('D', vector([2.0, 1.0]))
problem.add_constraint(AngleConstraint('B','A','C', math.pi / 8))
problem.add_constraint(AngleConstraint('A','B','C', math.pi / 8))
problem.add_constraint(AngleConstraint('B','C','D', math.pi / 8))
problem.add_constraint(AngleConstraint('C','D','B', math.pi / 8))
problem.add_constraint(DistanceConstraint('A', 'D', 6.0))
return problem
def balloons():
# for testing angle propagation via balloon
problem = GeometricProblem(dimension=2)
problem.add_point('A', vector([0.0, 0.0]))
problem.add_point('B', vector([0.0, 1.0]))
problem.add_point('C', vector([1.0, 1.0]))
problem.add_point('D', vector([2.0, 1.0]))
problem.add_constraint(AngleConstraint('B', 'A', 'C', math.pi / 8))
problem.add_constraint(AngleConstraint('A', 'B', 'C', math.pi / 8))
problem.add_constraint(AngleConstraint('B', 'C', 'D', math.pi / 8))
problem.add_constraint(AngleConstraint('C', 'D', 'B', math.pi / 8))
problem.add_constraint(DistanceConstraint('A', 'D', 6.0))
return problem
def twoscisors():
problem = GeometricProblem(dimension=2)
problem.add_point('A', vector([0.0, 0.0]))
problem.add_point('B', vector([0.0, 1.0]))
problem.add_point('C', vector([1.0, 1.0]))
problem.add_point('D', vector([2.0, 1.0]))
problem.add_constraint(AngleConstraint('B', 'A', 'C', math.pi / 8))
problem.add_constraint(AngleConstraint('B', 'D', 'C', math.pi / 8))
problem.add_constraint(DistanceConstraint('A', 'B', 6.0))
problem.add_constraint(DistanceConstraint('A', 'C', 6.0))
problem.add_constraint(DistanceConstraint('D', 'B', 6.0))
problem.add_constraint(DistanceConstraint('D', 'C', 6.0))
return problem
def twoscisors():
problem = GeometricProblem(dimension=2)
problem.add_point('A', vector([0.0, 0.0]))
problem.add_point('B', vector([0.0, 1.0]))
problem.add_point('C', vector([1.0, 1.0]))
problem.add_point('D', vector([2.0, 1.0]))
problem.add_constraint(AngleConstraint('B','A','C', math.pi / 8))
problem.add_constraint(AngleConstraint('B','D','C', math.pi / 8))
problem.add_constraint(DistanceConstraint('A', 'B', 6.0))
problem.add_constraint(DistanceConstraint('A', 'C', 6.0))
problem.add_constraint(DistanceConstraint('D', 'B', 6.0))
problem.add_constraint(DistanceConstraint('D', 'C', 6.0))
return problem
def hog1():
# double triangle with inter-angle (needs angle propagation)
problem = GeometricProblem(dimension=2)
problem.add_point('A', vector([0.0, 0.0]))
problem.add_point('B', vector([1.0, 0.0]))
problem.add_point('C', vector([1.0, 1.0]))
problem.add_point('D', vector([0.0, 1.0]))
problem.add_constraint(DistanceConstraint('A', 'B', 10.0))
problem.add_constraint(DistanceConstraint('B', 'C', 10.0))
problem.add_constraint(DistanceConstraint('C', 'D', 10.0))
problem.add_constraint(AngleConstraint('B', 'A', 'C', math.pi / 8))
problem.add_constraint(AngleConstraint('B', 'A', 'D', math.pi / 4))
return problem
def ada_3d_problem():
problem = GeometricProblem(dimension=3)
problem.add_point('v1', vector([random.random() for i in [1,2]]))
problem.add_point('v2', vector([random.random() for i in [1,2]]))
problem.add_point('v3', vector([random.random() for i in [1,2]]))
problem.add_constraint(DistanceConstraint('v1','v2',distance_2p(problem.get_point('v1'), problem.get_point('v2'))))
problem.add_constraint(AngleConstraint('v3', 'v1', 'v2',
angle_3p(problem.get_point('v3'), problem.get_point('v1'), problem.get_point('v2'))
))
problem.add_constraint(AngleConstraint('v1', 'v2', 'v3',
angle_3p(problem.get_point('v1'), problem.get_point('v2'), problem.get_point('v3'))
))
return problem
def double_banana_problem():
"""The double banana problem"""
problem = GeometricProblem(dimension=3)
problem.add_point('v1', vector([0.0, 0.0, 0.0]))
problem.add_point('v2', vector([1.0, 0.0, 0.0]))
problem.add_point('v3', vector([0.0, 1.0, 0.0]))
problem.add_point('v4', vector([0.5, 0.5, 1.0]))
problem.add_point('v5', vector([0.5, 0.5,-1.0]))
problem.add_constraint(DistanceConstraint('v1', 'v2', 10.0))
problem.add_constraint(DistanceConstraint('v1', 'v3', 10.0))
problem.add_constraint(DistanceConstraint('v2', 'v3', 10.0))
problem.add_constraint(DistanceConstraint('v1', 'v4', 10.0))
problem.add_constraint(DistanceConstraint('v2', 'v4', 10.0))
problem.add_constraint(DistanceConstraint('v3', 'v4', 10.0))
problem.add_constraint(DistanceConstraint('v1', 'v5', 10.0))
problem.add_constraint(DistanceConstraint('v2', 'v5', 10.0))
problem.add_constraint(DistanceConstraint('v3', 'v5', 10.0))
problem.add_point('w1', vector([0.0, 0.0, 0.0]))
problem.add_point('w2', vector([1.0, 0.0, 0.0]))
problem.add_point('w3', vector([0.0, 1.0, 0.0]))
problem.add_constraint(DistanceConstraint('w1', 'w2', 10.0))
problem.add_constraint(DistanceConstraint('w1', 'w3', 10.0))
problem.add_constraint(DistanceConstraint('w2', 'w3', 10.0))
problem.add_constraint(DistanceConstraint('w1', 'v4', 10.0))
problem.add_constraint(DistanceConstraint('w2', 'v4', 10.0))
problem.add_constraint(DistanceConstraint('w3', 'v4', 10.0))
problem.add_constraint(DistanceConstraint('w1', 'v5', 10.0))
problem.add_constraint(DistanceConstraint('w2', 'v5', 10.0))
problem.add_constraint(DistanceConstraint('w3', 'v5', 10.0))
return problem
def selection_test():
problem = GeometricProblem(dimension=3,use_prototype=False)
problem.add_point('v1', vector([0.0, 0.0, 0.0]))
problem.add_point('v2', vector([1.0, 0.0, 0.0]))
problem.add_point('v3', vector([0.0, 1.0, 0.0]))
problem.add_point('v4', vector([0.5, 0.5, 1.0]))
problem.add_point('v5', vector([0.5, 0.5,-1.0]))
problem.add_constraint(DistanceConstraint('v1', 'v2', 10.0))
problem.add_constraint(DistanceConstraint('v1', 'v3', 10.0))
problem.add_constraint(DistanceConstraint('v2', 'v3', 10.0))
problem.add_constraint(DistanceConstraint('v1', 'v4', 10.0))
problem.add_constraint(DistanceConstraint('v2', 'v4', 10.0))
problem.add_constraint(DistanceConstraint('v3', 'v4', 10.0))
problem.add_constraint(DistanceConstraint('v1', 'v5', 10.0))
problem.add_constraint(DistanceConstraint('v2', 'v5', 10.0))
problem.add_constraint(DistanceConstraint('v3', 'v5', 10.0))
s1 = RightHandedConstraint('v1','v2','v4','v5')
# add selection con
problem.add_constraint(s1)
# solve
solver = GeometricSolver(problem)
print len(solver.get_solutions()), "solutions"
# remove and add constraint
print "removing selection-constraint"
problem.rem_constraint(s1)
# solve again
print len(solver.get_solutions()), "solutions"
# remove and add constraint
print "re-adding selection constraint"
problem.add_constraint(s1)
# solve again
print len(solver.get_solutions()), "solutions"
# remove distance
print "removing and re-adding distance v1-v5"
problem.rem_constraint(problem.get_distance("v1","v5"))
problem.add_constraint(DistanceConstraint('v1', 'v5', 10.0))
# solve again
print len(solver.get_solutions()), "solutions"
def overconstrained_tetra():
problem = GeometricProblem(dimension=3)
problem.add_point('v1', vector([0.0, 0.0, 0.0]))
problem.add_point('v2', vector([1.0, 0.0, 0.0]))
problem.add_point('v3', vector([0.0, 1.0, 0.0]))
problem.add_point('v4', vector([0.5, 0.5, 1.0]))
problem.add_constraint(DistanceConstraint('v1', 'v2', 10.0))
problem.add_constraint(DistanceConstraint('v1', 'v3', 10.0))
problem.add_constraint(DistanceConstraint('v2', 'v3', 10.0))
problem.add_constraint(DistanceConstraint('v1', 'v4', 10.0))
problem.add_constraint(DistanceConstraint('v2', 'v4', 10.0))
problem.add_constraint(DistanceConstraint('v3', 'v4', 10.0))
# overconstrain me!
problem.add_constraint(AngleConstraint('v1', 'v2', 'v3', math.pi / 4.0))
return problem
def fix1_problem_3d():
"""A problem with a fix constraint"""
problem = GeometricProblem(dimension=3)
problem.add_point('v1', vector([0.0, 0.0, 0.0]))
problem.add_point('v2', vector([1.0, 0.0, 0.0]))
problem.add_point('v3', vector([0.0, 1.0, 0.0]))
problem.add_point('v4', vector([0.0, 0.0, 1.0]))
problem.add_constraint(DistanceConstraint('v1', 'v2', 10.0))
problem.add_constraint(DistanceConstraint('v1', 'v3', 10.0))
problem.add_constraint(DistanceConstraint('v2', 'v3', 10.0))
problem.add_constraint(DistanceConstraint('v1', 'v4', 10.0))
problem.add_constraint(DistanceConstraint('v2', 'v4', 10.0))
problem.add_constraint(DistanceConstraint('v3', 'v4', 10.0))
problem.add_constraint(FixConstraint('v1', vector([0.0,0.0,0.0])))
return problem
def transform_point(point, transform):
"""transform a point from from_cs to to_cs"""
hpoint = Vec(point)
hpoint.append(1.0)
hres = transform.mmul(hpoint)
res = vector(hres[1:-1]) / hres[-1]
return res
def buggy1():
problem = GeometricProblem(dimension=2)
p0 = "P0"
p1 = "P1"
p2 = "P2"
p3 = "P3"
problem.add_point(p2, vector([4.2516273494524803, -9.510959969336783]))
problem.add_point(p3, vector([0.96994030830283862, -3.6416260233938491]))
problem.add_point(p0, vector([6.6635607149389386, -8.5894325593219882]))
problem.add_point(p1, vector([-0.06750282559988996, 6.6760454282229134]))
problem.add_constraint(AngleConstraint(p1, p3, p0, 2.38643631762))
problem.add_constraint(DistanceConstraint(p2, p0, 2.58198282856))
problem.add_constraint(AngleConstraint(p1, p0, p2, -1.52046205861))
problem.add_constraint(DistanceConstraint(p3, p1, 10.3696977989))
problem.add_constraint(AngleConstraint(p3, p0, p1, 0.440080782652))
return problem
def buggy1():
problem = GeometricProblem(dimension=2)
p0 = "P0"
p1 = "P1"
p2 = "P2"
p3 = "P3"
problem.add_point(p2,vector([4.2516273494524803, -9.510959969336783]))
problem.add_point(p3,vector([0.96994030830283862, -3.6416260233938491]))
problem.add_point(p0,vector([6.6635607149389386, -8.5894325593219882]))
problem.add_point(p1,vector([-0.06750282559988996, 6.6760454282229134]))
problem.add_constraint(AngleConstraint(p1,p3,p0,2.38643631762))
problem.add_constraint(DistanceConstraint(p2,p0,2.58198282856))
problem.add_constraint(AngleConstraint(p1,p0,p2,-1.52046205861))
problem.add_constraint(DistanceConstraint(p3,p1,10.3696977989))
problem.add_constraint(AngleConstraint(p3,p0,p1,0.440080782652))
return problem
def random_problem_2D(numpoints, radius=10.0, roundoff=0.0, angleratio=0.5):
"""Generate a random problem with given number of points, a roundoff
value for the prototype points, a radius for the cloud of prototype points
and a ratio of angle constraints over distance constraints"""
group = {}
problem = GeometricProblem(dimension=2)
i = 0
while i < numpoints:
aname = 'p' + str(i)
apoint = vector([
_round(random.uniform(-radius, radius), roundoff),
_round(random.uniform(-radius, radius), roundoff)
])
unique = True
for v in group:
p = group[v]
if tol_eq(apoint[0], p[0]) and tol_eq(apoint[1], p[1]):
unique = False
break
if unique:
problem.add_point(aname, apoint)
group[aname] = apoint
i = i + 1
# next
_constraint_group(problem, group, None, angleratio)
return problem
def overconstrained_tetra():
problem = GeometricProblem(dimension=3)
problem.add_point('v1', vector([0.0, 0.0, 0.0]))
problem.add_point('v2', vector([1.0, 0.0, 0.0]))
problem.add_point('v3', vector([0.0, 1.0, 0.0]))
problem.add_point('v4', vector([0.5, 0.5, 1.0]))
problem.add_constraint(DistanceConstraint('v1', 'v2', 10.0))
problem.add_constraint(DistanceConstraint('v1', 'v3', 10.0))
problem.add_constraint(DistanceConstraint('v2', 'v3', 10.0))
problem.add_constraint(DistanceConstraint('v1', 'v4', 10.0))
problem.add_constraint(DistanceConstraint('v2', 'v4', 10.0))
problem.add_constraint(DistanceConstraint('v3', 'v4', 10.0))
# overconstrain me!
problem.add_constraint(AngleConstraint('v1', 'v2', 'v3', math.pi/3))
#problem.add_constraint(AngleConstraint('v1', 'v2', 'v3', math.pi/4))
return problem
def solve_shape(self, layers):
for layer in layers:
print("Solving shape ", layer.id)
pt0 = layer.named_pairs[0][0]
pt1 = layer.named_pairs[1][0]
pt2 = layer.named_pairs[2][0]
for i, point in enumerate(layer.named_pairs):
# Add initial points
self.problem.add_variable(point[0],
vector([point[1], point[2], 0]))
# Lock them together
if i > 0:
self.problem.add_constraint(
DistanceConstraint(
pt0, point[0],
distance_2p(self.problem.get_point(pt0),
self.problem.get_point(point[0]))))
if i > 1:
self.problem.add_constraint(
AngleConstraint(
pt0, pt1, point[0],
angle_3p(self.problem.get_point(pt0),
self.problem.get_point(pt1),
self.problem.get_point(point[0]))))
if i > 2:
self.problem.add_constraint(
AngleConstraint(
pt0, pt2, point[0],
angle_3p(self.problem.get_point(pt0),
self.problem.get_point(pt2),
self.problem.get_point(point[0]))))
def test_mergehogs():
diag_select(".")
problem = GeometricProblem(dimension=2)
problem.add_point('x',vector([0.0, 0.0]))
problem.add_point('a',vector([1.0, 0.0]))
problem.add_point('b',vector([0.0, 1.0]))
problem.add_point('c',vector([-1.0, 0.0]))
problem.add_point('d',vector([0.0, -1.0]))
problem.add_constraint(AngleConstraint('a','x','b', 30.0/180*math.pi))
problem.add_constraint(AngleConstraint('b','x','c', 30.0/180*math.pi))
problem.add_constraint(AngleConstraint('c','x','d', 30.0/180*math.pi))
solver = GeometricSolver(problem)
print solver.dr
for hog in solver.dr.hedgehogs():
conf = list(solver.mg.get(hog))[0]
print hog
print conf
print problem.verify(conf.map)
def ada_tetrahedron_problem():
"""The double tetrahedron problem with an angle"""
problem = GeometricProblem(dimension=3)
problem.add_point('v1', vector([0.0, 0.0, 0.0]))
problem.add_point('v2', vector([1.0, 0.0, 0.0]))
problem.add_point('v3', vector([0.0, 1.0, 0.0]))
problem.add_point('v4', vector([0.5, 0.5, 1.0]))
problem.add_point('v5', vector([0.5, 0.5,-1.0]))
problem.add_constraint(DistanceConstraint('v1', 'v2', 10.0))
problem.add_constraint(AngleConstraint('v3', 'v1','v2', 60.0*math.pi/180.0))
problem.add_constraint(AngleConstraint('v1', 'v2','v3', 60.0*math.pi/180.0))
problem.add_constraint(DistanceConstraint('v1', 'v4', 10.0))
problem.add_constraint(DistanceConstraint('v2', 'v4', 10.0))
problem.add_constraint(DistanceConstraint('v3', 'v4', 10.0))
problem.add_constraint(DistanceConstraint('v1', 'v5', 10.0))
problem.add_constraint(DistanceConstraint('v2', 'v5', 10.0))
problem.add_constraint(DistanceConstraint('v3', 'v5', 10.0))
return problem
def transform(self, t):
"""returns a new configuration, which is this one transformed by matrix t"""
newmap = {}
for v in self.map:
p = self.map[v]
ph = Vec(p)
ph.append(1.0)
ph = t.mmul(ph)
p = vector(ph[0:-1]) / ph[-1]
newmap[v] = p
return Configuration(newmap)
def solve_dad_3D(v1, v2, v3, d12, a123, d23):
"""returns a list of Configurations of v1,v2,v3 such that distance v1-v2=d12 etc.
v<x>: name of point variables
d<xy>: numeric distance values
a<xyz>: numeric angle in radians
"""
diag_print("solve_dad: %s %s %s %f %f %f" % (v1, v2, v3, d12, a123, d23),
"clmethods")
p2 = vector([0.0, 0.0])
p1 = vector([d12, 0.0])
p3s = [vector([d23 * math.cos(a123), d23 * math.sin(a123)])]
# extend coords to 3D!
p1.append(0.0)
p2.append(0.0)
solutions = []
for p3 in p3s:
p3.append(0.0)
solution = Configuration({v1: p1, v2: p2, v3: p3})
solutions.append(solution)
return solutions
def make_hcs_2d(a, b):
"""build a 2D homogeneus coordiate system from two vectors"""
u = b - a
if tol_eq(norm(u), 0.0): # 2006/6/30
return None
else:
u = u / norm(u)
v = vector([-u[1], u[0]])
hcs = matrix_factory([[u[0], v[0], a[0]], [u[1], v[1], a[1]],
[0.0, 0.0, 1.0]])
return hcs
def make_hcs_2d_scaled(a, b):
"""build a 2D homogeneus coordiate system from two vectors, but scale with distance between input point"""
u = b - a
if tol_eq(norm(u), 0.0): # 2006/6/30
return None
#else:
# u = u / norm(u)
v = vector([-u[1], u[0]])
hcs = matrix_factory([[u[0], v[0], a[0]], [u[1], v[1], a[1]],
[0.0, 0.0, 1.0]])
return hcs
def diamond_3d():
"""creates a diamond shape with point 'v1'...'v4' in 3D with one solution"""
# Following should be well-constraint, gives underconstrained (need extra rule/pattern)
L=10.0
problem = GeometricProblem(dimension=3, use_prototype=False) # no prototype based selection
problem.add_point('v1', vector([0.0, 0.0, 0.0]))
problem.add_point('v2', vector([-5.0, 5.0, 0.0]))
problem.add_point('v3', vector([5.0, 5.0, 0.0]))
problem.add_point('v4', vector([0.0, 10.0, 0.0]))
problem.add_constraint(DistanceConstraint('v1', 'v2', L))
problem.add_constraint(DistanceConstraint('v1', 'v3', L))
problem.add_constraint(DistanceConstraint('v2', 'v3', L))
problem.add_constraint(DistanceConstraint('v2', 'v4', L))
problem.add_constraint(DistanceConstraint('v3', 'v4', L))
# this bit of code constrains the points v1...v4 in a plane with point p above it
problem.add_point('p', vector([0.0, 0.0, 1.0]))
problem.add_constraint(DistanceConstraint('v1', 'p', 1.0))
problem.add_constraint(AngleConstraint('v2','v1','p', math.pi/2))
problem.add_constraint(AngleConstraint('v3','v1','p', math.pi/2))
problem.add_constraint(AngleConstraint('v4','v1','p', math.pi/2))
return problem
def solve_add_3D(a, b, c, a_cab, d_ab, d_bc):
"""returns a list of Configurations of v1,v2,v3 such that distance v1-v2=d12 etc.
v<x>: name of point variables
d<xy>: numeric distance values
a<xyz>: numeric angle in radians
"""
diag_print("solve_dad: %s %s %s %f %f %f" % (a, b, c, a_cab, d_ab, d_bc),
"clmethods")
p_a = vector([0.0, 0.0])
p_b = vector([d_ab, 0.0])
dir = vector([math.cos(-a_cab), math.sin(-a_cab)])
solutions = cr_int(p_b, d_bc, p_a, dir)
rval = []
p_a.append(0.0)
p_b.append(0.0)
for p_c in solutions:
p_c.append(0.0)
map = {a: p_a, b: p_b, c: p_c}
rval.append(Configuration(map))
return rval
def solve_fixed(self, fixed, layers):
for i, layer in enumerate(layers):
print("Solving fixed ", layer.id)
i = 0
for point in layer.named_pairs:
if point[0] in fixed:
self.problem.add_constraint(
FixConstraint(point[0], vector([point[1], point[2],
0])))
i += 1
def test_mergehogs():
diag_select(".")
problem = GeometricProblem(dimension=2)
problem.add_point('x', vector([0.0, 0.0]))
problem.add_point('a', vector([1.0, 0.0]))
problem.add_point('b', vector([0.0, 1.0]))
problem.add_point('c', vector([-1.0, 0.0]))
problem.add_point('d', vector([0.0, -1.0]))
problem.add_constraint(AngleConstraint('a', 'x', 'b',
30.0 / 180 * math.pi))
problem.add_constraint(AngleConstraint('b', 'x', 'c',
30.0 / 180 * math.pi))
problem.add_constraint(AngleConstraint('c', 'x', 'd',
30.0 / 180 * math.pi))
solver = GeometricSolver(problem)
print solver.dr
for hog in solver.dr.hedgehogs():
conf = list(solver.mg.get(hog))[0]
print hog
print conf
print problem.verify(conf.map)
def balloon_problem():
"""test angle propagation via balloon"""
problem = GeometricProblem(dimension=2)
problem.add_point('A', vector([0.0, 0.0]))
problem.add_point('B', vector([1.0, -1.0]))
problem.add_point('C', vector([1.0, +1.0]))
problem.add_point('D', vector([2.0, 0.0]))
problem.add_constraint(AngleConstraint('B','A','C',
angle_3p(problem.get_point('B'), problem.get_point('A'), problem.get_point('C'))
))
problem.add_constraint(AngleConstraint('A','B','C',
angle_3p(problem.get_point('A'), problem.get_point('B'), problem.get_point('C'))
))
problem.add_constraint(AngleConstraint('B','C','D',
angle_3p(problem.get_point('B'), problem.get_point('C'), problem.get_point('D'))
))
problem.add_constraint(AngleConstraint('C','D','B',
angle_3p(problem.get_point('C'), problem.get_point('D'), problem.get_point('B'))
))
problem.add_constraint(DistanceConstraint('A', 'D', 6.0))
return problem
def hog2():
# several triangles with inter-angles (needs angle propagation)
problem = GeometricProblem(dimension=2)
problem.add_point('M', vector([0.0, 0.0]))
problem.add_point('A', vector([0.0, 1.0]))
problem.add_point('B', vector([1.0, 1.0]))
problem.add_point('C', vector([2.0, 1.0]))
problem.add_point('D', vector([3.0, 1.0]))
problem.add_point('E', vector([4.0, 1.0]))
problem.add_constraint(DistanceConstraint('A', 'M', 10.0))
problem.add_constraint(DistanceConstraint('A', 'E', 10.0))
problem.add_constraint(DistanceConstraint('B', 'E', 7.0))
problem.add_constraint(DistanceConstraint('C', 'E', 6.0))
problem.add_constraint(DistanceConstraint('D', 'E', 5.0))
problem.add_constraint(AngleConstraint('A','M','B', math.pi / 20))
problem.add_constraint(AngleConstraint('B','M','C', math.pi / 20))
problem.add_constraint(AngleConstraint('D','M','C', math.pi / 20))
problem.add_constraint(AngleConstraint('D','M','E', math.pi / 20))
return problem
def test_mate():
problem = GeometricProblem(dimension=3)
# create and mate two blocks
add_block(problem, "A", 4.0, 2.0, 6.0)
add_block(problem, "B", 4.0, 2.0, 6.0)
mate_blocks(problem, "A", 'right-bot-front','right-bot-back','right-top-front',
"B", 'left-bot-front','left-bot-back','left-top-front',
0.5, 0.0)
# add global coordinate system
problem.add_point("origin",vector([0.0,0.0,0.0]))
problem.add_point("x-axis",vector([1.0,0.0,0.0]))
problem.add_point("y-axis",vector([0.0,1.0,0.0]))
problem.add_constraint(FixConstraint("origin",vector([0.0,0.0,0.0])))
problem.add_constraint(FixConstraint("x-axis",vector([1.0,0.0,0.0])))
problem.add_constraint(FixConstraint("y-axis",vector([0.0,1.0,0.0])))
# fix block1 to cs
problem.add_constraint(MateConstraint("origin","x-axis","y-axis",
block_var("A", "left-bot-front"),block_var("A", "right-bot-front"),block_var("A", "left-top-front"),
id_transform_3D()))
test(problem)
def line_problem_2d_0():
"""A problem with a Line (and no CoincicentConstraints)"""
problem = GeometricProblem(dimension=2)
problem.add_variable(Line('l1'),vector([0.0, 0.0, 1.0, 1.0]))
return problem
def add_block(problem,name,x,y,z):
"""A block with variables name+#1...8 and dimensions x,y,z"""
problem.add_point(block_var(name,'left-bot-front'), vector([-1.0, -1.0, -1.0]))
problem.add_point(block_var(name,'left-bot-back'), vector([-1.0, -1.0, 1.0]))
problem.add_point(block_var(name,'left-top-front'), vector([-1.0, 1.0, -1.0]))
problem.add_point(block_var(name,'left-top-back'), vector([-1.0, 1.0, 1.0]))
problem.add_point(block_var(name,'right-bot-front'), vector([1.0, -1.0, -1.0]))
problem.add_point(block_var(name,'right-bot-back'), vector([1.0, -1.0, 0.0]))
problem.add_point(block_var(name,'right-top-front'), vector([1.0, 1.0, -1.0]))
problem.add_point(block_var(name,'right-top-back'), vector([1.0, 1.0, 1.0]))
conf = Configuration({
block_var(name,'left-bot-front'):vector([-x/2, -y/2, -z/2]),
block_var(name,'left-bot-back'):vector([-x/2, -y/2, +z/2]),
block_var(name,'left-top-front'):vector([-x/2, +y/2, -z/2]),
block_var(name,'left-top-back'):vector([-x/2, +y/2, +z/2]),
block_var(name,'right-bot-front'):vector([+x/2, -y/2, -z/2]),
block_var(name,'right-bot-back'):vector([+x/2, -y/2, +z/2]),
block_var(name,'right-top-front'):vector([+x/2, +y/2, -z/2]),
block_var(name,'right-top-back'):vector([+x/2, +y/2, +z/2])
})
problem.add_constraint(RigidConstraint(conf))
return problem
