def test_smallest_triangle_sphere():
# this test is based on test_circum
p1 = np.array((0, 0, 0))
p2 = np.array((3, 0, 0))
p3 = np.array((0, 4, 0))
exp_r = 2.5
exp_center = (1.5, 2, 0)
tol = 1e-10
(r, center) = smallest_triangle_sphere(p1, p2, p3)
feqok_(exp_r, r, tol)
iter_ = iter(exp_center)
for item in center:
feqok_(next(iter_), item, tol)
p1 = np.array((0, 0, 0))
p2 = np.array((3, -1, 0))
p3 = np.array((0, 4, 0))
exp_r = sqrt(34) / 2
exp_center = (1.5, 1.5, 0)
tol = 1e-10
(r, center) = smallest_triangle_sphere(p1, p2, p3)
feqok_(exp_r, r, tol)
iter_ = iter(exp_center)
for item in center:
feqok_(next(iter_), item, tol)
def edge_polygon(self):
e = self.ale.pop()
p1 = e.start
p2 = e.end
p_s = (p1 + p2) / 2.0
#grd_s = norm_vec(self.func_gd(p_s))
pold = e.tri_pt
v12 = p2 - p1
grd_old = np.cross(v12, pold - p2)
# not like Cermak2005!!!
c0 = vec_len(grd_old) / vec_len(v12)
vinit = np.cross(v12, grd_old)
radius = self.estimate_spining_radius(p1, p2, vinit, c0)
pnew = self.search_on_plane(p_s, radius, v12, vinit)
v_succ = e.succ.end - e.end
v_pred = e.start - e.pred.start
alpha2 = intersec_angle(v_succ, -v12)
if np.cross(v12, v_succ).dot(grd_old) > 0:
alpha2 = 2 * pi - alpha2
alpha1 = intersec_angle(v12, -v_pred)
if np.cross(v_pred, v12).dot(grd_old) > 0:
alpha1 = 2 * pi - alpha1
alpha = min(alpha1, alpha2)
# MARK: alpha_n_assuming the pnew made by edge_spining is on the plan P:
# P across the mid point of e
# P is perpendicular to e
if pnew is not None:
alpha_n = intersec_angle(pnew - p1, v12)
alpha_shape = alpha_n + self.alpha_shape_min
else:
alpha_shape = self.alpha_shape_big
# neibourhood test
if alpha < alpha_shape:
if e.succ.succ is e.pred:
self.ale.remove(e.succ)
self.ale.remove(e.pred)
self.triangles.append((e.end_index, e.start_index, e.pred.start_index))
return
# situation a) in Fig8 & Fig9
if alpha == alpha1:
case = 1
(r, center) = smallest_triangle_sphere(p1, p2,
e.pred.start)
except_pts = (p1, p2, e.pred.start)
check_dir = p2 - e.pred.start
radius_check_pts = (e.pred.pred.start, e.succ.end)
else:
case = 2
(r, center) = smallest_triangle_sphere(p1, p2,
e.succ.end)
except_pts = (p1, p2, e.succ.end)
check_dir = e.succ.end - p1
radius_check_pts = (e.pred.start, e.succ.succ.end)
elif pnew is None:
r = vec_len(v12) * 0.5
center = (p1 + p2) * 0.5
except_pts = (p1, p2)
check_dir = e
radius_check_pts = (e.pred.start, e.succ.end)
case = 3
else:
(r, center) = smallest_triangle_sphere(p1, p2, pnew)
r = r * self.dist_test_cf
except_pts = (p1, p2)
check_dir = e
radius_check_pts = (e.pred.start, e.succ.end)
case = 4
# filet out a NAEL,distance test
emin = self._distance_test(e, r, center, check_dir, except_pts, radius_check_pts)
if emin is e.pred.pred:
emin = None
case = 1
elif emin is e.succ:
emin = None
case = 2
if emin is None:
if 1 == case:
self.ale.remove(e.pred)
self._add_tri_ale_A(e.pred, e)
elif 2 == case:
self.ale.remove(e.succ)
self._add_tri_ale_A(e, e.succ)
elif 3 == case:
self.ale.appendleft(e)
elif 4 == case:
pnew_index = len(self.points)
self.points.append(pnew)
self.triangles.append((pnew_index, e.end_index,
e.start_index))
e_new1 = _WingedEdge(e.start, pnew, e.start_index,
pnew_index, e.end)
e_new2 = _WingedEdge(pnew, e.end, pnew_index,
e.end_index, e.start)
e_new1.succ = e_new2
e_new1.pred = e.pred
e_new2.pred = e_new1
e_new2.succ = e.succ
e.pred.succ = e_new1
e.succ.pred = e_new2
self.ale.append(e_new1)
self.ale.append(e_new2)
else:
emin1 = emin
emin2 = emin.succ
alpha_m1 = intersec_angle(emin2.end - emin2.start, e.start
- emin2.start)
alpha_m2 = intersec_angle(emin1.start - emin1.end, e.end
- emin1.end)
if alpha_m1 < alpha_m2:
te = _WingedEdge(e.start, emin2.end)
(r, center) = smallest_triangle_sphere(e.start,
emin2.start, emin2.end)
except_pts = (emin2.start, emin2.end, e.start, e.end)
radius_check_pts = (emin2.succ.end, emin1.start, e.pred.start)
else:
te = _WingedEdge(emin1.start, e.end)
(r, center) = smallest_triangle_sphere(e.end,
emin1.start, emin1.end)
except_pts = (emin1.start, emin1.end, e.start, e.end)
radius_check_pts = (emin2.end, emin1.pred.start, e.succ.end)
check_dir = te.end - te.start
t_emin = self._distance_test(te, r, center, check_dir, except_pts, radius_check_pts)
if t_emin is not None:
self.ale.appendleft(e)
return
if alpha_m1 < alpha_m2:
self.ale.remove(emin2)
if emin2.succ is e.pred:
self.ale.remove(e.pred)
else:
enew1 = _WingedEdge(
e.start,
emin2.end,
e.start_index,
emin2.end_index,
emin2.start,
e.pred,
emin2.succ,
)
e.pred.succ = enew1
emin2.succ.pred = enew1
self.ale.append(enew1)
enew2 = _WingedEdge(
emin2.start,
e.end,
emin2.start_index,
e.end_index,
e.start,
emin1,
e.succ,
)
emin1.succ = enew2
e.succ.pred = enew2
self.ale.append(enew2)
self.triangles.append((emin2.end_index,
emin2.start_index, e.start_index))
else:
self.ale.remove(emin1)
if e.succ is emin1.pred:
self.ale.remove(emin1.pred)
else:
enew1 = _WingedEdge(
emin1.start,
e.end,
emin1.start_index,
e.end_index,
emin1.end,
emin1.pred,
e.succ,
)
emin1.pred.succ = enew1
e.succ.pred = enew1
self.ale.append(enew1)
enew2 = _WingedEdge(
e.start,
emin1.end,
e.start_index,
emin1.end_index,
e.end,
e.pred,
emin2,
)
e.pred.succ = enew2
emin2.pred = enew2
self.ale.append(enew2)
self.triangles.append((emin1.end_index,
emin1.start_index, e.end_index))
self.triangles.append((emin2.start_index, e.end_index,
e.start_index))
pass
