def test_intersec_angle():
a = np.array((1, 3, 4))
b = np.array((2, 6, 5))
tol = 1e-3
exp = 0.2328
feqok_(exp, intersec_angle(a, b), tol)
def test_norm_vec():
while True:
vec = random_vec(100)
if vec_len(vec) != 1:
break
normed_vec = norm_vec(vec)
feqok_(np.dot(normed_vec, normed_vec), 1, 1e-6)
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 test_rotation_matrix():
sample_count = 10
vec_len_range = 10000
theta_range = pi # if > pi, may cause test fail, but don't worry.
tol = 1e-4
for i in xrange(sample_count):
axis_dir = random_vec(vec_len_range)
vec_to_rotate = random_vec(vec_len_range)
theta = random_float(theta_range)
mat = rotation_array(theta, axis_dir)
rotated_vec = mat.dot(vec_to_rotate)
rotated_vec2 = mat.dot(rotated_vec)
act_theta = intersec_angle(projection_to_plan(vec_to_rotate,
axis_dir),
projection_to_plan(rotated_vec,
axis_dir))
act_theta *= cmp(np.dot(np.cross(vec_to_rotate, rotated_vec),
axis_dir), 0)
feqok_(act_theta, theta, tol)
if theta < pi * tol:
continue
feqok_(vec_len(vec_to_rotate), vec_len(rotated_vec), tol)
(r, center) = circum(vec_to_rotate, rotated_vec, rotated_vec2)
feqok_(vec_len(np.cross(center, axis_dir)), 0, tol
* max(vec_len(axis_dir), vec_len(center)))
ok_(cmp(np.dot(center, axis_dir), 0)
== cmp(np.dot(vec_to_rotate, axis_dir), 0))
def test_circum():
vec_len_range = 10000
sample_count = 1000
tol = 1e-6
for i in xrange(sample_count):
p1 = random_vec(vec_len_range)
p2 = random_vec(vec_len_range)
p3 = random_vec(vec_len_range)
(r, center) = circum(p1, p2, p3)
err = max(vec_len(p1 - p2), vec_len(p2 - p3), vec_len(p3 - p1)) \
* tol
feqok_(vec_len(p1 - center), r, err)
feqok_(vec_len(p2 - center), r, err)
feqok_(vec_len(p3 - center), r, err)
feqok_((p1 - center).dot(np.cross(p2 - center, p3 - center)),
0, tol * vec_len(np.cross(p2 - center, p3 - center))
* vec_len(p1 - center))