def test_arc_1(self):
circle = SvCircle(Matrix(), 1.0)
t_min = 0.1
t_max = 1.4
pt1 = circle.evaluate(t_max)
nurbs = circle._arc_to_nurbs(t_min, t_max)
pt2 = nurbs.evaluate(t_max)
self.assert_numpy_arrays_equal(pt1, pt2, precision=8)
def calc(point_a, point_b, tangent_a, tangent_b, p, planar_tolerance=1e-6):
xx = point_b - point_a
xx /= np.linalg.norm(xx)
tangent_normal = np.cross(tangent_a, tangent_b)
volume = np.dot(xx, tangent_normal)
if abs(volume) > planar_tolerance:
raise Exception(
f"Provided tangents are not coplanar, volume={volume}")
zz_a = np.cross(tangent_a, xx)
zz_b = np.cross(tangent_b, xx)
zz = (zz_a + zz_b)
zz /= np.linalg.norm(zz)
yy = np.cross(zz, xx)
c = np.linalg.norm(point_b - point_a) * 0.5
tangent_a /= np.linalg.norm(tangent_a)
tangent_b /= np.linalg.norm(tangent_b)
to_center_a = np.cross(zz, tangent_a)
to_center_b = -np.cross(zz, tangent_b)
matrix_inv = np.stack((xx, yy, zz))
matrix = np.linalg.inv(matrix_inv)
# TODO: sin(arccos(...)) = ...
alpha = acos(np.dot(tangent_a, xx))
beta = acos(np.dot(tangent_b, xx))
if np.dot(tangent_a, yy) > 0:
alpha = -alpha
if np.dot(tangent_b, yy) > 0:
beta = -beta
#print("A", alpha, "B", beta)
omega = (alpha + beta) * 0.5
r1 = c / (sin(alpha) + sin(omega) / p)
r2 = c / (sin(beta) + p * sin(omega))
#print("R1", r1, "R2", r2)
theta1 = 2 * arg(cexp(-1j * alpha) + cexp(-1j * omega) / p)
theta2 = 2 * arg(cexp(1j * beta) + p * cexp(1j * omega))
#print("T1", theta1, "T2", theta2)
vectorx_a = r1 * to_center_a
center1 = point_a + vectorx_a
center2 = point_b + r2 * to_center_b
arc1 = SvCircle( #radius = r1,
center=center1,
normal=-zz,
vectorx=point_a - center1)
if theta1 > 0:
arc1.u_bounds = (0.0, theta1)
else:
theta1 = -theta1
arc1.u_bounds = (0.0, theta1)
arc1.set_normal(-arc1.normal)
junction = arc1.evaluate(theta1)
#print("J", junction)
arc2 = SvCircle( #radius = r2,
center=center2,
normal=-zz,
vectorx=junction - center2)
if theta2 > 0:
arc2.u_bounds = (0.0, theta2)
else:
theta2 = -theta2
arc2.u_bounds = (0.0, theta2)
arc2.set_normal(-arc2.normal)
curve = SvBiArc(arc1, arc2)
curve.p = p
curve.junction = junction
return curve