def test_circle_1(self):
circle = SvCircle(Matrix(), 1.0)
circle.u_bounds = (0, pi / 6)
nurbs = circle.to_nurbs()
cpts = nurbs.get_control_points()
expected_cpts = np.array([[1.0, 0.0, 0.0], [1.0, 0.26794919, 0.0],
[0.8660254, 0.5, 0.0]])
self.assert_numpy_arrays_equal(cpts, expected_cpts, precision=6)
def test_circle_2(self):
circle = SvCircle(Matrix(), 1.0)
t_max = pi + 0.3
circle.u_bounds = (0, t_max)
nurbs = circle.to_nurbs()
ts = np.array([0, pi / 2, pi, t_max])
points = nurbs.evaluate_array(ts)
expected_points = circle.evaluate_array(ts)
self.assert_numpy_arrays_equal(points, expected_points, precision=6)
def get_circular_arc(self):
center = np.array(self.center)
normal = np.array(self.normal)
p1 = np.array(self.p1)
circle = SvCircle(center = center,
normal = -normal,
vectorx = p1 - center)
circle.u_bounds = (0.0, self.angle)
#circle.u_bounds = (-self.angle, 0.0)
return circle
def test_arc_2(self):
pt1 = (-5, 0, 0)
pt2 = (-4, 3, 0)
pt3 = (-3, 4, 0)
eq = circle_by_three_points(pt1, pt2, pt3)
matrix = eq.get_matrix()
arc = SvCircle(matrix, eq.radius)
arc.u_bounds = (0.0, eq.arc_angle)
nurbs = arc.to_nurbs()
u_min, u_max = nurbs.get_u_bounds()
self.assertEquals(u_min, 0, "U_min")
self.assertEquals(u_max, eq.arc_angle, "U_max")
startpoint = nurbs.evaluate(u_min)
self.assert_sverchok_data_equal(startpoint.tolist(), pt1, precision=8)
endpoint = nurbs.evaluate(u_max)
self.assert_sverchok_data_equal(endpoint.tolist(), pt3, precision=8)
def nurbs_revolution_surface(curve,
origin,
axis,
v_min=0,
v_max=2 * pi,
global_origin=True):
my_control_points = curve.get_control_points()
my_weights = curve.get_weights()
control_points = []
weights = []
any_circle = SvCircle(Matrix(), 1)
any_circle.u_bounds = (v_min, v_max)
any_circle = any_circle.to_nurbs()
# all circles with given (v_min, v_max)
# actually always have the same knotvector
# and the same number of control points
n = len(any_circle.get_control_points())
circle_knotvector = any_circle.get_knotvector()
circle_weights = any_circle.get_weights()
# TODO: vectorize with numpy? Or better let it so for better readability?
for my_control_point, my_weight in zip(my_control_points, my_weights):
eq = CircleEquation3D.from_axis_point(origin, axis, my_control_point)
if abs(eq.radius) < 1e-8:
parallel_points = np.empty((n, 3))
parallel_points[:] = np.array(eq.center) #[np.newaxis].T
else:
circle = SvCircle.from_equation(eq)
circle.u_bounds = (v_min, v_max)
nurbs_circle = circle.to_nurbs()
parallel_points = nurbs_circle.get_control_points()
parallel_weights = circle_weights * my_weight
control_points.append(parallel_points)
weights.append(parallel_weights)
control_points = np.array(control_points)
if global_origin:
control_points = control_points - origin
weights = np.array(weights)
degree_u = curve.get_degree()
degree_v = 2 # circle
return SvNurbsSurface.build(curve.get_nurbs_implementation(), degree_u,
degree_v, curve.get_knotvector(),
circle_knotvector, control_points, weights)
def test_arc_3(self):
pt1 = np.array((-4, 2, 0))
pt2 = np.array((0, 2.5, 0))
pt3 = np.array((4, 2, 0))
eq = circle_by_three_points(pt1, pt2, pt3)
#matrix = eq.get_matrix()
arc = SvCircle(center=np.array(eq.center),
vectorx=np.array(pt1 - eq.center),
normal=eq.normal)
arc.u_bounds = (0.0, eq.arc_angle)
nurbs = arc.to_nurbs()
u_min, u_max = nurbs.get_u_bounds()
self.assertEquals(u_min, 0, "U_min")
self.assertEquals(u_max, eq.arc_angle, "U_max")
startpoint = nurbs.evaluate(u_min)
self.assert_sverchok_data_equal(startpoint.tolist(), pt1, precision=6)
endpoint = nurbs.evaluate(u_max)
self.assert_sverchok_data_equal(endpoint.tolist(), pt3, precision=6)
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