def test_interpolate_1(self):
"NURBS interpolation in 3D"
points = np.array([[0, 0, 0], [1, 0, 0], [1, 1, 0]], dtype=np.float64)
degree = 2
curve = interpolate_nurbs_curve(SvNativeNurbsCurve, degree, points)
ts = np.array([0, 0.5, 1])
result = curve.evaluate_array(ts)
self.assert_numpy_arrays_equal(result, points, precision=6)
ctrlpts = curve.get_control_points()
expected_ctrlpts = np.array([[0.0, 0.0, 0.0], [1.5, -0.5, 0.0],
[1.0, 1.0, 0.0]])
self.assert_numpy_arrays_equal(ctrlpts, expected_ctrlpts, precision=6)
def test_interpolate_2(self):
"NURBS Interpolation in homogenous coordinates"
points = np.array([[0, 0, 0, 1], [1, 0, 0, 2], [1, 1, 0, 1]],
dtype=np.float64)
degree = 2
curve = interpolate_nurbs_curve(SvNativeNurbsCurve, degree, points)
ts = np.array([0, 0.5, 1])
result = curve.evaluate_array(ts)
expected = np.array([[0, 0, 0], [0.5, 0, 0], [1, 1, 0]])
self.assert_numpy_arrays_equal(result, expected, precision=6)
ctrlpts = curve.get_control_points()
expected_ctrlpts = np.array([[0.0, 0.0, 0.0], [0.5, -0.16666667, 0.0],
[1.0, 1.0, 0.0]])
self.assert_numpy_arrays_equal(ctrlpts, expected_ctrlpts, precision=6)
weights = curve.get_weights()
expected_weights = np.array([1, 3, 1])
self.assert_numpy_arrays_equal(weights, expected_weights, precision=6)
def interpolate(cls, degree, points, metric='DISTANCE'):
return interpolate_nurbs_curve(cls, degree, points, metric)
def simple_loft(curves,
degree_v=None,
knots_u='UNIFY',
metric='DISTANCE',
tknots=None,
implementation=SvNurbsSurface.NATIVE):
"""
Loft between given NURBS curves (a.k.a skinning).
inputs:
* degree_v - degree of resulting surface along V parameter; by default - use the same degree as provided curves
* knots_u - one of:
- 'UNIFY' - unify knotvectors of given curves by inserting additional knots
- 'AVERAGE' - average knotvectors of given curves; this will work only if all curves have the same number of control points
* metric - metric for interpolation; most useful are 'DISTANCE' and 'CENTRIPETAL'
* implementation - NURBS maths implementation
output: tuple:
* list of curves - input curves after unification
* list of NURBS curves along V direction
* generated NURBS surface.
"""
if knots_u not in {'UNIFY', 'AVERAGE'}:
raise Exception(f"Unsupported knots_u option: {knots_u}")
curve_class = type(curves[0])
curves = unify_curves_degree(curves)
if knots_u == 'UNIFY':
curves = unify_curves(curves)
else:
kvs = [len(curve.get_control_points()) for curve in curves]
max_kv, min_kv = max(kvs), min(kvs)
if max_kv != min_kv:
raise Exception(
f"U knotvector averaging is not applicable: Curves have different number of control points: {kvs}"
)
degree_u = curves[0].get_degree()
if degree_v is None:
degree_v = degree_u
if degree_v > len(curves):
raise Exception(
f"V degree ({degree_v}) must be not greater than number of curves ({len(curves)}) minus 1"
)
src_points = [curve.get_homogenous_control_points() for curve in curves]
# lens = [len(pts) for pts in src_points]
# max_len, min_len = max(lens), min(lens)
# if max_len != min_len:
# raise Exception(f"Unify error: curves have different number of control points: {lens}")
src_points = np.array(src_points)
#print("Src:", src_points)
src_points = np.transpose(src_points, axes=(1, 0, 2))
v_curves = [
interpolate_nurbs_curve(curve_class,
degree_v,
points,
metric=metric,
tknots=tknots) for points in src_points
]
control_points = [
curve.get_homogenous_control_points() for curve in v_curves
]
control_points = np.array(control_points)
#weights = [curve.get_weights() for curve in v_curves]
#weights = np.array([curve.get_weights() for curve in curves]).T
n, m, ndim = control_points.shape
control_points = control_points.reshape((n * m, ndim))
control_points, weights = from_homogenous(control_points)
control_points = control_points.reshape((n, m, 3))
weights = weights.reshape((n, m))
mean_v_vector = control_points.mean(axis=0)
tknots_v = Spline.create_knots(mean_v_vector, metric=metric)
knotvector_v = sv_knotvector.from_tknots(degree_v, tknots_v)
if knots_u == 'UNIFY':
knotvector_u = curves[0].get_knotvector()
else:
knotvectors = np.array([curve.get_knotvector() for curve in curves])
knotvector_u = knotvectors.mean(axis=0)
surface = SvNurbsSurface.build(implementation, degree_u, degree_v,
knotvector_u, knotvector_v, control_points,
weights)
surface.u_bounds = curves[0].get_u_bounds()
return curves, v_curves, surface
