def make_section(self, apex, cone_dir, alpha, cone_gen, count,
plane_center, plane_dir, maxd):
apex = Vector(apex)
cone_dir = Vector(cone_dir)
plane_dir = Vector(plane_dir)
cone_dir2 = cone_dir.orthogonal()
if self.cone_mode == 'ANGLE':
cone_vector = rotate_vector_around_vector(cone_dir, cone_dir2,
alpha)
else:
cone_vector = Vector(cone_gen)
theta = 2 * pi / count
angle = 0
plane = PlaneEquation.from_normal_and_point(plane_dir, plane_center)
cone_ort_plane = PlaneEquation.from_normal_and_point(cone_dir, apex)
def get_branch(v):
return cone_ort_plane.side_of_point(v) > 0
if plane.side_of_point(apex) == 0 or (
plane_dir.cross(cone_dir)).length < 1e-10:
def get_side(v):
return True
else:
apex_projection = plane.projection_of_point(apex)
apex_ort = apex_projection - apex
cone_sagital_plane = PlaneEquation.from_point_and_two_vectors(
apex, apex_ort, cone_dir)
def get_side(v):
return cone_sagital_plane.side_of_point(v) > 0
vertices = []
branch_mask = []
side_mask = []
breaks = []
i = 0
while angle < 2 * pi:
cone_line = LineEquation.from_direction_and_point(
cone_vector, apex)
vertex = plane.intersect_with_line(cone_line, min_det=1e-10)
if vertex is not None and (vertex - apex).length <= maxd:
vertices.append(tuple(vertex))
branch = get_branch(vertex)
side = get_side(vertex)
branch_mask.append(branch)
side_mask.append(side)
i += 1
else:
breaks.append(i)
cone_vector = rotate_vector_around_vector(cone_vector, cone_dir,
theta)
angle += theta
return SectionData(vertices, branch_mask, side_mask, get_branch,
get_side, breaks)
def test_intersect_with_plane(self):
plane1 = PlaneEquation.from_coordinate_plane('XY')
plane2 = PlaneEquation.from_coordinate_plane('XZ')
line = plane1.intersect_with_plane(plane2)
self.assert_sverchok_data_equal(tuple(line.direction.normalized()),
(1, 0, 0))
self.assert_sverchok_data_equal(tuple(line.point), (0, 0, 0))
def _pre_calc(self):
curve = self.curve
t_min, t_max = curve.get_u_bounds()
ts = np.linspace(t_min, t_max, num=self.resolution)
points = curve.evaluate_array(ts)
tangents, normals, binormals = curve.tangent_normal_binormal_array(ts)
tangents /= np.linalg.norm(tangents, axis=1, keepdims=True)
normal = normals[0]
if np.linalg.norm(normal) > 1e-4:
binormal = binormals[0]
binormal /= np.linalg.norm(binormal)
else:
tangent = tangents[0]
normal = Vector(tangent).orthogonal()
normal = np.array(normal)
binormal = np.cross(tangent, normal)
binormal /= np.linalg.norm(binormal)
out_normals = [normal]
out_binormals = [binormal]
for point, tangent in zip(points[1:], tangents[1:]):
plane = PlaneEquation.from_normal_and_point(Vector(tangent), Vector(point))
normal = plane.projection_of_vector(Vector(point), Vector(point + normal))
normal = np.array(normal.normalized())
binormal = np.cross(tangent, normal)
binormal /= np.linalg.norm(binormal)
out_normals.append(normal)
out_binormals.append(binormal)
self.quats = self._make_quats(points, tangents, np.array(out_normals), np.array(out_binormals))
self.tknots = ts
def to_curve(point, curve, u1, u2, raycast=None):
if support_nurbs and is_nurbs and raycast is not None:
segment = curve.cut_segment(u1, u2)
surface_u, surface_v = raycast.us[0], raycast.vs[0]
point_on_surface = raycast.points[0]
surface_normal = surface.normal(surface_u, surface_v)
plane = PlaneEquation.from_normal_and_point(
surface_normal, point_on_surface)
r = intersect_curve_plane_nurbs(segment,
plane,
init_samples=2,
tolerance=tolerance,
maxiter=maxiter)
if not r:
return None
else:
return r[0]
else:
ortho = ortho_project_curve(point,
curve,
subdomain=(u1, u2),
init_samples=2,
on_fail=RETURN_NONE)
if ortho is None:
return None
else:
return ortho.nearest_u, ortho.nearest
def test_nearest_to_origin(self):
p1 = (1, 0, 0)
p2 = (0, 1, 0)
p3 = (0, 0, 1)
plane = PlaneEquation.from_three_points(p1, p2, p3)
p = plane.nearest_point_to_origin()
self.assert_sverchok_data_equal(tuple(p), (0.3333, 0.3333, 0.3333), precision=4)
def process(self):
if not any(socket.is_linked for socket in self.outputs):
return
curves_s = self.inputs['Curve'].sv_get()
point_s = self.inputs['Point'].sv_get()
normal_s = self.inputs['Normal'].sv_get()
curves_s = ensure_nesting_level(curves_s,
2,
data_types=(SvCurve, ))
points_out = []
for curves, points, normals in zip_long_repeat(
curves_s, point_s, normal_s):
new_points = []
for curve, point, normal in zip_long_repeat(
curves, points, normals):
plane = PlaneEquation.from_normal_and_point(normal, point)
ps = intersect_curve_plane(curve,
plane,
init_samples=self.samples,
ortho_samples=self.samples)
new_points.extend(ps)
points_out.append(new_points)
self.outputs['Point'].sv_set(points_out)
def test_projection_2(self):
p1 = (1, 0, 0)
p2 = (0, 1, 0)
p3 = (0, 0, 1)
plane = PlaneEquation.from_three_points(p1, p2, p3)
point = (3, 3, 3)
result = plane.projection_of_point(point)
self.assert_sverchok_data_equal(tuple(result), (0.3333, 0.3333, 0.3333), precision=4)
def _faces_by_plane(self, topo, center, direction, radius):
plane = PlaneEquation.from_normal_and_point(direction, center)
def condition(points):
distances = plane.distance_to_points(points)
return distances < radius
return topo.get_faces_by_location_mask(condition, self.include_partial)
def test_nearest_to_origin(self):
p1 = (1, 0, 0)
p2 = (0, 1, 0)
p3 = (0, 0, 1)
plane = PlaneEquation.from_three_points(p1, p2, p3)
p = plane.nearest_point_to_origin()
self.assert_sverchok_data_equal(tuple(p), (0.3333, 0.3333, 0.3333),
precision=4)
def __init__(self, curve, point, normal, coefficient):
self.curve = curve
self.point = point
self.normal = normal
self.coefficient = coefficient
self.plane = PlaneEquation.from_normal_and_point(normal, point)
self.tangent_delta = 0.001
self.__description__ = "{} casted to Plane".format(curve)
def test_plane_from_three_points(self):
p1 = (1, 0, 0)
p2 = (0, 1, 0)
p3 = (0, 0, 1)
plane = PlaneEquation.from_three_points(p1, p2, p3)
self.assertEquals(plane.a, 1)
self.assertEquals(plane.b, 1)
self.assertEquals(plane.c, 1)
self.assertEquals(plane.d, -1)
def test_projection_3(self):
plane = PlaneEquation.from_coordinate_plane('XY')
point1 = (1, 2, 3)
point2 = (4, 5, 6)
point3 = (7, 8, 9)
point4 = (2, 5, 9)
result = plane.projection_of_points([point1, point2, point3, point4])
expected = np.array([[1, 2, 0], [4, 5, 0], [7, 8, 0], [2, 5, 0]])
self.assert_numpy_arrays_equal(result, expected)
def test_projection_3(self):
plane = PlaneEquation.from_coordinate_plane('XY')
point1 = (1, 2, 3)
point2 = (4, 5, 6)
point3 = (7, 8, 9)
point4 = (2, 5, 9)
result = plane.projection_of_points([point1, point2, point3, point4])
expected = np.array([[1, 2, 0], [4, 5, 0], [7, 8, 0], [2, 5, 0]])
self.assert_numpy_arrays_equal(result, expected)
def test_plane_from_three_points(self):
p1 = (1, 0, 0)
p2 = (0, 1, 0)
p3 = (0, 0, 1)
plane = PlaneEquation.from_three_points(p1, p2, p3)
self.assertEquals(plane.a, 1)
self.assertEquals(plane.b, 1)
self.assertEquals(plane.c, 1)
self.assertEquals(plane.d, -1)
def test_projection_2(self):
p1 = (1, 0, 0)
p2 = (0, 1, 0)
p3 = (0, 0, 1)
plane = PlaneEquation.from_three_points(p1, p2, p3)
point = (3, 3, 3)
result = plane.projection_of_point(point)
self.assert_sverchok_data_equal(tuple(result),
(0.3333, 0.3333, 0.3333),
precision=4)
def test_two_vectors(self):
p1 = (2, 0, 0)
p2 = (0, 1, 0)
p3 = (0, 0, 2)
plane = PlaneEquation.from_three_points(p1, p2, p3)
normal = plane.normal
v1, v2 = plane.two_vectors()
self.assertTrue(abs(normal.dot(v1)) < 1e-8)
self.assertTrue(abs(normal.dot(v2)) < 1e-8)
self.assertTrue(abs(v1.dot(v2)) < 1e-8)
def get_ridges_per_site(voronoi):
result = defaultdict(list)
for ridge_idx in range(len(voronoi.ridge_points)):
site1_idx, site2_idx = tuple(voronoi.ridge_points[ridge_idx])
site1 = voronoi.points[site1_idx]
site2 = voronoi.points[site2_idx]
middle = (site1 + site2) * 0.5
normal = site2 - site1
plane = PlaneEquation.from_normal_and_point(normal, middle)
result[site1_idx].append(plane)
result[site2_idx].append(plane)
return result
def test_two_vectors(self):
p1 = (2, 0, 0)
p2 = (0, 1, 0)
p3 = (0, 0, 2)
plane = PlaneEquation.from_three_points(p1, p2, p3)
normal = plane.normal
v1, v2 = plane.two_vectors()
self.assertTrue(abs(normal.dot(v1)) < 1e-8)
self.assertTrue(abs(normal.dot(v2)) < 1e-8)
self.assertTrue(abs(v1.dot(v2)) < 1e-8)
def test_projection_4(self):
p1 = (1, 0, 0)
p2 = (0, 1, 0)
p3 = (0, 0, 1)
plane = PlaneEquation.from_three_points(p1, p2, p3)
point1 = (-3, -3, -3)
point2 = (2, 1, 1)
point3 = (1, 1, 2)
point4 = (1, 2, 1)
result = plane.projection_of_points([point1, point2, point3, point4])
expected = np.array([[0.3333, 0.3333, 0.3333], [1,0,0], [0, 0, 1], [0, 1, 0]])
info(result)
self.assert_numpy_arrays_equal(result, expected, precision=4)
def test_projection_4(self):
p1 = (1, 0, 0)
p2 = (0, 1, 0)
p3 = (0, 0, 1)
plane = PlaneEquation.from_three_points(p1, p2, p3)
point1 = (-3, -3, -3)
point2 = (2, 1, 1)
point3 = (1, 1, 2)
point4 = (1, 2, 1)
result = plane.projection_of_points([point1, point2, point3, point4])
expected = np.array([[0.3333, 0.3333, 0.3333], [1, 0, 0], [0, 0, 1],
[0, 1, 0]])
info(result)
self.assert_numpy_arrays_equal(result, expected, precision=4)
def process(self):
if not any(socket.is_linked for socket in self.outputs):
return
curves_s = self.inputs['Curve'].sv_get()
point_s = self.inputs['Point'].sv_get()
normal_s = self.inputs['Normal'].sv_get()
curves_s = ensure_nesting_level(curves_s,
2,
data_types=(SvCurve, ))
points_out = []
t_out = []
tolerance = 10**(-self.accuracy)
for curves, points, normals in zip_long_repeat(
curves_s, point_s, normal_s):
new_points = []
new_ts = []
for curve, point, normal in zip_long_repeat(
curves, points, normals):
method = EQUATION
if self.use_nurbs:
c = SvNurbsCurve.to_nurbs(curve)
if c is not None:
curve = c
method = NURBS
plane = PlaneEquation.from_normal_and_point(normal, point)
ps = intersect_curve_plane(curve,
plane,
method=method,
init_samples=self.samples,
tolerance=tolerance)
ts = [p[0] for p in ps]
points = [p[1].tolist() for p in ps]
if self.join:
new_points.extend(points)
new_ts.extend(ts)
else:
new_points.append(points)
new_ts.append(ts)
points_out.append(new_points)
t_out.append(new_ts)
self.outputs['Point'].sv_set(points_out)
self.outputs['T'].sv_set(t_out)
def _cast_nurbs(self, curve, center, direction, radius, coeff):
curve = SvNurbsCurve.to_nurbs(curve)
if curve is None:
raise Exception("Provided curve is not a NURBS")
if self.form == 'PLANE':
target = PlaneEquation.from_normal_and_point(direction, center)
elif self.form == 'SPHERE':
target = SphereEquation(center, radius)
elif self.form == 'CYLINDER':
target = CylinderEquation.from_point_direction_radius(center, direction, radius)
else:
raise Exception("Unsupported target form")
return cast_nurbs_curve(curve, target, coeff=coeff)
def process(self):
if not any(socket.is_linked for socket in self.outputs):
return
surfaces_s = self.inputs['Surface'].sv_get()
point_s = self.inputs['Point'].sv_get()
normal_s = self.inputs['Normal'].sv_get()
samples_u_s = self.inputs['SamplesU'].sv_get()
samples_v_s = self.inputs['SamplesV'].sv_get()
surfaces_s = ensure_nesting_level(surfaces_s,
2,
data_types=(SvSurface, ))
need_points = self.outputs['Points'].is_linked
uv_out = []
points_out = []
for surfaces, points, normals, samples_u_i, samples_v_i in zip_long_repeat(
surfaces_s, point_s, normal_s, samples_u_s, samples_v_s):
uv_new = []
points_new = []
for surface, point, normal, samples_u, samples_v in zip_long_repeat(
surfaces, points, normals, samples_u_i, samples_v_i):
plane = PlaneEquation.from_normal_and_point(normal, point)
if self.algorithm == 'skimage':
uv_new, points_new = intersect_surface_plane_msquares(
surface,
plane,
need_points=need_points,
samples_u=samples_u,
samples_v=samples_v)
else:
points_new = intersect_surface_plane_uv(
surface,
plane,
samples_u=samples_u,
samples_v=samples_v,
init_samples=self.init_samples,
ortho_samples=self.init_samples)
points_new = [points_new]
uv_out.extend(uv_new)
points_out.extend(points_new)
self.outputs['Points'].sv_set(points_out)
self.outputs['UVPoints'].sv_set(uv_out)
def cut_cell(verts, faces, planes, site):
src_mesh = bmesh_from_pydata(verts, [], faces, normal_update=True)
n_cuts = 0
for plane in planes:
if len(src_mesh.verts) == 0:
break
geom_in = src_mesh.verts[:] + src_mesh.edges[:] + src_mesh.faces[:]
plane_co = plane.projection_of_point(site)
plane_no = plane.normal.normalized()
if plane.side_of_point(site) > 0:
plane_no = -plane_no
plane_co = plane_co - 0.5 * spacing * plane_no
current_verts = np.array([tuple(v.co) for v in src_mesh.verts])
signs = PlaneEquation.from_normal_and_point(
plane_no, plane_co).side_of_points(current_verts)
#print(f"Plane co {plane_co}, no {plane_no}, signs {signs}")
if (signs <= 0).all(): # or (signs <= 0).all():
continue
res = bmesh.ops.bisect_plane(src_mesh,
geom=geom_in,
dist=precision,
plane_co=plane_co,
plane_no=plane_no,
use_snap_center=False,
clear_outer=True,
clear_inner=False)
n_cuts += 1
if fill:
surround = [
e for e in res['geom_cut']
if isinstance(e, bmesh.types.BMEdge)
]
if surround:
fres = bmesh.ops.edgenet_prepare(src_mesh, edges=surround)
if fres['edges']:
bmesh.ops.edgeloop_fill(src_mesh, edges=fres['edges'])
if n_cuts == 0:
return None
return pydata_from_bmesh(src_mesh)
def matrix_to_curve(curve,
matrix,
z_axis,
init_samples=10,
tolerance=1e-3,
maxiter=50):
plane = PlaneEquation.from_matrix(matrix, normal_axis=z_axis)
# Or take nearest point?
solutions = intersect_curve_plane(curve,
plane,
init_samples=init_samples,
tolerance=tolerance,
maxiter=maxiter)
t, point = nearest_solution(matrix.translation, solutions)
if t is None:
raise Exception(
f"Can't project the matrix {matrix} to the {curve}!")
#matrix.translation = Vector(point)
return t, matrix.to_quaternion()
def process(self):
if not any(socket.is_linked for socket in self.outputs):
return
vertices_s = self.inputs['Vertices'].sv_get()
edges_s = self.inputs['Edges'].sv_get()
faces_s = self.inputs['Faces'].sv_get()
vertex_weight_s = self.inputs['VertexWeight'].sv_get()
edge_weight_s = self.inputs['EdgeWeight'].sv_get()
face_weight_s = self.inputs['FaceWeight'].sv_get()
tangent_weight_s = self.inputs['TangentWeight'].sv_get()
degree_u_s = self.inputs['DegreeU'].sv_get()
degree_v_s = self.inputs['DegreeV'].sv_get()
surface_out = []
control_points_out = []
weights_out = []
inputs = zip_long_repeat(vertices_s, edges_s, faces_s, degree_u_s,
degree_v_s, vertex_weight_s,
edge_weight_s, face_weight_s,
tangent_weight_s)
for vertices, edges, faces, degree_u, degree_v, vertex_weights, edge_weights, face_weights, tangent_weights in inputs:
fullList(degree_u, len(faces))
fullList(degree_v, len(faces))
if not edges:
edges = polygons_to_edges([faces], True)[0]
fullList(vertex_weights, len(vertices))
fullList(tangent_weights, len(vertices))
fullList(edge_weights, len(edges))
fullList(face_weights, len(faces))
bm = bmesh_from_pydata(vertices,
edges,
faces,
normal_update=True,
markup_edge_data=True)
normals = [vertex.normal for vertex in bm.verts]
edge_planes_dict = dict()
for edge in bm.edges:
edge_v = edge.verts[1].co - edge.verts[0].co
edge_c = (edge.verts[0].co + edge.verts[1].co) / 2.0
edge_ort_plane = PlaneEquation.from_normal_and_point(
edge_v, edge_c)
face_normals = [face.normal for face in edge.link_faces]
faces_normal = sum(face_normals, Vector())
projected_faces_normal = edge_ort_plane.projection_of_point(
faces_normal)
#print("EV: %s, No.sum: %s, Pr.N: %s" % (edge_v, faces_normal, projected_faces_normal))
edge_plane = PlaneEquation.from_normal_and_point(
projected_faces_normal, edge_c)
edge_planes_dict[(edge.verts[0].index,
edge.verts[1].index)] = edge_plane
edge_planes_dict[(edge.verts[1].index,
edge.verts[0].index)] = edge_plane
bm.free()
vert_planes = [
PlaneEquation.from_normal_and_point(normal, point)
for normal, point in zip(normals, vertices)
]
edge_weights_dict = dict()
#edge_planes_dict = dict()
for (i, j), edge_weight in zip(edges, edge_weights):
edge_weights_dict[(i, j)] = edge_weight
edge_weights_dict[(j, i)] = edge_weight
#edge_planes_dict[(i, j)] = edge_plane
#edge_planes_dict[(j, i)] = edge_plane
for i, (face, degree_u, degree_v, face_weight) in enumerate(
zip(faces, degree_u, degree_v, face_weights)):
if len(face) != 4:
self.info("Face #%s is not a Quad, skip it", i)
continue
face_verts = [vertices[i] for i in face]
face_planes = [vert_planes[i] for i in face]
face_vert_weights = [vertex_weights[i] for i in face]
face_tangent_weights = [tangent_weights[i] for i in face]
#face_edges = list(zip(face, face[1:])) + [(face[-1], face[0])]
#face_edge_weights = [edge_weights_dict[edge] for edge in face_edges]
surface, ctrlpts, weights = self.make_surface(
face, degree_u, degree_v, face_verts, face_planes,
face_vert_weights, face_tangent_weights, face_weight,
edge_weights_dict, edge_planes_dict)
surface_out.append(surface)
control_points_out.append(list(map(tuple, ctrlpts)))
weights_out.append(weights)
self.outputs['Surfaces'].sv_set(surface_out)
self.outputs['ControlPoints'].sv_set(control_points_out)
self.outputs['Weights'].sv_set(weights_out)
def _verts_by_plane(self, topo, center, direction, radius):
plane = PlaneEquation.from_normal_and_point(direction, center)
condition = lambda v: plane.distance_to_point(v) < radius
return topo.get_vertices_by_location_mask(condition)
def test_projection_1(self):
plane = PlaneEquation.from_coordinate_plane('XY')
point = (1, 2, 3)
result = plane.projection_of_point(point)
self.assert_sverchok_data_equal(tuple(result), (1, 2, 0))
def test_intersect_with_line(self):
plane = PlaneEquation.from_coordinate_plane('XY')
line = LineEquation.from_direction_and_point((1, 1, 1), (1, 1, 1))
point = plane.intersect_with_line(line)
self.assert_sverchok_data_equal(tuple(point), (0, 0, 0))
def test_check_no(self):
plane = PlaneEquation.from_coordinate_plane('XY')
p = (7, 8, 1)
self.assertFalse(plane.check(p))
def test_check_yes(self):
plane = PlaneEquation.from_coordinate_plane('XY')
p = (7, 8, 0)
self.assertTrue(plane.check(p))
def test_check_yes(self):
plane = PlaneEquation.from_coordinate_plane('XY')
p = (7, 8, 0)
self.assertTrue(plane.check(p))
def test_intersect_with_plane(self):
plane1 = PlaneEquation.from_coordinate_plane('XY')
plane2 = PlaneEquation.from_coordinate_plane('XZ')
line = plane1.intersect_with_plane(plane2)
self.assert_sverchok_data_equal(tuple(line.direction.normalized()), (1, 0, 0))
self.assert_sverchok_data_equal(tuple(line.point), (0, 0, 0))
def test_check_no(self):
plane = PlaneEquation.from_coordinate_plane('XY')
p = (7, 8, 1)
self.assertFalse(plane.check(p))
def test_projection_1(self):
plane = PlaneEquation.from_coordinate_plane('XY')
point = (1, 2, 3)
result = plane.projection_of_point(point)
self.assert_sverchok_data_equal(tuple(result), (1, 2, 0))
def test_distance_to_points(self):
plane = PlaneEquation.from_coordinate_plane('XY')
points = [(1, 2, 3), (4, 5, 6)]
distances = plane.distance_to_points(points)
self.assert_numpy_arrays_equal(distances, np.array([3, 6]))
def test_intersect_with_line(self):
plane = PlaneEquation.from_coordinate_plane('XY')
line = LineEquation.from_direction_and_point((1, 1, 1), (1, 1, 1))
point = plane.intersect_with_line(line)
self.assert_sverchok_data_equal(tuple(point), (0, 0, 0))
def test_distance_to_point(self):
plane = PlaneEquation.from_coordinate_plane('XY')
point = (1, 2, 3)
distance = plane.distance_to_point(point)
self.assertEquals(distance, 3)
def test_distance_to_point(self):
plane = PlaneEquation.from_coordinate_plane('XY')
point = (1, 2, 3)
distance = plane.distance_to_point(point)
self.assertEquals(distance, 3)
def test_distance_to_points(self):
plane = PlaneEquation.from_coordinate_plane('XY')
points = [(1, 2, 3), (4, 5, 6)]
distances = plane.distance_to_points(points)
self.assert_numpy_arrays_equal(distances, np.array([3, 6]))