def fit_plane_scipy(P=None):
from skspatial.objects import Points, Plane
from skspatial.plotting import plot_3d
points = Points([[0, 0, 0], [1, 3, 5], [-5, 6, 3], [3, 6, 7], [-2, 6, 7]
]) if P is None else Points(P)
plane = Plane.best_fit(points)
plot_3d(
points.plotter(c='k', s=0.1, depthshade=False),
plane.plotter(alpha=0.8, lims_x=(-5, 5), lims_y=(-5, 5)),
)
plt.show()
"""
3D Line of Best Fit
===================
Fit a line to multiple 3D points.
"""
from skspatial.objects import Line
from skspatial.objects import Points
from skspatial.plotting import plot_3d
points = Points([
[0, 0, 0],
[1, 1, 0],
[2, 3, 2],
[3, 2, 3],
[4, 5, 4],
[6, 5, 5],
[6, 6, 5],
[7, 6, 7],
], )
line_fit = Line.best_fit(points)
plot_3d(
line_fit.plotter(t_1=-7, t_2=7, c='k'),
points.plotter(c='b', depthshade=False),
)
"""
3D Plane of Best Fit
====================
Fit a plane to multiple 3D points.
"""
from skspatial.objects import Plane
from skspatial.objects import Points
from skspatial.plotting import plot_3d
points = Points([[0, 0, 0], [1, 3, 5], [-5, 6, 3], [3, 6, 7], [-2, 6, 7]])
plane = Plane.best_fit(points)
plot_3d(
points.plotter(c='k', s=50, depthshade=False),
plane.plotter(alpha=0.2, lims_x=(-5, 5), lims_y=(-5, 5)),
)
"""
Sphere-Line Intersection
========================
"""
from skspatial.objects import Sphere, Line
from skspatial.plotting import plot_3d
sphere = Sphere([0, 0, 0], 1)
line = Line([0, 0, 0], [1, 1, 1])
point_a, point_b = sphere.intersect_line(line)
plot_3d(
line.plotter(t_1=-1, c='k'),
sphere.plotter(alpha=0.2),
point_a.plotter(c='r', s=100),
point_b.plotter(c='r', s=100),
)
"""
3D Line-Line Intersection
=========================
"""
from skspatial.objects import Line
from skspatial.plotting import plot_3d
line_a = Line(point=[0, 0, 0], direction=[1, 1, 1])
line_b = Line(point=[1, 1, 0], direction=[-1, -1, 1])
point_intersection = line_a.intersect_line(line_b)
plot_3d(
line_a.plotter(),
line_b.plotter(),
point_intersection.plotter(c='k', s=75),
)
"""
Vector-Plane Projection
=======================
Project a vector onto a plane.
"""
from skspatial.objects import Plane
from skspatial.objects import Vector
from skspatial.plotting import plot_3d
plane = Plane([0, 0, 0], [0, 0, 1])
vector = Vector([1, 1, 1])
vector_projected = plane.project_vector(vector)
_, ax = plot_3d(
plane.plotter(lims_x=(-5, 5), lims_y=(-5, 5), alpha=0.3),
vector.plotter(point=plane.point, color='k'),
vector_projected.plotter(point=plane.point,
color='r',
linewidth=2,
zorder=3),
)
ax.set_zlim([-1, 1])
"""
3D Vector-Line Projection
=========================
Project a vector onto a line.
"""
from skspatial.objects import Vector, Line
from skspatial.plotting import plot_3d
line = Line([0, 0, 0], [1, 1, 2])
vector = Vector([1, 1, 0.1])
vector_projected = line.project_vector(vector)
plot_3d(
line.plotter(t_1=-1, c='k', linestyle='--'),
vector.plotter(point=line.point, color='k'),
vector_projected.plotter(point=line.point,
color='r',
linewidth=2,
zorder=3),
)
"""
Plane-Line Intersection
=======================
"""
from skspatial.objects import Line, Plane
from skspatial.plotting import plot_3d
plane = Plane(point=[0, 0, 0], normal=[1, 1, 1])
line = Line(point=[-1, -1, 0], direction=[0, 0, 1])
point_intersection = plane.intersect_line(line)
plot_3d(
plane.plotter(lims_x=[-2, 2], lims_y=[-2, 2], alpha=0.2),
line.plotter(t_2=5),
point_intersection.plotter(c='k', s=75),
)
cordi_after = np.zeros_like(cordi)
for i in range(len(cordi)):
point_tem = plane.project_point(cordi[i])
cordi_after[i] = np.array(point_tem)
# print(cordi_after)
points_after = Points(cordi_after)
# print(points)
# print(type(points))
plot_3d(
points_after.plotter(c='k', s=5, depthshade=False),
plane.plotter(alpha=0.2, lims_x=(-1, 1), lims_y=(-1, 1)),
)
# fig = plt.figure()
# ax = Axes3D(fig)
# ax.scatter(cordi[:, 0], cordi[:, 1], cordi[:, 2])
# plt.show()
def rotation(normal_vector_, support_vector):
a = np.array(normal_vector_)
b = np.array(support_vector)
theta_ = np.arccos(np.dot(a, b) / (np.linalg.norm(a) * np.linalg.norm(b)))
rotation_axis = np.cross(a, b)
"""
Point-Plane Projection
======================
Project a point onto a plane.
"""
from skspatial.objects import Plane
from skspatial.objects import Point
from skspatial.objects import Vector
from skspatial.plotting import plot_3d
plane = Plane(point=[0, 0, 2], normal=[1, 0, 2])
point = Point([5, 9, 3])
point_projected = plane.project_point(point)
vector_projection = Vector.from_points(point, point_projected)
plot_3d(
plane.plotter(lims_x=(0, 10), lims_y=(0, 15), alpha=0.3),
point.plotter(s=75, c='k'),
point_projected.plotter(c='r', s=75, zorder=3),
vector_projection.plotter(point=point, c='k', linestyle='--'),
)
"""
Plane-Plane Intersection
========================
"""
from skspatial.objects import Plane
from skspatial.plotting import plot_3d
plane_a = Plane([0, 0, 0], [1, 0, 0])
plane_b = Plane([0, 0, 0], [1, 0, 1])
line_intersection = plane_a.intersect_plane(plane_b)
plot_3d(
plane_a.plotter(alpha=0.2),
plane_b.plotter(alpha=0.2),
line_intersection.plotter(t_1=-1, c='k'),
)
