"""Three-dimensional mobjects."""
from __future__ import annotations
__all__ = [
"ThreeDVMobject",
"Surface",
"Sphere",
"Dot3D",
"Cube",
"Prism",
"Cone",
"Arrow3D",
"Cylinder",
"Line3D",
"Torus",
]
from typing import *
import numpy as np
from colour import Color
from manim import config, logger
from manim.constants import *
from manim.mobject.geometry.arc import Circle
from manim.mobject.geometry.polygram import Square
from manim.mobject.mobject import *
from manim.mobject.opengl.opengl_compatibility import ConvertToOpenGL
from manim.mobject.opengl.opengl_mobject import OpenGLMobject
from manim.mobject.types.vectorized_mobject import VGroup, VMobject
from manim.utils.color import *
from manim.utils.color import Colors
from manim.utils.deprecation import deprecated_params
from manim.utils.iterables import tuplify
from manim.utils.space_ops import normalize, perpendicular_bisector, z_to_vector
[docs]class ThreeDVMobject(VMobject, metaclass=ConvertToOpenGL):
def __init__(self, shade_in_3d=True, **kwargs):
super().__init__(shade_in_3d=shade_in_3d, **kwargs)
[docs]class Surface(VGroup, metaclass=ConvertToOpenGL):
"""Creates a Parametric Surface using a checkerboard pattern.
Parameters
----------
func
The function defining the :class:`Surface`.
u_range
The range of the ``u`` variable: ``(u_min, u_max)``.
v_range
The range of the ``v`` variable: ``(v_min, v_max)``.
resolution
The number of samples taken of the :class:`Surface`. A tuple can be
used to define different resolutions for ``u`` and ``v`` respectively.
fill_color
The color of the :class:`Surface`. Ignored if ``checkerboard_colors``
is set.
fill_opacity
The opacity of the :class:`Surface`, from 0 being fully transparent
to 1 being fully opaque. Defaults to 1.
checkerboard_colors
Colors individual faces alternating colors. Overrides ``fill_color``.
stroke_color
Color of the stroke surrounding each face of :class:`Surface`.
stroke_width
Width of the stroke surrounding each face of :class:`Surface`.
Defaults to 0.5.
should_make_jagged
Changes the anchor mode of the Bézier curves from smooth to jagged.
Defaults to ``False``.
Examples
--------
.. manim:: ParaSurface
:save_last_frame:
class ParaSurface(ThreeDScene):
def func(self, u, v):
return np.array([np.cos(u) * np.cos(v), np.cos(u) * np.sin(v), u])
def construct(self):
axes = ThreeDAxes(x_range=[-4,4], x_length=8)
surface = Surface(
lambda u, v: axes.c2p(*self.func(u, v)),
u_range=[-PI, PI],
v_range=[0, TAU],
resolution=8,
)
self.set_camera_orientation(theta=70 * DEGREES, phi=75 * DEGREES)
self.add(axes, surface)
"""
def __init__(
self,
func: Callable[[float, float], np.ndarray],
u_range: Sequence[float] = [0, 1],
v_range: Sequence[float] = [0, 1],
resolution: Sequence[int] = 32,
surface_piece_config: dict = {},
fill_color: Color = BLUE_D,
fill_opacity: float = 1.0,
checkerboard_colors: Sequence[Color] = [BLUE_D, BLUE_E],
stroke_color: Color = LIGHT_GREY,
stroke_width: float = 0.5,
should_make_jagged: bool = False,
pre_function_handle_to_anchor_scale_factor: float = 0.00001,
**kwargs,
) -> None:
self.u_range = u_range
self.v_range = v_range
super().__init__(**kwargs)
self.resolution = resolution
self.surface_piece_config = surface_piece_config
self.fill_color = fill_color
self.fill_opacity = fill_opacity
self.checkerboard_colors = checkerboard_colors
self.stroke_color = stroke_color
self.stroke_width = stroke_width
self.should_make_jagged = should_make_jagged
self.pre_function_handle_to_anchor_scale_factor = (
pre_function_handle_to_anchor_scale_factor
)
self._func = func
self._setup_in_uv_space()
self.apply_function(lambda p: func(p[0], p[1]))
if self.should_make_jagged:
self.make_jagged()
def func(self, u: float, v: float):
return self._func(u, v)
def _get_u_values_and_v_values(self):
res = tuplify(self.resolution)
if len(res) == 1:
u_res = v_res = res[0]
else:
u_res, v_res = res
u_values = np.linspace(*self.u_range, u_res + 1)
v_values = np.linspace(*self.v_range, v_res + 1)
return u_values, v_values
def _setup_in_uv_space(self):
u_values, v_values = self._get_u_values_and_v_values()
faces = VGroup()
for i in range(len(u_values) - 1):
for j in range(len(v_values) - 1):
u1, u2 = u_values[i : i + 2]
v1, v2 = v_values[j : j + 2]
face = ThreeDVMobject()
face.set_points_as_corners(
[
[u1, v1, 0],
[u2, v1, 0],
[u2, v2, 0],
[u1, v2, 0],
[u1, v1, 0],
],
)
faces.add(face)
face.u_index = i
face.v_index = j
face.u1 = u1
face.u2 = u2
face.v1 = v1
face.v2 = v2
faces.set_fill(color=self.fill_color, opacity=self.fill_opacity)
faces.set_stroke(
color=self.stroke_color,
width=self.stroke_width,
opacity=self.stroke_opacity,
)
self.add(*faces)
if self.checkerboard_colors:
self.set_fill_by_checkerboard(*self.checkerboard_colors)
[docs] def set_fill_by_checkerboard(self, *colors, opacity=None):
"""Sets the fill_color of each face of :class:`Surface` in
an alternating pattern.
Parameters
----------
colors
List of colors for alternating pattern.
opacity
The fill_opacity of :class:`Surface`, from 0 being fully transparent
to 1 being fully opaque.
Returns
-------
:class:`~.Surface`
The parametric surface with an alternating pattern.
"""
n_colors = len(colors)
for face in self:
c_index = (face.u_index + face.v_index) % n_colors
face.set_fill(colors[c_index], opacity=opacity)
return self
[docs] @deprecated_params("colors", since="v0.16.0")
def set_fill_by_value(
self,
axes: Mobject,
colorscale: Union[Iterable[Color], Color] | None = None,
axis: int = 2,
**kwargs,
):
"""Sets the color of each mobject of a parametric surface to a color
relative to its axis-value.
Parameters
----------
axes
The axes for the parametric surface, which will be used to map
axis-values to colors.
colorscale
A list of colors, ordered from lower axis-values to higher axis-values.
If a list of tuples is passed containing colors paired with numbers,
then those numbers will be used as the pivots.
axis
The chosen axis to use for the color mapping. (0 = x, 1 = y, 2 = z)
Returns
-------
:class:`~.Surface`
The parametric surface with a gradient applied by value. For chaining.
Examples
--------
.. manim:: FillByValueExample
:save_last_frame:
class FillByValueExample(ThreeDScene):
def construct(self):
resolution_fa = 8
self.set_camera_orientation(phi=75 * DEGREES, theta=-160 * DEGREES)
axes = ThreeDAxes(x_range=(0, 5, 1), y_range=(0, 5, 1), z_range=(-1, 1, 0.5))
def param_surface(u, v):
x = u
y = v
z = np.sin(x) * np.cos(y)
return z
surface_plane = Surface(
lambda u, v: axes.c2p(u, v, param_surface(u, v)),
resolution=(resolution_fa, resolution_fa),
v_range=[0, 5],
u_range=[0, 5],
)
surface_plane.set_style(fill_opacity=1)
surface_plane.set_fill_by_value(axes=axes, colorscale=[(RED, -0.5), (YELLOW, 0), (GREEN, 0.5)], axis=2)
self.add(axes, surface_plane)
"""
if "colors" in kwargs and colorscale is None:
colorscale = kwargs.pop("colors")
if kwargs:
raise ValueError(
"Unsupported keyword argument(s): "
f"{', '.join(str(key) for key in kwargs)}"
)
if colorscale is None:
logger.warning(
"The value passed to the colorscale keyword argument was None, "
"the surface fill color has not been changed"
)
return self
ranges = [axes.x_range, axes.y_range, axes.z_range]
if type(colorscale[0]) is tuple:
new_colors, pivots = [
[i for i, j in colorscale],
[j for i, j in colorscale],
]
else:
new_colors = colorscale
pivot_min = ranges[axis][0]
pivot_max = ranges[axis][1]
pivot_frequency = (pivot_max - pivot_min) / (len(new_colors) - 1)
pivots = np.arange(
start=pivot_min,
stop=pivot_max + pivot_frequency,
step=pivot_frequency,
)
for mob in self.family_members_with_points():
axis_value = axes.point_to_coords(mob.get_midpoint())[axis]
if axis_value <= pivots[0]:
mob.set_color(new_colors[0])
elif axis_value >= pivots[-1]:
mob.set_color(new_colors[-1])
else:
for i, pivot in enumerate(pivots):
if pivot > axis_value:
color_index = (axis_value - pivots[i - 1]) / (
pivots[i] - pivots[i - 1]
)
color_index = min(color_index, 1)
mob_color = interpolate_color(
new_colors[i - 1],
new_colors[i],
color_index,
)
if config.renderer == RendererType.OPENGL:
mob.set_color(mob_color, recurse=False)
elif config.renderer == RendererType.CAIRO:
mob.set_color(mob_color, family=False)
break
return self
# Specific shapes
[docs]class Sphere(Surface):
"""An three-dimensional sphere.
Parameters
----------
center
Center of the :class:`Sphere`.
radius
The radius of the :class:`Sphere`.
resolution
The number of samples taken of the :class:`Sphere`. A tuple can be used
to define different resolutions for ``u`` and ``v`` respectively.
u_range
The range of the ``u`` variable: ``(u_min, u_max)``.
v_range
The range of the ``v`` variable: ``(v_min, v_max)``.
Examples
--------
.. manim:: ExampleSphere
:save_last_frame:
class ExampleSphere(ThreeDScene):
def construct(self):
self.set_camera_orientation(phi=PI / 6, theta=PI / 6)
sphere1 = Sphere(
center=(3, 0, 0),
radius=1,
resolution=(20, 20),
u_range=[0.001, PI - 0.001],
v_range=[0, TAU]
)
sphere1.set_color(RED)
self.add(sphere1)
sphere2 = Sphere(center=(-1, -3, 0), radius=2, resolution=(18, 18))
sphere2.set_color(GREEN)
self.add(sphere2)
sphere3 = Sphere(center=(-1, 2, 0), radius=2, resolution=(16, 16))
sphere3.set_color(BLUE)
self.add(sphere3)
"""
def __init__(
self,
center=ORIGIN,
radius=1,
resolution=None,
u_range=(0, TAU),
v_range=(0, PI),
**kwargs,
):
if config.renderer == RendererType.OPENGL:
res_value = (101, 51)
elif config.renderer == RendererType.CAIRO:
res_value = (24, 12)
else:
raise Exception("Unknown renderer")
resolution = resolution if resolution is not None else res_value
self.radius = radius
super().__init__(
self.func,
resolution=resolution,
u_range=u_range,
v_range=v_range,
**kwargs,
)
self.shift(center)
def func(self, u, v):
return self.radius * np.array(
[np.cos(u) * np.sin(v), np.sin(u) * np.sin(v), -np.cos(v)],
)
[docs]class Dot3D(Sphere):
"""A spherical dot.
Parameters
----------
point
The location of the dot.
radius
The radius of the dot.
color
The color of the :class:`Dot3D`.
resolution
The number of samples taken of the :class:`Dot3D`. A tuple can be
used to define different resolutions for ``u`` and ``v`` respectively.
Examples
--------
.. manim:: Dot3DExample
:save_last_frame:
class Dot3DExample(ThreeDScene):
def construct(self):
self.set_camera_orientation(phi=75*DEGREES, theta=-45*DEGREES)
axes = ThreeDAxes()
dot_1 = Dot3D(point=axes.coords_to_point(0, 0, 1), color=RED)
dot_2 = Dot3D(point=axes.coords_to_point(2, 0, 0), radius=0.1, color=BLUE)
dot_3 = Dot3D(point=[0, 0, 0], radius=0.1, color=ORANGE)
self.add(axes, dot_1, dot_2,dot_3)
"""
def __init__(
self,
point: list | np.ndarray = ORIGIN,
radius: float = DEFAULT_DOT_RADIUS,
color: Colors = WHITE,
resolution=(8, 8),
**kwargs,
):
super().__init__(center=point, radius=radius, resolution=resolution, **kwargs)
self.set_color(color)
[docs]class Cube(VGroup):
"""A three-dimensional cube.
Parameters
----------
side_length
Length of each side of the :class:`Cube`.
fill_opacity
The opacity of the :class:`Cube`, from 0 being fully transparent to 1 being
fully opaque. Defaults to 0.75.
fill_color
The color of the :class:`Cube`.
stroke_width
The width of the stroke surrounding each face of the :class:`Cube`.
Examples
--------
.. manim:: CubeExample
:save_last_frame:
class CubeExample(ThreeDScene):
def construct(self):
self.set_camera_orientation(phi=75*DEGREES, theta=-45*DEGREES)
axes = ThreeDAxes()
cube = Cube(side_length=3, fill_opacity=0.7, fill_color=BLUE)
self.add(cube)
"""
def __init__(
self,
side_length=2,
fill_opacity=0.75,
fill_color=BLUE,
stroke_width=0,
**kwargs,
):
self.side_length = side_length
super().__init__(
fill_color=fill_color,
fill_opacity=fill_opacity,
stroke_width=stroke_width,
**kwargs,
)
[docs] def generate_points(self):
for vect in IN, OUT, LEFT, RIGHT, UP, DOWN:
face = Square(
side_length=self.side_length,
shade_in_3d=True,
)
face.flip()
face.shift(self.side_length * OUT / 2.0)
face.apply_matrix(z_to_vector(vect))
self.add(face)
init_points = generate_points
[docs]class Prism(Cube):
"""A right rectangular prism (or rectangular cuboid).
Defined by the length of each side in ``[x, y, z]`` format.
Parameters
----------
dimensions
Dimensions of the :class:`Prism` in ``[x, y, z]`` format.
Examples
--------
.. manim:: ExamplePrism
:save_last_frame:
class ExamplePrism(ThreeDScene):
def construct(self):
self.set_camera_orientation(phi=60 * DEGREES, theta=150 * DEGREES)
prismSmall = Prism(dimensions=[1, 2, 3]).rotate(PI / 2)
prismLarge = Prism(dimensions=[1.5, 3, 4.5]).move_to([2, 0, 0])
self.add(prismSmall, prismLarge)
"""
def __init__(self, dimensions=[3, 2, 1], **kwargs):
self.dimensions = dimensions
super().__init__(**kwargs)
[docs] def generate_points(self):
super().generate_points()
for dim, value in enumerate(self.dimensions):
self.rescale_to_fit(value, dim, stretch=True)
[docs]class Cone(Surface):
"""A circular cone.
Can be defined using 2 parameters: its height, and its base radius.
The polar angle, theta, can be calculated using arctan(base_radius /
height) The spherical radius, r, is calculated using the pythagorean
theorem.
Parameters
----------
base_radius
The base radius from which the cone tapers.
height
The height measured from the plane formed by the base_radius to
the apex of the cone.
direction
The direction of the apex.
show_base
Whether to show the base plane or not.
v_range
The azimuthal angle to start and end at.
u_min
The radius at the apex.
checkerboard_colors
Show checkerboard grid texture on the cone.
Examples
--------
.. manim:: ExampleCone
:save_last_frame:
class ExampleCone(ThreeDScene):
def construct(self):
axes = ThreeDAxes()
cone = Cone(direction=X_AXIS+Y_AXIS+2*Z_AXIS, resolution=8)
self.set_camera_orientation(phi=5*PI/11, theta=PI/9)
self.add(axes, cone)
"""
def __init__(
self,
base_radius: float = 1,
height: float = 1,
direction: np.ndarray = Z_AXIS,
show_base: bool = False,
v_range: Sequence[float] = [0, TAU],
u_min: float = 0,
checkerboard_colors: bool = False,
**kwargs,
):
self.direction = direction
self.theta = PI - np.arctan(base_radius / height)
super().__init__(
self.func,
v_range=v_range,
u_range=[u_min, np.sqrt(base_radius**2 + height**2)],
checkerboard_colors=checkerboard_colors,
**kwargs,
)
# used for rotations
self._current_theta = 0
self._current_phi = 0
if show_base:
self.base_circle = Circle(
radius=base_radius,
color=self.fill_color,
fill_opacity=self.fill_opacity,
stroke_width=0,
)
self.base_circle.shift(height * IN)
self.add(self.base_circle)
self._rotate_to_direction()
[docs] def func(self, u: float, v: float):
"""Converts from spherical coordinates to cartesian.
Parameters
----------
u
The radius.
v
The azimuthal angle.
"""
r = u
phi = v
return np.array(
[
r * np.sin(self.theta) * np.cos(phi),
r * np.sin(self.theta) * np.sin(phi),
r * np.cos(self.theta),
],
)
def _rotate_to_direction(self):
x, y, z = self.direction
r = np.sqrt(x**2 + y**2 + z**2)
if r > 0:
theta = np.arccos(z / r)
else:
theta = 0
if x == 0:
if y == 0: # along the z axis
phi = 0
else:
phi = np.arctan(np.inf)
if y < 0:
phi += PI
else:
phi = np.arctan(y / x)
if x < 0:
phi += PI
# Undo old rotation (in reverse order)
self.rotate(-self._current_phi, Z_AXIS, about_point=ORIGIN)
self.rotate(-self._current_theta, Y_AXIS, about_point=ORIGIN)
# Do new rotation
self.rotate(theta, Y_AXIS, about_point=ORIGIN)
self.rotate(phi, Z_AXIS, about_point=ORIGIN)
# Store values
self._current_theta = theta
self._current_phi = phi
[docs] def set_direction(self, direction):
"""Changes the direction of the apex of the :class:`Cone`.
Parameters
----------
direction : :class:`numpy.array`
The direction of the apex.
"""
self.direction = direction
self._rotate_to_direction()
[docs] def get_direction(self):
"""Returns the current direction of the apex of the :class:`Cone`.
Returns
-------
direction : :class:`numpy.array`
The direction of the apex.
"""
return self.direction
[docs]class Cylinder(Surface):
"""A cylinder, defined by its height, radius and direction,
Parameters
----------
radius
The radius of the cylinder.
height
The height of the cylinder.
direction
The direction of the central axis of the cylinder.
v_range
The height along the height axis (given by direction) to start and end on.
show_ends
Whether to show the end caps or not.
resolution
The number of samples taken of the :class:`Cylinder`. A tuple can be used
to define different resolutions for ``u`` and ``v`` respectively.
Examples
--------
.. manim:: ExampleCylinder
:save_last_frame:
class ExampleCylinder(ThreeDScene):
def construct(self):
axes = ThreeDAxes()
cylinder = Cylinder(radius=2, height=3)
self.set_camera_orientation(phi=75 * DEGREES, theta=30 * DEGREES)
self.add(axes, cylinder)
"""
def __init__(
self,
radius: float = 1,
height: float = 2,
direction: np.ndarray = Z_AXIS,
v_range: Sequence[float] = [0, TAU],
show_ends: bool = True,
resolution=(24, 24),
**kwargs,
):
self._height = height
self.radius = radius
super().__init__(
self.func,
resolution=resolution,
u_range=[-self._height / 2, self._height / 2],
v_range=v_range,
**kwargs,
)
if show_ends:
self.add_bases()
self._current_phi = 0
self._current_theta = 0
self.set_direction(direction)
[docs] def func(self, u: float, v: float):
"""Converts from cylindrical coordinates to cartesian.
Parameters
----------
u
The height.
v
The azimuthal angle.
"""
height = u
phi = v
r = self.radius
return np.array([r * np.cos(phi), r * np.sin(phi), height])
[docs] def add_bases(self):
"""Adds the end caps of the cylinder."""
if config.renderer == RendererType.OPENGL:
color = self.color
opacity = self.opacity
elif config.renderer == RendererType.CAIRO:
color = self.fill_color
opacity = self.fill_opacity
self.base_top = Circle(
radius=self.radius,
color=color,
fill_opacity=opacity,
shade_in_3d=True,
stroke_width=0,
)
self.base_top.shift(self.u_range[1] * IN)
self.base_bottom = Circle(
radius=self.radius,
color=color,
fill_opacity=opacity,
shade_in_3d=True,
stroke_width=0,
)
self.base_bottom.shift(self.u_range[0] * IN)
self.add(self.base_top, self.base_bottom)
def _rotate_to_direction(self):
x, y, z = self.direction
r = np.sqrt(x**2 + y**2 + z**2)
if r > 0:
theta = np.arccos(z / r)
else:
theta = 0
if x == 0:
if y == 0: # along the z axis
phi = 0
else: # along the x axis
phi = np.arctan(np.inf)
if y < 0:
phi += PI
else:
phi = np.arctan(y / x)
if x < 0:
phi += PI
# undo old rotation (in reverse direction)
self.rotate(-self._current_phi, Z_AXIS, about_point=ORIGIN)
self.rotate(-self._current_theta, Y_AXIS, about_point=ORIGIN)
# do new rotation
self.rotate(theta, Y_AXIS, about_point=ORIGIN)
self.rotate(phi, Z_AXIS, about_point=ORIGIN)
# store new values
self._current_theta = theta
self._current_phi = phi
[docs] def set_direction(self, direction):
"""Sets the direction of the central axis of the :class:`Cylinder`.
Parameters
----------
direction
The direction of the central axis of the :class:`Cylinder`.
"""
# if get_norm(direction) is get_norm(self.direction):
# pass
self.direction = direction
self._rotate_to_direction()
[docs] def get_direction(self):
"""Returns the direction of the central axis of the :class:`Cylinder`.
Returns
-------
direction
The direction of the central axis of the :class:`Cylinder`.
"""
return self.direction
[docs]class Line3D(Cylinder):
"""A cylindrical line, for use in ThreeDScene.
Parameters
----------
start
The start point of the line.
end
The end point of the line.
thickness
The thickness of the line.
color
The color of the line.
Examples
--------
.. manim:: ExampleLine3D
:save_last_frame:
class ExampleLine3D(ThreeDScene):
def construct(self):
axes = ThreeDAxes()
line = Line3D(start=np.array([0, 0, 0]), end=np.array([2, 2, 2]))
self.set_camera_orientation(phi=75 * DEGREES, theta=30 * DEGREES)
self.add(axes, line)
"""
def __init__(
self,
start: np.ndarray = LEFT,
end: np.ndarray = RIGHT,
thickness: float = 0.02,
color=None,
**kwargs,
):
self.thickness = thickness
self.set_start_and_end_attrs(start, end, **kwargs)
if color is not None:
self.set_color(color)
[docs] def set_start_and_end_attrs(self, start, end, **kwargs):
"""Sets the start and end points of the line.
If either ``start`` or ``end`` are :class:`Mobjects <.Mobject>`,
this gives their centers.
Parameters
----------
start
Starting point or :class:`Mobject`.
end
Ending point or :class:`Mobject`.
"""
rough_start = self.pointify(start)
rough_end = self.pointify(end)
self.vect = rough_end - rough_start
self.length = np.linalg.norm(self.vect)
self.direction = normalize(self.vect)
# Now that we know the direction between them,
# we can the appropriate boundary point from
# start and end, if they're mobjects
self.start = self.pointify(start, self.direction)
self.end = self.pointify(end, -self.direction)
super().__init__(
height=np.linalg.norm(self.vect),
radius=self.thickness,
direction=self.direction,
**kwargs,
)
self.shift((self.start + self.end) / 2)
def pointify(self, mob_or_point, direction=None):
if isinstance(mob_or_point, (Mobject, OpenGLMobject)):
mob = mob_or_point
if direction is None:
return mob.get_center()
else:
return mob.get_boundary_point(direction)
return np.array(mob_or_point)
[docs] def get_start(self):
"""Returns the starting point of the :class:`Line3D`.
Returns
-------
start : :class:`numpy.array`
Starting point of the :class:`Line3D`.
"""
return self.start
[docs] def get_end(self):
"""Returns the ending point of the :class:`Line3D`.
Returns
-------
end : :class:`numpy.array`
Ending point of the :class:`Line3D`.
"""
return self.end
[docs] @classmethod
def parallel_to(
cls, line: Line3D, point: Sequence[float] = ORIGIN, length: float = 5, **kwargs
):
"""Returns a line parallel to another line going through
a given point.
Parameters
----------
line
The line to be parallel to.
point
The point to pass through.
kwargs
Additional parameters to be passed to the class.
Examples
--------
.. manim:: ParallelLineExample
:save_last_frame:
class ParallelLineExample(ThreeDScene):
def construct(self):
self.set_camera_orientation(PI / 3, -PI / 4)
ax = ThreeDAxes((-5, 5), (-5, 5), (-5, 5), 10, 10, 10)
line1 = Line3D(RIGHT * 2, UP + OUT, color=RED)
line2 = Line3D.parallel_to(line1, color=YELLOW)
self.add(ax, line1, line2)
"""
point = np.array(point)
vect = normalize(line.vect)
return cls(
point + vect * length / 2,
point - vect * length / 2,
**kwargs,
)
[docs] @classmethod
def perpendicular_to(
cls, line: Line3D, point: Sequence[float] = ORIGIN, length: float = 5, **kwargs
):
"""Returns a line perpendicular to another line going through
a given point.
Parameters
----------
line
The line to be perpendicular to.
point
The point to pass through.
kwargs
Additional parameters to be passed to the class.
Examples
--------
.. manim:: PerpLineExample
:save_last_frame:
class PerpLineExample(ThreeDScene):
def construct(self):
self.set_camera_orientation(PI / 3, -PI / 4)
ax = ThreeDAxes((-5, 5), (-5, 5), (-5, 5), 10, 10, 10)
line1 = Line3D(RIGHT * 2, UP + OUT, color=RED)
line2 = Line3D.perpendicular_to(line1, color=BLUE)
self.add(ax, line1, line2)
"""
point = np.array(point)
norm = np.cross(line.vect, point - line.start)
if all(np.linalg.norm(norm) == np.zeros(3)):
raise ValueError("Could not find the perpendicular.")
start, end = perpendicular_bisector([line.start, line.end], norm)
vect = normalize(end - start)
return cls(
point + vect * length / 2,
point - vect * length / 2,
**kwargs,
)
[docs]class Arrow3D(Line3D):
"""An arrow made out of a cylindrical line and a conical tip.
Parameters
----------
start
The start position of the arrow.
end
The end position of the arrow.
thickness
The thickness of the arrow.
height
The height of the conical tip.
base_radius
The base radius of the conical tip.
color
The color of the arrow.
Examples
--------
.. manim:: ExampleArrow3D
:save_last_frame:
class ExampleArrow3D(ThreeDScene):
def construct(self):
axes = ThreeDAxes()
arrow = Arrow3D(
start=np.array([0, 0, 0]),
end=np.array([2, 2, 2]),
resolution=8
)
self.set_camera_orientation(phi=75 * DEGREES, theta=30 * DEGREES)
self.add(axes, arrow)
"""
def __init__(
self,
start: np.ndarray = LEFT,
end: np.ndarray = RIGHT,
thickness: float = 0.02,
height: float = 0.3,
base_radius: float = 0.08,
color=WHITE,
**kwargs,
):
super().__init__(
start=start, end=end, thickness=thickness, color=color, **kwargs
)
self.length = np.linalg.norm(self.vect)
self.set_start_and_end_attrs(
self.start,
self.end - height * self.direction,
**kwargs,
)
self.cone = Cone(
direction=self.direction, base_radius=base_radius, height=height, **kwargs
)
self.cone.shift(end)
self.add(self.cone)
self.set_color(color)
[docs]class Torus(Surface):
"""A torus.
Parameters
----------
major_radius
Distance from the center of the tube to the center of the torus.
minor_radius
Radius of the tube.
u_range
The range of the ``u`` variable: ``(u_min, u_max)``.
v_range
The range of the ``v`` variable: ``(v_min, v_max)``.
resolution
The number of samples taken of the :class:`Torus`. A tuple can be
used to define different resolutions for ``u`` and ``v`` respectively.
Examples
--------
.. manim :: ExampleTorus
:save_last_frame:
class ExampleTorus(ThreeDScene):
def construct(self):
axes = ThreeDAxes()
torus = Torus()
self.set_camera_orientation(phi=75 * DEGREES, theta=30 * DEGREES)
self.add(axes, torus)
"""
def __init__(
self,
major_radius: float = 3,
minor_radius: float = 1,
u_range=(0, TAU),
v_range=(0, TAU),
resolution=None,
**kwargs,
):
if config.renderer == RendererType.OPENGL:
res_value = (101, 101)
elif config.renderer == RendererType.CAIRO:
res_value = (24, 24)
resolution = resolution if resolution is not None else res_value
self.R = major_radius
self.r = minor_radius
super().__init__(
self.func,
u_range=u_range,
v_range=v_range,
resolution=resolution,
**kwargs,
)
def func(self, u, v):
P = np.array([np.cos(u), np.sin(u), 0])
return (self.R - self.r * np.cos(v)) * P - self.r * np.sin(v) * OUT