"""A camera that can be positioned and oriented in three-dimensional space."""
from __future__ import annotations
__all__ = ["ThreeDCamera"]
from typing import Callable
import numpy as np
from manim.mobject.mobject import Mobject
from manim.mobject.three_d.three_d_utils import (
get_3d_vmob_end_corner,
get_3d_vmob_end_corner_unit_normal,
get_3d_vmob_start_corner,
get_3d_vmob_start_corner_unit_normal,
)
from manim.mobject.value_tracker import ValueTracker
from .. import config
from ..camera.camera import Camera
from ..constants import *
from ..mobject.types.point_cloud_mobject import Point
from ..utils.color import get_shaded_rgb
from ..utils.family import extract_mobject_family_members
from ..utils.space_ops import rotation_about_z, rotation_matrix
[docs]class ThreeDCamera(Camera):
def __init__(
self,
focal_distance=20.0,
shading_factor=0.2,
default_distance=5.0,
light_source_start_point=9 * DOWN + 7 * LEFT + 10 * OUT,
should_apply_shading=True,
exponential_projection=False,
phi=0,
theta=-90 * DEGREES,
gamma=0,
zoom=1,
**kwargs,
):
"""Initializes the ThreeDCamera
Parameters
----------
*kwargs
Any keyword argument of Camera.
"""
self._frame_center = Point(kwargs.get("frame_center", ORIGIN), stroke_width=0)
super().__init__(**kwargs)
self.focal_distance = focal_distance
self.phi = phi
self.theta = theta
self.gamma = gamma
self.zoom = zoom
self.shading_factor = shading_factor
self.default_distance = default_distance
self.light_source_start_point = light_source_start_point
self.light_source = Point(self.light_source_start_point)
self.should_apply_shading = should_apply_shading
self.exponential_projection = exponential_projection
self.max_allowable_norm = 3 * config["frame_width"]
self.phi_tracker = ValueTracker(self.phi)
self.theta_tracker = ValueTracker(self.theta)
self.focal_distance_tracker = ValueTracker(self.focal_distance)
self.gamma_tracker = ValueTracker(self.gamma)
self.zoom_tracker = ValueTracker(self.zoom)
self.fixed_orientation_mobjects = {}
self.fixed_in_frame_mobjects = set()
self.reset_rotation_matrix()
@property
def frame_center(self):
return self._frame_center.points[0]
@frame_center.setter
def frame_center(self, point):
self._frame_center.move_to(point)
[docs] def capture_mobjects(self, mobjects, **kwargs):
self.reset_rotation_matrix()
super().capture_mobjects(mobjects, **kwargs)
[docs] def get_value_trackers(self):
"""A list of :class:`ValueTrackers <.ValueTracker>` of phi, theta, focal_distance,
gamma and zoom.
Returns
-------
list
list of ValueTracker objects
"""
return [
self.phi_tracker,
self.theta_tracker,
self.focal_distance_tracker,
self.gamma_tracker,
self.zoom_tracker,
]
def modified_rgbas(self, vmobject, rgbas):
if not self.should_apply_shading:
return rgbas
if vmobject.shade_in_3d and (vmobject.get_num_points() > 0):
light_source_point = self.light_source.points[0]
if len(rgbas) < 2:
shaded_rgbas = rgbas.repeat(2, axis=0)
else:
shaded_rgbas = np.array(rgbas[:2])
shaded_rgbas[0, :3] = get_shaded_rgb(
shaded_rgbas[0, :3],
get_3d_vmob_start_corner(vmobject),
get_3d_vmob_start_corner_unit_normal(vmobject),
light_source_point,
)
shaded_rgbas[1, :3] = get_shaded_rgb(
shaded_rgbas[1, :3],
get_3d_vmob_end_corner(vmobject),
get_3d_vmob_end_corner_unit_normal(vmobject),
light_source_point,
)
return shaded_rgbas
return rgbas
[docs] def get_stroke_rgbas(
self,
vmobject,
background=False,
): # NOTE : DocStrings From parent
return self.modified_rgbas(vmobject, vmobject.get_stroke_rgbas(background))
[docs] def get_fill_rgbas(self, vmobject): # NOTE : DocStrings From parent
return self.modified_rgbas(vmobject, vmobject.get_fill_rgbas())
[docs] def get_mobjects_to_display(self, *args, **kwargs): # NOTE : DocStrings From parent
mobjects = super().get_mobjects_to_display(*args, **kwargs)
rot_matrix = self.get_rotation_matrix()
def z_key(mob):
if not (hasattr(mob, "shade_in_3d") and mob.shade_in_3d):
return np.inf
# Assign a number to a three dimensional mobjects
# based on how close it is to the camera
return np.dot(mob.get_z_index_reference_point(), rot_matrix.T)[2]
return sorted(mobjects, key=z_key)
[docs] def get_phi(self):
"""Returns the Polar angle (the angle off Z_AXIS) phi.
Returns
-------
float
The Polar angle in radians.
"""
return self.phi_tracker.get_value()
[docs] def get_theta(self):
"""Returns the Azimuthal i.e the angle that spins the camera around the Z_AXIS.
Returns
-------
float
The Azimuthal angle in radians.
"""
return self.theta_tracker.get_value()
[docs] def get_focal_distance(self):
"""Returns focal_distance of the Camera.
Returns
-------
float
The focal_distance of the Camera in MUnits.
"""
return self.focal_distance_tracker.get_value()
[docs] def get_gamma(self):
"""Returns the rotation of the camera about the vector from the ORIGIN to the Camera.
Returns
-------
float
The angle of rotation of the camera about the vector
from the ORIGIN to the Camera in radians
"""
return self.gamma_tracker.get_value()
[docs] def get_zoom(self):
"""Returns the zoom amount of the camera.
Returns
-------
float
The zoom amount of the camera.
"""
return self.zoom_tracker.get_value()
[docs] def set_phi(self, value: float):
"""Sets the polar angle i.e the angle between Z_AXIS and Camera through ORIGIN in radians.
Parameters
----------
value
The new value of the polar angle in radians.
"""
self.phi_tracker.set_value(value)
[docs] def set_theta(self, value: float):
"""Sets the azimuthal angle i.e the angle that spins the camera around Z_AXIS in radians.
Parameters
----------
value
The new value of the azimuthal angle in radians.
"""
self.theta_tracker.set_value(value)
[docs] def set_focal_distance(self, value: float):
"""Sets the focal_distance of the Camera.
Parameters
----------
value
The focal_distance of the Camera.
"""
self.focal_distance_tracker.set_value(value)
[docs] def set_gamma(self, value: float):
"""Sets the angle of rotation of the camera about the vector from the ORIGIN to the Camera.
Parameters
----------
value
The new angle of rotation of the camera.
"""
self.gamma_tracker.set_value(value)
[docs] def set_zoom(self, value: float):
"""Sets the zoom amount of the camera.
Parameters
----------
value
The zoom amount of the camera.
"""
self.zoom_tracker.set_value(value)
[docs] def reset_rotation_matrix(self):
"""Sets the value of self.rotation_matrix to
the matrix corresponding to the current position of the camera
"""
self.rotation_matrix = self.generate_rotation_matrix()
[docs] def get_rotation_matrix(self):
"""Returns the matrix corresponding to the current position of the camera.
Returns
-------
np.array
The matrix corresponding to the current position of the camera.
"""
return self.rotation_matrix
[docs] def generate_rotation_matrix(self):
"""Generates a rotation matrix based off the current position of the camera.
Returns
-------
np.array
The matrix corresponding to the current position of the camera.
"""
phi = self.get_phi()
theta = self.get_theta()
gamma = self.get_gamma()
matrices = [
rotation_about_z(-theta - 90 * DEGREES),
rotation_matrix(-phi, RIGHT),
rotation_about_z(gamma),
]
result = np.identity(3)
for matrix in matrices:
result = np.dot(matrix, result)
return result
[docs] def project_points(self, points: np.ndarray | list):
"""Applies the current rotation_matrix as a projection
matrix to the passed array of points.
Parameters
----------
points
The list of points to project.
Returns
-------
np.array
The points after projecting.
"""
frame_center = self.frame_center
focal_distance = self.get_focal_distance()
zoom = self.get_zoom()
rot_matrix = self.get_rotation_matrix()
points = points - frame_center
points = np.dot(points, rot_matrix.T)
zs = points[:, 2]
for i in 0, 1:
if self.exponential_projection:
# Proper projection would involve multiplying
# x and y by d / (d-z). But for points with high
# z value that causes weird artifacts, and applying
# the exponential helps smooth it out.
factor = np.exp(zs / focal_distance)
lt0 = zs < 0
factor[lt0] = focal_distance / (focal_distance - zs[lt0])
else:
factor = focal_distance / (focal_distance - zs)
factor[(focal_distance - zs) < 0] = 10**6
points[:, i] *= factor * zoom
return points
[docs] def project_point(self, point: list | np.ndarray):
"""Applies the current rotation_matrix as a projection
matrix to the passed point.
Parameters
----------
point
The point to project.
Returns
-------
np.array
The point after projection.
"""
return self.project_points(point.reshape((1, 3)))[0, :]
def transform_points_pre_display(
self,
mobject,
points,
): # TODO: Write Docstrings for this Method.
points = super().transform_points_pre_display(mobject, points)
fixed_orientation = mobject in self.fixed_orientation_mobjects
fixed_in_frame = mobject in self.fixed_in_frame_mobjects
if fixed_in_frame:
return points
if fixed_orientation:
center_func = self.fixed_orientation_mobjects[mobject]
center = center_func()
new_center = self.project_point(center)
return points + (new_center - center)
else:
return self.project_points(points)
[docs] def add_fixed_orientation_mobjects(
self,
*mobjects: Mobject,
use_static_center_func: bool = False,
center_func: Callable[[], np.ndarray] | None = None,
):
"""This method allows the mobject to have a fixed orientation,
even when the camera moves around.
E.G If it was passed through this method, facing the camera, it
will continue to face the camera even as the camera moves.
Highly useful when adding labels to graphs and the like.
Parameters
----------
*mobjects
The mobject whose orientation must be fixed.
use_static_center_func
Whether or not to use the function that takes the mobject's
center as centerpoint, by default False
center_func
The function which returns the centerpoint
with respect to which the mobject will be oriented, by default None
"""
# This prevents the computation of mobject.get_center
# every single time a projection happens
def get_static_center_func(mobject):
point = mobject.get_center()
return lambda: point
for mobject in mobjects:
if center_func:
func = center_func
elif use_static_center_func:
func = get_static_center_func(mobject)
else:
func = mobject.get_center
for submob in mobject.get_family():
self.fixed_orientation_mobjects[submob] = func
[docs] def add_fixed_in_frame_mobjects(self, *mobjects: Mobject):
"""This method allows the mobject to have a fixed position,
even when the camera moves around.
E.G If it was passed through this method, at the top of the frame, it
will continue to be displayed at the top of the frame.
Highly useful when displaying Titles or formulae or the like.
Parameters
----------
**mobjects
The mobject to fix in frame.
"""
for mobject in extract_mobject_family_members(mobjects):
self.fixed_in_frame_mobjects.add(mobject)
[docs] def remove_fixed_orientation_mobjects(self, *mobjects: Mobject):
"""If a mobject was fixed in its orientation by passing it through
:meth:`.add_fixed_orientation_mobjects`, then this undoes that fixing.
The Mobject will no longer have a fixed orientation.
Parameters
----------
mobjects
The mobjects whose orientation need not be fixed any longer.
"""
for mobject in extract_mobject_family_members(mobjects):
if mobject in self.fixed_orientation_mobjects:
del self.fixed_orientation_mobjects[mobject]
[docs] def remove_fixed_in_frame_mobjects(self, *mobjects: Mobject):
"""If a mobject was fixed in frame by passing it through
:meth:`.add_fixed_in_frame_mobjects`, then this undoes that fixing.
The Mobject will no longer be fixed in frame.
Parameters
----------
mobjects
The mobjects which need not be fixed in frame any longer.
"""
for mobject in extract_mobject_family_members(mobjects):
if mobject in self.fixed_in_frame_mobjects:
self.fixed_in_frame_mobjects.remove(mobject)