Source code for manim.camera.three_d_camera

"""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)