3b1b-manim/manimlib/mobject/three_dimensions.py

from manimlib.constants import *
from manimlib.mobject.geometry import Square
from manimlib.mobject.types.vectorized_mobject import VGroup
from manimlib.mobject.types.vectorized_mobject import VMobject
from manimlib.utils.iterables import listify
from manimlib.utils.space_ops import z_to_vector

##############


# TODO, replace these with a special 3d type, not VMobject


class ThreeDVMobject(VMobject):
    CONFIG = {
        "shade_in_3d": True,
    }


class ParametricSurface(VGroup):
    CONFIG = {
        "u_min": 0,
        "u_max": 1,
        "v_min": 0,
        "v_max": 1,
        "resolution": 32,
        "surface_piece_config": {},
        "fill_color": BLUE_D,
        "fill_opacity": 1.0,
        "checkerboard_colors": [BLUE_D, BLUE_E],
        "stroke_color": LIGHT_GREY,
        "stroke_width": 0.5,
        "should_make_jagged": False,
        "pre_function_handle_to_anchor_scale_factor": 0.00001,
    }

    def __init__(self, func, **kwargs):
        VGroup.__init__(self, **kwargs)
        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 get_u_values_and_v_values(self):
        res = listify(self.resolution)
        if len(res) == 1:
            u_res = v_res = res[0]
        else:
            u_res, v_res = res
        u_min = self.u_min
        u_max = self.u_max
        v_min = self.v_min
        v_max = self.v_max

        u_values = np.linspace(u_min, u_max, u_res + 1)
        v_values = np.linspace(v_min, v_max, 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)

    def set_fill_by_checkerboard(self, *colors, opacity=None):
        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)


# Specific shapes


class Sphere(ParametricSurface):
    CONFIG = {
        "resolution": (12, 24),
        "radius": 1,
        "u_min": 0.001,
        "u_max": PI - 0.001,
        "v_min": 0,
        "v_max": TAU,
    }

    def __init__(self, **kwargs):
        ParametricSurface.__init__(
            self, self.func, **kwargs
        )
        self.scale(self.radius)

    def func(self, u, v):
        return np.array([
            np.cos(v) * np.sin(u),
            np.sin(v) * np.sin(u),
            np.cos(u)
        ])


class Cube(VGroup):
    CONFIG = {
        "fill_opacity": 0.75,
        "fill_color": BLUE,
        "stroke_width": 0,
        "side_length": 2,
    }

    def init_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)


class Prism(Cube):
    CONFIG = {
        "dimensions": [3, 2, 1]
    }

    def init_points(self):
        Cube.init_points(self)
        for dim, value in enumerate(self.dimensions):
            self.rescale_to_fit(value, dim, stretch=True)