coordinate_systems.py

import numpy as np
import numbers

from manimlib.constants import *
from manimlib.mobject.functions import ParametricCurve
from manimlib.mobject.geometry import Arrow
from manimlib.mobject.geometry import Line
from manimlib.mobject.number_line import NumberLine
from manimlib.mobject.svg.tex_mobject import TexMobject
from manimlib.mobject.types.vectorized_mobject import VGroup
from manimlib.utils.config_ops import merge_dicts_recursively
from manimlib.utils.simple_functions import binary_search
from manimlib.utils.space_ops import angle_of_vector

# TODO: There should be much more code reuse between Axes, NumberPlane and GraphScene


class CoordinateSystem():
    """
    Abstract class for Axes and NumberPlane
    """
    CONFIG = {
        "dimension": 2,
        "x_range": [-8, 8, 1],
        "y_range": [-4, 4, 1],
        "width": None,
        "height": None,
    }

    def coords_to_point(self, *coords):
        raise Exception("Not implemented")

    def point_to_coords(self, point):
        raise Exception("Not implemented")

    def c2p(self, *coords):
        """Abbreviation for coords_to_point"""
        return self.coords_to_point(*coords)

    def p2c(self, point):
        """Abbreviation for point_to_coords"""
        return self.point_to_coords(point)

    def get_axes(self):
        raise Exception("Not implemented")

    def get_axis(self, index):
        return self.get_axes()[index]

    def get_x_axis(self):
        return self.get_axis(0)

    def get_y_axis(self):
        return self.get_axis(1)

    def get_z_axis(self):
        return self.get_axis(2)

    def get_x_axis_label(self, label_tex, edge=RIGHT, direction=DL, **kwargs):
        return self.get_axis_label(
            label_tex, self.get_x_axis(),
            edge, direction, **kwargs
        )

    def get_y_axis_label(self, label_tex, edge=UP, direction=DR, **kwargs):
        return self.get_axis_label(
            label_tex, self.get_y_axis(),
            edge, direction, **kwargs
        )

    def get_axis_label(self, label_tex, axis, edge, direction, buff=MED_SMALL_BUFF):
        label = TexMobject(label_tex)
        label.next_to(
            axis.get_edge_center(edge), direction,
            buff=buff
        )
        label.shift_onto_screen(buff=MED_SMALL_BUFF)
        return label

    def get_axis_labels(self, x_label_tex="x", y_label_tex="y"):
        self.axis_labels = VGroup(
            self.get_x_axis_label(x_label_tex),
            self.get_y_axis_label(y_label_tex),
        )
        return self.axis_labels

    def get_graph(self, function, x_range=None, **kwargs):
        if x_range is None:
            x_range = self.x_range
        graph = ParametricCurve(
            lambda t: self.coords_to_point(t, function(t)),
            t_range=x_range,
            **kwargs
        )
        graph.underlying_function = function
        return graph

    def get_parametric_curve(self, function, **kwargs):
        dim = self.dimension
        graph = ParametricCurve(
            lambda t: self.coords_to_point(*function(t)[:dim]),
            **kwargs
        )
        graph.underlying_function = function
        return graph

    def input_to_graph_point(self, x, graph):
        if hasattr(graph, "underlying_function"):
            return self.coords_to_point(x, graph.underlying_function(x))
        else:
            alpha = binary_search(
                function=lambda a: self.point_to_coords(
                    graph.point_from_proportion(a)
                )[0],
                target=x,
                lower_bound=self.x_range[0],
                upper_bound=self.x_range[1],
            )
            if alpha is not None:
                return graph.point_from_proportion(alpha)
            else:
                return None


class Axes(VGroup, CoordinateSystem):
    CONFIG = {
        "axis_config": {
            "include_tip": True,
        },
        "x_axis_config": {},
        "y_axis_config": {
            "line_to_number_direction": LEFT,
        },
    }

    def __init__(self, x_range=None, y_range=None, **kwargs):
        VGroup.__init__(self, **kwargs)
        self.x_axis = self.create_axis(
            x_range or self.x_range,
            self.x_axis_config,
            self.width,
        )
        self.y_axis = self.create_axis(
            y_range or self.y_range,
            self.y_axis_config,
            self.height
        )
        self.y_axis.rotate(90 * DEGREES, about_point=ORIGIN)
        # Add as a separate group in case various other
        # mobjects are added to self, as for example in
        # NumberPlane below
        self.axes = VGroup(self.x_axis, self.y_axis)
        self.add(*self.axes)
        self.center()

    def create_axis(self, range_terms, axis_config, length):
        new_config = merge_dicts_recursively(self.axis_config, axis_config)
        new_config["width"] = length
        axis = NumberLine(range_terms, **new_config)
        axis.shift(-axis.n2p(0))
        return axis

    def coords_to_point(self, *coords):
        origin = self.x_axis.number_to_point(0)
        result = np.array(origin)
        for axis, coord in zip(self.get_axes(), coords):
            result += (axis.number_to_point(coord) - origin)
        return result

    def point_to_coords(self, point):
        return tuple([
            axis.point_to_number(point)
            for axis in self.get_axes()
        ])

    def get_axes(self):
        return self.axes

    def add_coordinate_labels(self, x_values=None, y_values=None):
        axes = self.get_axes()
        self.coordinate_labels = VGroup()
        for axis, values in zip(axes, [x_values, y_values]):
            numbers = axis.add_numbers(values, excluding=[0])
            self.coordinate_labels.add(numbers)
        return self.coordinate_labels


class ThreeDAxes(Axes):
    CONFIG = {
        "dimension": 3,
        "x_range": (-6, 6, 1),
        "y_range": (-5, 5, 1),
        "z_range": (-4, 4, 1),
        "z_axis_config": {},
        "z_normal": DOWN,
        "depth": None,
        "num_axis_pieces": 20,
        "gloss": 0.5,
    }

    def __init__(self, x_range=None, y_range=None, z_range=None, **kwargs):
        Axes.__init__(self, x_range, y_range, **kwargs)

        z_axis = self.create_axis(
            z_range or self.z_range,
            self.z_axis_config,
            self.depth,
        )
        z_axis.rotate(-PI / 2, UP, about_point=ORIGIN)
        z_axis.rotate(
            angle_of_vector(self.z_normal), OUT,
            about_point=ORIGIN
        )
        z_axis.shift(self.x_axis.n2p(0))
        self.axes.add(z_axis)
        self.add(z_axis)
        self.z_axis = z_axis

        for axis in self.axes:
            axis.insert_n_curves(self.num_axis_pieces - 1)


class NumberPlane(Axes):
    CONFIG = {
        "axis_config": {
            "stroke_color": WHITE,
            "stroke_width": 2,
            "include_ticks": False,
            "include_tip": False,
            "line_to_number_buff": SMALL_BUFF,
            "line_to_number_direction": DL,
            "decimal_number_config": {
                "height": 0.2,
            }
        },
        "y_axis_config": {
            "line_to_number_direction": DL,
        },
        "background_line_style": {
            "stroke_color": BLUE_D,
            "stroke_width": 2,
            "stroke_opacity": 1,
        },
        # Defaults to a faded version of line_config
        "faded_line_style": None,
        "faded_line_ratio": 1,
        "make_smooth_after_applying_functions": True,
    }

    def __init__(self, x_range=None, y_range=None, **kwargs):
        super().__init__(x_range, y_range, **kwargs)
        self.init_background_lines()

    def init_background_lines(self):
        if self.faded_line_style is None:
            style = dict(self.background_line_style)
            # For anything numerical, like stroke_width
            # and stroke_opacity, chop it in half
            for key in style:
                if isinstance(style[key], numbers.Number):
                    style[key] *= 0.5
            self.faded_line_style = style

        self.background_lines, self.faded_lines = self.get_lines()
        self.background_lines.set_style(**self.background_line_style)
        self.faded_lines.set_style(**self.faded_line_style)
        self.add_to_back(
            self.faded_lines,
            self.background_lines,
        )

    def get_lines(self):
        x_axis = self.get_x_axis()
        y_axis = self.get_y_axis()

        x_lines1, x_lines2 = self.get_lines_parallel_to_axis(x_axis, y_axis)
        y_lines1, y_lines2 = self.get_lines_parallel_to_axis(y_axis, x_axis)
        lines1 = VGroup(*x_lines1, *y_lines1)
        lines2 = VGroup(*x_lines2, *y_lines2)
        return lines1, lines2

    def get_lines_parallel_to_axis(self, axis1, axis2):
        freq = axis1.x_step
        ratio = self.faded_line_ratio
        line = Line(axis1.get_start(), axis1.get_end())
        dense_freq = (1 + ratio)
        step = (1 / dense_freq) * freq

        lines1 = VGroup()
        lines2 = VGroup()
        inputs = np.arange(axis2.x_min, axis2.x_max + step, step)
        for i, x in enumerate(inputs):
            new_line = line.copy()
            new_line.shift(axis2.n2p(x) - axis2.n2p(0))
            if i % (1 + ratio) == 0:
                lines1.add(new_line)
            else:
                lines2.add(new_line)
        return lines1, lines2

    def get_x_unit_size(self):
        return self.get_x_axis().get_unit_size()

    def get_y_unit_size(self):
        return self.get_x_axis().get_unit_size()

    def get_axes(self):
        return self.axes

    def get_vector(self, coords, **kwargs):
        kwargs["buff"] = 0
        return Arrow(self.c2p(0, 0), self.c2p(*coords), **kwargs)

    def prepare_for_nonlinear_transform(self, num_inserted_curves=50):
        for mob in self.family_members_with_points():
            num_curves = mob.get_num_curves()
            if num_inserted_curves > num_curves:
                mob.insert_n_curves(num_inserted_curves - num_curves)
        return self


class ComplexPlane(NumberPlane):
    CONFIG = {
        "color": BLUE,
        "line_frequency": 1,
    }

    def number_to_point(self, number):
        number = complex(number)
        return self.coords_to_point(number.real, number.imag)

    def n2p(self, number):
        return self.number_to_point(number)

    def point_to_number(self, point):
        x, y = self.point_to_coords(point)
        return complex(x, y)

    def p2n(self, point):
        return self.point_to_number(point)

    def get_default_coordinate_values(self):
        x_numbers = self.get_x_axis().get_tick_range()[1:]
        y_numbers = self.get_y_axis().get_tick_range()[1:]
        y_numbers = [complex(0, y) for y in y_numbers if y != 0]
        return [*x_numbers, *y_numbers]

    def add_coordinate_labels(self, numbers=None, **kwargs):
        if numbers is None:
            numbers = self.get_default_coordinate_values()

        self.coordinate_labels = VGroup()
        for number in numbers:
            z = complex(number)
            if abs(z.imag) > abs(z.real):
                axis = self.get_y_axis()
                value = z.imag
                kwargs = merge_dicts_recursively(
                    kwargs,
                    {"number_config": {"unit": "i"}},
                )
            else:
                axis = self.get_x_axis()
                value = z.real
            number_mob = axis.get_number_mobject(value, **kwargs)
            self.coordinate_labels.add(number_mob)
        self.add(self.coordinate_labels)
        return self