graph_scene.py

import itertools as it

from manimlib.animation.creation import Write, DrawBorderThenFill, ShowCreation
from manimlib.animation.transform import Transform
from manimlib.animation.update import UpdateFromAlphaFunc
from manimlib.constants import *
from manimlib.mobject.functions import ParametricCurve
from manimlib.mobject.geometry import Line
from manimlib.mobject.geometry import Rectangle
from manimlib.mobject.geometry import RegularPolygon
from manimlib.mobject.number_line import NumberLine
from manimlib.mobject.svg.tex_mobject import Tex
from manimlib.mobject.svg.tex_mobject import TexText
from manimlib.mobject.types.vectorized_mobject import VGroup
from manimlib.mobject.types.vectorized_mobject import VectorizedPoint
from manimlib.scene.scene import Scene
from manimlib.utils.bezier import interpolate
from manimlib.utils.color import color_gradient
from manimlib.utils.color import invert_color
from manimlib.utils.space_ops import angle_of_vector

# TODO, this class should be deprecated, with all its
# functionality moved to Axes and handled at the mobject
# level rather than the scene level


class GraphScene(Scene):
    x_min = -1
    x_max = 10
    x_axis_width = 9
    x_tick_frequency = 1
    x_leftmost_tick = None  # Change if different from x_min
    x_labeled_nums = None
    x_axis_label = "$x$"
    y_min = -1
    y_max = 10
    y_axis_height = 6
    y_tick_frequency = 1
    y_bottom_tick = None  # Change if different from y_min
    y_labeled_nums = None
    y_axis_label = "$y$"
    axes_color = GREY
    graph_origin = 2.5 * DOWN + 4 * LEFT
    exclude_zero_label = True
    default_graph_colors = [BLUE, GREEN, YELLOW]
    default_derivative_color = GREEN
    default_input_color = YELLOW
    default_riemann_start_color = BLUE
    default_riemann_end_color = GREEN
    area_opacity = 0.8
    num_rects = 50

    def setup(self):
        self.default_graph_colors_cycle = it.cycle(self.default_graph_colors)

        self.left_T_label = VGroup()
        self.left_v_line = VGroup()
        self.right_T_label = VGroup()
        self.right_v_line = VGroup()

    def setup_axes(self, animate=False):
        # TODO, once eoc is done, refactor this to be less redundant.
        x_num_range = float(self.x_max - self.x_min)
        self.space_unit_to_x = self.x_axis_width / x_num_range
        if self.x_labeled_nums is None:
            self.x_labeled_nums = []
        if self.x_leftmost_tick is None:
            self.x_leftmost_tick = self.x_min
        x_axis = NumberLine(
            x_min=self.x_min,
            x_max=self.x_max,
            unit_size=self.space_unit_to_x,
            tick_frequency=self.x_tick_frequency,
            leftmost_tick=self.x_leftmost_tick,
            big_tick_numbers=self.x_labeled_nums,
            color=self.axes_color
        )
        x_axis.shift(self.graph_origin - x_axis.number_to_point(0))
        if len(self.x_labeled_nums) > 0:
            if self.exclude_zero_label:
                self.x_labeled_nums = [x for x in self.x_labeled_nums if x != 0]
            x_axis.add_numbers(self.x_labeled_nums)
        if self.x_axis_label:
            x_label = OldTexText(self.x_axis_label)
            x_label.next_to(
                x_axis.get_tick_marks(), UP + RIGHT,
                buff=SMALL_BUFF
            )
            x_label.shift_onto_screen()
            x_axis.add(x_label)
            self.x_axis_label_mob = x_label

        y_num_range = float(self.y_max - self.y_min)
        self.space_unit_to_y = self.y_axis_height / y_num_range

        if self.y_labeled_nums is None:
            self.y_labeled_nums = []
        if self.y_bottom_tick is None:
            self.y_bottom_tick = self.y_min
        y_axis = NumberLine(
            x_min=self.y_min,
            x_max=self.y_max,
            unit_size=self.space_unit_to_y,
            tick_frequency=self.y_tick_frequency,
            leftmost_tick=self.y_bottom_tick,
            big_tick_numbers=self.y_labeled_nums,
            color=self.axes_color,
            line_to_number_vect=LEFT,
            label_direction=LEFT,
        )
        y_axis.shift(self.graph_origin - y_axis.number_to_point(0))
        y_axis.rotate(np.pi / 2, about_point=y_axis.number_to_point(0))
        if len(self.y_labeled_nums) > 0:
            if self.exclude_zero_label:
                self.y_labeled_nums = [y for y in self.y_labeled_nums if y != 0]
            y_axis.add_numbers(self.y_labeled_nums)
        if self.y_axis_label:
            y_label = OldTexText(self.y_axis_label)
            y_label.next_to(
                y_axis.get_corner(UP + RIGHT), UP + RIGHT,
                buff=SMALL_BUFF
            )
            y_label.shift_onto_screen()
            y_axis.add(y_label)
            self.y_axis_label_mob = y_label

        if animate:
            self.play(Write(VGroup(x_axis, y_axis)))
        else:
            self.add(x_axis, y_axis)
        self.x_axis, self.y_axis = self.axes = VGroup(x_axis, y_axis)
        self.default_graph_colors = it.cycle(self.default_graph_colors)

    def coords_to_point(self, x, y):
        assert(hasattr(self, "x_axis") and hasattr(self, "y_axis"))
        result = self.x_axis.number_to_point(x)[0] * RIGHT
        result += self.y_axis.number_to_point(y)[1] * UP
        return result

    def point_to_coords(self, point):
        return (self.x_axis.point_to_number(point),
                self.y_axis.point_to_number(point))

    def get_graph(
        self, func,
        color=None,
        x_min=None,
        x_max=None,
        **kwargs
    ):
        if color is None:
            color = next(self.default_graph_colors_cycle)
        if x_min is None:
            x_min = self.x_min
        if x_max is None:
            x_max = self.x_max

        def parameterized_function(alpha):
            x = interpolate(x_min, x_max, alpha)
            y = func(x)
            if not np.isfinite(y):
                y = self.y_max
            return self.coords_to_point(x, y)

        graph = ParametricCurve(
            parameterized_function,
            color=color,
            **kwargs
        )
        graph.underlying_function = func
        return graph

    def input_to_graph_point(self, x, graph):
        return self.coords_to_point(x, graph.underlying_function(x))

    def angle_of_tangent(self, x, graph, dx=0.01):
        vect = self.input_to_graph_point(
            x + dx, graph) - self.input_to_graph_point(x, graph)
        return angle_of_vector(vect)

    def slope_of_tangent(self, *args, **kwargs):
        return np.tan(self.angle_of_tangent(*args, **kwargs))

    def get_derivative_graph(self, graph, dx=0.01, **kwargs):
        if "color" not in kwargs:
            kwargs["color"] = self.default_derivative_color

        def deriv(x):
            return self.slope_of_tangent(x, graph, dx) / self.space_unit_to_y
        return self.get_graph(deriv, **kwargs)

    def get_graph_label(
        self,
        graph,
        label="f(x)",
        x_val=None,
        direction=RIGHT,
        buff=MED_SMALL_BUFF,
        color=None,
    ):
        label = OldTex(label)
        color = color or graph.get_color()
        label.set_color(color)
        if x_val is None:
            # Search from right to left
            for x in np.linspace(self.x_max, self.x_min, 100):
                point = self.input_to_graph_point(x, graph)
                if point[1] < FRAME_Y_RADIUS:
                    break
            x_val = x
        label.next_to(
            self.input_to_graph_point(x_val, graph),
            direction,
            buff=buff
        )
        label.shift_onto_screen()
        return label

    def get_riemann_rectangles(
        self,
        graph,
        x_min=None,
        x_max=None,
        dx=0.1,
        input_sample_type="left",
        stroke_width=1,
        stroke_color=BLACK,
        fill_opacity=1,
        start_color=None,
        end_color=None,
        show_signed_area=True,
        width_scale_factor=1.001
    ):
        x_min = x_min if x_min is not None else self.x_min
        x_max = x_max if x_max is not None else self.x_max
        if start_color is None:
            start_color = self.default_riemann_start_color
        if end_color is None:
            end_color = self.default_riemann_end_color
        rectangles = VGroup()
        x_range = np.arange(x_min, x_max, dx)
        colors = color_gradient([start_color, end_color], len(x_range))
        for x, color in zip(x_range, colors):
            if input_sample_type == "left":
                sample_input = x
            elif input_sample_type == "right":
                sample_input = x + dx
            elif input_sample_type == "center":
                sample_input = x + 0.5 * dx
            else:
                raise Exception("Invalid input sample type")
            graph_point = self.input_to_graph_point(sample_input, graph)
            points = VGroup(*list(map(VectorizedPoint, [
                self.coords_to_point(x, 0),
                self.coords_to_point(x + width_scale_factor * dx, 0),
                graph_point
            ])))

            rect = Rectangle()
            rect.replace(points, stretch=True)
            if graph_point[1] < self.graph_origin[1] and show_signed_area:
                fill_color = invert_color(color)
            else:
                fill_color = color
            rect.set_fill(fill_color, opacity=fill_opacity)
            rect.set_stroke(stroke_color, width=stroke_width)
            rectangles.add(rect)
        return rectangles

    def get_riemann_rectangles_list(
        self,
        graph,
        n_iterations,
        max_dx=0.5,
        power_base=2,
        stroke_width=1,
        **kwargs
    ):
        return [
            self.get_riemann_rectangles(
                graph=graph,
                dx=float(max_dx) / (power_base**n),
                stroke_width=float(stroke_width) / (power_base**n),
                **kwargs
            )
            for n in range(n_iterations)
        ]

    def get_area(self, graph, t_min, t_max):
        numerator = max(t_max - t_min, 0.0001)
        dx = float(numerator) / self.num_rects
        return self.get_riemann_rectangles(
            graph,
            x_min=t_min,
            x_max=t_max,
            dx=dx,
            stroke_width=0,
        ).set_fill(opacity=self.area_opacity)

    def transform_between_riemann_rects(self, curr_rects, new_rects, **kwargs):
        transform_kwargs = {
            "run_time": 2,
            "lag_ratio": 0.5
        }
        added_anims = kwargs.get("added_anims", [])
        transform_kwargs.update(kwargs)
        curr_rects.align_family(new_rects)
        x_coords = set()  # Keep track of new repetitions
        for rect in curr_rects:
            x = rect.get_center()[0]
            if x in x_coords:
                rect.set_fill(opacity=0)
            else:
                x_coords.add(x)
        self.play(
            Transform(curr_rects, new_rects, **transform_kwargs),
            *added_anims
        )

    def get_vertical_line_to_graph(
        self,
        x, graph,
        line_class=Line,
        **line_kwargs
    ):
        if "color" not in line_kwargs:
            line_kwargs["color"] = graph.get_color()
        return line_class(
            self.coords_to_point(x, 0),
            self.input_to_graph_point(x, graph),
            **line_kwargs
        )

    def get_vertical_lines_to_graph(
        self, graph,
        x_min=None,
        x_max=None,
        num_lines=20,
        **kwargs
    ):
        x_min = x_min or self.x_min
        x_max = x_max or self.x_max
        return VGroup(*[
            self.get_vertical_line_to_graph(x, graph, **kwargs)
            for x in np.linspace(x_min, x_max, num_lines)
        ])

    def get_secant_slope_group(
        self,
        x, graph,
        dx=None,
        dx_line_color=None,
        df_line_color=None,
        dx_label=None,
        df_label=None,
        include_secant_line=True,
        secant_line_color=None,
        secant_line_length=10,
    ):
        """
        Resulting group is of the form VGroup(
            dx_line,
            df_line,
            dx_label, (if applicable)
            df_label, (if applicable)
            secant_line, (if applicable)
        )
        with attributes of those names.
        """
        kwargs = locals()
        kwargs.pop("self")
        group = VGroup()
        group.kwargs = kwargs

        dx = dx or float(self.x_max - self.x_min) / 10
        dx_line_color = dx_line_color or self.default_input_color
        df_line_color = df_line_color or graph.get_color()

        p1 = self.input_to_graph_point(x, graph)
        p2 = self.input_to_graph_point(x + dx, graph)
        interim_point = p2[0] * RIGHT + p1[1] * UP

        group.dx_line = Line(
            p1, interim_point,
            color=dx_line_color
        )
        group.df_line = Line(
            interim_point, p2,
            color=df_line_color
        )
        group.add(group.dx_line, group.df_line)

        labels = VGroup()
        if dx_label is not None:
            group.dx_label = OldTex(dx_label)
            labels.add(group.dx_label)
            group.add(group.dx_label)
        if df_label is not None:
            group.df_label = OldTex(df_label)
            labels.add(group.df_label)
            group.add(group.df_label)

        if len(labels) > 0:
            max_width = 0.8 * group.dx_line.get_width()
            max_height = 0.8 * group.df_line.get_height()
            if labels.get_width() > max_width:
                labels.set_width(max_width)
            if labels.get_height() > max_height:
                labels.set_height(max_height)

        if dx_label is not None:
            group.dx_label.next_to(
                group.dx_line,
                np.sign(dx) * DOWN,
                buff=group.dx_label.get_height() / 2
            )
            group.dx_label.set_color(group.dx_line.get_color())

        if df_label is not None:
            group.df_label.next_to(
                group.df_line,
                np.sign(dx) * RIGHT,
                buff=group.df_label.get_height() / 2
            )
            group.df_label.set_color(group.df_line.get_color())

        if include_secant_line:
            secant_line_color = secant_line_color or self.default_derivative_color
            group.secant_line = Line(p1, p2, color=secant_line_color)
            group.secant_line.scale(
                secant_line_length / group.secant_line.get_length()
            )
            group.add(group.secant_line)

        return group

    def add_T_label(self, x_val, side=RIGHT, label=None, color=WHITE, animated=False, **kwargs):
        triangle = RegularPolygon(n=3, start_angle=np.pi / 2)
        triangle.set_height(MED_SMALL_BUFF)
        triangle.move_to(self.coords_to_point(x_val, 0), UP)
        triangle.set_fill(color, 1)
        triangle.set_stroke(width=0)
        if label is None:
            T_label = OldTex(self.variable_point_label, fill_color=color)
        else:
            T_label = OldTex(label, fill_color=color)

        T_label.next_to(triangle, DOWN)
        v_line = self.get_vertical_line_to_graph(
            x_val, self.v_graph,
            color=YELLOW
        )

        if animated:
            self.play(
                DrawBorderThenFill(triangle),
                ShowCreation(v_line),
                Write(T_label, run_time=1),
                **kwargs
            )

        if np.all(side == LEFT):
            self.left_T_label_group = VGroup(T_label, triangle)
            self.left_v_line = v_line
            self.add(self.left_T_label_group, self.left_v_line)
        elif np.all(side == RIGHT):
            self.right_T_label_group = VGroup(T_label, triangle)
            self.right_v_line = v_line
            self.add(self.right_T_label_group, self.right_v_line)

    def get_animation_integral_bounds_change(
        self,
        graph,
        new_t_min,
        new_t_max,
        fade_close_to_origin=True,
        run_time=1.0
    ):
        curr_t_min = self.x_axis.point_to_number(self.area.get_left())
        curr_t_max = self.x_axis.point_to_number(self.area.get_right())
        if new_t_min is None:
            new_t_min = curr_t_min
        if new_t_max is None:
            new_t_max = curr_t_max

        group = VGroup(self.area)
        group.add(self.left_v_line)
        group.add(self.left_T_label_group)
        group.add(self.right_v_line)
        group.add(self.right_T_label_group)

        def update_group(group, alpha):
            area, left_v_line, left_T_label, right_v_line, right_T_label = group
            t_min = interpolate(curr_t_min, new_t_min, alpha)
            t_max = interpolate(curr_t_max, new_t_max, alpha)
            new_area = self.get_area(graph, t_min, t_max)

            new_left_v_line = self.get_vertical_line_to_graph(
                t_min, graph
            )
            new_left_v_line.set_color(left_v_line.get_color())
            left_T_label.move_to(new_left_v_line.get_bottom(), UP)

            new_right_v_line = self.get_vertical_line_to_graph(
                t_max, graph
            )
            new_right_v_line.set_color(right_v_line.get_color())
            right_T_label.move_to(new_right_v_line.get_bottom(), UP)

            # Fade close to 0
            if fade_close_to_origin:
                if len(left_T_label) > 0:
                    left_T_label[0].set_fill(opacity=min(1, np.abs(t_min)))
                if len(right_T_label) > 0:
                    right_T_label[0].set_fill(opacity=min(1, np.abs(t_max)))

            Transform(area, new_area).update(1)
            Transform(left_v_line, new_left_v_line).update(1)
            Transform(right_v_line, new_right_v_line).update(1)
            return group

        return UpdateFromAlphaFunc(group, update_group, run_time=run_time)

    def animate_secant_slope_group_change(
        self, secant_slope_group,
        target_dx=None,
        target_x=None,
        run_time=3,
        added_anims=None,
        **anim_kwargs
    ):
        if target_dx is None and target_x is None:
            raise Exception(
                "At least one of target_x and target_dx must not be None")
        if added_anims is None:
            added_anims = []

        start_dx = secant_slope_group.kwargs["dx"]
        start_x = secant_slope_group.kwargs["x"]
        if target_dx is None:
            target_dx = start_dx
        if target_x is None:
            target_x = start_x

        def update_func(group, alpha):
            dx = interpolate(start_dx, target_dx, alpha)
            x = interpolate(start_x, target_x, alpha)
            kwargs = dict(secant_slope_group.kwargs)
            kwargs["dx"] = dx
            kwargs["x"] = x
            new_group = self.get_secant_slope_group(**kwargs)
            group.become(new_group)
            return group

        self.play(
            UpdateFromAlphaFunc(
                secant_slope_group, update_func,
                run_time=run_time,
                **anim_kwargs
            ),
            *added_anims
        )
        secant_slope_group.kwargs["x"] = target_x
        secant_slope_group.kwargs["dx"] = target_dx