3b1b-manim/mobject/geometry.py

from __future__ import absolute_import

from constants import *

import itertools as it
import numpy as np

from mobject.mobject import Mobject
from mobject.types.vectorized_mobject import VGroup
from mobject.types.vectorized_mobject import VMobject
from utils.bezier import interpolate
from utils.config_ops import digest_config
from utils.config_ops import digest_locals
from utils.paths import path_along_arc
from utils.space_ops import angle_of_vector
from utils.space_ops import center_of_mass
from utils.space_ops import compass_directions
from utils.space_ops import rotate_vector


class Arc(VMobject):
    CONFIG = {
        "radius": 1.0,
        "start_angle": 0,
        "num_anchors": 9,
        "anchors_span_full_range": True,
    }

    def __init__(self, angle, **kwargs):
        self.angle = angle
        VMobject.__init__(self, **kwargs)

    def generate_points(self):
        anchors = np.array([
            np.cos(a) * RIGHT + np.sin(a) * UP
            for a in np.linspace(
                self.start_angle,
                self.start_angle + self.angle,
                self.num_anchors
            )
        ])
        # Figure out which control points will give the
        # Appropriate tangent lines to the circle
        d_theta = self.angle / (self.num_anchors - 1.0)
        tangent_vectors = np.zeros(anchors.shape)
        tangent_vectors[:, 1] = anchors[:, 0]
        tangent_vectors[:, 0] = -anchors[:, 1]
        handles1 = anchors[:-1] + (d_theta / 3) * tangent_vectors[:-1]
        handles2 = anchors[1:] - (d_theta / 3) * tangent_vectors[1:]
        self.set_anchors_and_handles(
            anchors, handles1, handles2
        )
        self.scale(self.radius, about_point=ORIGIN)

    def add_tip(self, tip_length=0.25, at_start=False, at_end=True):
        # clear out any old tips
        for submob in self.submobjects:
            if submob.mark_paths_closed:
                self.remove(submob)

        # TODO, do this a better way
        p1 = p2 = p3 = p4 = None
        start_arrow = end_arrow = None
        if at_end:
            p1, p2 = self.points[-3:-1]
            # self.points[-2:] did overshoot
            start_arrow = Arrow(
                p1, 2 * p2 - p1,
                tip_length=tip_length,
                max_tip_length_to_length_ratio=2.0
            )
            self.add(start_arrow.split()[-1])  # just the tip

        if at_start:
            p4, p3 = self.points[1:3]
            # self.points[:2] did overshoot
            end_arrow = Arrow(
                p3, 2 * p4 - p3,
                tip_length=tip_length,
                max_tip_length_to_length_ratio=2.0
            )
            self.add(end_arrow.split()[-1])

        self.set_color(self.get_color())
        return self

    def get_arc_center(self):
        first_point = self.points[0]
        radial_unit_vector = np.array(
            [np.cos(self.start_angle), np.sin(self.start_angle), 0])
        arc_center = first_point - self.radius * radial_unit_vector
        return arc_center

    def move_arc_center_to(self, point):
        v = point - self.get_arc_center()
        self.shift(v)
        return self

    def stop_angle(self):
        return self.start_angle + self.angle

    def set_bound_angles(self, start=0, stop=np.pi):
        self.start_angle = start
        self.angle = stop - start

        return self


class ArcBetweenPoints(Arc):

    def __init__(self, start_point, end_point, angle=TAU / 4, **kwargs):
        if angle == 0:
            raise Exception("Arc with zero curve angle: use Line instead.")

        midpoint = 0.5 * (start_point + end_point)
        distance_vector = end_point - start_point
        normal_vector = np.array([-distance_vector[1], distance_vector[0], 0])
        distance = np.linalg.norm(normal_vector)
        normal_vector /= distance
        if angle < 0:
            normal_vector *= -1

        radius = distance / 2 / np.sin(0.5 * np.abs(angle))
        length = distance / 2 / np.tan(0.5 * np.abs(angle))
        arc_center = midpoint + length * normal_vector
        w = start_point - arc_center
        if w[0] != 0:
            start_angle = np.arctan2(w[1], w[0])
        else:
            start_angle = np.pi / 2

        Arc.__init__(self, angle,
                     radius=radius,
                     start_angle=start_angle,
                     **kwargs)

        self.move_arc_center_to(arc_center)


class CurvedArrow(ArcBetweenPoints):

    def __init__(self, start_point, end_point, angle=TAU / 4, **kwargs):
        # I know this is in reverse, but it works
        if angle >= 0:
            ArcBetweenPoints.__init__(
                self, start_point, end_point, angle=angle, **kwargs)
            self.add_tip(at_start=True, at_end=False)
        else:
            ArcBetweenPoints.__init__(
                self, end_point, start_point, angle=-angle, **kwargs)
            self.add_tip(at_start=False, at_end=True)


class CurvedDoubleArrow(ArcBetweenPoints):

    def __init__(self, start_point, end_point, angle=TAU / 4, **kwargs):
        ArcBetweenPoints.__init__(
            self, start_point, end_point, angle=angle, **kwargs)
        self.add_tip(at_start=True, at_end=True)


class Circle(Arc):
    CONFIG = {
        "color": RED,
        "close_new_points": True,
        "anchors_span_full_range": False
    }

    def __init__(self, **kwargs):
        Arc.__init__(self, 2 * np.pi, **kwargs)

    def surround(self, mobject, dim_to_match=0, stretch=False, buffer_factor=1.2):
        # Ignores dim_to_match and stretch; result will always be a circle
        # TODO: Perhaps create an ellipse class to handle singele-dimension stretching

        # Something goes wrong here when surrounding lines?
        # TODO: Figure out and fix
        self.replace(mobject, dim_to_match, stretch)

        self.scale_to_fit_width(
            np.sqrt(mobject.get_width()**2 + mobject.get_height()**2))
        self.scale(buffer_factor)


class Dot(Circle):
    CONFIG = {
        "radius": 0.08,
        "stroke_width": 0,
        "fill_opacity": 1.0,
        "color": WHITE
    }

    def __init__(self, point=ORIGIN, **kwargs):
        Circle.__init__(self, **kwargs)
        self.shift(point)
        self.init_colors()


class Ellipse(VMobject):
    CONFIG = {
        "width": 2,
        "height": 1
    }

    def generate_points(self):
        circle = Circle(radius=1)
        circle = circle.stretch_to_fit_width(self.width)
        circle = circle.stretch_to_fit_height(self.height)
        self.points = circle.points


class AnnularSector(VMobject):
    CONFIG = {
        "inner_radius": 1,
        "outer_radius": 2,
        "angle": TAU / 4,
        "start_angle": 0,
        "fill_opacity": 1,
        "stroke_width": 0,
        "color": WHITE,
        "mark_paths_closed": True,
    }

    def generate_points(self):
        arc1 = Arc(
            angle=self.angle,
            start_angle=self.start_angle,
            radius=self.inner_radius,
        )
        arc2 = Arc(
            angle=-1 * self.angle,
            start_angle=self.start_angle + self.angle,
            radius=self.outer_radius,
        )
        a1_to_a2_points = np.array([
            interpolate(arc1.points[-1], arc2.points[0], alpha)
            for alpha in np.linspace(0, 1, 4)
        ])
        a2_to_a1_points = np.array([
            interpolate(arc2.points[-1], arc1.points[0], alpha)
            for alpha in np.linspace(0, 1, 4)
        ])
        self.points = np.array(arc1.points)
        self.add_control_points(a1_to_a2_points[1:])
        self.add_control_points(arc2.points[1:])
        self.add_control_points(a2_to_a1_points[1:])

    def get_arc_center(self):
        first_point = self.points[0]
        last_point = self.points[-2]
        v = last_point - first_point
        radial_unit_vector = v / np.linalg.norm(v)
        arc_center = first_point - self.inner_radius * radial_unit_vector
        return arc_center

    def move_arc_center_to(self, point):
        v = point - self.get_arc_center()
        self.shift(v)
        return self


class Sector(AnnularSector):
    CONFIG = {
        "outer_radius": 1,
        "inner_radius": 0
    }

    @property
    def radius(self):
        return self.outer_radius

    @radius.setter
    def radius(self, new_radius):
        self.outer_radius = new_radius


class Annulus(Circle):
    CONFIG = {
        "inner_radius": 1,
        "outer_radius": 2,
        "fill_opacity": 1,
        "stroke_width": 0,
        "color": WHITE,
        "mark_paths_closed": False,
        "propagate_style_to_family": True
    }

    def generate_points(self):
        self.points = []
        self.radius = self.outer_radius
        outer_circle = Circle(radius=self.outer_radius)
        inner_circle = Circle(radius=self.inner_radius)
        inner_circle.flip()
        self.points = outer_circle.points
        self.add_subpath(inner_circle.points)


class Line(VMobject):
    CONFIG = {
        "buff": 0,
        "path_arc": None,  # angle of arc specified here
        "n_arc_anchors": 10,  # Only used if path_arc is not None
    }

    def __init__(self, start, end, **kwargs):
        digest_config(self, kwargs)
        self.set_start_and_end(start, end)
        VMobject.__init__(self, **kwargs)

    def generate_points(self):
        if self.path_arc is None:
            self.set_points_as_corners([self.start, self.end])
        else:
            path_func = path_along_arc(self.path_arc)
            self.set_points_smoothly([
                path_func(self.start, self.end, alpha)
                for alpha in np.linspace(0, 1, self.n_arc_anchors)
            ])
        self.account_for_buff()

    def set_path_arc(self, new_value):
        self.path_arc = new_value
        self.generate_points()

    def account_for_buff(self):
        length = self.get_arc_length()
        if length < 2 * self.buff or self.buff == 0:
            return
        buff_proportion = self.buff / length
        self.pointwise_become_partial(
            self, buff_proportion, 1 - buff_proportion
        )

    def set_start_and_end(self, start, end):
        start_to_end = self.pointify(end) - self.pointify(start)
        vect = np.zeros(len(start_to_end))
        longer_dim = np.argmax(map(abs, start_to_end))
        vect[longer_dim] = start_to_end[longer_dim]
        self.start, self.end = [
            arg.get_edge_center(unit * vect)
            if isinstance(arg, Mobject)
            else np.array(arg)
            for arg, unit in zip([start, end], [1, -1])
        ]

    def pointify(self, mob_or_point):
        if isinstance(mob_or_point, Mobject):
            return mob_or_point.get_center()
        return np.array(mob_or_point)

    def get_length(self):
        start, end = self.get_start_and_end()
        return np.linalg.norm(start - end)

    def get_arc_length(self):
        if self.path_arc:
            anchors = self.get_anchors()
            return sum([
                np.linalg.norm(a2 - a1)
                for a1, a2 in zip(anchors, anchors[1:])
            ])
        else:
            return self.get_length()

    def get_start_and_end(self):
        return self.get_start(), self.get_end()

    def get_vector(self):
        return self.get_end() - self.get_start()

    def get_start(self):
        return np.array(self.points[0])

    def get_end(self):
        return np.array(self.points[-1])

    def get_slope(self):
        start, end = self.get_start_and_end()
        rise, run = [
            float(end[i] - start[i])
            for i in [1, 0]
        ]
        return np.inf if run == 0 else rise / run

    def get_angle(self):
        start, end = self.get_start_and_end()
        return angle_of_vector(end - start)

    # def put_start_and_end_on(self, new_start, new_end):
    #     self.set_start_and_end(new_start, new_end)
    #     self.buff = 0
    #     self.generate_points()

    def put_start_and_end_on(self, new_start, new_end):
        self.start = new_start
        self.end = new_end
        self.buff = 0
        self.generate_points()
        return

    def put_start_and_end_on_with_projection(self, new_start, new_end):
        target_vect = np.array(new_end) - np.array(new_start)
        curr_vect = self.get_vector()
        curr_norm = np.linalg.norm(curr_vect)
        if curr_norm == 0:
            self.put_start_and_end_on(new_start, new_end)
            return
        target_norm = np.linalg.norm(target_vect)
        if target_norm == 0:
            epsilon = 0.001
            self.scale(epsilon / curr_norm)
            self.move_to(new_start)
            return
        unit_target = target_vect / target_norm
        unit_curr = curr_vect / curr_norm
        normal = np.cross(unit_target, unit_curr)
        if np.linalg.norm(normal) == 0:
            if unit_curr[0] == 0 and unit_curr[1] == 0:
                normal = UP
            else:
                normal = OUT
        angle_diff = np.arccos(
            np.clip(np.dot(unit_target, unit_curr), -1, 1)
        )
        self.scale(target_norm / curr_norm)
        self.rotate(-angle_diff, normal)
        self.shift(new_start - self.get_start())
        return self

    def insert_n_anchor_points(self, n):
        if not self.path_arc:
            n_anchors = self.get_num_anchor_points()
            new_num_points = 3 * (n_anchors + n) - 2
            self.points = np.array([
                self.point_from_proportion(alpha)
                for alpha in np.linspace(0, 1, new_num_points)
            ])
        else:
            VMobject.insert_n_anchor_points(self, n)


class DashedLine(Line):
    CONFIG = {
        "dashed_segment_length": 0.05
    }

    def __init__(self, *args, **kwargs):
        self.init_kwargs = kwargs
        Line.__init__(self, *args, **kwargs)

    def generate_points(self):
        length = np.linalg.norm(self.end - self.start)
        num_interp_points = int(length / self.dashed_segment_length)
        points = [
            interpolate(self.start, self.end, alpha)
            for alpha in np.linspace(0, 1, num_interp_points)
        ]
        includes = it.cycle([True, False])
        self.submobjects = [
            Line(p1, p2, **self.init_kwargs)
            for p1, p2, include in zip(points, points[1:], includes)
            if include
        ]
        self.put_start_and_end_on_with_projection(self.start, self.end)
        return self

    def get_start(self):
        if len(self.points) > 0:
            return self[0].points[0]
        else:
            return self.start

    def get_end(self):
        if len(self) > 0:
            return self[-1].points[-1]
        else:
            return self.end


class Arrow(Line):
    CONFIG = {
        "tip_length": 0.25,
        "tip_width_to_length_ratio": 1,
        "max_tip_length_to_length_ratio": 0.35,
        "max_stem_width_to_tip_width_ratio": 0.3,
        "buff": MED_SMALL_BUFF,
        "propagate_style_to_family": False,
        "preserve_tip_size_when_scaling": True,
        "normal_vector": OUT,
        "use_rectangular_stem": True,
        "rectangular_stem_width": 0.05,
    }

    def __init__(self, *args, **kwargs):
        points = map(self.pointify, args)
        if len(args) == 1:
            args = (points[0] + UP + LEFT, points[0])
        Line.__init__(self, *args, **kwargs)
        self.init_tip()
        if self.use_rectangular_stem and not hasattr(self, "rect"):
            self.add_rectangular_stem()
        self.init_colors()

    def init_tip(self):
        self.add_tip()

    def add_tip(self, add_at_end=True):
        tip = VMobject(
            close_new_points=True,
            mark_paths_closed=True,
            fill_color=self.color,
            fill_opacity=1,
            stroke_color=self.color,
            stroke_width=0,
        )
        tip.add_at_end = add_at_end
        self.set_tip_points(tip, add_at_end, preserve_normal=False)
        self.add(tip)
        if not hasattr(self, 'tip'):
            self.tip = VGroup()
            self.tip.match_style(tip)
        self.tip.add(tip)
        return tip

    def add_rectangular_stem(self):
        self.rect = Rectangle(
            stroke_width=0,
            fill_color=self.tip.get_fill_color(),
            fill_opacity=self.tip.get_fill_opacity()
        )
        self.add_to_back(self.rect)
        self.set_stroke(width=0)
        self.set_rectangular_stem_points()

    def set_rectangular_stem_points(self):
        start, end = self.get_start_and_end()
        tip_base_points = self.tip[0].get_anchors()[1:]
        tip_base = center_of_mass(tip_base_points)
        tbp1, tbp2 = tip_base_points
        perp_vect = tbp2 - tbp1
        tip_base_width = np.linalg.norm(perp_vect)
        if tip_base_width > 0:
            perp_vect /= tip_base_width
        width = min(
            self.rectangular_stem_width,
            self.max_stem_width_to_tip_width_ratio * tip_base_width,
        )
        if hasattr(self, "second_tip"):
            start = center_of_mass(
                self.second_tip.get_anchors()[1:]
            )
        self.rect.set_points_as_corners([
            tip_base + perp_vect * width / 2,
            start + perp_vect * width / 2,
            start - perp_vect * width / 2,
            tip_base - perp_vect * width / 2,
        ])
        return self

    def set_tip_points(
        self, tip,
        add_at_end=True,
        tip_length=None,
        preserve_normal=True,
    ):
        if tip_length is None:
            tip_length = self.tip_length
        if preserve_normal:
            normal_vector = self.get_normal_vector()
        else:
            normal_vector = self.normal_vector
        line_length = np.linalg.norm(self.points[-1] - self.points[0])
        tip_length = min(
            tip_length, self.max_tip_length_to_length_ratio * line_length
        )

        indices = (-2, -1) if add_at_end else (1, 0)
        pre_end_point, end_point = [
            self.get_anchors()[index]
            for index in indices
        ]
        vect = end_point - pre_end_point
        perp_vect = np.cross(vect, normal_vector)
        for v in vect, perp_vect:
            if np.linalg.norm(v) == 0:
                v[0] = 1
            v *= tip_length / np.linalg.norm(v)
        ratio = self.tip_width_to_length_ratio
        tip.set_points_as_corners([
            end_point,
            end_point - vect + perp_vect * ratio / 2,
            end_point - vect - perp_vect * ratio / 2,
        ])

        return self

    def get_normal_vector(self):
        p0, p1, p2 = self.tip[0].get_anchors()
        result = np.cross(p2 - p1, p1 - p0)
        norm = np.linalg.norm(result)
        if norm == 0:
            return self.normal_vector
        else:
            return result / norm

    def reset_normal_vector(self):
        self.normal_vector = self.get_normal_vector()
        return self

    def get_end(self):
        if hasattr(self, "tip"):
            return self.tip[0].get_anchors()[0]
        else:
            return Line.get_end(self)

    def get_tip(self):
        return self.tip

    def put_start_and_end_on(self, *args, **kwargs):
        Line.put_start_and_end_on(self, *args, **kwargs)
        self.set_tip_points(self.tip[0], preserve_normal=False)
        self.set_rectangular_stem_points()
        return self

    def scale(self, scale_factor, **kwargs):
        Line.scale(self, scale_factor, **kwargs)
        if self.preserve_tip_size_when_scaling:
            for t in self.tip:
                self.set_tip_points(t, add_at_end=t.add_at_end)
        if self.use_rectangular_stem:
            self.set_rectangular_stem_points()
        return self

    def copy(self):
        return self.deepcopy()


class Vector(Arrow):
    CONFIG = {
        "color": YELLOW,
        "buff": 0,
    }

    def __init__(self, direction, **kwargs):
        if len(direction) == 2:
            direction = np.append(np.array(direction), 0)
        Arrow.__init__(self, ORIGIN, direction, **kwargs)


class DoubleArrow(Arrow):
    def init_tip(self):
        self.tip = VGroup()
        for b in True, False:
            t = self.add_tip(add_at_end=b)
            t.add_at_end = b
            self.tip.add(t)
        self.tip.match_style(self.tip[0])


class CubicBezier(VMobject):
    def __init__(self, points, **kwargs):
        VMobject.__init__(self, **kwargs)
        self.set_points(points)


class Polygon(VMobject):
    CONFIG = {
        "color": GREEN_D,
        "mark_paths_closed": True,
        "close_new_points": True,
    }

    def __init__(self, *vertices, **kwargs):
        assert len(vertices) > 1
        digest_locals(self)
        VMobject.__init__(self, **kwargs)

    def generate_points(self):
        self.set_anchor_points(self.vertices, mode="corners")

    def get_vertices(self):
        return self.get_anchors_and_handles()[0]


class RegularPolygon(Polygon):
    CONFIG = {
        "start_angle": 0
    }

    def __init__(self, n=3, **kwargs):
        digest_config(self, kwargs, locals())
        start_vect = rotate_vector(RIGHT, self.start_angle)
        vertices = compass_directions(n, start_vect)
        Polygon.__init__(self, *vertices, **kwargs)


class Rectangle(VMobject):
    CONFIG = {
        "color": WHITE,
        "height": 2.0,
        "width": 4.0,
        "mark_paths_closed": True,
        "close_new_points": True,
    }

    def generate_points(self):
        y, x = self.height / 2., self.width / 2.
        self.set_anchor_points([
            x * LEFT + y * UP,
            x * RIGHT + y * UP,
            x * RIGHT + y * DOWN,
            x * LEFT + y * DOWN
        ], mode="corners")


class Square(Rectangle):
    CONFIG = {
        "side_length": 2.0,
    }

    def __init__(self, **kwargs):
        digest_config(self, kwargs)
        Rectangle.__init__(
            self,
            height=self.side_length,
            width=self.side_length,
            **kwargs
        )


class Grid(VMobject):
    CONFIG = {
        "height": 6.0,
        "width": 6.0,
    }

    def __init__(self, rows, columns, **kwargs):
        digest_config(self, kwargs, locals())
        VMobject.__init__(self, **kwargs)

    def generate_points(self):
        x_step = self.width / self.columns
        y_step = self.height / self.rows

        for x in np.arange(0, self.width + x_step, x_step):
            self.add(Line(
                [x - self.width / 2., -self.height / 2., 0],
                [x - self.width / 2., self.height / 2., 0],
            ))
        for y in np.arange(0, self.height + y_step, y_step):
            self.add(Line(
                [-self.width / 2., y - self.height / 2., 0],
                [self.width / 2., y - self.height / 2., 0]
            ))