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

import numpy as np

from manimlib.constants import *
from manimlib.mobject.mobject import Mobject
from manimlib.mobject.types.vectorized_mobject import VGroup
from manimlib.mobject.types.vectorized_mobject import VMobject
from manimlib.mobject.types.vectorized_mobject import DashedVMobject
from manimlib.utils.config_ops import digest_config
from manimlib.utils.iterables import adjacent_n_tuples
from manimlib.utils.iterables import adjacent_pairs
from manimlib.utils.simple_functions import fdiv
from manimlib.utils.simple_functions import clip
from manimlib.utils.space_ops import angle_of_vector
from manimlib.utils.space_ops import angle_between_vectors
from manimlib.utils.space_ops import compass_directions
from manimlib.utils.space_ops import find_intersection
from manimlib.utils.space_ops import get_norm
from manimlib.utils.space_ops import normalize
from manimlib.utils.space_ops import rotate_vector


DEFAULT_DOT_RADIUS = 0.08
DEFAULT_SMALL_DOT_RADIUS = 0.04
DEFAULT_DASH_LENGTH = 0.05
DEFAULT_ARROW_TIP_LENGTH = 0.35
DEFAULT_ARROW_TIP_WIDTH = 0.35


class TipableVMobject(VMobject):
    """
    Meant for shared functionality between Arc and Line.
    Functionality can be classified broadly into these groups:

        * Adding, Creating, Modifying tips
            - add_tip calls create_tip, before pushing the new tip
                into the TipableVMobject's list of submobjects
            - stylistic and positional configuration

        * Checking for tips
            - Boolean checks for whether the TipableVMobject has a tip
                and a starting tip

        * Getters
            - Straightforward accessors, returning information pertaining
                to the TipableVMobject instance's tip(s), its length etc
    """
    CONFIG = {
        "tip_config": {
            "fill_opacity": 1,
            "stroke_width": 0,
        },
        "normal_vector": OUT,
    }

    # Adding, Creating, Modifying tips
    def add_tip(self, at_start=False, **kwargs):
        """
        Adds a tip to the TipableVMobject instance, recognising
        that the endpoints might need to be switched if it's
        a 'starting tip' or not.
        """
        tip = self.create_tip(at_start, **kwargs)
        self.reset_endpoints_based_on_tip(tip, at_start)
        self.asign_tip_attr(tip, at_start)
        self.add(tip)
        return self

    def create_tip(self, at_start=False, **kwargs):
        """
        Stylises the tip, positions it spacially, and returns
        the newly instantiated tip to the caller.
        """
        tip = self.get_unpositioned_tip(**kwargs)
        self.position_tip(tip, at_start)
        return tip

    def get_unpositioned_tip(self, **kwargs):
        """
        Returns a tip that has been stylistically configured,
        but has not yet been given a position in space.
        """
        config = self.get_style()
        config.update(self.tip_config)
        config.update(kwargs)
        return ArrowTip(**config)

    def position_tip(self, tip, at_start=False):
        # Last two control points, defining both
        # the end, and the tangency direction
        if at_start:
            anchor = self.get_start()
            handle = self.get_first_handle()
        else:
            handle = self.get_last_handle()
            anchor = self.get_end()
        tip.rotate(angle_of_vector(handle - anchor) - PI - tip.get_angle())
        tip.shift(anchor - tip.get_tip_point())
        return tip

    def reset_endpoints_based_on_tip(self, tip, at_start):
        if self.get_length() == 0:
            # Zero length, put_start_and_end_on wouldn't
            # work
            return self

        if at_start:
            start = tip.get_base()
            end = self.get_end()
        else:
            start = self.get_start()
            end = tip.get_base()
        self.put_start_and_end_on(start, end)
        return self

    def asign_tip_attr(self, tip, at_start):
        if at_start:
            self.start_tip = tip
        else:
            self.tip = tip
        return self

    # Checking for tips
    def has_tip(self):
        return hasattr(self, "tip") and self.tip in self

    def has_start_tip(self):
        return hasattr(self, "start_tip") and self.start_tip in self

    # Getters
    def pop_tips(self):
        start, end = self.get_start_and_end()
        result = VGroup()
        if self.has_tip():
            result.add(self.tip)
            self.remove(self.tip)
        if self.has_start_tip():
            result.add(self.start_tip)
            self.remove(self.start_tip)
        self.put_start_and_end_on(start, end)
        return result

    def get_tips(self):
        """
        Returns a VGroup (collection of VMobjects) containing
        the TipableVMObject instance's tips.
        """
        result = VGroup()
        if hasattr(self, "tip"):
            result.add(self.tip)
        if hasattr(self, "start_tip"):
            result.add(self.start_tip)
        return result

    def get_tip(self):
        """Returns the TipableVMobject instance's (first) tip,
        otherwise throws an exception."""
        tips = self.get_tips()
        if len(tips) == 0:
            raise Exception("tip not found")
        else:
            return tips[0]

    def get_default_tip_length(self):
        return self.tip_length

    def get_first_handle(self):
        return self.points[1]

    def get_last_handle(self):
        return self.points[-2]

    def get_end(self):
        if self.has_tip():
            return self.tip.get_start()
        else:
            return VMobject.get_end(self)

    def get_start(self):
        if self.has_start_tip():
            return self.start_tip.get_start()
        else:
            return VMobject.get_start(self)

    def get_length(self):
        start, end = self.get_start_and_end()
        return get_norm(start - end)


class Arc(TipableVMobject):
    CONFIG = {
        "radius": 1.0,
        "n_components": 8,
        "anchors_span_full_range": True,
        "arc_center": ORIGIN,
    }

    def __init__(self, start_angle=0, angle=TAU / 4, **kwargs):
        self.start_angle = start_angle
        self.angle = angle
        VMobject.__init__(self, **kwargs)

    def init_points(self):
        self.set_pre_positioned_points()
        self.scale(self.radius, about_point=ORIGIN)
        self.shift(self.arc_center)

    def set_pre_positioned_points(self):
        samples = np.array([
            np.cos(a) * RIGHT + np.sin(a) * UP
            for a in np.linspace(
                self.start_angle,
                self.start_angle + self.angle,
                2 * self.n_components + 1,
            )
        ])
        theta = self.angle / self.n_components
        samples[1::2] /= np.cos(theta / 2)

        self.points = np.zeros((3 * self.n_components, self.dim))
        self.points[0::3] = samples[0:-1:2]
        self.points[1::3] = samples[1::2]
        self.points[2::3] = samples[2::2]

    def get_arc_center(self):
        """
        Looks at the normals to the first two
        anchors, and finds their intersection points
        """
        # First two anchors and handles
        a1, h, a2 = self.points[:3]
        # Tangent vectors
        t1 = h - a1
        t2 = h - a2
        # Normals
        n1 = rotate_vector(t1, TAU / 4)
        n2 = rotate_vector(t2, TAU / 4)
        return find_intersection(a1, n1, a2, n2)

    def get_start_angle(self):
        angle = angle_of_vector(self.get_start() - self.get_arc_center())
        return angle % TAU

    def get_stop_angle(self):
        angle = angle_of_vector(self.get_end() - self.get_arc_center())
        return angle % TAU

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


class ArcBetweenPoints(Arc):
    def __init__(self, start, end, angle=TAU / 4, **kwargs):
        Arc.__init__(self, angle=angle, **kwargs)
        if angle == 0:
            self.set_points_as_corners([LEFT, RIGHT])
        self.put_start_and_end_on(start, end)


class CurvedArrow(ArcBetweenPoints):
    def __init__(self, start_point, end_point, **kwargs):
        ArcBetweenPoints.__init__(self, start_point, end_point, **kwargs)
        self.add_tip()


class CurvedDoubleArrow(CurvedArrow):
    def __init__(self, start_point, end_point, **kwargs):
        CurvedArrow.__init__(self, start_point, end_point, **kwargs)
        self.add_tip(at_start=True)


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

    def __init__(self, **kwargs):
        Arc.__init__(self, 0, TAU, **kwargs)

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

        self.replace(mobject, dim_to_match, stretch)
        self.stretch((self.get_width() + 2 * buff) / self.get_width(), 0)
        self.stretch((self.get_height() + 2 * buff) / self.get_height(), 1)

    def point_at_angle(self, angle):
        start_angle = self.get_start_angle()
        return self.point_from_proportion(
            (angle - start_angle) / TAU
        )


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

    def __init__(self, point=ORIGIN, **kwargs):
        Circle.__init__(self, arc_center=point, **kwargs)
        self.lock_triangulation()


class SmallDot(Dot):
    CONFIG = {
        "radius": DEFAULT_SMALL_DOT_RADIUS,
    }


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

    def __init__(self, **kwargs):
        Circle.__init__(self, **kwargs)
        self.set_width(self.width, stretch=True)
        self.set_height(self.height, stretch=True)


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

    def init_points(self):
        inner_arc, outer_arc = [
            Arc(
                start_angle=self.start_angle,
                angle=self.angle,
                radius=radius,
                arc_center=self.arc_center,
            )
            for radius in (self.inner_radius, self.outer_radius)
        ]
        outer_arc.reverse_points()
        self.append_points(inner_arc.points)
        self.add_line_to(outer_arc.points[0])
        self.append_points(outer_arc.points)
        self.add_line_to(inner_arc.points[0])


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


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

    def init_points(self):
        self.radius = self.outer_radius
        outer_circle = Circle(radius=self.outer_radius)
        inner_circle = Circle(radius=self.inner_radius)
        inner_circle.reverse_points()
        self.append_points(outer_circle.points)
        self.append_points(inner_circle.points)
        self.shift(self.arc_center)


class Line(TipableVMobject):
    CONFIG = {
        "buff": 0,
        # Angle of arc specified here
        "path_arc": None,
    }

    def __init__(self, start=LEFT, end=RIGHT, **kwargs):
        digest_config(self, kwargs)
        self.set_start_and_end_attrs(start, end)
        VMobject.__init__(self, **kwargs)

    def init_points(self):
        if self.path_arc:
            arc = ArcBetweenPoints(
                self.start, self.end,
                angle=self.path_arc
            )
            self.set_points(arc.points)
        else:
            self.set_points_as_corners([self.start, self.end])
        self.account_for_buff()

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

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

    def set_start_and_end_attrs(self, start, end):
        # If either start or end are Mobjects, this
        # gives their centers
        rough_start = self.pointify(start)
        rough_end = self.pointify(end)
        vect = normalize(rough_end - rough_start)
        # Now that we know the direction between them,
        # we can find the appropriate boundary point from
        # start and end, if they're mobjects
        self.start = self.pointify(start, vect)
        self.end = self.pointify(end, -vect)

    def pointify(self, mob_or_point, direction=None):
        if isinstance(mob_or_point, Mobject):
            mob = mob_or_point
            if direction is None:
                return mob.get_center()
            else:
                return mob.get_boundary_point(direction)
        return mob_or_point

    def put_start_and_end_on(self, start, end):
        curr_start, curr_end = self.get_start_and_end()
        if np.all(curr_start == curr_end):
            # TODO, any problems with resetting
            # these attrs?
            self.start = start
            self.end = end
            self.init_points()
        return super().put_start_and_end_on(start, end)

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

    def get_unit_vector(self):
        return normalize(self.get_vector())

    def get_angle(self):
        return angle_of_vector(self.get_vector())

    def get_slope(self):
        return np.tan(self.get_angle())

    def set_angle(self, angle):
        self.rotate(
            angle - self.get_angle(),
            about_point=self.get_start(),
        )

    def set_length(self, length):
        self.scale(length / self.get_length())


class DashedLine(Line):
    CONFIG = {
        "dash_length": DEFAULT_DASH_LENGTH,
        "dash_spacing": None,
        "positive_space_ratio": 0.5,
    }

    def __init__(self, *args, **kwargs):
        Line.__init__(self, *args, **kwargs)
        ps_ratio = self.positive_space_ratio
        num_dashes = self.calculate_num_dashes(ps_ratio)
        dashes = DashedVMobject(
            self,
            num_dashes=num_dashes,
            positive_space_ratio=ps_ratio
        )
        self.clear_points()
        self.add(*dashes)

    def calculate_num_dashes(self, positive_space_ratio):
        try:
            full_length = self.dash_length / positive_space_ratio
            return int(np.ceil(self.get_length() / full_length))
        except ZeroDivisionError:
            return 1

    def calculate_positive_space_ratio(self):
        return fdiv(
            self.dash_length,
            self.dash_length + self.dash_spacing,
        )

    def get_start(self):
        if len(self.submobjects) > 0:
            return self.submobjects[0].get_start()
        else:
            return Line.get_start(self)

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

    def get_first_handle(self):
        return self.submobjects[0].points[1]

    def get_last_handle(self):
        return self.submobjects[-1].points[-2]


class TangentLine(Line):
    CONFIG = {
        "length": 1,
        "d_alpha": 1e-6
    }

    def __init__(self, vmob, alpha, **kwargs):
        digest_config(self, kwargs)
        da = self.d_alpha
        a1 = clip(alpha - da, 0, 1)
        a2 = clip(alpha + da, 0, 1)
        super().__init__(
            vmob.point_from_proportion(a1),
            vmob.point_from_proportion(a2),
            **kwargs
        )
        self.scale(self.length / self.get_length())


class Elbow(VMobject):
    CONFIG = {
        "width": 0.2,
        "angle": 0,
    }

    def __init__(self, **kwargs):
        VMobject.__init__(self, **kwargs)
        self.set_points_as_corners([UP, UP + RIGHT, RIGHT])
        self.set_width(self.width, about_point=ORIGIN)
        self.rotate(self.angle, about_point=ORIGIN)


class Arrow(Line):
    CONFIG = {
        "stroke_width": 6,
        "buff": MED_SMALL_BUFF,
        # TODO, the interface is terrible
        "max_tip_length_to_length_ratio": 0.25,
        "max_stroke_width_to_length_ratio": 5,
        "preserve_tip_size_when_scaling": True,
    }

    def __init__(self, *args, **kwargs):
        super().__init__(*args, **kwargs)
        # TODO, should this be affected when
        # Arrow.set_stroke is called?
        self.initial_stroke_width = self.stroke_width
        self.add_tip()
        self.set_stroke_width_from_length()

    def scale(self, factor, **kwargs):
        if self.get_length() == 0:
            return self

        has_tip = self.has_tip()
        has_start_tip = self.has_start_tip()
        if has_tip or has_start_tip:
            old_tips = self.pop_tips()

        VMobject.scale(self, factor, **kwargs)
        self.set_stroke_width_from_length()

        # So horribly confusing, must redo
        if has_tip:
            self.add_tip()
            old_tips[0].points[:, :] = self.tip.points
            self.remove(self.tip)
            self.tip = old_tips[0]
            self.add(self.tip)
        if has_start_tip:
            self.add_tip(at_start=True)
            old_tips[1].points[:, :] = self.start_tip.points
            self.remove(self.start_tip)
            self.start_tip = old_tips[1]
            self.add(self.start_tip)
        return self

    def get_normal_vector(self):
        p0, p1, p2 = self.tip.get_start_anchors()[:3]
        return normalize(np.cross(p2 - p1, p1 - p0))

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

    def get_default_tip_length(self):
        max_ratio = self.max_tip_length_to_length_ratio
        return min(
            self.tip_length,
            max_ratio * self.get_length(),
        )

    def set_stroke_width_from_length(self):
        mr = self.max_stroke_width_to_length_ratio
        width = min(self.initial_stroke_width, mr * self.get_length())
        self.set_stroke(width=width)
        return self


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

    def __init__(self, direction=RIGHT, **kwargs):
        if len(direction) == 2:
            direction = np.hstack([direction, 0])
        Arrow.__init__(self, ORIGIN, direction, **kwargs)


class DoubleArrow(Arrow):
    def __init__(self, *args, **kwargs):
        Arrow.__init__(self, *args, **kwargs)
        self.add_tip(at_start=True)


class CubicBezier(VMobject):
    def __init__(self, a0, h0, h1, a1, **kwargs):
        VMobject.__init__(self, **kwargs)
        self.add_cubic_bezier_curve(a0, h0, h1, a1)


class Polygon(VMobject):
    CONFIG = {
        "color": BLUE,
    }

    def __init__(self, *vertices, **kwargs):
        self.vertices = vertices
        super().__init__(**kwargs)

    def init_points(self):
        verts = self.vertices
        self.set_points_as_corners([*verts, verts[0]])

    def get_vertices(self):
        return self.get_start_anchors()

    def round_corners(self, radius=0.5):
        vertices = self.get_vertices()
        arcs = []
        for v1, v2, v3 in adjacent_n_tuples(vertices, 3):
            vect1 = v2 - v1
            vect2 = v3 - v2
            unit_vect1 = normalize(vect1)
            unit_vect2 = normalize(vect2)
            angle = angle_between_vectors(vect1, vect2)
            # Negative radius gives concave curves
            angle *= np.sign(radius)
            # Distance between vertex and start of the arc
            cut_off_length = radius * np.tan(angle / 2)
            # Determines counterclockwise vs. clockwise
            sign = np.sign(np.cross(vect1, vect2)[2])
            arc = ArcBetweenPoints(
                v2 - unit_vect1 * cut_off_length,
                v2 + unit_vect2 * cut_off_length,
                angle=sign * angle,
                n_components=2,
            )
            arcs.append(arc)

        self.clear_points()
        # To ensure that we loop through starting with last
        arcs = [arcs[-1], *arcs[:-1]]
        for arc1, arc2 in adjacent_pairs(arcs):
            self.append_points(arc1.points)
            line = Line(arc1.get_end(), arc2.get_start())
            # Make sure anchors are evenly distributed
            len_ratio = line.get_length() / arc1.get_arc_length()
            line.insert_n_curves(
                int(arc1.get_num_curves() * len_ratio)
            )
            self.append_points(line.get_points())
        return self


class RegularPolygon(Polygon):
    CONFIG = {
        "start_angle": None,
    }

    def __init__(self, n=6, **kwargs):
        digest_config(self, kwargs, locals())
        if self.start_angle is None:
            # 0 for odd, 90 for even
            self.start_angle = (n % 2) * 90 * DEGREES
        start_vect = rotate_vector(RIGHT, self.start_angle)
        vertices = compass_directions(n, start_vect)
        super().__init__(*vertices, **kwargs)


class Triangle(RegularPolygon):
    def __init__(self, **kwargs):
        super().__init__(n=3, **kwargs)


class ArrowTip(Triangle):
    CONFIG = {
        "fill_opacity": 1,
        "stroke_width": 0,
        "width": DEFAULT_ARROW_TIP_WIDTH,
        "length": DEFAULT_ARROW_TIP_LENGTH,
        "angle": 0,
    }

    def __init__(self, **kwargs):
        Triangle.__init__(self, start_angle=0, **kwargs)
        self.set_height(self.width)
        self.set_width(self.length, stretch=True)
        self.rotate(self.angle)

    def get_base(self):
        return self.point_from_proportion(0.5)

    def get_tip_point(self):
        return self.points[0]

    def get_vector(self):
        return self.get_tip_point() - self.get_base()

    def get_angle(self):
        return angle_of_vector(self.get_vector())

    def get_length(self):
        return get_norm(self.get_vector())


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

    def __init__(self, width=None, height=None, **kwargs):
        Polygon.__init__(self, UR, UL, DL, DR, **kwargs)
        self.width = width or self.width
        self.height = height or self.height
        self.set_width(self.width, stretch=True)
        self.set_height(self.height, stretch=True)


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 RoundedRectangle(Rectangle):
    CONFIG = {
        "corner_radius": 0.5,
    }

    def __init__(self, **kwargs):
        Rectangle.__init__(self, **kwargs)
        self.round_corners(self.corner_radius)