3b1b-manim/mobject/number_line.py

from __future__ import absolute_import

from constants import *

from mobject.svg.tex_mobject import TexMobject
from mobject.types.vectorized_mobject import VGroup
from mobject.types.vectorized_mobject import VMobject
from mobject.geometry import Arrow
from mobject.geometry import Line
from utils.bezier import interpolate
from utils.config_ops import digest_config

class NumberLine(VMobject):
    CONFIG = {
        "color" : BLUE,
        "x_min" : -FRAME_X_RADIUS,
        "x_max" : FRAME_X_RADIUS,
        "unit_size" : 1,
        "tick_size" : 0.1,
        "tick_frequency" : 1,
        "leftmost_tick" : None, #Defaults to value near x_min s.t. 0 is a tick
        "numbers_with_elongated_ticks" : [0],
        "numbers_to_show" : None,
        "longer_tick_multiple" : 2,
        "number_at_center" : 0,
        "number_scale_val" : 0.75,
        "label_direction" : DOWN,
        "line_to_number_buff" : MED_SMALL_BUFF,
        "include_tip" : False,
        "propagate_style_to_family" : True,
    }

    def __init__(self, **kwargs):
        digest_config(self, kwargs)
        if self.leftmost_tick is None:
            tf = self.tick_frequency
            self.leftmost_tick = tf*np.ceil(self.x_min/tf)
        VMobject.__init__(self, **kwargs)
        if self.include_tip:
            self.add_tip()

    def generate_points(self):
        self.main_line = Line(self.x_min*RIGHT, self.x_max*RIGHT)
        self.tick_marks = VGroup()
        self.add(self.main_line, self.tick_marks)
        rounding_value = int(-np.log10(0.1*self.tick_frequency))
        rounded_numbers_with_elongated_ticks = np.round(
            self.numbers_with_elongated_ticks, 
            rounding_value
        )

        for x in self.get_tick_numbers():
            rounded_x = np.round(x, rounding_value)
            if rounded_x in rounded_numbers_with_elongated_ticks:
                tick_size_used = self.longer_tick_multiple*self.tick_size
            else:
                tick_size_used = self.tick_size
            self.add_tick(x, tick_size_used)

        self.stretch(self.unit_size, 0)
        self.shift(-self.number_to_point(self.number_at_center))

    def add_tick(self, x, size = None):
        self.tick_marks.add(self.get_tick(x, size))
        return self

    def get_tick(self, x, size = None):
        if size is None: size = self.tick_size
        result = Line(size*DOWN, size*UP)
        result.rotate(self.main_line.get_angle())
        result.move_to(self.number_to_point(x))
        return result

    def get_tick_marks(self):
        return self.tick_marks

    def get_tick_numbers(self):
        epsilon = 0.001
        return np.arange(
            self.leftmost_tick, self.x_max+epsilon,
            self.tick_frequency
        )

    def number_to_point(self, number):
        alpha = float(number-self.x_min)/(self.x_max - self.x_min)
        return interpolate(
            self.main_line.get_start(),
            self.main_line.get_end(),
            alpha
        )

    def point_to_number(self, point):
        left_point, right_point = self.main_line.get_start_and_end()
        full_vect = right_point-left_point
        def distance_from_left(p):
            return np.dot(p-left_point, full_vect)/np.linalg.norm(full_vect)

        return interpolate(
            self.x_min, self.x_max, 
            distance_from_left(point)/distance_from_left(right_point)
        )

    def default_numbers_to_display(self):
        if self.numbers_to_show is not None:
            return self.numbers_to_show
        return np.arange(int(self.leftmost_tick), int(self.x_max)+1)

    def get_number_mobjects(self, *numbers, **kwargs):
        #TODO, handle decimals
        if len(numbers) == 0:
            numbers = self.default_numbers_to_display()
        if "force_integers" in kwargs and kwargs["force_integers"]:
            numbers = map(int, numbers)
        result = VGroup()
        for number in numbers:
            mob = TexMobject(str(number))
            mob.scale(self.number_scale_val)
            mob.next_to(
                self.number_to_point(number),
                self.label_direction,
                self.line_to_number_buff,
            )
            result.add(mob)
        return result

    def get_labels(self):
        return self.get_number_mobjects()

    def add_numbers(self, *numbers, **kwargs):
        self.numbers = self.get_number_mobjects(
            *numbers, **kwargs
        )
        self.add(*self.numbers)
        return self

    def add_tip(self):
        start, end = self.main_line.get_start_and_end()
        vect = (end - start)/np.linalg.norm(end-start)
        arrow = Arrow(start, end + MED_SMALL_BUFF*vect, buff = 0)
        tip = arrow.tip
        tip.set_color(self.color)
        self.tip = tip
        self.add(tip)

class UnitInterval(NumberLine):
    CONFIG = {
        "x_min" : 0,
        "x_max" : 1,
        "unit_size" : 6,
        "tick_frequency" : 0.1,
        "numbers_with_elongated_ticks" : [0, 1],
        "number_at_center" : 0.5,
    }