from helpers import * from mobject import Mobject1D from mobject.vectorized_mobject import VMobject from mobject.tex_mobject import TexMobject from topics.geometry import Line, Arrow from scene import Scene class NumberLine(VMobject): CONFIG = { "color" : BLUE, "x_min" : -SPACE_WIDTH, "x_max" : SPACE_WIDTH, "space_unit_to_num" : 1, "tick_size" : 0.1, "tick_frequency" : 0.5, "leftmost_tick" : None, #Defaults to ceil(x_min) "numbers_with_elongated_ticks" : [0], "longer_tick_multiple" : 2, "number_at_center" : 0, "propogate_style_to_family" : True } def __init__(self, **kwargs): digest_config(self, kwargs) if self.leftmost_tick is None: self.leftmost_tick = np.ceil(self.x_min) VMobject.__init__(self, **kwargs) def generate_points(self): self.main_line = Line(self.x_min*RIGHT, self.x_max*RIGHT) self.add(self.main_line) for x in self.get_tick_numbers(): self.add_tick(x, self.tick_size) for x in self.numbers_with_elongated_ticks: self.add_tick(x, self.longer_tick_multiple*self.tick_size) self.stretch(self.space_unit_to_num, 0) self.shift(-self.number_to_point(self.number_at_center)) def add_tick(self, x, size): self.add(Line( x*RIGHT+size*DOWN, x*RIGHT+size*UP, )) return self def get_tick_numbers(self): return np.arange(self.leftmost_tick, self.x_max, self.tick_frequency) def number_to_point(self, number): return interpolate( self.main_line.get_left(), self.main_line.get_right(), float(number-self.x_min)/(self.x_max - self.x_min) ) def point_to_number(self, point): dist_from_left = (point[0]-self.main_line.get_left()[0]) num_dist_from_left = num_dist_from_left/self.space_unit_to_num return self.x_min + dist_from_left def default_numbers_to_display(self): return self.get_tick_numbers()[::2] def get_vertical_number_offset(self, direction = DOWN): return 4*direction*self.tick_size def get_number_mobjects(self, *numbers, **kwargs): #TODO, handle decimals if len(numbers) == 0: numbers = self.default_numbers_to_display() result = [] for number in numbers: mob = TexMobject(str(int(number))) mob.scale_to_fit_height(2*self.tick_size) mob.shift( self.number_to_point(number), self.get_vertical_number_offset(**kwargs) ) result.append(mob) return result def add_numbers(self, *numbers, **kwargs): self.numbers = self.get_number_mobjects( *numbers, **kwargs ) self.add(*self.numbers) return self class UnitInterval(NumberLine): CONFIG = { "x_min" : 0, "x_max" : 1, "space_unit_to_num" : 6, "tick_frequency" : 0.1, "numbers_with_elongated_ticks" : [0, 1], "number_at_center" : 0.5, } class Axes(VMobject): CONFIG = { "propogate_style_to_family" : True } def generate_points(self, **kwargs): self.x_axis = NumberLine(**kwargs) self.y_axis = NumberLine(**kwargs).rotate(np.pi/2) self.add(self.x_axis, self.y_axis) class NumberPlane(VMobject): CONFIG = { "color" : BLUE_D, "secondary_color" : BLUE_E, "axes_color" : WHITE, "x_radius": SPACE_WIDTH, "y_radius": SPACE_HEIGHT, "space_unit_to_x_unit" : 1, "space_unit_to_y_unit" : 1, "x_line_frequency" : 1, "y_line_frequency" : 1, "secondary_line_ratio" : 1, "written_coordinate_height" : 0.2, "written_coordinate_nudge" : 0.1*(DOWN+RIGHT), "num_pair_at_center" : (0, 0), "propogate_style_to_family" : False, } def generate_points(self): self.axes = VMobject() self.main_lines = VMobject() self.secondary_lines = VMobject() tuples = [ ( self.x_radius, self.x_line_frequency, self.y_radius*DOWN, self.y_radius*UP, RIGHT ), ( self.y_radius, self.y_line_frequency, self.x_radius*LEFT, self.x_radius*RIGHT, UP, ), ] for radius, freq, start, end, unit in tuples: main_range = np.arange(0, radius, freq) step = freq/float(freq + self.secondary_line_ratio) for v in np.arange(0, radius, step): line1 = Line(start+v*unit, end+v*unit) line2 = Line(start-v*unit, end-v*unit) if v == 0: self.axes.add(line1) elif v in main_range: self.main_lines.add(line1, line2) else: self.secondary_lines.add(line1, line2) self.add(self.axes, self.main_lines, self.secondary_lines) self.stretch(self.space_unit_to_x_unit, 0) self.stretch(self.space_unit_to_y_unit, 1) def init_colors(self): VMobject.init_colors(self) self.axes.set_stroke(self.axes_color) self.main_lines.set_stroke(self.color) self.secondary_lines.set_stroke(self.secondary_color, 1) return self def get_center_point(self): return self.num_pair_to_point(self.num_pair_at_center) def num_pair_to_point(self, pair): pair = np.array(pair) + self.num_pair_at_center result = self.get_center() result[0] += pair[0]*self.space_unit_to_x_unit result[1] += pair[1]*self.space_unit_to_y_unit return result def point_to_num_pair(self, point): new_point = point-self.get_center() center_x, center_y = self.num_pair_at_center x = center_x + point[0]/self.space_unit_to_x_unit y = center_y + point[1]/self.space_unit_to_y_unit return x, y def get_coordinate_labels(self, x_vals = None, y_vals = None): result = [] if x_vals == None and y_vals == None: x_vals = range(-int(self.x_radius), int(self.x_radius)) y_vals = range(-int(self.y_radius), int(self.y_radius)) for index, vals in enumerate([x_vals, y_vals]): num_pair = [0, 0] for val in vals: num_pair[index] = val point = self.num_pair_to_point(num_pair) num = TexMobject(str(val)) num.scale_to_fit_height( self.written_coordinate_height ) num.shift( point-num.get_corner(UP+LEFT), self.written_coordinate_nudge ) result.append(num) return result def add_coordinates(self, x_vals = None, y_vals = None): self.add(*self.get_coordinate_labels(x_vals, y_vals)) return self def get_vector(self, coords, **kwargs): point = coords[0]*RIGHT + coords[1]*UP arrow = Arrow(ORIGIN, coords, **kwargs) return arrow def prepare_for_nonlinear_transform(self): for mob in self.submobject_family(): if mob.get_num_points() > 0: mob.insert_n_anchor_points(20) mob.change_anchor_mode("smooth")