More moser, count method of scene implemented

animation.py

@@ -14,7 +14,7 @@ from constants import *
 from mobject import Mobject
 
 class Animation(object):
-    def __init__(self, 
+    def __init__(self,
                  mobject,
                  run_time = DEFAULT_ANIMATION_RUN_TIME,
                  alpha_func = high_inflection_0_to_1,
@@ -217,6 +217,18 @@ class Transform(Animation):
                         )[self.non_redundant_m2_indices]
                     )
 
+class FadeToColor(Transform):
+    def __init__(self, mobject, color, *args, **kwargs):
+        target = copy.deepcopy(mobject).highlight(color)
+        Transform.__init__(self, mobject, target, *args, **kwargs)
+
+class ScaleInPlace(Transform):
+    def __init__(self, mobject, scale_factor, *args, **kwargs):
+        target = copy.deepcopy(mobject)
+        center = mobject.get_center()
+        target.shift(-center).scale(scale_factor).shift(center)
+        Transform.__init__(self, mobject, target, *args, **kwargs)
+
 class ApplyMethod(Transform):
     def __init__(self, method, mobject, *args, **kwargs):
         """
@@ -232,7 +244,7 @@ class ApplyMethod(Transform):
             mobject, 
             method(copy.deepcopy(mobject), *method_args),
             *args, **kwargs
-        )        
+        )
 
 class ApplyFunction(Transform):
     def __init__(self, function, mobject, run_time = DEFAULT_ANIMATION_RUN_TIME,

mobject.py

@@ -130,6 +130,7 @@ class Mobject(object):
         """
         Condition is function which takes in one arguments, (x, y, z).
         """
+        #TODO, Should self.color change?
         to_change = np.apply_along_axis(condition, 1, self.points)
         self.rgbs[to_change, :] *= 0
         self.rgbs[to_change, :] += Color(color).get_rgb()

moser/main.py

@@ -36,10 +36,17 @@ class CircleScene(Scene):
 ##################################################
 
 def count_lines(*radians):
+    #TODO, Count things explicitly?
     sc = CircleScene(radians)
-    text = tex_mobject(r"\text{How Many Lines?}", size = r"\large")
     text_center = (sc.radius + 1, sc.radius -1, 0)
-    text.scale(0.4).shift(text_center)
+    scale_factor = 0.4
+    text = tex_mobject(r"\text{How Many Lines?}", size = r"\large")
+    n = len(radians)
+    formula, answer = tex_mobject([
+        r"{%d \choose 2} = \frac{%d(%d - 1)}{2} = "%(n, n, n),
+        str(choose(n, 2))
+    ])
+    text.scale(scale_factor).shift(text_center)
     x = text_center[0]
     new_lines = [
         Line((x-1, y, 0), (x+1, y, 0))
@@ -55,6 +62,16 @@ def count_lines(*radians):
        Transform(line1, line2, run_time = 2)
        for line1, line2 in zip(sc.lines, new_lines)
     ])
+    sc.dither()
+    sc.remove(text)
+    sc.count(new_lines)
+    anims = [FadeIn(formula)]
+    for mob in sc.mobjects:
+        if mob == sc.number: #put in during animate_count
+            anims.append(Transform(mob, answer))
+        else:
+            anims.append(FadeOut(mob))
+    sc.animate(*anims, run_time = 1)
     return sc
 
 
@@ -63,35 +80,44 @@ def count_intersection_points(*radians):
     radians.sort()
     sc = CircleScene(radians)
     intersection_points = [
-        intersection([p[0], p[2]], [p[1], p[3]])
+        intersection((p[0], p[2]), (p[1], p[3]))
         for p in it.combinations(sc.points, 4)
     ]
-    intersection_dots = CompoundMobject(*[
-        Dot(point) for point in intersection_points
-    ])
-    how_many = tex_mobject(r"""
-        \text{How many}\\
-        \text{intersection points?}
-    """, size = r"\large")
-    text_center = (sc.radius + 1, sc.radius -1, 0)
-    how_many.scale(0.4).shift(text_center)
-    new_points = [
-        (text_center[0], y, 0)
-        for y in np.arange(
-            -(sc.radius - 1), 
-            sc.radius - 1, 
-            (2*sc.radius - 2)/choose(len(sc.points), 4)
-        )
-    ]
-    new_dots = CompoundMobject(*[
-        Dot(point) for point in new_points
+    intersection_dots = [Dot(point) for point in intersection_points]
+    text_center = (sc.radius + 1, sc.radius -0.5, 0)
+    size = r"\large"
+    scale_factor = 0.4
+    text = tex_mobject(r"\text{How Many Intersection Points?}", size = size)
+    n = len(radians)
+    formula, answer = tex_mobjects([
+        r"{%d \choose 4} = \frac{%d(%d - 1)(%d - 2)(%d-3)}{1\cdot 2\cdot 3 \cdot 4}="%(n, n, n, n, n),
+        str(choose(n, 4))
     ])
+    text.scale(scale_factor).shift(text_center)
+    # new_points = [
+    #     (text_center[0], y, 0)
+    #     for y in np.arange(
+    #         -(sc.radius - 1), 
+    #         sc.radius - 1, 
+    #         (2*sc.radius - 2)/choose(len(sc.points), 4)
+    #     )
+    # ]
+    # new_dots = CompoundMobject(*[
+    #     Dot(point) for point in new_points
+    # ])
 
-    sc.add(how_many)
-    sc.animate(ShowCreation(intersection_dots))
-    sc.add(intersection_dots)
-    sc.animate(Transform(intersection_dots, new_dots))
-    sc.add(tex_mobject(str(len(new_points))).center())
+    sc.add(text)
+    sc.count(intersection_dots, "show_creation", num_offset = (0, 0, 0))
+    sc.dither()
+    # sc.animate(Transform(intersection_dots, new_dots))
+    anims = []
+    for mob in sc.mobjects:
+        if mob == sc.number: #put in during animate_count
+            anims.append(Transform(mob, answer))
+        else:
+            anims.append(FadeOut(mob))
+    anims.append(FadeIn(formula)) #Put here to so they are foreground
+    sc.animate(*anims, run_time = 1)
     return sc
 
 def non_general_position():
@@ -127,11 +153,52 @@ def non_general_position():
     ])
     return sc1
 
+def line_corresponds_with_pair(radians, r1, r2):
+    sc = CircleScene(radians)
+    #Remove from sc.lines list, so they won't be faded out
+    assert r1 in radians and r2 in radians
+    line_index = list(it.combinations(radians, 2)).index((r1, r2))
+    radians = list(radians)
+    dot0_index, dot1_index = radians.index(r1), radians.index(r2)
+    line, dot0, dot1 = sc.lines[line_index], sc.dots[dot0_index], sc.dots[dot1_index]
+    sc.lines.remove(line)
+    sc.dots.remove(dot0)
+    sc.dots.remove(dot1)
+    sc.dither()
+    sc.animate(*[FadeOut(mob) for mob in sc.lines + sc.dots])
+    sc.add(sc.circle)
+    sc.animate(*[
+        ScaleInPlace(mob, 3, alpha_func = there_and_back) 
+        for mob in (dot0, dot1)
+    ])
+    sc.animate(Transform(line, dot0))
+    return sc
+
+def illustrate_n_choose_2(n):
+    #TODO, maybe make this snazzy
+    sc = Scene()
+    nrange = range(1, n+1)
+    nrange_im = tex_mobject(str(nrange))
+    pairs_str = str(list(it.combinations(nrange, 2)))
+    exp = tex_mobject(r"{{%d \choose 2} = %d \text{ total pairs}}"%(n, choose(n, 2)))
+    pairs_im  = tex_mobject(r"\underbrace{%s}"%pairs_str, size=r"\tiny")
+    nrange_im.shift((0, 2, 0))
+    pairs_im.scale(0.7)
+    exp.shift((0, -2, 0))
+    sc.add(nrange_im)
+    sc.dither()
+    sc.animate(FadeIn(pairs_im), FadeIn(exp))
+    sc.add(pairs_im)
+    return sc
+    
 
 ##################################################
 
 if __name__ == '__main__':
     radians = np.arange(0, 6, 6.0/7)
-    count_lines(*radians).write_to_movie("moser/CountLines")
+    # count_lines(*radians).write_to_movie("moser/CountLines")
     count_intersection_points(*radians).write_to_movie("moser/CountIntersectionPoints")
-    non_general_position().write_to_movie("moser/NonGeneralPosition")
+    # non_general_position().write_to_movie("moser/NonGeneralPosition")
+    # line_corresponds_with_pair(radians, radians[3], radians[4]).write_to_movie("moser/LineCorrespondsWithPair34")
+    # line_corresponds_with_pair(radians, radians[2], radians[5]).write_to_movie("moser/LineCorrespondsWithPair25")
+    # illustrate_n_choose_2(6).write_to_movie("moser/IllustrateNChoose2with6")

moser/moser_helpers.py

@@ -2,6 +2,9 @@ import numpy as np
 import operator as op
 import itertools as it
 
+from constants import *
+from image_mobject import *
+
 def choose(n, r):
     if n < r: return 0
     if r == 0: return 1
@@ -32,3 +35,6 @@ def intersection(line1, line2):
     result = np.dot(transform, [[x_intercept], [0]])
     result = result.reshape((2,)) + p0
     return result
+
+
+

scene.py

@@ -12,6 +12,7 @@ import inspect
 
 from helpers import *
 from mobject import *
+from image_mobject import *
 from animation import *
 import displayer as disp
 
@@ -98,6 +99,37 @@ class Scene(object):
         self.add(*moving_mobjects)
         progress_bar.finish()
 
+    def count(self, mobjects, mode = "highlight",
+              color = "red", 
+              num_offset = (SPACE_WIDTH - 1, SPACE_HEIGHT - 1, 0),
+              run_time = 5.0):
+        """
+        Note: Leaves scene with a "number" attribute 
+        for the final number mobject
+        """
+        if len(mobjects) > 50: #TODO
+            raise Exception("I don't know if you should be counting \
+                             too many mobjects...")
+        if mode not in ["highlight", "show_creation"]:
+            raise Exception("Invalid mode")
+        frame_time = run_time / len(mobjects)
+        if mode == "highlight":
+            self.add(*mobjects)
+        for mob, num in zip(mobjects, it.count(1)):
+            num_mob = tex_mobject(str(num))
+            num_mob.center().shift(num_offset)
+            self.add(num_mob)
+            if mode == "highlight":
+                original_color = mob.color
+                mob.highlight(color)
+                self.dither(frame_time)
+                mob.highlight(original_color)
+            if mode == "show_creation":
+                self.animate(ShowCreation(mob, run_time = frame_time))
+            self.remove(num_mob)
+        self.add(num_mob)
+        self.number = num_mob
+
     def get_frame(self):
         frame = self.background
         for mob in self.mobjects: