A few 3d updates

animation/animation.py

@@ -64,14 +64,17 @@ class Animation(object):
         #Typically ipmlemented by subclass
         pass
 
-    def get_all_families_zipped(self):
+    def get_all_mobjects(self):
         """
         Ordering must match the ording of arguments to update_submobject
         """ 
-        return zip(
-            self.mobject.submobject_family(),
-            self.starting_mobject.submobject_family()
-        )
+        return self.mobject, self.starting_mobject
+
+    def get_all_families_zipped(self):
+        return zip(*map(
+            Mobject.family_members_with_points,
+            self.get_all_mobjects()
+        ))
 
     def get_sub_alpha(self, alpha, index, num_submobjects):
         if self.submobject_mode in ["lagged_start", "smoothed_lagged_start"]:

animation/transform.py

@@ -13,6 +13,7 @@ from mobject import Mobject, Point, VMobject, Group
 class Transform(Animation):
     CONFIG = {
         "path_arc" : 0,
+        "path_arc_axis" : OUT,
         "path_func" : None,
         "submobject_mode" : "all_at_once",
         "replace_mobject_with_target_in_scene" : False,
@@ -31,7 +32,10 @@ class Transform(Animation):
     def update_config(self, **kwargs):
         Animation.update_config(self, **kwargs)
         if "path_arc" in kwargs:
-            self.path_func = path_along_arc(kwargs["path_arc"])
+            self.path_func = path_along_arc(
+                kwargs["path_arc"],
+                kwargs["path_arc_axis"]
+            )
 
     def init_path_func(self):
         if self.path_func is not None:
@@ -39,13 +43,13 @@ class Transform(Animation):
         if self.path_arc == 0:
             self.path_func = straight_path
         else:
-            self.path_func = path_along_arc(self.path_arc)
+            self.path_func = path_along_arc(
+                self.path_arc,
+                self.path_arc_axis,
+            )
 
-    def get_all_families_zipped(self):
-        return zip(*map(
-            Mobject.submobject_family,
-            [self.mobject, self.starting_mobject, self.target_mobject]
-        ))
+    def get_all_mobjects(self):
+        return self.mobject, self.starting_mobject, self.target_mobject
 
     def update_submobject(self, submob, start, end, alpha):
         submob.interpolate(start, end, alpha, self.path_func)
@@ -169,6 +173,8 @@ class Rotate(ApplyMethod):
     def __init__(self, mobject, angle = np.pi, axis = OUT, **kwargs):
         if "path_arc" not in kwargs:
             kwargs["path_arc"] = angle
+        if "path_arc_axis" not in kwargs:
+            kwargs["path_arc_axis"] = axis
         digest_config(self, kwargs, locals())
         target = mobject.copy()
         if self.in_place:

camera.py

@@ -288,47 +288,6 @@ class MovingCamera(Camera):
             0 if self.aligned_dimension == "height" else 1
         )
 
-class ShadingCamera(Camera):
-    CONFIG = {
-        # "sun_vect" : OUT+LEFT+UP,
-        "sun_vect" : UP+LEFT,
-        "shading_factor" : 0.5,
-    }
-    def __init__(self, *args, **kwargs):
-        Camera.__init__(self, *args, **kwargs)
-        self.unit_sun_vect = self.sun_vect/np.linalg.norm(self.sun_vect)
-
-    def get_stroke_color(self, vmobject):
-        return Color(rgb = self.get_shaded_rgb(
-            color_to_rgb(vmobject.get_stroke_color()),
-            normal_vect = self.get_unit_normal_vect(vmobject)
-        ))
-
-    def get_fill_color(self, vmobject):
-        return Color(rgb = self.get_shaded_rgb(
-            color_to_rgb(vmobject.get_fill_color()),
-            normal_vect = self.get_unit_normal_vect(vmobject)
-        ))
-
-    def get_shaded_rgb(self, rgb, normal_vect):
-        brightness = np.dot(normal_vect, self.unit_sun_vect)
-        if brightness > 0:
-            alpha = self.shading_factor*brightness
-            return interpolate(rgb, np.ones(3), alpha)
-        else:
-            alpha = -self.shading_factor*brightness
-            return interpolate(rgb, np.zeros(3), alpha)
-
-    def get_unit_normal_vect(self, vmobject):
-        anchors = vmobject.get_anchors()
-        if len(anchors) < 3:
-            return OUT
-        normal = np.cross(anchors[1]-anchors[0], anchors[2]-anchors[1])
-        length = np.linalg.norm(normal)
-        if length == 0:
-            return OUT
-        return normal/length
-
 
 
 

eoc/chapter1.py

@@ -2597,7 +2597,6 @@ class PatreonThanks(Scene):
         special_thanks.to_edge(UP)
 
         patreon_logo = PatreonLogo()
-        # patreon_logo.scale_to_fit_width(morty.get_width())
         patreon_logo.next_to(morty, UP, buff = MED_LARGE_BUFF)
 
         left_patrons = VGroup(*map(TextMobject, 

helpers.py

@@ -318,7 +318,7 @@ def random_color():
 def straight_path(start_points, end_points, alpha):
     return interpolate(start_points, end_points, alpha)
 
-def path_along_arc(arc_angle):
+def path_along_arc(arc_angle, axis = OUT):
     """
     If vect is vector from start to end, [vect[:,1], -vect[:,0]] is 
     perpendicualr to vect in the left direction.
@@ -333,7 +333,7 @@ def path_along_arc(arc_angle):
                 centers[:,i] += 0.5*b*vects[:,1-i]/np.tan(arc_angle/2)
         return centers + np.dot(
             start_points-centers, 
-            np.transpose(rotation_about_z(alpha*arc_angle))
+            np.transpose(rotation_matrix(alpha*arc_angle, axis))
         )
     return path
 

old_projects/borsuk.py

@@ -19,7 +19,7 @@ from topics.numerals import *
 from topics.three_dimensions import *
 from scene import Scene
 from scene.reconfigurable_scene import ReconfigurableScene
-from camera import Camera, ShadingCamera
+from camera import Camera
 from mobject.svg_mobject import *
 from mobject.tex_mobject import *
 
@@ -148,9 +148,8 @@ class CheckOutMathologer(PiCreatureScene):
         logo.highlight(BLACK)
         return ApplyMethod(logo.restore)
 
-class IntroduceStolenNecklaceProblem(Scene):
+class IntroduceStolenNecklaceProblem(ThreeDScene):
     CONFIG = {
-        "camera_class" : ShadingCamera,
         "jewel_colors" : [BLUE, GREEN, WHITE, RED],
         "num_per_jewel" : [8, 10, 4, 6],
         "num_shuffles" : 1,
@@ -994,10 +993,7 @@ class FormLoopTransverseToEquator(ExternallyAnimatedScene):
 class AntipodalWalkAroundTransverseLoop(ExternallyAnimatedScene):
     pass
 
-class MentionGenerality(TeacherStudentsScene):
-    CONFIG = {
-        "camera_class" : ShadingCamera,
-    }
+class MentionGenerality(TeacherStudentsScene, ThreeDScene):
     def construct(self):
         necklace = Necklace(width = SPACE_WIDTH)
         necklace.shift(2*UP)
@@ -1274,7 +1270,6 @@ class MentionMakingNecklaceProblemContinuous(TeacherStudentsScene):
 
 class MakeTwoJewelCaseContinuous(IntroduceStolenNecklaceProblem):
     CONFIG = {
-        "camera_class" : ShadingCamera,
         "jewel_colors" : [BLUE, GREEN],
         "num_per_jewel" : [8, 10],
         "random_seed" : 2,
@@ -2170,9 +2165,8 @@ class NecklaceDivisionSphereAssociation(ChoicesInNecklaceCutting):
 class SimpleRotatingSphereWithAntipodes(ExternallyAnimatedScene):
     pass
 
-class TotalLengthOfEachJewelEquals(NecklaceDivisionSphereAssociation):
+class TotalLengthOfEachJewelEquals(NecklaceDivisionSphereAssociation, ThreeDScene):
     CONFIG = {
-        "camera_class" : ShadingCamera,
         "random_seed" : 1,
         "thief_box_offset" : 1.2,
     }
@@ -2310,7 +2304,7 @@ class ExclaimBorsukUlam(TeacherStudentsScene):
 class ShowFunctionDiagram(TotalLengthOfEachJewelEquals, ReconfigurableScene):
     CONFIG = {
         "necklace_center" : ORIGIN,
-        "camera_class" : ShadingCamera,
+        "camera_class" : ThreeDCamera,
         "thief_box_offset" : 0.3,
         "make_up_fair_division_indices" : False,
     }
@@ -2407,7 +2401,7 @@ class ShowFunctionDiagram(TotalLengthOfEachJewelEquals, ReconfigurableScene):
 
 class JewelPairPlane(GraphScene):
     CONFIG = {
-        "camera_class" : ShadingCamera,
+        "camera_class" : ThreeDCamera,
         "x_labeled_nums" : [],
         "y_labeled_nums" : [],
         "thief_number" : 1,
@@ -2639,7 +2633,7 @@ class MortyLookingAtRectangle(Scene):
 
 class RotatingThreeDSphereProjection(Scene):
     CONFIG = {
-        "camera_class" : ShadingCamera,
+        "camera_class" : ThreeDCamera,
     }
     def construct(self):
         sphere = VGroup(*[
@@ -2659,8 +2653,21 @@ class FourDSphereProjectTo4D(ExternallyAnimatedScene):
     pass
 
 
-
-
+class Test(Scene):
+    CONFIG = {
+        "camera_class" : ThreeDCamera,
+    }
+    def construct(self):
+        randy = Randolph()
+        necklace = Necklace()
+        necklace.insert_n_anchor_points(20)
+        # necklace.apply_function(
+        #     lambda (x, y, z) : x*RIGHT + (y + 0.1*x**2)*UP
+        # )
+        necklace.scale_to_fit_width(randy.get_width() + 1)
+        necklace.move_to(randy)
+
+        self.add(randy, necklace)
 
 
 

old_projects/three_dimensions.py

@@ -0,0 +1,113 @@
+import numpy as np
+import itertools as it
+
+from mobject import Mobject, Mobject1D, Mobject2D, Mobject
+from geometry import Line
+from helpers import *
+
+class Stars(Mobject1D):
+    CONFIG = {
+        "stroke_width" : 1,
+        "radius"          : SPACE_WIDTH,
+        "num_points"      : 1000,
+    }
+    def generate_points(self):
+        radii, phis, thetas = [
+            scalar*np.random.random(self.num_points)
+            for scalar in [self.radius, np.pi, 2*np.pi]
+        ]
+        self.add_points([
+            (
+                r * np.sin(phi)*np.cos(theta), 
+                r * np.sin(phi)*np.sin(theta), 
+                r * np.cos(phi)
+            )
+            for r, phi, theta in zip(radii, phis, thetas)
+        ])
+
+class CubeWithFaces(Mobject2D):
+    def generate_points(self):
+        self.add_points([
+            sgn * np.array(coords)
+            for x in np.arange(-1, 1, self.epsilon)
+            for y in np.arange(x, 1, self.epsilon) 
+            for coords in it.permutations([x, y, 1]) 
+            for sgn in [-1, 1]
+        ])
+        self.pose_at_angle()
+        self.set_color(BLUE)
+
+    def unit_normal(self, coords):
+        return np.array(map(lambda x : 1 if abs(x) == 1 else 0, coords))
+
+class Cube(Mobject1D):
+    def generate_points(self):
+        self.add_points([
+            ([a, b, c][p[0]], [a, b, c][p[1]], [a, b, c][p[2]])
+            for p in [(0, 1, 2), (2, 0, 1), (1, 2, 0)]
+            for a, b, c in it.product([-1, 1], [-1, 1], np.arange(-1, 1, self.epsilon))
+        ])
+        self.pose_at_angle()
+        self.set_color(YELLOW)
+
+class Octohedron(Mobject1D):
+    def generate_points(self):
+        x = np.array([1, 0, 0])
+        y = np.array([0, 1, 0])
+        z = np.array([0, 0, 1])
+        vertex_pairs = [(x+y, x-y), (x+y,-x+y), (-x-y,-x+y), (-x-y,x-y)]
+        vertex_pairs += [
+            (b[0]*x+b[1]*y, b[2]*np.sqrt(2)*z)
+            for b in it.product(*[(-1, 1)]*3)
+        ]
+        for pair in vertex_pairs:
+            self.add_points(
+                Line(pair[0], pair[1], density = 1/self.epsilon).points
+            )
+        self.pose_at_angle()
+        self.set_color(MAROON_D)
+
+class Dodecahedron(Mobject1D):
+    def generate_points(self):
+        phi = (1 + np.sqrt(5)) / 2
+        x = np.array([1, 0, 0])
+        y = np.array([0, 1, 0])
+        z = np.array([0, 0, 1])
+        v1, v2 = (phi, 1/phi, 0), (phi, -1/phi, 0)
+        vertex_pairs = [
+            (v1, v2),
+            (x+y+z, v1),
+            (x+y-z, v1),
+            (x-y+z, v2),
+            (x-y-z, v2),
+        ]
+        five_lines_points = Mobject(*[
+            Line(pair[0], pair[1], density = 1.0/self.epsilon)
+            for pair in vertex_pairs
+        ]).points
+        #Rotate those 5 edges into all 30.
+        for i in range(3):
+            perm = map(lambda j : j%3, range(i, i+3))
+            for b in [-1, 1]:
+                matrix = b*np.array([x[perm], y[perm], z[perm]])
+                self.add_points(np.dot(five_lines_points, matrix))
+        self.pose_at_angle()
+        self.set_color(GREEN)
+
+class Sphere(Mobject2D):
+    def generate_points(self):
+        self.add_points([
+            (
+                np.sin(phi) * np.cos(theta),
+                np.sin(phi) * np.sin(theta),
+                np.cos(phi)
+            )
+            for phi in np.arange(self.epsilon, np.pi, self.epsilon)
+            for theta in np.arange(0, 2 * np.pi, 2 * self.epsilon / np.sin(phi)) 
+        ])
+        self.set_color(BLUE)
+
+    def unit_normal(self, coords):
+        return np.array(coords) / np.linalg.norm(coords)
+
+        

scene/scene.py

@@ -424,8 +424,6 @@ class Scene(object):
 
 
 
-
-
 
 
 

topics/three_dimensions.py

@@ -1,114 +1,91 @@
-import numpy as np
-import itertools as it
 
-from mobject import Mobject, Mobject1D, Mobject2D, Mobject
-from geometry import Line
 from helpers import *
 
+from scene import Scene
+from camera import Camera
 
-class Stars(Mobject1D):
+class ThreeDCamera(Camera):
     CONFIG = {
-        "stroke_width" : 1,
-        "radius"          : SPACE_WIDTH,
-        "num_points"      : 1000,
+        "sun_vect" : UP+LEFT,
+        "shading_factor" : 0.5,
     }
-    def generate_points(self):
-        radii, phis, thetas = [
-            scalar*np.random.random(self.num_points)
-            for scalar in [self.radius, np.pi, 2*np.pi]
-        ]
-        self.add_points([
-            (
-                r * np.sin(phi)*np.cos(theta), 
-                r * np.sin(phi)*np.sin(theta), 
-                r * np.cos(phi)
-            )
-            for r, phi, theta in zip(radii, phis, thetas)
-        ])
+    def __init__(self, *args, **kwargs):
+        Camera.__init__(self, *args, **kwargs)
+        self.unit_sun_vect = self.sun_vect/np.linalg.norm(self.sun_vect)
+
+    def display_multiple_vectorized_mobjects(self, vmobjects):
+        def cmp_vmobs(vm1, vm2):
+            return cmp(vm1.get_center()[2], vm2.get_center()[2])
+        Camera.display_multiple_vectorized_mobjects(
+            self, 
+            sorted(vmobjects, cmp = cmp_vmobs)
+        )
+
+    def get_stroke_color(self, vmobject):
+        return Color(rgb = self.get_shaded_rgb(
+            color_to_rgb(vmobject.get_stroke_color()),
+            normal_vect = self.get_unit_normal_vect(vmobject)
+        ))
+
+    def get_fill_color(self, vmobject):
+        return Color(rgb = self.get_shaded_rgb(
+            color_to_rgb(vmobject.get_fill_color()),
+            normal_vect = self.get_unit_normal_vect(vmobject)
+        ))
+
+    def get_shaded_rgb(self, rgb, normal_vect):
+        brightness = np.dot(normal_vect, self.unit_sun_vect)
+        if brightness > 0:
+            alpha = self.shading_factor*brightness
+            return interpolate(rgb, np.ones(3), alpha)
+        else:
+            alpha = -self.shading_factor*brightness
+            return interpolate(rgb, np.zeros(3), alpha)
+
+    def get_unit_normal_vect(self, vmobject):
+        anchors = vmobject.get_anchors()
+        if len(anchors) < 3:
+            return OUT
+        normal = np.cross(anchors[1]-anchors[0], anchors[2]-anchors[1])
+        if normal[2] < 0:
+            normal = -normal
+        length = np.linalg.norm(normal)
+        if length == 0:
+            return OUT
+        return normal/length
+
+
+class ThreeDScene(Scene):
+    CONFIG = {
+        "camera_class" : ThreeDCamera,
+    }
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
 
-class CubeWithFaces(Mobject2D):
-    def generate_points(self):
-        self.add_points([
-            sgn * np.array(coords)
-            for x in np.arange(-1, 1, self.epsilon)
-            for y in np.arange(x, 1, self.epsilon) 
-            for coords in it.permutations([x, y, 1]) 
-            for sgn in [-1, 1]
-        ])
-        self.pose_at_angle()
-        self.set_color(BLUE)
 
-    def unit_normal(self, coords):
-        return np.array(map(lambda x : 1 if abs(x) == 1 else 0, coords))
 
-class Cube(Mobject1D):
-    def generate_points(self):
-        self.add_points([
-            ([a, b, c][p[0]], [a, b, c][p[1]], [a, b, c][p[2]])
-            for p in [(0, 1, 2), (2, 0, 1), (1, 2, 0)]
-            for a, b, c in it.product([-1, 1], [-1, 1], np.arange(-1, 1, self.epsilon))
-        ])
-        self.pose_at_angle()
-        self.set_color(YELLOW)
 
-class Octohedron(Mobject1D):
-    def generate_points(self):
-        x = np.array([1, 0, 0])
-        y = np.array([0, 1, 0])
-        z = np.array([0, 0, 1])
-        vertex_pairs = [(x+y, x-y), (x+y,-x+y), (-x-y,-x+y), (-x-y,x-y)]
-        vertex_pairs += [
-            (b[0]*x+b[1]*y, b[2]*np.sqrt(2)*z)
-            for b in it.product(*[(-1, 1)]*3)
-        ]
-        for pair in vertex_pairs:
-            self.add_points(
-                Line(pair[0], pair[1], density = 1/self.epsilon).points
-            )
-        self.pose_at_angle()
-        self.set_color(MAROON_D)
 
-class Dodecahedron(Mobject1D):
-    def generate_points(self):
-        phi = (1 + np.sqrt(5)) / 2
-        x = np.array([1, 0, 0])
-        y = np.array([0, 1, 0])
-        z = np.array([0, 0, 1])
-        v1, v2 = (phi, 1/phi, 0), (phi, -1/phi, 0)
-        vertex_pairs = [
-            (v1, v2),
-            (x+y+z, v1),
-            (x+y-z, v1),
-            (x-y+z, v2),
-            (x-y-z, v2),
-        ]
-        five_lines_points = Mobject(*[
-            Line(pair[0], pair[1], density = 1.0/self.epsilon)
-            for pair in vertex_pairs
-        ]).points
-        #Rotate those 5 edges into all 30.
-        for i in range(3):
-            perm = map(lambda j : j%3, range(i, i+3))
-            for b in [-1, 1]:
-                matrix = b*np.array([x[perm], y[perm], z[perm]])
-                self.add_points(np.dot(five_lines_points, matrix))
-        self.pose_at_angle()
-        self.set_color(GREEN)
-
-class Sphere(Mobject2D):
-    def generate_points(self):
-        self.add_points([
-            (
-                np.sin(phi) * np.cos(theta),
-                np.sin(phi) * np.sin(theta),
-                np.cos(phi)
-            )
-            for phi in np.arange(self.epsilon, np.pi, self.epsilon)
-            for theta in np.arange(0, 2 * np.pi, 2 * self.epsilon / np.sin(phi)) 
-        ])
-        self.set_color(BLUE)
-
-    def unit_normal(self, coords):
-        return np.array(coords) / np.linalg.norm(coords)