First few animations of shadows project

active_projects/shadows.py

@@ -0,0 +1,330 @@
+from big_ol_pile_of_manim_imports import *
+
+
+# Helpers
+def get_shadow(mobject, opacity=0.5):
+    result = mobject.deepcopy()
+    result.apply_function(lambda p: [p[0], p[1], 0])
+    result.set_fill(BLACK, opacity=opacity)
+    result.set_stroke(BLACK, 0)
+    result.set_shade_in_3d(False)
+    return result
+
+
+def get_boundary_points(shadow, n_points=20):
+    points = shadow.get_points_defining_boundary()
+    return np.array([
+        points[np.argmax(np.dot(points, vect.T))]
+        for vect in compass_directions(n_points)
+    ])
+
+
+def get_area(planar_mobject):
+    boundary = get_boundary_points(planar_mobject, 100)
+    xs = boundary[:, 0]
+    ys = boundary[:, 1]
+    dxs = np.append(xs[-1], xs[:-1]) - xs
+    dys = np.append(ys[-1], ys[:-1]) - ys
+    return abs(sum([
+        0.5 * (x * dy - y * dx)
+        for x, dx, y, dy in zip(xs, dxs, ys, dys)
+    ]))
+
+
+def get_xy_plane_projection_point(p1, p2):
+    """
+    Draw a line from source to p1 to p2.  Where does it
+    intersect the xy plane?
+    """
+    vect = p2 - p1
+    return p1 - (p1[2] / vect[2]) * vect
+
+
+# Scenes
+
+
+class ShowShadows(ThreeDScene):
+    CONFIG = {
+        "object_center": [0, 0, 3],
+        "area_label_center": [0, -1.5, 0],
+        "surface_area": 6.0,
+        "num_reorientations": 10,
+        "camera_config": {
+            "light_source_start_point": 10 * OUT,
+            "frame_center": [0, 0, 0.5],
+        }
+    }
+
+    def setup(self):
+        self.add_plane()
+        self.set_camera_orientation(
+            phi=60 * DEGREES,
+            theta=-90 * DEGREES,
+        )
+        # self.begin_ambient_camera_rotation(0.02)
+        self.setup_orientation_trackers()
+        self.setup_object_and_shadow()
+        self.add_shadow_area_label()
+        self.add_surface_area_label()
+
+    def add_plane(self):
+        plane = self.plane = Rectangle(
+            width=FRAME_WIDTH,
+            height=24.2,
+            stroke_width=0,
+            fill_color=WHITE,
+            fill_opacity=0.5,
+        )
+        grid = NumberPlane(
+            color=LIGHT_GREY,
+            secondary_color=DARK_GREY,
+            y_radius=int(plane.get_height() / 2),
+            stroke_width=1,
+            secondary_line_ratio=0,
+        )
+        plane.add(grid)
+        plane.add(VectorizedPoint(10 * IN))
+        plane.set_shade_in_3d(True, z_index_as_group=True)
+        self.add(plane)
+
+    def setup_orientation_trackers(self):
+        # Euler angles
+        self.alpha_tracker = ValueTracker(0)
+        self.beta_tracker = ValueTracker(0)
+        self.gamma_tracker = ValueTracker(0)
+
+    def setup_object_and_shadow(self):
+        self.obj3d = updating_mobject_from_func(self.get_reoriented_object)
+        self.shadow = updating_mobject_from_func(lambda: get_shadow(self.obj3d))
+
+    def add_shadow_area_label(self):
+        text = TextMobject("Shadow area: ")
+        decimal = DecimalNumber(0)
+        label = VGroup(text, decimal)
+        label.arrange_submobjects(RIGHT)
+        label.scale(1.5)
+        label.move_to(self.area_label_center)
+        self.shadow_area_label = label
+        continual_update = ContinualChangingDecimal(
+            decimal, lambda a: get_area(self.shadow)
+        )
+
+        self.add(label)
+        self.add(continual_update)
+
+    def add_surface_area_label(self):
+        text = TextMobject("Surface area: ")
+        decimal = DecimalNumber(self.surface_area)
+        label = VGroup(text, decimal)
+        label.arrange_submobjects(RIGHT)
+        label.scale(1.25)
+        label.next_to(self.obj3d, RIGHT, MED_LARGE_BUFF)
+        self.surface_area_label = label
+        self.add_fixed_orientation_mobjects(label)
+
+    def construct(self):
+        obj3d = self.obj3d.copy()
+        obj3d.clear_updaters()
+        temp_shadow = updating_mobject_from_func(lambda: get_shadow(obj3d))
+        self.add(temp_shadow)
+        self.play(LaggedStart(DrawBorderThenFill, obj3d))
+        self.remove(obj3d, temp_shadow)
+        self.add(self.obj3d, self.shadow)
+        for n in range(self.num_reorientations):
+            self.randomly_reorient()
+            self.wait()
+
+    def randomly_reorient(self, run_time=3):
+        a, b, c = TAU * np.random.random(3)
+        self.play(
+            self.alpha_tracker.set_value, a,
+            self.beta_tracker.set_value, b,
+            self.gamma_tracker.set_value, c,
+            run_time=run_time
+        )
+
+    #
+    def get_object(self):
+        cube = Cube()
+        cube.set_height(1)
+        # cube.set_width(2, stretch=True)
+        cube.set_stroke(WHITE, 0.5)
+        return cube
+
+    def get_reoriented_object(self):
+        obj3d = self.get_object()
+        angles = [
+            self.alpha_tracker.get_value(),
+            self.beta_tracker.get_value(),
+            self.gamma_tracker.get_value(),
+        ]
+        vects = [OUT, RIGHT, OUT]
+
+        center = self.object_center
+        obj3d.move_to(center)
+        for angle, vect in zip(angles, vects):
+            obj3d.rotate(angle, vect, about_point=center)
+        return obj3d
+
+
+class ShowInfinitelyFarLightSource(ShowShadows):
+    CONFIG = {
+        "num_reorientations": 1,
+        "camera_center": [0, 0, 1]
+    }
+
+    def construct(self):
+        self.force_skipping()
+        ShowShadows.construct(self)
+        self.revert_to_original_skipping_status()
+
+        self.add_light_source_based_shadow_updater()
+        self.add_light()
+        self.move_light_around()
+        self.show_vertical_lines()
+
+    def add_light(self):
+        light = self.light = self.get_light()
+        light_source = self.camera.light_source
+        light.move_to(light_source)
+        light_source.add_updater(lambda m: m.move_to(light))
+        self.add(light_source)
+        self.add_fixed_orientation_mobjects(light)
+
+    def move_light_around(self):
+        light = self.light
+        self.play(
+            light.move_to, 5 * OUT + DOWN,
+            run_time=3
+        )
+        self.play(Rotating(
+            light, angle=TAU, about_point=5 * OUT,
+            rate_func=smooth, run_time=3
+        ))
+        self.play(
+            light.move_to, 30 * OUT,
+            run_time=3,
+        )
+        self.remove(light)
+
+    def show_vertical_lines(self):
+        lines = self.get_vertical_lines()
+        self.play(LaggedStart(ShowCreation, lines))
+        lines.add_updater(lambda m: m.become(self.get_vertical_lines()))
+        self.wait()
+        for x in range(5):
+            self.randomly_reorient()
+
+    def add_light_source_based_shadow_updater(self):
+        shadow = self.shadow
+        light_source = self.camera.light_source
+        obj3d = self.obj3d
+        center = obj3d.get_center()
+        right = center + RIGHT
+        up = center + UP
+
+        def update(shadow):
+            lsp = light_source.get_center()
+            proj_center, proj_right, proj_up = [
+                get_xy_plane_projection_point(lsp, point)
+                for point in [center, right, up]
+            ]
+            matrix = np.array([
+                proj_right - proj_center,
+                proj_up - proj_center
+            ]).T
+            shadow.apply_matrix(matrix)
+            shadow.move_to(proj_center)
+            return shadow
+        shadow.add_updater(update)
+
+    def get_light(self):
+        n_rings = 40
+        radii = np.linspace(0, 2, n_rings)
+        rings = VGroup(*[
+            Annulus(inner_radius=r1, outer_radius=r2)
+            for r1, r2 in zip(radii, radii[1:])
+        ])
+        opacities = np.linspace(1, 0, n_rings)**1.5
+        for opacity, ring in zip(opacities, rings):
+            ring.set_fill(YELLOW, opacity)
+            ring.set_stroke(YELLOW, width=0.1, opacity=opacity)
+        return rings
+
+    def get_vertical_lines(self):
+        shadow = self.shadow
+        points = get_boundary_points(shadow, 10)
+        half_points = [(p1 + p2) / 2 for p1, p2 in adjacent_pairs(points)]
+        points = np.append(points, half_points, axis=0)
+        light_source = self.light.get_center()
+        lines = VGroup(*[
+            DashedLine(light_source, point)
+            for point in points
+        ])
+        lines.set_shade_in_3d(True)
+        for line in lines:
+            line.remove(*line[:int(0.8 * len(line))])
+            line[-10:].set_shade_in_3d(False)
+            line.set_stroke(YELLOW, 1)
+        return lines
+
+
+class CylinderShadows(ShowShadows):
+    CONFIG = {
+        "surface_area": 2 * PI + 2 * PI * 2
+    }
+
+    def get_object(self):
+        height = 2
+        cylinder = ParametricSurface(
+            lambda u, v: np.array([
+                np.cos(TAU * v),
+                np.sin(TAU * v),
+                height * (1 - u)
+            ]),
+            resolution=(6, 32)
+        )
+        # circle = Circle(radius=1)
+        circle = ParametricSurface(
+            lambda u, v: np.array([
+                (v + 0.01) * np.cos(TAU * u),
+                (v + 0.01) * np.sin(TAU * u),
+                0,
+            ]),
+            resolution=(16, 8)
+        )
+        # circle.set_fill(GREEN, opacity=0.5)
+        for surface in cylinder, circle:
+            surface.set_fill_by_checkerboard(GREEN, GREEN_E, opacity=1.0)
+            # surface.set_fill(GREEN, opacity=0.5)
+        cylinder.add(circle)
+        cylinder.add(circle.copy().flip().move_to(height * OUT))
+        cylinder.set_shade_in_3d(True)
+        cylinder.set_stroke(width=0)
+        cylinder.scale(1.003)
+        return cylinder
+
+
+class PrismShadows(ShowShadows):
+    CONFIG = {
+        "surface_area": 3 * np.sqrt(3) / 2 + 3 * (np.sqrt(3) * 2),
+        "object_center": [0, 0, 3],
+        "area_label_center": [0, -2.25, 0],
+    }
+
+    def get_object(self):
+        height = 2
+        prism = VGroup()
+        triangle = RegularPolygon(3)
+        verts = triangle.get_anchors()[:3]
+        rects = [
+            Polygon(v1, v2, v2 + height * OUT, v1 + height * OUT)
+            for v1, v2 in adjacent_pairs(verts)
+        ]
+        prism.add(triangle, *rects)
+        prism.add(triangle.copy().shift(height * OUT))
+        triangle.reverse_points()
+        prism.set_shade_in_3d(True)
+        prism.set_fill(PINK, 0.8)
+        prism.set_stroke(WHITE, 1)
+        return prism

big_ol_pile_of_manim_imports.py

@@ -56,6 +56,7 @@ from mobject.three_dimensions import *
 from mobject.types.image_mobject import *
 from mobject.types.point_cloud_mobject import *
 from mobject.types.vectorized_mobject import *
+from mobject.updater import *
 from mobject.value_tracker import *
 
 from for_3b1b_videos.common_scenes import *