mirror of
https://github.com/3b1b/videos.git
synced 2022-02-13 01:35:58 +03:00
Resume efforts on shadows project
This commit is contained in:
Grant Sanderson
@@ -2,20 +2,60 @@ from manim_imports_ext import *
|
||||
|
||||
|
||||
# Helpers
|
||||
def get_shadow(mobject, opacity=0.5):
|
||||
def project_to_xy_plane(p1, p2):
|
||||
"""
|
||||
Draw a line from source to p1 to p2. Where does it
|
||||
intersect the xy plane?
|
||||
"""
|
||||
x1, y1, z1 = p1
|
||||
x2, y2, z2 = p2
|
||||
if z2 < z1:
|
||||
z2 = z1 + 1e-2 # TODO, bad hack
|
||||
vect = p2 - p1
|
||||
return p1 - (z2 / vect[2]) * vect
|
||||
|
||||
|
||||
def flat_project(point):
|
||||
return [*point[:2], 0]
|
||||
|
||||
|
||||
def get_pre_shadow(mobject, opacity):
|
||||
result = mobject.deepcopy()
|
||||
result.apply_function(lambda p: [p[0], p[1], 0])
|
||||
result.clear_updaters()
|
||||
|
||||
color = interpolate_color(
|
||||
mobject.get_fill_color(), BLACK,
|
||||
mobject.get_fill_opacity()
|
||||
mobject[0].get_fill_color(), BLACK,
|
||||
mobject[0].get_fill_opacity()
|
||||
)
|
||||
# color = BLACK
|
||||
result.set_fill(color, opacity=opacity)
|
||||
result.set_stroke(BLACK, 0.5, opacity=opacity)
|
||||
result.set_shade_in_3d(False)
|
||||
for sm in result.family_members_with_points():
|
||||
sm.set_fill(color, opacity=opacity)
|
||||
sm.set_stroke(BLACK, 0.5, opacity=opacity)
|
||||
sm.set_gloss(sm.get_gloss() * 0.5)
|
||||
sm.set_shadow(0)
|
||||
sm.set_reflectiveness(0)
|
||||
return result
|
||||
|
||||
|
||||
def update_shadow(shadow, mobject, light_source):
|
||||
lp = light_source.get_center() if light_source is not None else None
|
||||
|
||||
def project(point):
|
||||
if lp is None:
|
||||
return flat_project(point)
|
||||
else:
|
||||
return project_to_xy_plane(lp, point)
|
||||
|
||||
for sm, mm in zip(shadow.family_members_with_points(), mobject.family_members_with_points()):
|
||||
sm.set_points(np.apply_along_axis(project, 1, mm.get_points()))
|
||||
|
||||
|
||||
def get_shadow(mobject, light_source=None, opacity=0.5):
|
||||
shadow = get_pre_shadow(mobject, opacity)
|
||||
shadow.add_updater(lambda s: update_shadow(s, mobject, light_source))
|
||||
return shadow
|
||||
|
||||
|
||||
def get_boundary_points(shadow, n_points=20):
|
||||
points = shadow.get_points_defining_boundary()
|
||||
return np.array([
|
||||
@@ -36,72 +76,98 @@ def get_area(planar_mobject):
|
||||
]))
|
||||
|
||||
|
||||
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],
|
||||
},
|
||||
"initial_orientation_config": {
|
||||
"phi": 60 * DEGREES,
|
||||
"theta": -120 * DEGREES,
|
||||
}
|
||||
class ShadowScene(ThreeDScene):
|
||||
object_center = [0, 0, 3]
|
||||
frame_center = [0, 0, 2]
|
||||
area_label_center = [0, -1.5, 0]
|
||||
surface_area = 6.0
|
||||
num_reorientations = 10
|
||||
plane_dims = (20, 20)
|
||||
plane_style = {
|
||||
"stroke_width": 0,
|
||||
"fill_color": GREY_A,
|
||||
"fill_opacity": 0.5,
|
||||
"gloss": 0.5,
|
||||
"shadow": 0.2,
|
||||
}
|
||||
inf_light = False
|
||||
glow_radius = 10
|
||||
glow_factor = 10
|
||||
|
||||
def setup(self):
|
||||
self.camera.frame.reorient(-30, 75)
|
||||
self.camera.frame.move_to(self.frame_center)
|
||||
self.add_plane()
|
||||
self.setup_orientation_trackers()
|
||||
self.setup_object_and_shadow()
|
||||
self.add_shadow_area_label()
|
||||
self.add_surface_area_label()
|
||||
self.add_solid()
|
||||
self.add_shadow()
|
||||
self.setup_light_source()
|
||||
|
||||
def add_plane(self):
|
||||
plane = self.plane = Rectangle(
|
||||
width=FRAME_WIDTH,
|
||||
height=24.2,
|
||||
stroke_width=0,
|
||||
fill_color=WHITE,
|
||||
fill_opacity=0.35,
|
||||
)
|
||||
plane.set_sheen(0.2, DR)
|
||||
width, height = self.plane_dims
|
||||
plane = self.plane = Rectangle(width, height)
|
||||
plane.set_style(**self.plane_style)
|
||||
|
||||
grid = NumberPlane(
|
||||
color=GREY_B,
|
||||
secondary_color=GREY_D,
|
||||
y_radius=int(plane.get_height() / 2),
|
||||
stroke_width=1,
|
||||
secondary_line_ratio=0,
|
||||
x_range=(-width // 2, width // 2, 2),
|
||||
y_range=(-height // 2, height // 2, 2),
|
||||
background_line_style={
|
||||
"stroke_color": GREY_B,
|
||||
"stroke_width": 1,
|
||||
},
|
||||
faded_line_ratio=4,
|
||||
)
|
||||
grid.axes.match_style(grid.background_lines)
|
||||
grid.set_flat_stroke(True)
|
||||
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 add_solid(self):
|
||||
self.solid = self.get_object()
|
||||
self.solid.move_to(self.object_center)
|
||||
self.solid.add_updater(lambda m: self.sort_to_camera(m))
|
||||
self.add(self.solid)
|
||||
|
||||
def setup_object_and_shadow(self):
|
||||
self.obj3d = always_redraw(self.get_reoriented_object)
|
||||
self.shadow = always_redraw(lambda: get_shadow(self.obj3d))
|
||||
def get_object(self):
|
||||
cube = VCube()
|
||||
cube.deactivate_depth_test()
|
||||
cube.set_height(2)
|
||||
cube.set_stroke(WHITE, 0.5)
|
||||
cube.set_fill(BLUE_E, 0.8)
|
||||
cube.set_reflectiveness(0.3)
|
||||
cube.set_gloss(0.1)
|
||||
cube.set_shadow(0.5)
|
||||
# Wrap in group so that strokes and fills
|
||||
# are rendered in separate passes
|
||||
cube = self.cube = Group(*cube)
|
||||
return cube
|
||||
|
||||
def add_shadow(self):
|
||||
light_source = None if self.inf_light else self.camera.light_source
|
||||
shadow = get_shadow(self.solid, light_source)
|
||||
|
||||
self.add(shadow, self.solid)
|
||||
self.shadow = shadow
|
||||
|
||||
def setup_light_source(self):
|
||||
self.light = self.camera.light_source
|
||||
glow = self.glow = TrueDot(
|
||||
radius=self.glow_radius,
|
||||
glow_factor=self.glow_factor,
|
||||
)
|
||||
glow.set_color(interpolate_color(YELLOW, WHITE, 0.5))
|
||||
glow.add_updater(lambda m: m.move_to(self.light))
|
||||
self.add(glow)
|
||||
|
||||
def sort_to_camera(self, mobject):
|
||||
cl = self.camera.get_location()
|
||||
mobject.sort(lambda p: -get_norm(p - cl))
|
||||
for sm in mobject:
|
||||
sm.refresh_unit_normal()
|
||||
return mobject
|
||||
|
||||
# TODO
|
||||
def add_shadow_area_label(self):
|
||||
text = TexText("Shadow area: ")
|
||||
decimal = DecimalNumber(0)
|
||||
@@ -129,6 +195,7 @@ class ShowShadows(ThreeDScene):
|
||||
self.add(label)
|
||||
self.add(decimal)
|
||||
|
||||
# TODO
|
||||
def add_surface_area_label(self):
|
||||
text = TexText("Surface area: ")
|
||||
decimal = DecimalNumber(self.surface_area)
|
||||
@@ -142,65 +209,7 @@ class ShowShadows(ThreeDScene):
|
||||
self.surface_area_label = label
|
||||
self.add_fixed_orientation_mobjects(label)
|
||||
|
||||
def construct(self):
|
||||
# Show creation
|
||||
obj3d = self.obj3d.copy()
|
||||
obj3d.clear_updaters()
|
||||
temp_shadow = always_redraw(lambda: get_shadow(obj3d))
|
||||
self.add(temp_shadow)
|
||||
self.move_camera(
|
||||
**self.initial_orientation_config,
|
||||
added_anims=[
|
||||
LaggedStartMap(DrawBorderThenFill, obj3d)
|
||||
],
|
||||
run_time=2
|
||||
)
|
||||
self.begin_ambient_camera_rotation(0.01)
|
||||
self.remove(obj3d, temp_shadow)
|
||||
|
||||
average_label = self.get_average_label()
|
||||
# Reorient
|
||||
self.add(self.obj3d, self.shadow)
|
||||
for n in range(self.num_reorientations):
|
||||
self.randomly_reorient()
|
||||
if n == 3:
|
||||
self.add_fixed_in_frame_mobjects(average_label)
|
||||
self.play(Write(average_label, run_time=2))
|
||||
else:
|
||||
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
|
||||
|
||||
# TODO
|
||||
def get_average_label(self):
|
||||
rect = SurroundingRectangle(
|
||||
self.shadow_area_decimal,
|
||||
@@ -223,7 +232,21 @@ class ShowShadows(ThreeDScene):
|
||||
return VGroup(rect, words)
|
||||
|
||||
|
||||
class ShowInfinitelyFarLightSource(ShowShadows):
|
||||
class IntroduceShadow(ShadowScene):
|
||||
def construct(self):
|
||||
light = self.light
|
||||
cube = self.cube
|
||||
|
||||
self.play(
|
||||
light.animate.next_to(cube, OUT, 2),
|
||||
run_time=5,
|
||||
)
|
||||
self.wait()
|
||||
|
||||
self.embed()
|
||||
|
||||
|
||||
class ShowInfinitelyFarLightSource(ShadowScene):
|
||||
CONFIG = {
|
||||
"num_reorientations": 1,
|
||||
"camera_center": [0, 0, 1],
|
||||
@@ -345,7 +368,7 @@ class ShowInfinitelyFarLightSource(ShowShadows):
|
||||
return lines
|
||||
|
||||
|
||||
class CylinderShadows(ShowShadows):
|
||||
class CylinderShadows(ShadowScene):
|
||||
CONFIG = {
|
||||
"surface_area": 2 * PI + 2 * PI * 2,
|
||||
"area_label_center": [0, -2, 0],
|
||||
@@ -382,7 +405,7 @@ class CylinderShadows(ShowShadows):
|
||||
return cylinder
|
||||
|
||||
|
||||
class PrismShadows(ShowShadows):
|
||||
class PrismShadows(ShadowScene):
|
||||
CONFIG = {
|
||||
"surface_area": 3 * np.sqrt(3) / 2 + 3 * (np.sqrt(3) * 2),
|
||||
"object_center": [0, 0, 3],
|
||||
@@ -18,4 +18,5 @@ style:
|
||||
camera_qualities:
|
||||
default_quality: "ultra_high"
|
||||
window_position: UR
|
||||
window_monitor: 0
|
||||
window_monitor: 0
|
||||
full_screen: False
|
||||
Reference in New Issue
Block a user