def update_shadow(self):
point = self.get_source_point()
projected_screen_points = []
if not self.has_screen():
return
for point in self.screen.get_anchors():
projected_screen_points.append(self.spotlight.project(point))
projected_source = project_along_vector(
self.get_source_point(), self.spotlight.projection_direction())
projected_point_cloud_3d = np.append(
projected_screen_points,
np.reshape(projected_source, (1, 3)),
axis=0
)
# z_to_vector(self.spotlight.projection_direction())
rotation_matrix = self.rotation_matrix()
back_rotation_matrix = rotation_matrix.T # i. e. its inverse
rotated_point_cloud_3d = np.dot(
projected_point_cloud_3d, back_rotation_matrix.T)
# these points now should all have z = 0
point_cloud_2d = rotated_point_cloud_3d[:, :2]
# now we can compute the convex hull
hull_2d = ConvexHull(point_cloud_2d) # guaranteed to run ccw
hull = []
# we also need the projected source point
source_point_2d = np.dot(self.spotlight.project(
self.get_source_point()), back_rotation_matrix.T)[:2]
index = 0
for point in point_cloud_2d[hull_2d.vertices]:
if np.all(np.abs(point - source_point_2d) < 1.0e-6):
source_index = index
index += 1
continue
point_3d = np.array([point[0], point[1], 0])
hull.append(point_3d)
index += 1
hull_mobject = VMobject()
hull_mobject.set_points_as_corners(hull)
hull_mobject.apply_matrix(rotation_matrix)
anchors = hull_mobject.get_anchors()
# add two control points for the outer cone
if np.size(anchors) == 0:
self.shadow.points = []
return
ray1 = anchors[source_index - 1] - projected_source
ray1 = ray1 / np.linalg.norm(ray1) * 100
ray2 = anchors[source_index] - projected_source
ray2 = ray2 / np.linalg.norm(ray2) * 100
outpoint1 = anchors[source_index - 1] + ray1
outpoint2 = anchors[source_index] + ray2
new_anchors = anchors[:source_index]
new_anchors = np.append(new_anchors, np.array(
[outpoint1, outpoint2]), axis=0)
new_anchors = np.append(new_anchors, anchors[source_index:], axis=0)
self.shadow.set_points_as_corners(new_anchors)
# shift it closer to the camera so it is in front of the spotlight
self.shadow.mark_paths_closed = True
def update_shadow(self):
point = self.get_source_point()
projected_screen_points = []
if not self.has_screen():
return
for point in self.screen.get_anchors():
projected_screen_points.append(self.spotlight.project(point))
projected_source = project_along_vector(
self.get_source_point(), self.spotlight.projection_direction())
projected_point_cloud_3d = np.append(projected_screen_points,
np.reshape(
projected_source, (1, 3)),
axis=0)
rotation_matrix = self.rotation_matrix(
) # z_to_vector(self.spotlight.projection_direction())
back_rotation_matrix = rotation_matrix.T # i. e. its inverse
rotated_point_cloud_3d = np.dot(projected_point_cloud_3d,
back_rotation_matrix.T)
# these points now should all have z = 0
point_cloud_2d = rotated_point_cloud_3d[:, :2]
# now we can compute the convex hull
hull_2d = ConvexHull(point_cloud_2d) # guaranteed to run ccw
hull = []
# we also need the projected source point
source_point_2d = np.dot(
self.spotlight.project(self.get_source_point()),
back_rotation_matrix.T)[:2]
index = 0
for point in point_cloud_2d[hull_2d.vertices]:
if np.all(np.abs(point - source_point_2d) < 1.0e-6):
source_index = index
index += 1
continue
point_3d = np.array([point[0], point[1], 0])
hull.append(point_3d)
index += 1
hull_mobject = VMobject()
hull_mobject.set_points_as_corners(hull)
hull_mobject.apply_matrix(rotation_matrix)
anchors = hull_mobject.get_anchors()
# add two control points for the outer cone
if np.size(anchors) == 0:
self.shadow.points = []
return
ray1 = anchors[source_index - 1] - projected_source
ray1 = ray1 / np.linalg.norm(ray1) * 100
ray2 = anchors[source_index] - projected_source
ray2 = ray2 / np.linalg.norm(ray2) * 100
outpoint1 = anchors[source_index - 1] + ray1
outpoint2 = anchors[source_index] + ray2
new_anchors = anchors[:source_index]
new_anchors = np.append(new_anchors,
np.array([outpoint1, outpoint2]),
axis=0)
new_anchors = np.append(new_anchors, anchors[source_index:], axis=0)
self.shadow.set_points_as_corners(new_anchors)
# shift it closer to the camera so it is in front of the spotlight
self.shadow.mark_paths_closed = True
class LightSource(VMobject):
# combines:
# a lighthouse
# an ambient light
# a spotlight
# and a shadow
CONFIG = {
"source_point": VectorizedPoint(location=ORIGIN, stroke_width=0, fill_opacity=0),
"color": LIGHT_COLOR,
"num_levels": 10,
"radius": 10.0,
"screen": None,
"opacity_function": inverse_quadratic(1, 2, 1),
"max_opacity_ambient": AMBIENT_FULL,
"max_opacity_spotlight": SPOTLIGHT_FULL,
"camera_mob": None
}
def generate_points(self):
self.add(self.source_point)
self.lighthouse = Lighthouse()
self.ambient_light = AmbientLight(
source_point=VectorizedPoint(location=self.get_source_point()),
color=self.color,
num_levels=self.num_levels,
radius=self.radius,
opacity_function=self.opacity_function,
max_opacity=self.max_opacity_ambient
)
if self.has_screen():
self.spotlight = Spotlight(
source_point=VectorizedPoint(location=self.get_source_point()),
color=self.color,
num_levels=self.num_levels,
radius=self.radius,
screen=self.screen,
opacity_function=self.opacity_function,
max_opacity=self.max_opacity_spotlight,
camera_mob=self.camera_mob
)
else:
self.spotlight = Spotlight()
self.shadow = VMobject(fill_color=SHADOW_COLOR,
fill_opacity=1.0, stroke_color=BLACK)
self.lighthouse.next_to(self.get_source_point(), DOWN, buff=0)
self.ambient_light.move_source_to(self.get_source_point())
if self.has_screen():
self.spotlight.move_source_to(self.get_source_point())
self.update_shadow()
self.add(self.ambient_light, self.spotlight,
self.lighthouse, self.shadow)
def has_screen(self):
if self.screen is None:
return False
elif np.size(self.screen.points) == 0:
return False
else:
return True
def dim_ambient(self):
self.set_max_opacity_ambient(AMBIENT_DIMMED)
def set_max_opacity_ambient(self, new_opacity):
self.max_opacity_ambient = new_opacity
self.ambient_light.dimming(new_opacity)
def dim_spotlight(self):
self.set_max_opacity_spotlight(SPOTLIGHT_DIMMED)
def set_max_opacity_spotlight(self, new_opacity):
self.max_opacity_spotlight = new_opacity
self.spotlight.dimming(new_opacity)
def set_camera_mob(self, new_cam_mob):
self.camera_mob = new_cam_mob
self.spotlight.camera_mob = new_cam_mob
def set_screen(self, new_screen):
if self.has_screen():
self.spotlight.screen = new_screen
else:
# Note: See below
index = self.submobjects.index(self.spotlight)
camera_mob = self.spotlight.camera_mob
self.remove(self.spotlight)
self.spotlight = Spotlight(
source_point=VectorizedPoint(location=self.get_source_point()),
color=self.color,
num_levels=self.num_levels,
radius=self.radius,
screen=new_screen,
camera_mob=self.camera_mob,
opacity_function=self.opacity_function,
max_opacity=self.max_opacity_spotlight,
)
self.spotlight.move_source_to(self.get_source_point())
# Note: This line will make spotlight show up at the end
# of the submojects list, which can make it show up on
# top of the shadow. To make it show up in the
# same spot, you could try the following line,
# where "index" is what I defined above:
self.submobjects.insert(index, self.spotlight)
# self.add(self.spotlight)
# in any case
self.screen = new_screen
def move_source_to(self, point):
apoint = np.array(point)
v = apoint - self.get_source_point()
# Note: As discussed, things stand to behave better if source
# point is a submobject, so that it automatically interpolates
# during an animation, and other updates can be defined wrt
# that source point's location
self.source_point.set_location(apoint)
# self.lighthouse.next_to(apoint,DOWN,buff = 0)
# self.ambient_light.move_source_to(apoint)
self.lighthouse.shift(v)
# self.ambient_light.shift(v)
self.ambient_light.move_source_to(apoint)
if self.has_screen():
self.spotlight.move_source_to(apoint)
self.update()
return self
def change_spotlight_opacity_function(self, new_of):
self.spotlight.change_opacity_function(new_of)
def set_radius(self, new_radius):
self.radius = new_radius
self.ambient_light.radius = new_radius
self.spotlight.radius = new_radius
def update(self):
self.update_lighthouse()
self.update_ambient()
self.spotlight.update_sectors()
self.update_shadow()
def update_lighthouse(self):
self.lighthouse.move_to(self.get_source_point())
# new_lh = Lighthouse()
# new_lh.move_to(ORIGIN)
# new_lh.apply_matrix(self.rotation_matrix())
# new_lh.shift(self.get_source_point())
# self.lighthouse.submobjects = new_lh.submobjects
def update_ambient(self):
new_ambient_light = AmbientLight(
source_point=VectorizedPoint(location=ORIGIN),
color=self.color,
num_levels=self.num_levels,
radius=self.radius,
opacity_function=self.opacity_function,
max_opacity=self.max_opacity_ambient
)
new_ambient_light.apply_matrix(self.rotation_matrix())
new_ambient_light.move_source_to(self.get_source_point())
self.ambient_light.submobjects = new_ambient_light.submobjects
def get_source_point(self):
return self.source_point.get_location()
def rotation_matrix(self):
if self.camera_mob is None:
return np.eye(3)
phi = self.camera_mob.get_center()[0]
theta = self.camera_mob.get_center()[1]
R1 = np.array([
[1, 0, 0],
[0, np.cos(phi), -np.sin(phi)],
[0, np.sin(phi), np.cos(phi)]
])
R2 = np.array([
[np.cos(theta + TAU / 4), -np.sin(theta + TAU / 4), 0],
[np.sin(theta + TAU / 4), np.cos(theta + TAU / 4), 0],
[0, 0, 1]
])
R = np.dot(R2, R1)
return R
def update_shadow(self):
point = self.get_source_point()
projected_screen_points = []
if not self.has_screen():
return
for point in self.screen.get_anchors():
projected_screen_points.append(self.spotlight.project(point))
projected_source = project_along_vector(
self.get_source_point(), self.spotlight.projection_direction())
projected_point_cloud_3d = np.append(
projected_screen_points,
np.reshape(projected_source, (1, 3)),
axis=0
)
# z_to_vector(self.spotlight.projection_direction())
rotation_matrix = self.rotation_matrix()
back_rotation_matrix = rotation_matrix.T # i. e. its inverse
rotated_point_cloud_3d = np.dot(
projected_point_cloud_3d, back_rotation_matrix.T)
# these points now should all have z = 0
point_cloud_2d = rotated_point_cloud_3d[:, :2]
# now we can compute the convex hull
hull_2d = ConvexHull(point_cloud_2d) # guaranteed to run ccw
hull = []
# we also need the projected source point
source_point_2d = np.dot(self.spotlight.project(
self.get_source_point()), back_rotation_matrix.T)[:2]
index = 0
for point in point_cloud_2d[hull_2d.vertices]:
if np.all(np.abs(point - source_point_2d) < 1.0e-6):
source_index = index
index += 1
continue
point_3d = np.array([point[0], point[1], 0])
hull.append(point_3d)
index += 1
hull_mobject = VMobject()
hull_mobject.set_points_as_corners(hull)
hull_mobject.apply_matrix(rotation_matrix)
anchors = hull_mobject.get_anchors()
# add two control points for the outer cone
if np.size(anchors) == 0:
self.shadow.points = []
return
ray1 = anchors[source_index - 1] - projected_source
ray1 = ray1 / np.linalg.norm(ray1) * 100
ray2 = anchors[source_index] - projected_source
ray2 = ray2 / np.linalg.norm(ray2) * 100
outpoint1 = anchors[source_index - 1] + ray1
outpoint2 = anchors[source_index] + ray2
new_anchors = anchors[:source_index]
new_anchors = np.append(new_anchors, np.array(
[outpoint1, outpoint2]), axis=0)
new_anchors = np.append(new_anchors, anchors[source_index:], axis=0)
self.shadow.set_points_as_corners(new_anchors)
# shift it closer to the camera so it is in front of the spotlight
self.shadow.mark_paths_closed = True
class LightSource(VMobject):
# combines:
# a lighthouse
# an ambient light
# a spotlight
# and a shadow
CONFIG = {
"source_point":
VectorizedPoint(location=ORIGIN, stroke_width=0, fill_opacity=0),
"color":
LIGHT_COLOR,
"num_levels":
10,
"radius":
10.0,
"screen":
None,
"opacity_function":
inverse_quadratic(1, 2, 1),
"max_opacity_ambient":
AMBIENT_FULL,
"max_opacity_spotlight":
SPOTLIGHT_FULL,
"camera_mob":
None
}
def generate_points(self):
self.add(self.source_point)
self.lighthouse = Lighthouse()
self.ambient_light = AmbientLight(
source_point=VectorizedPoint(location=self.get_source_point()),
color=self.color,
num_levels=self.num_levels,
radius=self.radius,
opacity_function=self.opacity_function,
max_opacity=self.max_opacity_ambient)
if self.has_screen():
self.spotlight = Spotlight(
source_point=VectorizedPoint(location=self.get_source_point()),
color=self.color,
num_levels=self.num_levels,
radius=self.radius,
screen=self.screen,
opacity_function=self.opacity_function,
max_opacity=self.max_opacity_spotlight,
camera_mob=self.camera_mob)
else:
self.spotlight = Spotlight()
self.shadow = VMobject(fill_color=SHADOW_COLOR,
fill_opacity=1.0,
stroke_color=BLACK)
self.lighthouse.next_to(self.get_source_point(), DOWN, buff=0)
self.ambient_light.move_source_to(self.get_source_point())
if self.has_screen():
self.spotlight.move_source_to(self.get_source_point())
self.update_shadow()
self.add(self.ambient_light, self.spotlight, self.lighthouse,
self.shadow)
def has_screen(self):
if self.screen == None:
return False
elif np.size(self.screen.points) == 0:
return False
else:
return True
def dim_ambient(self):
self.set_max_opacity_ambient(AMBIENT_DIMMED)
def set_max_opacity_ambient(self, new_opacity):
self.max_opacity_ambient = new_opacity
self.ambient_light.dimming(new_opacity)
def dim_spotlight(self):
self.set_max_opacity_spotlight(SPOTLIGHT_DIMMED)
def set_max_opacity_spotlight(self, new_opacity):
self.max_opacity_spotlight = new_opacity
self.spotlight.dimming(new_opacity)
def set_camera_mob(self, new_cam_mob):
self.camera_mob = new_cam_mob
self.spotlight.camera_mob = new_cam_mob
def set_screen(self, new_screen):
if self.has_screen():
self.spotlight.screen = new_screen
else:
# Note: See below
index = self.submobjects.index(self.spotlight)
camera_mob = self.spotlight.camera_mob
self.remove(self.spotlight)
self.spotlight = Spotlight(
source_point=VectorizedPoint(location=self.get_source_point()),
color=self.color,
num_levels=self.num_levels,
radius=self.radius,
screen=new_screen,
camera_mob=self.camera_mob,
opacity_function=self.opacity_function,
max_opacity=self.max_opacity_spotlight,
)
self.spotlight.move_source_to(self.get_source_point())
# Note: This line will make spotlight show up at the end
# of the submojects list, which can make it show up on
# top of the shadow. To make it show up in the
# same spot, you could try the following line,
# where "index" is what I defined above:
self.submobjects.insert(index, self.spotlight)
#self.add(self.spotlight)
# in any case
self.screen = new_screen
def move_source_to(self, point):
apoint = np.array(point)
v = apoint - self.get_source_point()
# Note: As discussed, things stand to behave better if source
# point is a submobject, so that it automatically interpolates
# during an animation, and other updates can be defined wrt
# that source point's location
self.source_point.set_location(apoint)
#self.lighthouse.next_to(apoint,DOWN,buff = 0)
#self.ambient_light.move_source_to(apoint)
self.lighthouse.shift(v)
#self.ambient_light.shift(v)
self.ambient_light.move_source_to(apoint)
if self.has_screen():
self.spotlight.move_source_to(apoint)
self.update()
return self
def change_spotlight_opacity_function(self, new_of):
self.spotlight.change_opacity_function(new_of)
def set_radius(self, new_radius):
self.radius = new_radius
self.ambient_light.radius = new_radius
self.spotlight.radius = new_radius
def update(self):
self.update_lighthouse()
self.update_ambient()
self.spotlight.update_sectors()
self.update_shadow()
def update_lighthouse(self):
self.lighthouse.move_to(self.get_source_point())
# new_lh = Lighthouse()
# new_lh.move_to(ORIGIN)
# new_lh.apply_matrix(self.rotation_matrix())
# new_lh.shift(self.get_source_point())
# self.lighthouse.submobjects = new_lh.submobjects
def update_ambient(self):
new_ambient_light = AmbientLight(
source_point=VectorizedPoint(location=ORIGIN),
color=self.color,
num_levels=self.num_levels,
radius=self.radius,
opacity_function=self.opacity_function,
max_opacity=self.max_opacity_ambient)
new_ambient_light.apply_matrix(self.rotation_matrix())
new_ambient_light.move_source_to(self.get_source_point())
self.ambient_light.submobjects = new_ambient_light.submobjects
def get_source_point(self):
return self.source_point.get_location()
def rotation_matrix(self):
if self.camera_mob == None:
return np.eye(3)
phi = self.camera_mob.get_center()[0]
theta = self.camera_mob.get_center()[1]
R1 = np.array([[1, 0, 0], [0, np.cos(phi), -np.sin(phi)],
[0, np.sin(phi), np.cos(phi)]])
R2 = np.array([[np.cos(theta + TAU / 4), -np.sin(theta + TAU / 4), 0],
[np.sin(theta + TAU / 4),
np.cos(theta + TAU / 4), 0], [0, 0, 1]])
R = np.dot(R2, R1)
return R
def update_shadow(self):
point = self.get_source_point()
projected_screen_points = []
if not self.has_screen():
return
for point in self.screen.get_anchors():
projected_screen_points.append(self.spotlight.project(point))
projected_source = project_along_vector(
self.get_source_point(), self.spotlight.projection_direction())
projected_point_cloud_3d = np.append(projected_screen_points,
np.reshape(
projected_source, (1, 3)),
axis=0)
rotation_matrix = self.rotation_matrix(
) # z_to_vector(self.spotlight.projection_direction())
back_rotation_matrix = rotation_matrix.T # i. e. its inverse
rotated_point_cloud_3d = np.dot(projected_point_cloud_3d,
back_rotation_matrix.T)
# these points now should all have z = 0
point_cloud_2d = rotated_point_cloud_3d[:, :2]
# now we can compute the convex hull
hull_2d = ConvexHull(point_cloud_2d) # guaranteed to run ccw
hull = []
# we also need the projected source point
source_point_2d = np.dot(
self.spotlight.project(self.get_source_point()),
back_rotation_matrix.T)[:2]
index = 0
for point in point_cloud_2d[hull_2d.vertices]:
if np.all(np.abs(point - source_point_2d) < 1.0e-6):
source_index = index
index += 1
continue
point_3d = np.array([point[0], point[1], 0])
hull.append(point_3d)
index += 1
hull_mobject = VMobject()
hull_mobject.set_points_as_corners(hull)
hull_mobject.apply_matrix(rotation_matrix)
anchors = hull_mobject.get_anchors()
# add two control points for the outer cone
if np.size(anchors) == 0:
self.shadow.points = []
return
ray1 = anchors[source_index - 1] - projected_source
ray1 = ray1 / np.linalg.norm(ray1) * 100
ray2 = anchors[source_index] - projected_source
ray2 = ray2 / np.linalg.norm(ray2) * 100
outpoint1 = anchors[source_index - 1] + ray1
outpoint2 = anchors[source_index] + ray2
new_anchors = anchors[:source_index]
new_anchors = np.append(new_anchors,
np.array([outpoint1, outpoint2]),
axis=0)
new_anchors = np.append(new_anchors, anchors[source_index:], axis=0)
self.shadow.set_points_as_corners(new_anchors)
# shift it closer to the camera so it is in front of the spotlight
self.shadow.mark_paths_closed = True
