class ThreeDCamera(CameraWithPerspective):
CONFIG = {
"sun_vect" : 5*UP+LEFT,
"shading_factor" : 0.5,
"distance" : 5,
"phi" : 0, #Angle off z axis
"theta" : -np.pi/2, #Rotation about z axis
}
def __init__(self, *args, **kwargs):
Camera.__init__(self, *args, **kwargs)
self.unit_sun_vect = self.sun_vect/np.linalg.norm(self.sun_vect)
self.position_mobject = VectorizedPoint()
self.set_position(self.phi, self.theta, self.distance)
def get_color(self, method):
color = method()
vmobject = method.im_self
if should_shade_in_3d(vmobject):
return Color(rgb = self.get_shaded_rgb(
color_to_rgb(color),
normal_vect = self.get_unit_normal_vect(vmobject)
))
else:
return color
def get_stroke_color(self, vmobject):
return self.get_color(vmobject.get_stroke_color)
def get_fill_color(self, vmobject):
return self.get_color(vmobject.get_fill_color)
def get_shaded_rgb(self, rgb, normal_vect):
brightness = np.dot(normal_vect, self.unit_sun_vect)**2
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
def display_multiple_vectorized_mobjects(self, vmobjects):
def z_cmp(*vmobs):
#Compare to three dimensional mobjects based on their
#z value, otherwise don't compare.
three_d_status = map(should_shade_in_3d, vmobs)
has_points = [vm.get_num_points() > 0 for vm in vmobs]
if all(three_d_status) and all(has_points):
cmp_vect = self.get_unit_normal_vect(vmobs[1])
return cmp(*[
np.dot(vm.get_center(), cmp_vect)
for vm in vmobs
])
else:
return 0
Camera.display_multiple_vectorized_mobjects(
self, sorted(vmobjects, cmp = z_cmp)
)
def get_position(self):
return self.position_mobject.points[0]
def get_phi(self):
x, y, z = self.get_position()
return angle_of_vector([z, np.sqrt(x**2 + y**2)])
def get_theta(self):
x, y, z = self.get_position()
return angle_of_vector([x, y])
def get_distance(self):
return np.linalg.norm(self.get_position())
def spherical_coords_to_point(self, phi, theta, distance):
phi = phi or self.get_phi()
theta = theta or self.get_theta()
distance = distance or self.get_distance()
return distance*np.array([
np.sin(phi)*np.cos(theta),
np.sin(phi)*np.sin(theta),
np.cos(phi)
])
def set_position(self, phi = None, theta = None, distance = None):
point = self.spherical_coords_to_point(phi, theta, distance)
self.position_mobject.move_to(point)
self.phi = self.get_phi()
self.theta = self.get_theta()
self.distance = self.get_distance()
def get_view_transformation_matrix(self):
return np.dot(
rotation_matrix(self.get_phi(), LEFT),
rotation_about_z(-self.get_theta() - np.pi/2),
)
def points_to_pixel_coords(self, points):
matrix = self.get_view_transformation_matrix()
new_points = np.dot(points, matrix.T)
return Camera.points_to_pixel_coords(self, new_points)
class ThreeDCamera(CameraWithPerspective):
CONFIG = {
"sun_vect": 5 * UP + LEFT,
"shading_factor": 0.2,
"distance": 5.,
"default_distance": 5.,
"phi": 0, #Angle off z axis
"theta": -TAU / 4, #Rotation about z axis
}
def __init__(self, *args, **kwargs):
Camera.__init__(self, *args, **kwargs)
self.unit_sun_vect = self.sun_vect / np.linalg.norm(self.sun_vect)
## rotation_mobject lives in the phi-theta-distance space
self.rotation_mobject = VectorizedPoint()
## moving_center lives in the x-y-z space
## It representes the center of rotation
self.moving_center = VectorizedPoint(self.space_center)
self.set_position(self.phi, self.theta, self.distance)
def modified_rgb(self, vmobject, rgb):
if should_shade_in_3d(vmobject):
return self.get_shaded_rgb(rgb,
self.get_unit_normal_vect(vmobject))
else:
return rgb
def get_stroke_rgb(self, vmobject):
return self.modified_rgb(vmobject, vmobject.get_stroke_rgb())
def get_fill_rgb(self, vmobject):
return self.modified_rgb(vmobject, vmobject.get_fill_rgb())
def get_shaded_rgb(self, rgb, normal_vect):
brightness = np.dot(normal_vect, self.unit_sun_vect)**2
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
def display_multiple_vectorized_mobjects(self, vmobjects):
camera_point = self.spherical_coords_to_point(
*self.get_spherical_coords())
def z_cmp(*vmobs):
# Compare to three dimensional mobjects based on
# how close they are to the camera
# return cmp(*[
# -np.linalg.norm(vm.get_center()-camera_point)
# for vm in vmobs
# ])
three_d_status = map(should_shade_in_3d, vmobs)
has_points = [vm.get_num_points() > 0 for vm in vmobs]
if all(three_d_status) and all(has_points):
cmp_vect = self.get_unit_normal_vect(vmobs[1])
return cmp(
*[np.dot(vm.get_center(), cmp_vect) for vm in vmobs])
else:
return 0
Camera.display_multiple_vectorized_mobjects(
self, sorted(vmobjects, cmp=z_cmp))
def get_spherical_coords(self, phi=None, theta=None, distance=None):
curr_phi, curr_theta, curr_d = self.rotation_mobject.points[0]
if phi is None: phi = curr_phi
if theta is None: theta = curr_theta
if distance is None: distance = curr_d
return np.array([phi, theta, distance])
def get_cartesian_coords(self, phi=None, theta=None, distance=None):
spherical_coords_array = self.get_spherical_coords(
phi, theta, distance)
phi2 = spherical_coords_array[0]
theta2 = spherical_coords_array[1]
d2 = spherical_coords_array[2]
return self.spherical_coords_to_point(phi2, theta2, d2)
def get_phi(self):
return self.get_spherical_coords()[0]
def get_theta(self):
return self.get_spherical_coords()[1]
def get_distance(self):
return self.get_spherical_coords()[2]
def spherical_coords_to_point(self, phi, theta, distance):
return distance * np.array([
np.sin(phi) * np.cos(theta),
np.sin(phi) * np.sin(theta),
np.cos(phi)
])
def get_center_of_rotation(self, x=None, y=None, z=None):
curr_x, curr_y, curr_z = self.moving_center.points[0]
if x is None:
x = curr_x
if y is None:
y = curr_y
if z is None:
z = curr_z
return np.array([x, y, z])
def set_position(self,
phi=None,
theta=None,
distance=None,
center_x=None,
center_y=None,
center_z=None):
point = self.get_spherical_coords(phi, theta, distance)
self.rotation_mobject.move_to(point)
self.phi, self.theta, self.distance = point
center_of_rotation = self.get_center_of_rotation(
center_x, center_y, center_z)
self.moving_center.move_to(center_of_rotation)
self.space_center = self.moving_center.points[0]
def get_view_transformation_matrix(self):
return (self.default_distance / self.get_distance()) * np.dot(
rotation_matrix(self.get_phi(), LEFT),
rotation_about_z(-self.get_theta() - np.pi / 2),
)
def points_to_pixel_coords(self, points):
matrix = self.get_view_transformation_matrix()
new_points = np.dot(points, matrix.T)
self.space_center = self.moving_center.points[0]
return Camera.points_to_pixel_coords(self, new_points)
class ThreeDCamera(CameraWithPerspective):
CONFIG = {
"sun_vect" : 5*UP+LEFT,
"shading_factor" : 0.2,
"distance" : 5.,
"default_distance" : 5.,
"phi" : 0, #Angle off z axis
"theta" : -TAU/4, #Rotation about z axis
}
def __init__(self, *args, **kwargs):
Camera.__init__(self, *args, **kwargs)
self.unit_sun_vect = self.sun_vect/np.linalg.norm(self.sun_vect)
## Lives in the phi-theta-distance space
self.rotation_mobject = VectorizedPoint()
self.set_position(self.phi, self.theta, self.distance)
def get_color(self, method):
color = method()
vmobject = method.im_self
if should_shade_in_3d(vmobject):
return Color(rgb = self.get_shaded_rgb(
color_to_rgb(color),
normal_vect = self.get_unit_normal_vect(vmobject)
))
else:
return color
def get_stroke_color(self, vmobject):
return self.get_color(vmobject.get_stroke_color)
def get_fill_color(self, vmobject):
return self.get_color(vmobject.get_fill_color)
def get_shaded_rgb(self, rgb, normal_vect):
brightness = np.dot(normal_vect, self.unit_sun_vect)**2
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
def display_multiple_vectorized_mobjects(self, vmobjects):
camera_point = self.spherical_coords_to_point(
*self.get_spherical_coords()
)
def z_cmp(*vmobs):
#Compare to three dimensional mobjects based on
#how close they are to the camera
return cmp(*[
-np.linalg.norm(vm.get_center()-camera_point)
for vm in vmobs
])
# three_d_status = map(should_shade_in_3d, vmobs)
# has_points = [vm.get_num_points() > 0 for vm in vmobs]
# if all(three_d_status) and all(has_points):
# cmp_vect = self.get_unit_normal_vect(vmobs[1])
# return cmp(*[
# np.dot(vm.get_center(), cmp_vect)
# for vm in vmobs
# ])
# else:
# return 0
Camera.display_multiple_vectorized_mobjects(
self, sorted(vmobjects, cmp = z_cmp)
)
def get_spherical_coords(self, phi = None, theta = None, distance = None):
curr_phi, curr_theta, curr_d = self.rotation_mobject.points[0]
if phi is None: phi = curr_phi
if theta is None: theta = curr_theta
if distance is None: distance = curr_d
return np.array([phi, theta, distance])
def get_phi(self):
return self.get_spherical_coords()[0]
def get_theta(self):
return self.get_spherical_coords()[1]
def get_distance(self):
return self.get_spherical_coords()[2]
def spherical_coords_to_point(self, phi, theta, distance):
return distance*np.array([
np.sin(phi)*np.cos(theta),
np.sin(phi)*np.sin(theta),
np.cos(phi)
])
def set_position(self, phi = None, theta = None, distance = None):
point = self.get_spherical_coords(phi, theta, distance)
self.rotation_mobject.move_to(point)
self.phi, self.theta, self.distance = point
def get_view_transformation_matrix(self):
return (self.default_distance / self.get_distance()) * np.dot(
rotation_matrix(self.get_phi(), LEFT),
rotation_about_z(-self.get_theta() - np.pi/2),
)
def points_to_pixel_coords(self, points):
matrix = self.get_view_transformation_matrix()
new_points = np.dot(points, matrix.T)
return Camera.points_to_pixel_coords(self, new_points)