def look_at_matrix(camera_position: np.ndarray, camera_target: np.ndarray,
camera_up: np.ndarray):
z_axis = Utils.normalize(np.array(camera_position - camera_target))
x_axis = Utils.normalize(np.cross(camera_up, z_axis))
y_axis = np.cross(z_axis, x_axis)
translation_x = -np.dot(x_axis, camera_position)
translation_y = -np.dot(y_axis, camera_position)
translation_z = -np.dot(z_axis, camera_position)
translation = np.array([translation_x, translation_y,
translation_z]).reshape((3, 1))
x_axis = x_axis.reshape((3, 1))
y_axis = y_axis.reshape((3, 1))
z_axis = z_axis.reshape((3, 1))
translation = translation.reshape((3, 1))
#TODO: Make this more efficient
mat = np.append(np.append(np.append(x_axis, y_axis, axis=1),
z_axis,
axis=1),
translation,
axis=1)
return np.append(mat, Utils.homogenous_for_SE3(), axis=0)
def render(self):
(height, width) = self.resolution
for x in range(0, width):
for y in range(0, height):
ray_direction_camera_space = self.camera.camera_ray_direction_camera_space(
x, y, width, height, self.fov)
camera_to_world = self.camera.se3_inv
rot = SE3.extract_rotation(camera_to_world)
ray_world_space = Utils.normalize(
np.matmul(rot, ray_direction_camera_space))
ray = Geometry.Ray(self.camera.origin_ws[0:3], ray_world_space)
(b, t, sphere) = self.find_closest_intersection(ray)
if sphere.is_intersection_acceptable(b, t):
intersection_point = Geometry.point_for_ray(ray, t)
normal = sphere.normal_for_point(intersection_point)
depth = intersection_point[2]
self.depth_buffer[y, x] = fabs(depth)
self.frame_buffer[y, x] = phong_shading(
self.light_ws, intersection_point, normal)
def camera_ray_direction_camera_space(self, pixel_x, pixel_y, width,
height, fov):
(camera_x, camera_y) = self.pixel_to_camera(pixel_x, pixel_y, width,
height, fov)
ray_cs = np.array([camera_x, camera_y, -1]).reshape(3, 1)
return Utils.normalize(ray_cs)
def normal_for_point(self,point_on_shpere):
return Utils.normalize(point_on_shpere - self.origin)
def phong_shading(light_ws, position_ws, normal):
view = Utils.normalize(light_ws - position_ws)
return Utils.fast_dot(view, normal)