def refracted(self, ray: Ray) -> Optional[Ray]:
position = self.intersection_position(ray)
if position is None:
return None
direction = self._refracted_direction(ray, position)
if direction is None:
return None
return Ray(ray.dim, position, direction)
def show_two_dim_render_demo():
ray = Ray(2, np.array([3, 6]), np.array([-1, -7]))
plane = Plane(2, 1.4, 1, np.array([-6, -1]), np.array([-2, -2]))
two_dim_render.plane_render(ray, plane)
r1 = Ray(2, np.array([-2, 2]), np.array([1, 1]))
r2 = Ray(2, np.array([7, 5]), np.array([1, 2]))
sphere1 = Sphere(2, 1, 1.8, np.array([5, 6]), 4.3)
two_dim_render.sphere_render(r1, sphere1, 100)
sphere2 = Sphere(2, 1, 1.8, np.array([5, 6]), 4)
two_dim_render.sphere_render(r2, sphere2, 100)
ellipse1 = Ellipse(2, 1.2, 1, np.array([5, 6]), np.array([60, 30]))
two_dim_render.ellipse_render(r1, ellipse1, 300)
ellipse2 = Ellipse(2, 1.2, 1, np.array([15, 25]), np.array([6, 10]))
two_dim_render.ellipse_render(r2, ellipse2, 200)
def intersection_position(self, ray: Ray) -> Optional[np.ndarray]:
pc = ray.position - self.center
a = 1
b = 2*np.dot(pc, ray.direction)
c = np.dot(pc, pc) - self.radius**2
t1, t2 = np.roots([a, b, c])
min_t = min(t1, t2)
t = min_t if min_t >= 10**-10 else max(t1, t2)
return ray.point(t) if super().valid_t(t) else None
def intersection_position(self, ray: Ray) -> Optional[np.ndarray]:
md = self.m.dot(ray.direction)
mpc = self.m.dot(ray.position - self.center)
a = md.dot(md)
b = 2*md.dot(mpc)
c = mpc.dot(mpc) - self.semi_axes.prod()**2
t1, t2 = np.roots([a, b, c])
min_t = min(t1, t2)
t = min_t if min_t >= 10**-10 else max(t1, t2)
return ray.point(t) if super().valid_t(t) else None
def _draw_ray(ax: Axes3D,
ray: Ray,
length: float,
color: str = "blue",
line_style: str = "-",
label: str = None):
end_point = ray.point(length)
x = np.array([ray.position[0], end_point[0]])
y = np.array([ray.position[1], end_point[1]])
z = np.array([ray.position[2], end_point[2]])
ax.plot(x, y, z, color=color, linestyle=line_style, label=label)
def three_d_plane():
ray = Ray(3, np.array([4, 1, -10]), np.array([0, 1, 1]))
plane = Plane(3, 1, 2, np.array([5, 5, 10]), np.array([0, 0, 1]))
three_dim_render.plane_render(ray,
plane,
figsize=(7, 7),
plane_length=30,
ray_length=30,
normal_length=30,
xlim=(-15, 35),
ylim=(-15, 35),
zlim=(-10, 60))
def three_d_ellipse():
ray = Ray(3, np.array([0, 5, 0]), np.array([-1.3, 1, 0.5]))
ellipse = Ellipse(3, 1.23, 1, np.array([0, 0, 0]), np.array([12, 30, 12]))
three_dim_render.ellipse_render(ray,
ellipse,
100,
sphere_color="#470180",
ray_color="#0245d4",
reflected_color="#ffc400",
refracted_color="#ff0000",
ray_length=20,
figsize=(7, 7),
xlim=(-30, 30),
ylim=(-30, 30),
zlim=(-30, 30))
def three_d_sphere():
ray = Ray(3, np.array([0, 5, 0]), np.array([-1.3, 1, 0.5]))
sphere = Sphere(3, 1.23, 1, np.array([0, 0, 0]), 20)
three_dim_render.sphere_render(ray,
sphere,
100,
sphere_color="#470180",
ray_color="#0245d4",
reflected_color="#ffc400",
refracted_color="#ff0000",
ray_length=20,
figsize=(7, 7),
xlim=(-30, 30),
ylim=(-30, 30),
zlim=(-30, 30))
def three_d_multiple_plane():
ray_point = np.array([0, 0, 70])
plane = Plane(3, 1.230, 1, np.array([0, 0, 10]), np.array([0, 0, 1]))
ray_direction = np.array([40, 40, -100])
rays = [
Ray(3, ray_point,
transform3d_z(i).dot(ray_direction))
for i in np.linspace(0, 2 * np.pi, 150)
]
three_dim_render.multiple_rays_plane_render(rays,
plane,
figsize=(7, 7),
plane_length=70,
ray_length=40,
xlim=(-60, 60),
ylim=(-60, 60),
zlim=(-20, 100))
def _ray_coords(ray: Ray, length: float = 5) -> Tuple[list, list]:
end_point = ray.point(length)
return [ray.position[0], end_point[0]], [ray.position[1], end_point[1]]
def intersection_position(self, ray: Ray) -> Optional[np.ndarray]:
t = np.dot(self.n, self.position - ray.position) / \
np.dot(self.n, ray.direction)
return ray.point(t) if super().valid_t(t) else None
def _get_normal_rays(normal: np.ndarray,
position: np.ndarray) -> Tuple[Ray, Ray]:
return (
Ray(3, position, normal),
Ray(3, position, -normal),
)
def _get_orthogonal_rays(point: np.array,
normal: np.array) -> Tuple[Ray, Ray, Ray, Ray]:
first, second, third, fourth = _get_orthogonal_directions(normal)
return (Ray(3, point, first), Ray(3, point, second), Ray(3, point, third),
Ray(3, point, fourth))