This commit is contained in:
Yingjie Wang 2023-10-30 00:41:13 -04:00
commit 386db2d6b8
5 changed files with 541 additions and 0 deletions

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78
rainbow.py Normal file
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import numpy as np
from raytrace_2D import Disk
import csv
class Ray:
def __init__(self, origin, direction, intensity):
self.origin = np.array(origin)
self.direction = np.array(direction) / np.linalg.norm(direction)
self.intensity = intensity
center = [0,0]
r = 1
n = 1.3
disk = Disk(center, r, n)
dx = 0.01
N = int(2*r /dx - 1)
min_intensity = 0.001
stack = []
result = []
points = []
def init():
for x in np.linspace(-r + dx, r-dx, N):
stack.append(Ray([x, 2*r], [0,-1], 1))
print(np.linspace(-r + dx, r-dx, N))
def reflection_and_refraction(ray:Ray, intersection_point, normal, n):
print("reflection/refraction at the point:", intersection_point)
k_n = np.dot(ray.direction, normal)
if k_n > 0:
n1,n2 = n,1
else:
n1, n2 = 1,n
kp = ray.direction - k_n*normal
k2p = n1*kp/n2
if np.dot(k2p, k2p) >= 1:
ray1 = Ray(intersection_point, ray.direction-2*k_n*normal, ray.intensity)
return ray1,None
else:
k2n = np.sqrt(1 - np.dot(k2p, k2p))*np.sign(k_n)
Rs = (n1*k_n - n2*k2n)*(n1*k_n - n2*k2n)/((n1*k_n + n2*k2n)*(n1*k_n + n2*k2n))
Rp = (n1*k2n - n2*k_n)*(n1*k2n - n2*k_n)/((n1*k2n + n2*k_n)*(n1*k2n + n2*k_n))
R = (Rs+Rp)/2
ray1 = Ray(intersection_point, ray.direction-2*k_n*normal, ray.intensity*R)
ray2 = Ray(intersection_point, k2n*normal+k2p, ray.intensity*(1-R))
return ray1,ray2
def trace(disk:Disk, stack:list):
while stack:
ray = stack.pop()
if ray is None:
continue
if isinstance(ray, Ray):
if ray.intensity < min_intensity:
continue
direction = ray.direction
t,intersection_point = disk.find_intersection(ray)
if intersection_point is not None:
points.append(np.concatenate((ray.origin, intersection_point,[ray.intensity])))
normal = disk.get_normal(intersection_point)
stack.extend(reflection_and_refraction(ray, intersection_point, normal, disk.refractive_index))
else:
points.append(np.concatenate((ray.origin, ray.origin+ray.direction,[ray.intensity])))
if direction[1] > 0:
result.append([np.arccos(direction[1]), ray.intensity*direction[1]])
# init()
stack.append(Ray([0.8, 2*r], [0,-1], 1))
trace(disk, stack)
with open("result.csv", 'w', newline='') as f:
writer = csv.writer(f)
writer.writerows(result)
with open("points.csv", 'w', newline='') as f:
writer = csv.writer(f)
writer.writerows(points)

78
raytrace_2D.py Normal file
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@ -0,0 +1,78 @@
import numpy as np
from abc import ABC, abstractmethod
class Ray:
def __init__(self, origin, direction):
self.origin = np.array(origin)
self.direction = np.array(direction) / np.linalg.norm(direction)
class Shapes(ABC):
def __init__(self,refractive_index) -> None:
self.refractive_index = refractive_index
@abstractmethod
def find_intersection(self, ray:Ray):
pass
def get_normal(self, point):
pass
class Scheme:
def __init__(self, shapes, rays) -> None:
self.shapes = shapes
self.rays = rays
self.raytrace()
def raytrace(self):
for ray in self.rays:
t, intersection_point, first_shape = None, None, None
for shape in self.shapes:
t1,intersection_point1 = shape.find_intersection(ray)
if t is None or ((t1 is not None) and (t1 < t)):
t, intersection_point, first_shape = t1, intersection_point1, shape
if t is None:
continue
else:
self.reflection_and_refraction(ray, first_shape, intersection_point)
def reflection_and_refraction(ray:Ray, shape:Shapes, intersection_point):
pass
class Disk(Shapes):
def __init__(self, center, radius, refractive_index):
super().__init__(refractive_index)
self.center = np.array(center)
self.radius = radius
def find_intersection(self, ray:Ray):
oc = ray.origin - self.center
a = np.dot(ray.direction, ray.direction)
b = 2.0 * np.dot(oc, ray.direction)
c = np.dot(oc, oc) - self.radius * self.radius
discriminant = b*b - 4*a*c
if discriminant < 0:
return None, None # 没有交点
else:
if np.dot(oc, oc) <= self.radius * self.radius + 1e-10:
t = (-b + np.sqrt(discriminant)) / (2.0 * a)
else:
t = (-b - np.sqrt(discriminant)) / (2.0 * a)
if t < 0:
return None, None
intersection_point = ray.origin + t * ray.direction
intersection_point = intersection_point/np.linalg.norm(intersection_point)
return t,intersection_point
def get_normal(self, point):
normal = (point - self.center)/self.radius
normal = normal / np.linalg.norm(normal)
return normal
class half_plane(Shapes):
def __init__(self, point, normal, refractive_index) -> None:
super().__init__(refractive_index)
self.point = point
self.normal = normal/np.linalg.norm(normal)
def find_intersection(self, ray:Ray):
dot = np.dot(ray.direction, self.normal)
if dot == 0:
return None,None
else:
t = np.dot(self.point - ray.origin, self.normal) / dot
return t, ray.origin + t*ray.direction
def get_normal(self, point):
return self.normal

5
result.csv Normal file
View File

@ -0,0 +1,5 @@
0.7993010857076976,0.0007048815056688454
1.3928938872949743,0.003657341850518903
1.2482567878728648,0.0003454071966921608
0.8743957180247236,0.0006520310605573929
0.1162362891411113,0.0010096197790698755
1 0.7993010857076976 0.0007048815056688454
2 1.3928938872949743 0.003657341850518903
3 1.2482567878728648 0.0003454071966921608
4 0.8743957180247236 0.0006520310605573929
5 0.1162362891411113 0.0010096197790698755