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||||||
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||||||
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||||||
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|
||||||
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||||||
|
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||||||
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||||||
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||||||
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||||||
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|
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||||||
|
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||||||
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||||||
|
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||||||
|
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0.3154791712274903,0.9489325015624747,1.2639126752139642,1.2659086655179674,0.0010896945447944162
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0.38799246954563393,-0.9216625432206087,-0.9882567011996567,-0.1528027896799413,0.03301052172860067
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||||||
|
0.7511512707196144,0.6601301148230615,0.8440472660316307,-0.5362687877403735,0.03188226482313869
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0.8440472660316307,-0.5362687877403735,-0.27848480174190304,-0.9604406359576698,0.03188226482313869
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-0.2784848017419032,-0.9604406359576697,-0.27848480174190327,-0.9604406359576696,0.030792570278344276
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0.5505197827681364,0.8348221180472662,0.9555747725004538,-0.2947487984041771,0.028568995792213343
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0.9555747725004538,-0.2947487984041771,0.9555747725004536,-0.2947487984041773,0.028568995792213343
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0.09151669908378514,0.9958035417635388,0.09151669908378514,0.9958035417635388,0.0010896945447944162
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|
0.09151669908378514,0.9958035417635388,0.981596075836457,0.19096896057335733,0.0010896945447944162
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0.981596075836457,0.19096896057335733,0.4581771033846308,-0.888860923842459,0.0010896945447944162
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|
0.4581771033846308,-0.888860923842459,0.4581771033846306,-0.888860923842459,0.0010896945447944162
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0.4581771033846306,-0.888860923842459,-0.9734620546103817,-0.2288484831361885,0.00105245019570122
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-0.9734620546103817,-0.2288484831361885,-1.7406180738855612,0.412612070670404,0.0010164788102527463
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0.8000000000000002,0.5999999999999998,0.8000000000000002,0.5999999999999998,0.034178705648400684
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|
0.8000000000000002,0.5999999999999998,0.8000000000000005,-0.5999999999999994,0.034178705648400684
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0.8000000000000005,-0.5999999999999994,-0.35199999999999854,-0.9360000000000006,0.034178705648400684
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|
0.31547917122748886,0.9489325015624751,0.31547917122748886,0.9489325015624751,0.03188226482313869
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|
0.31547917122748886,0.9489325015624751,0.999309369443673,-0.03715890394089538,0.03188226482313869
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0.999309369443673,-0.03715890394089538,0.24413407566096978,-0.9697414877693765,0.03188226482313869
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0.842350634412331,0.5389298736432632,1.77890491397434,0.18840729029935604,0.02974012008264305
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|
0.842350634412331,0.5389298736432632,0.842350634412331,0.5389298736432631,0.0010524501957012206
|
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|
0.842350634412331,0.5389298736432631,-0.015397910167872508,-0.9998814451536053,0.001031520068892143
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|
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|
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|
||||||
|
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|
||||||
|
0.4553696362771245,0.8903024735205668,0.4553696362771246,0.8903024735205666,0.001089694544794418
|
||||||
|
0.4553696362771246,0.8903024735205666,0.7532308563329863,-0.657756244415723,0.0010524501957012214
|
||||||
|
0.7532308563329863,-0.657756244415723,0.7532308563329863,-0.657756244415723,0.0010164788102527476
|
||||||
|
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|
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|
||||||
|
0.31547917122748886,0.9489325015624751,0.8440472660316329,-0.5362687877403698,0.0011282569054619782
|
||||||
|
0.8440472660316329,-0.5362687877403698,0.8440472660316329,-0.5362687877403698,0.0010896945447944177
|
||||||
|
0.8440472660316329,-0.5362687877403698,-0.27848480174189666,-0.9604406359576716,0.0010896945447944177
|
||||||
|
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|
||||||
|
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|
||||||
|
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|
||||||
|
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|
||||||
|
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|
||||||
|
-0.20638720000000324,0.9784703999999994,-0.20638720000000307,0.9784703999999994,0.0011681839198000176
|
||||||
|
-0.20638720000000307,0.9784703999999994,0.999309369443673,-0.03715890394089493,0.001128256905461978
|
||||||
|
0.999309369443673,-0.03715890394089493,0.999309369443673,-0.03715890394089493,0.0010896945447944175
|
||||||
|
0.999309369443673,-0.03715890394089493,0.24413407566097078,-0.9697414877693763,0.0010896945447944175
|
||||||
|
0.24413407566097078,-0.9697414877693763,-0.8625942870735287,-0.5058963292099586,0.0010896945447944175
|
||||||
|
-0.8625942870735287,-0.5058963292099586,-0.7271868764221492,0.6864395434117981,0.0010896945447944175
|
||||||
|
-0.7271868764221492,0.6864395434117981,0.4553696362771229,0.8903024735205675,0.0010896945447944175
|
||||||
|
0.4553696362771229,0.8903024735205675,0.9821938727373396,-0.18787015824027742,0.0010896945447944175
|
||||||
|
0.9821938727373396,-0.18787015824027742,0.09465893245579027,-0.9955097621351237,0.0010896945447944175
|
||||||
|
0.09465893245579027,-0.9955097621351237,0.09465893245579007,-0.9955097621351235,0.0010896945447944175
|
||||||
|
0.09465893245579007,-0.9955097621351235,-0.9887340150578674,0.1496831569267193,0.0010524501957012212
|
||||||
|
-0.9887340150578674,0.1496831569267193,-0.9887340150578674,0.1496831569267193,0.0010164788102527474
|
||||||
|
-0.9887340150578674,0.1496831569267193,-0.13314969356655304,0.9910959383950341,0.0010164788102527474
|
||||||
|
-0.13314969356655304,0.9910959383950341,0.9141701866605978,0.4053305685745008,0.0010164788102527474
|
||||||
|
0.9141701866605978,0.4053305685745008,0.9141701866605978,0.40533056857450056,0.0010164788102527474
|
||||||
|
78
rainbow.py
Normal file
78
rainbow.py
Normal file
@ -0,0 +1,78 @@
|
|||||||
|
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
78
raytrace_2D.py
Normal file
@ -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
5
result.csv
Normal 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
|
||||||
|
Loading…
Reference in New Issue
Block a user