update: save ram by trace ray one by one

.gitignore

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+*.csv
+__pycache__/

README.md

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+# 几何光学模拟及彩虹模拟
+
+写了几何光学正向光追。考虑了阳光在水珠中的折射反射，统计角度分布从而模拟彩虹
+
+## 使用的数据
+
+- 水的密度：$$\rho(t) = 999.974950 \frac{1 - (t - 3.983035)^2 (t + 301.797)}{522528.9(t+69.34881)}$$
+其中 $t$ 是摄氏温度
+- 水的折射率：
+  $$ n = \sqrt{\frac{2C + 1}{1- C}}, \\ C = \bar{\rho} \left( a_0 + a_1 \bar{\rho} + a_2 \bar{T} + a_{3}{\bar{\lambda }}^{2}{\bar{T}}+{\frac {a_{4}}{{\bar{\lambda }}^{2}}}+{\frac {a_{5}}{{\bar{\lambda }}^{2}-{\bar{\lambda }}_{\mathit {UV}}^{2}}}+{\frac {a_{6}}{{\bar{\lambda }}^{2}-{\bar{\lambda }}_{\mathit {IR}}^{2}}}+a_{7}{\bar{\rho }}^{2} \right)$$
+  其中：$\bar{T} = T/T^*$, $\bar{\rho} = \rho/\rho^*$, $\bar{\lambda} = \lambda/\lambda^*$ 是约化量，$a_{0} = 0.244257733$, $a_{1} = 0.00974634476$, $a_{2} = −0.00373234996$, $a_{3} = 0.000268678472$, $a_4 = 0.0015892057$, $a_{5} = 0.00245934259$, $a_{6} = 0.90070492$, $a_{7} = −0.0166626219$, $T^{*} = 273.15 \ \mathrm{K}$, $\rho^{*} = 1000\ \mathrm{kg/m^3}$, $\lambda^{*} = 589\ \mathrm{nm}$, $\bar\lambda_{\text{IR}} = 5.432937$, $\bar\lambda_{\text{UV}} = 0.229202$。
+- 单色光引起的色觉：见 CIE 1931，详细数据在 `colorspace.py` 中的 `_CIEXYZ_1931_table`。
+- 阳光设为 $5250\ {}\degree\rm C$ 的黑体辐射。这与大气上层吻合较好，但与大气底层相比，忽略了水分子的大量吸收峰和氧分子、二氧化碳分子等的吸收峰。
+
+## 模拟过程
+
+- 给定温度
+- 对每隔 $1\ \rm{nm}$ 的单色光：
+  - 计算折射率，进行正向光追。假设光只与单个水珠相遇。入射光的瞄准距离 $d_i = r \sqrt{u_i}$，其中 $u$ 在 $[0,1)$ 中均匀分布；入射光按照黑体辐射设置
+  - 统计背向出射的光强 - 角度分布
+  - 转化为 XYZ - 角度分布
+- 求和，得到整个频谱的 XYZ - 角度分布
+- 转化为 sRGB - 角度分布，作图
+
+### TODO：
+- 考虑散射效应：
+  - 这将导致背景不是黑色，而是天空蓝
+  - 这将导致水珠反射回的光强被削弱

colorspace.py

@@ -0,0 +1,512 @@
+import numpy as np
+
+XYZ2RGB_matrix = np.array([[3.2404542, -1.5371385, -0.4985314],
+                       [-0.9692660,  1.8760108,  0.0415560],
+                       [ 0.0556434, -0.2040259,  1.0572252]])
+RGB2XYZ_matrix = np.linalg.inv(XYZ2RGB_matrix)
+
+_CIEXYZ_1931_table = [
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+    [ 830,  0.000001251141,  0.000000451810,  0.000000000000 ]
+]
+
+data_wavelength = np.array(_CIEXYZ_1931_table)[:,0]
+data_x = np.array(_CIEXYZ_1931_table)[:,1]
+data_y = np.array(_CIEXYZ_1931_table)[:,2]
+data_z = np.array(_CIEXYZ_1931_table)[:,3]
+
+def XYZ2RGB(XYZ):
+	return np.dot(XYZ2RGB_matrix, XYZ)
+
+def RGB2XYZ(RGB):
+	return np.dot(RGB2XYZ_matrix, RGB)
+
+def gamma_correct(c):
+    if c <= 0.0031308:
+        return 12.92 * c
+    else:
+        return 1.055 * (c ** (1 / 2.4)) - 0.055
+
+def vectorized_gamma_correct(array):
+	return np.where(array <= 0.0031308, 12.92*array, 1.055*np.power(array, 1/2.4)-0.055)
+
+def wavelength2XYZ(wavelength):
+	X = np.interp(wavelength, data_wavelength, data_x, 0, 0)
+	Y = np.interp(wavelength, data_wavelength, data_y, 0, 0)
+	Z = np.interp(wavelength, data_wavelength, data_z, 0, 0)
+	return np.array([X,Y,Z])
+
+def spectral2XYZ(spectral):
+	X = np.dot(spectral, data_x)
+	Y = np.dot(spectral, data_y)
+	Z = np.dot(spectral, data_z)
+	return np.array([X,Y,Z])

rainbow.py

@@ -1,6 +1,10 @@
 import numpy as np
 from raytrace_2D import Disk
 import csv
+import colorspace
+from rich.progress import Progress, track
+from PIL import Image
+from concurrent.futures import ProcessPoolExecutor, ThreadPoolExecutor, as_completed
 
 class Ray:
 	def __init__(self, origin, direction, intensity):
@@ -10,24 +14,24 @@ class Ray:
 
 center = [0,0]
 r = 1
-n = 1.3
-disk = Disk(center, r, n)
-dx = 0.005
-N = int(2*r /dx - 1)
-min_intensity = 0.001
-max_ray = 10000
+# n = 1.3
+# disk = Disk(center, r, n)
+N = 100000
+min_intensity = 0.00001
+max_ray = 100
 
 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 init():
+# 	stack = []
+# 	for x in np.linspace(-r + dx, r-dx, N):
+# 		stack.append(Ray([x, 2*r], [0,-1], 10*np.abs(x)))
+# 	return stack
 
 def reflection_and_refraction(ray:Ray, intersection_point, normal, n):
-	print("reflection/refraction at the point:", intersection_point)
+	# print("reflection/refraction at the point:", intersection_point)
 	k_n = np.dot(ray.direction, normal)
 	if k_n > 0:
 		n1,n2 = n,1
@@ -49,6 +53,7 @@ def reflection_and_refraction(ray:Ray, intersection_point, normal, n):
 
 def trace(disk:Disk, stack:list, max_ray:int):
 	ray_count = 0
+	result = []
 	while stack and ray_count < max_ray:
 		ray = stack.pop()
 		ray_count += 1
@@ -67,15 +72,161 @@ def trace(disk:Disk, stack:list, max_ray:int):
 				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]])
+	# print("ray trace finish, total ray count:",ray_count)
+	return result
 
-init()
-# stack.append(Ray([0.8, 2*r], [0,-1], 1))
-trace(disk, stack, max_ray)
+def water_density(t):
+	data_t = np.linspace(0,101,102)
+	data_rho = np.array([999.79,999.84,999.88,999.92,999.97,999.92,999.88,999.84,999.79,999.72,999.65,999.55,999.44,999.32,999.19,999.05,998.90,998.74,998.56,998.36,998.16,997.96,997.74,997.50,997.25,996.99,996.74,996.48,996.20,995.90,995.59,995.29,995.97,994.65,994.33,994.98,993.64,993.28,992.93,992.55,992.17,991.78,991.39,990.99,990.57,990.16,989.75,989.33,988.90,988.45,988.04,987.55,987.06,986.58,986.19,985.70,985.22,984.73,984.67,983.18,983.13,982.70,982.22,981.64,981.06,980.48,979.91,979.33,978.85,978.28,977.70,977.13,976.56,975.99,975.41,974.84,974.27,973.70,973.14,972.47,971.81,971.25,970.59,969.93,969.27,968.61,967.96,967.30,966.65,965.99,965.34,964.69,964.04,963.39,962.64,961.90,961.26,960.52,959.78,959.04,958.40,957.67])
+	return np.interp(t, data_t, data_rho)
 
-with open("result.csv", 'w', newline='') as f:
-    writer = csv.writer(f)
-    writer.writerows(result)
+def water_refraction_index(t, wavelength):
+	rhobar = 0.999974950 * (1 - (t - 3.983035)*(t - 3.983035)*(t + 301.797)/(522528.9*(t+69.34881)))
+	# print(rhobar)
+	a0 = 0.244257733
+	a1 = 0.00974634476
+	a2 = -0.00373234996
+	a3 = 0.000268678472
+	a4 = 0.0015892057
+	a5 = 0.00245934259
+	a6 = 0.90070492
+	a7 = -0.0166626219
+	Tstar = 273.15
+	Tbar = 1 + t/Tstar
+	lambdastar = 589
+	lambdabar = wavelength/lambdastar
+	lambda_IR = 5.432937
+	lambda_UV = 0.229202
+	C = a0 + a1*rhobar + a2*Tbar + a3*lambdabar*lambdabar*Tbar + a4/(lambdabar*lambdabar) + a5/((lambdabar+lambda_UV)*(lambdabar-lambda_UV)) + a6/((lambdabar + lambda_IR)*(lambdabar - lambda_IR)) + a7*rhobar*rhobar
+	C *= rhobar
+	n = np.sqrt((2*C+1)/(1-C))
+	return n
 
-with open("points.csv", 'w', newline='') as f:
-    writer = csv.writer(f)
-    writer.writerows(points)
+def sun_spectral(wavelength):
+	return 1e16/(np.power(wavelength,5)*(np.exp(6.62607015e6*2.99792458/(wavelength*1.380649*(5250+273.15)))-1))
+
+def modified_trace(wavelength, temp, center, r, N, n_theta, d_theta, min_intensity, max_ray, max_angle):
+	n = water_refraction_index(temp, wavelength)
+	disk = Disk(center, r, n)
+	stack = []
+	XYZ = colorspace.wavelength2XYZ(wavelength)*sun_spectral(wavelength)
+	own_angle_XYZ = np.zeros((n_theta, 3))
+	for u in np.linspace(0, 1, N, endpoint=False):
+		stack=[Ray([r*np.sqrt(u), 2*r], [0,-1], 1)]
+		ray_count = 0
+		while stack and ray_count < max_ray:
+			ray = stack.pop()
+			ray_count += 1
+			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:
+						angle = np.arccos(direction[1])
+						if angle < max_angle:
+							own_angle_XYZ[int(angle/d_theta)] += XYZ*ray.intensity*direction[1]
+	return own_angle_XYZ
+
+def rainbow(n_theta, max_theta, temp):
+	angles, d_theta = np.linspace(0,max_theta,n_theta, retstep=True)
+
+	angle_XYZ = np.zeros((n_theta, 3))
+	angle_sRGB = np.zeros((n_theta, 3))
+
+	num_wavelength = len(colorspace.data_wavelength)
+
+	with Progress() as progress:
+		# 创建一个进度条
+		task = progress.add_task("[green]Simulating...", total=num_wavelength)
+
+		# 使用 ThreadPoolExecutor 并行执行
+		with ProcessPoolExecutor() as executor:
+			futures = [executor.submit(modified_trace, wavelength, temp, center, r, N, n_theta, d_theta, min_intensity, max_ray, max_theta) for wavelength in colorspace.data_wavelength]
+
+			for future in as_completed(futures):
+				result = future.result()
+				angle_XYZ += result
+				progress.update(task, advance=1)
+
+	for i,XYZ in enumerate(angle_XYZ):
+		angle_sRGB[i] = colorspace.XYZ2RGB(XYZ)
+
+	maxRGB = np.max(angle_sRGB)
+	angle_sRGB/= maxRGB
+	angle_sRGB = np.clip(angle_sRGB, 0, 1)
+	colorspace.vectorized_gamma_correct(angle_sRGB)
+	return angles,angle_sRGB
+
+def bin_find(x, list, start):
+	l,r = 0, len(list)-1
+
+	if x < list[l]:
+		return 0
+	if x >= list[r]:
+		return r
+
+	if list[start] <= x < list[start + 1]:
+		return start
+	elif list[start] < x:
+		l = start
+	else:
+		r = start
+
+	while l <= r:
+		mid = l + (r-l)//2
+		if list[mid] <= x < list[mid + 1]:
+			return mid
+		elif list[mid] < x:
+			l = mid + 1
+		else:
+			r = mid - 1
+	return -1
+
+def draw_column(i, w, h, radius, angle_sRGB):
+		index = 0
+		column = np.zeros((h, 3), dtype=np.int8)
+		for j in range(h):
+			r = np.linalg.norm(np.array([i,j]) - [w/2, 0])
+			index = bin_find(r, radius, index)
+			ratio = (r - radius[index])/(radius[index+1] - radius[index])
+			column[j] = ((1-ratio)*angle_sRGB[index]+ratio*angle_sRGB[index+1])*255
+		return i,column
+
+def take_picture(angles, angle_sRGB, w, h, distance, filename="image.png"):
+	image_array = np.zeros((w, h, 3), dtype=np.uint8)
+	radius = distance * np.tan(angles)
+
+	with Progress() as progress:
+		# 创建一个进度条
+		task2 = progress.add_task("[green]Rendering...", total=w)
+
+		# 使用 ThreadPoolExecutor 并行执行
+		with ProcessPoolExecutor() as executor:
+			futures2 = [executor.submit(draw_column, i, w,h,radius,angle_sRGB) for i in range(w)]
+
+			for future in as_completed(futures2):
+				ind,column = future.result()
+				image_array[ind] = column
+				progress.update(task2, advance=1)
+	image = Image.fromarray(image_array, "RGB")
+	image.save(filename)
+
+if __name__=="__main__":
+	w = 7680 *2
+	h = 4320 *2
+	dis = 2400 *2
+	max_angle = 1.1*np.arctan(np.sqrt(1+(h*h+w*w/4)/(dis*dis)))
+	angles,sRGB=rainbow(10000, max_angle, 10)
+	np.savez_compressed("saved.npz", a=angles, b=sRGB)
+	# loaded = np.load("saved.npz")
+	# angles, sRGB = loaded['a'], loaded['b']
+	take_picture(angles,sRGB, w, h, dis, "image16k.png")

result.csv

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