commit 386db2d6b84c09c403b2e44c9763ac44cf43942b Author: GaugeAndGravity Date: Mon Oct 30 00:41:13 2023 -0400 init diff --git a/__pycache__/raytrace_2D.cpython-311.pyc b/__pycache__/raytrace_2D.cpython-311.pyc new file mode 100644 index 0000000..55b0696 Binary files /dev/null and b/__pycache__/raytrace_2D.cpython-311.pyc differ diff --git a/points.csv b/points.csv new file mode 100644 index 0000000..061d8d8 --- /dev/null +++ b/points.csv @@ -0,0 +1,380 @@ +0.8,2.0,0.8000000000000002,0.5999999999999998,1.0 +0.8000000000000002,0.5999999999999998,0.38799246954563393,-0.9216625432206087,0.9658212943515994 +0.38799246954563393,-0.9216625432206087,0.38799246954563393,-0.9216625432206087,0.9328107726229987 +0.38799246954563393,-0.9216625432206087,-0.7761581500190065,-0.6305382828655796,0.9328107726229987 +-0.7761581500190065,-0.6305382828655796,-0.8226410335562787,0.5685611048158833,0.9328107726229987 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/dev/null +++ b/rainbow.py @@ -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) diff --git a/raytrace_2D.py b/raytrace_2D.py new file mode 100644 index 0000000..d7e37a5 --- /dev/null +++ b/raytrace_2D.py @@ -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 diff --git a/result.csv b/result.csv new file mode 100644 index 0000000..22349c0 --- /dev/null +++ b/result.csv @@ -0,0 +1,5 @@ +0.7993010857076976,0.0007048815056688454 +1.3928938872949743,0.003657341850518903 +1.2482567878728648,0.0003454071966921608 +0.8743957180247236,0.0006520310605573929 +0.1162362891411113,0.0010096197790698755