-
Notifications
You must be signed in to change notification settings - Fork 1
/
Copy pathutil.py
272 lines (244 loc) · 10.5 KB
/
util.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
import numpy as np
import numbers, time, os
from PIL import Image
from functools import reduce
from abc import ABC, abstractmethod
def extract(cond, x):
if isinstance(x, numbers.Number):
return x
else:
return np.extract(cond, x)
class vec4():
def __init__(self, t, x, y, z):
self.t, self.x, self.y, self.z = (t, x, y, z)
def __mul__(self, other):
return vec4(self.t * other, self.x * other, self.y * other, self.z * other)
def __add__(self, other):
return vec4(self.t + other.t, self.x + other.x, self.y + other.y, self.z + other.z)
def __sub__(self, other):
return vec4(self.t - other.t, self.x - other.x, self.y - other.y, self.z - other.z)
def __neg__(self):
return vec4(-self.t, -self.x, -self.y, -self.z)
def dot(self, other):
return (self.t * other.t) + (self.x * other.x) + (self.y * other.y) + (self.z * other.z)
def apply_matrix(self, matrix):
vec= np.array([self.t, self.x, self.y, self.z])
t,x,y,z= np.dot(matrix, vec)
return vec4(t,x,y,z)
def __abs__(self): #注意，该方法改为向量求模
return np.sqrt(self.dot(self))
def __str__(self):
return 'vec4(%s, %s, %s, %s)'%(self.t, self.x,self.y,self.z)
def components(self):
return (self.t, self.x, self.y, self.z)
def space_info(self):
return np.array([self.x, self.y, self.z])
def extract(self, cond):
return vec4(extract(cond, self.t),
extract(cond, self.x),
extract(cond, self.y),
extract(cond, self.z))
def place(self, cond):
r = vec4(np.zeros(cond.shape), np.zeros(cond.shape), np.zeros(cond.shape), np.zeros(cond.shape))
np.place(r.t, cond, self.t)
np.place(r.x, cond, self.x)
np.place(r.y, cond, self.y)
np.place(r.z, cond, self.z)
return r
def points(self):
arr= np.array([self.x, self.y, self.z])
return np.transpose(arr)
def vec3(self):
return vec3(self.x, self.y, self.z)
class vec3():
'''这是一个三维坐标。例如当计算交点时，用不到四维坐标，可以暂时转换为三维减少计算量。'''
def __init__(self, x, y, z):
(self.x, self.y, self.z) = (x, y, z)
def __mul__(self, other):
return vec3(self.x * other, self.y * other, self.z * other)
def __truediv__(self, other): #
return vec3(self.x / other, self.y / other, self.z / other)
def __rtruediv__(self, other):
return vec3(other.x / self.x, other.y / self.y, other.z / self.z)
def __add__(self, other):
return vec3(self.x + other.x, self.y + other.y, self.z + other.z)
def __sub__(self, other):
return vec3(self.x - other.x, self.y - other.y, self.z - other.z)
def __neg__(self):
return vec3(-self.x, -self.y, -self.z)
def dot(self, other):
return (self.x * other.x) + (self.y * other.y) + (self.z * other.z)
def __abs__(self):
return self.dot(self)
def __str__(self):
return 'vec3(%s,%s,%s)'%(self.x,self.y,self.z)
def norm(self):
return np.sqrt(abs(self))
def normalize(self):
return self * (1/self.norm())
def components(self):
return (self.x, self.y, self.z)
def points(self):
arr= np.array([self.x, self.y, self.z])
return np.transpose(arr)
def extract(self, cond):
return vec3(extract(cond, self.x),
extract(cond, self.y),
extract(cond, self.z))
def place(self, cond):
r = vec3(np.zeros(cond.shape), np.zeros(cond.shape), np.zeros(cond.shape))
np.place(r.x, cond, self.x)
np.place(r.y, cond, self.y)
np.place(r.z, cond, self.z)
return r
def vec4(self, t):
return vec4(t, self.x, self.y, self.z)
rgb=vec3
def quadratic_eqn_roots(a, b, c):
np.seterr(all='ignore')
discriminant = b ** 2 - 4 * a * c
sqrt_discriminant = np.sqrt(discriminant)
root1= (-b - sqrt_discriminant) / (2 * a)
root2= (-b + sqrt_discriminant) / (2 * a)
return root1, root2
def lorentz_boost(beta):
beta = np.asarray(beta)
beta_squared = np.inner(beta, beta)
if beta_squared >= 1:
raise ValueError(f"beta²= {beta_squared} 超光速")
if beta_squared == 0:
return np.identity(4)
gamma = 1 / np.sqrt(1 - beta_squared)
lambda_00 = np.matrix([[gamma]])
lambda_0j = -gamma * np.matrix(beta)
lambda_i0 = lambda_0j.transpose()
lambda_ij = np.identity(3) + (gamma - 1) * np.outer(beta, beta) / beta_squared
return np.asarray(np.bmat([[lambda_00, lambda_0j], [lambda_i0, lambda_ij]]))
def spherical_angles(point: vec3):
x, y, z = point.components()
radius = point.norm()
theta = np.arccos(z / radius)
phi = np.arctan2(y, x) + np.pi
return theta, phi
def checkerboard(point, color1= rgb(0.5,0.5,0.5), color2= rgb(1,1,1), ranks= 12):
theta, phi = spherical_angles(point)
n_theta = np.floor((theta / np.pi) * ranks)
n_phi = np.floor((phi / (2 * np.pi)) * ranks)
return color1 + (color2 - color1) * ((n_theta + n_phi) % 2)
def get_checkerboard_color_func(color1, color2, ranks= 12):
return lambda p: checkerboard(p,color1, color2, ranks)
def checkerboard(point:vec3, color1= rgb(0.5,0.5,0.5), color2= rgb(1,1,1), ranks= 12):
theta, phi = spherical_angles(point)
n_theta = np.floor((theta / np.pi) * ranks)
n_phi = np.floor((phi / (2 * np.pi)) * ranks)
return color1 + (color2 - color1) * ((n_theta + n_phi) % 2)
def get_cubical_checkerboard_color_func(color1, color2, width= .1, offset: vec3 = vec3(.001,.001,.001)):
return lambda p: cubical_checkerboard(p + offset ,color1, color2, width)
def cubical_checkerboard(point: vec3, color1= rgb(0.5,0.5,0.5), color2= rgb(1,1,1), width= .1):
x, y, z = point.components()
cond_x= np.floor(x/width)
cond_y= np.floor(y/width)
cond_z= np.floor(z/width)
cond= np.mod(cond_x + cond_y + cond_z, 2)
return color1 + (color2 - color1) * cond
def range_func_from_image(filename, resize= (1.920, 1.080), offset= (0, 0), black= True):
image = Image.open(filename).convert('1')
image_width, image_height= image.size
real_width, real_height= resize
pixels= black ^ np.array(image)
def x_transform_to_image(x): # array
return np.int32(np.floor(x * (image_width/real_width) + offset[0] + image_width/2))
def y_transform_to_image(y):
return np.int32(np.floor(image_height/2 - (y * (image_height/real_height) + offset[1])))
def range_func(inter: vec3):
transformed_inter= vec3(x_transform_to_image(inter.x), y_transform_to_image(inter.y), 0)
hit_image= reduce(np.logical_and, (
transformed_inter.x >= 0,
transformed_inter.x < image_width,
transformed_inter.y >= 0,
transformed_inter.y < image_height
)
)
hit_image_inter= transformed_inter.extract(hit_image)
hit_image_inter_hit_white_pixel= pixels[hit_image_inter.y, hit_image_inter.x]
hit= np.zeros(len(inter.x))
np.place(hit, hit_image, hit_image_inter_hit_white_pixel)
return hit
return range_func
def timeit(func):
def time_func(*args, **kwargs):
t0= time.time()
output= func(*args, **kwargs)
print(f'耗时{time.time() - t0}s...', end= '')
return output
return time_func
FARAWAY= 1.0e39
DEFAUT_CAMERA_HEIGHT= 200
DEFAUT_FOCAL_LENGTH= 200
ORIGIN= vec4(0, 0, 0, 0)
DEFAUT_LIGHT_POS= vec3(2, 2, -2)# 默认光源位置
LOW_DEFINITION= (533.3, 300)
DEFAUT_DEFINITION= (1920, 1080)
HIGH_DEFINITION= (4096, 3112)
DEFAULT_OBJ_COLOR = rgb(1,1,1)
BILIBILIPINK= rgb(1.0, 0.44140625, 0.62109375) # B站粉
BILIBILIBLUE_A= rgb(0.41796875, 0.7578125, 0.92578125) # B站青
BILIBILIBLUE= rgb(0.00390625, 0.640625, 0.93359375) # B站蓝
DARK_BLUE= rgb(0.140625, 0.421875, 0.55859375)
DARK_BROWN= rgb(0.546875, 0.2734375, 0.078125)
LIGHT_BROWN= rgb(0.8046875, 0.5234375, 0.25)
BLUE_E= rgb(0.11328125, 0.4609375, 0.54296875)
BLUE_D= rgb(0.1640625, 0.671875, 0.79296875)
BLUE_C= rgb(0.34765625, 0.76953125, 0.8671875)
BLUE_B= rgb(0.61328125, 0.86328125, 0.921875)
BLUE_A= rgb(0.78125, 0.9140625, 0.9453125)
TEAL_E= rgb(0.2890625, 0.66015625, 0.5625)
TEAL_D= rgb(0.3359375, 0.7578125, 0.65625)
TEAL_C= rgb(0.36328125, 0.81640625, 0.703125)
TEAL_B= rgb(0.46484375, 0.8671875, 0.75390625)
TEAL_A= rgb(0.67578125, 0.91796875, 0.84375)
GREEN_E= rgb(0.4140625, 0.61328125, 0.32421875)
GREEN_D= rgb(0.46875, 0.69140625, 0.3671875)
GREEN_C= rgb(0.515625, 0.7578125, 0.40625)
GREEN_B= rgb(0.65234375, 0.8125, 0.55078125)
GREEN_A= rgb(0.7890625, 0.88671875, 0.68359375)
YELLOW_E= rgb(0.91015625, 0.7578125, 0.11328125)
YELLOW_D= rgb(0.95703125, 0.828125, 0.2734375)
YELLOW_C= rgb(1.0, 1.0, 0.00390625)
YELLOW_B= rgb(1.0, 0.91796875, 0.58203125)
YELLOW_A= rgb(1.0, 0.9453125, 0.71484375)
GOLD_E= rgb(0.78125, 0.5546875, 0.27734375)
GOLD_D= rgb(0.8828125, 0.6328125, 0.34765625)
GOLD_C= rgb(0.94140625, 0.67578125, 0.375)
GOLD_B= rgb(0.9765625, 0.71875, 0.4609375)
GOLD_A= rgb(0.96875, 0.78125, 0.59375)
RED_E= rgb(0.8125, 0.31640625, 0.26953125)
RED_D= rgb(0.90234375, 0.35546875, 0.30078125)
RED_C= rgb(0.98828125, 0.38671875, 0.3359375)
RED_B= rgb(1.0, 0.50390625, 0.50390625)
RED_A= rgb(0.96875, 0.6328125, 0.640625)
MAROON_E= rgb(0.58203125, 0.26171875, 0.3125)
MAROON_D= rgb(0.63671875, 0.3046875, 0.3828125)
MAROON_C= rgb(0.7734375, 0.375, 0.453125)
MAROON_B= rgb(0.92578125, 0.57421875, 0.671875)
MAROON_A= rgb(0.92578125, 0.671875, 0.7578125)
PURPLE_E= rgb(0.39453125, 0.2578125, 0.44921875)
PURPLE_D= rgb(0.4453125, 0.3359375, 0.51171875)
PURPLE_C= rgb(0.60546875, 0.44921875, 0.67578125)
PURPLE_B= rgb(0.6953125, 0.5390625, 0.77734375)
PURPLE_A= rgb(0.79296875, 0.640625, 0.91015625)
WHITE= rgb(1.0, 1.0, 1.0)
BLACK= rgb(0.00390625, 0.00390625, 0.00390625)
LIGHT_GRAY= rgb(0.734375, 0.734375, 0.734375)
LIGHT_GREY= rgb(0.734375, 0.734375, 0.734375)
GRAY= rgb(0.53515625, 0.53515625, 0.53515625)
GREY= rgb(0.53515625, 0.53515625, 0.53515625)
DARK_GREY= rgb(0.26953125, 0.26953125, 0.26953125)
DARK_GRAY= rgb(0.26953125, 0.26953125, 0.26953125)
DARKER_GREY= rgb(0.13671875, 0.13671875, 0.13671875)
DARKER_GRAY= rgb(0.13671875, 0.13671875, 0.13671875)
GREY_BROWN= rgb(0.453125, 0.390625, 0.34375)
PINK= rgb(0.8203125, 0.28125, 0.7421875)
LIGHT_PINK= rgb(0.86328125, 0.4609375, 0.8046875)
GREEN_SCREEN= rgb(0.00390625, 1.0, 0.00390625)
ORANGE= rgb(1.0, 0.52734375, 0.1875)