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convert.py
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#!/usr/bin/env python
#-*- coding: utf-8 -*-
import sys
from PIL import Image
from math import pi,sin,cos,tan,atan2,asin,acos,hypot,floor,fabs,sqrt,radians
from numpy import clip,array,matrix
# convertCoordinate from coordinate A to B
# x 是沿所求坐标系转换为原坐标系X轴旋转的角度
# y 是沿所求坐标系转换为原坐标系y轴旋转的角度
# z 是沿所求坐标系转换为原坐标系z轴旋转的角度
# sequence 是矩阵旋转的次序，0是x->y->z，1是x->z->y，2是y->x->z，3是y->z->x，4是z->x->y，5是z->y->x
def convertCoordinate(x, y, z, sequence):
mx = matrix([
[1, 0, 0],
[0, cos(x), -sin(x)],
[0, sin(x), cos(x)]
])
my = matrix([
[cos(y), 0, sin(y)],
[0, 1, 0],
[-sin(y), 0, cos(y)]
])
mz = matrix([
[cos(z), -sin(z), 0],
[sin(z), cos(z), 0],
[0, 0, 1]
])
if sequence == 0:
A = (mz.dot(my)).dot(mx)
elif sequence == 1:
A = (my.dot(mz)).dot(mx)
elif sequence == 2:
A = (mz.dot(mx)).dot(my)
elif sequence == 3:
A = (mx.dot(mz)).dot(my)
elif sequence == 4:
A = (my.dot(mx)).dot(mz)
elif sequence == 5:
A = (mx.dot(my)).dot(mz)
return A
A1 = convertCoordinate(radians(0), radians(90), radians(-45), 5)
B1 = convertCoordinate(radians(45), -asin(1.0/sqrt(3))-pi/2.0, radians(0), 2)
A2 = convertCoordinate(radians(0), radians(0), radians(45), 2)
B2 = convertCoordinate(radians(-45), asin(1.0/sqrt(3))-pi, radians(0), 2)
A3 = convertCoordinate(radians(180), radians(90), radians(-45), 1)
B3 = convertCoordinate(radians(135), asin(1.0/sqrt(3))-pi/2.0, radians(0), 2)
A4 = convertCoordinate(radians(45), radians(-90), radians(0), 3)
B4 = convertCoordinate(radians(45), asin(1.0/sqrt(3))-pi/2.0, radians(0), 2)
# get x,y,z coords from out image pixels coords
# i,j 是输出图像的xy坐标
# face 是面的号码
# halfOutSize 输出图像宽度的一半
# 将输出图像的xy值转换为三维空间中的xyz坐标，对应成一个坐标值由-1到1的立方体
def outImgToXYZ(i,j,face,halfOutSize,toward):
if (toward == 0): # front face
a = i * 4.0 / (halfOutSize * 2)
b = j * 4.0 / (halfOutSize * 2)
if face==0: # down
a = a - 2.0
b = 2.0 - b
(x,y,z) = (sqrt(3) - 1, a, b)
elif face==1: # left top
# first coordinate conversion
c = A1.dot(matrix([b-1, a-1, 0]).T)
c[2] = c[2] * sqrt(3) # stretch
# second coordinate conversion
c[0] = c[0] - (1 - sqrt(3))
c[1] = c[1] - 0
c[2] = c[2] - sqrt(2)
d = B1.dot(c)
(x,y,z) = (d[0], d[1], d[2])
elif face==2: # left bottom
# first coordinate conversion
c = A2.dot(matrix([b-3, a-1, 0]).T)
c[0] = c[0] * sqrt(3) # stretch
# second coordinate conversion
c[0] = c[0] - sqrt(2)
c[1] = c[1] - 0
c[2] = c[2] - (1 - sqrt(3))
d = B2.dot(c)
(x,y,z) = (d[0], d[1], d[2])
elif face==3: # right top
# first coordinate conversion
c = A3.dot(matrix([b-1, a-3, 0]).T)
c[2] = c[2] * sqrt(3) # stretch
# second coordinate conversion
c[0] = c[0] - (sqrt(3) - 1)
c[1] = c[1] - 0
c[2] = c[2] - sqrt(2)
d = B3.dot(c)
(x,y,z) = (d[0], d[1], d[2])
elif face==4: # right bottom
# first coordinate conversion
c = A4.dot(matrix([b-3, a-3, 0]).T)
c[2] = c[2] * sqrt(3) # stretch
# second coordinate conversion
c[0] = c[0] - (sqrt(3) - 1)
c[1] = c[1] - 0
c[2] = c[2] - sqrt(2)
d = B4.dot(c)
(x,y,z) = (d[0], d[1], d[2])
return (x,y,z)
# convert using an inverse transformation
def convertBack(imgIn,imgOut):
inSize = imgIn.size
outSize = imgOut.size
inPix = imgIn.load()
outPix = imgOut.load()
edge = inSize[0]/4 # 视角宽度
halfOutSize = outSize[0] / 2;
for i in xrange(outSize[0]):
for j in xrange(outSize[1]):
face = 0
if fabs(halfOutSize - i) + fabs(halfOutSize - j) <= halfOutSize:
face = 0
elif (i < halfOutSize) and (j < halfOutSize):
face = 1 # 左上角
elif (i < halfOutSize) and (j > halfOutSize):
face = 2 # 左下角
elif (i > halfOutSize) and (j < halfOutSize):
face = 3 # 右上角
elif (i > halfOutSize) and (j > halfOutSize):
face = 4 # 右下角
(x,y,z) = outImgToXYZ(i,j,face,halfOutSize, 0)
theta = atan2(y,x) # 水平方向夹角
r = hypot(x,y)
phi = atan2(z,r) # 垂直方向夹角
# 对应原图像的坐标值
uf = ( 2.0*edge*(theta + pi) / pi )
vf = ( 2.0*edge * (pi/2 - phi)/pi)
outPix[i,j] = inPix[int(uf) % inSize[0], clip(vf,0,inSize[1]-1)]
imgIn = Image.open("2.jpg")
inSize = imgIn.size
imgOut = Image.new("RGB",((int)(inSize[0] / 4 * sqrt(2)) , (int)(inSize[0] / 4 * sqrt(2))),"black")
convertBack(imgIn,imgOut)
imgOut.save("out.jpg")
imgOut.show()