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Image projection onto sphere using Equirectangular map projection.

 ``` 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``` ```# Image Projection onto Sphere # https://en.wikipedia.org/wiki/Equirectangular_projection # Download the test image from the Wikipedia page! # FB36 - 20160731 import math, random from PIL import Image imgxOutput = 768; imgyOutput = 768 pi2 = math.pi * 2 # 3D Sphere Rotation Angles (arbitrary) xy = -pi2 * random.random() xz = -pi2 * random.random() yz = -pi2 * random.random() sxy = math.sin(xy); cxy = math.cos(xy) sxz = math.sin(xz); cxz = math.cos(xz) syz = math.sin(yz); cyz = math.cos(yz) imageInput = Image.open("Equirectangular_projection_SW.jpg") (imgxInput, imgyInput) = imageInput.size pixelsInput = imageInput.load() imageOutput = Image.new("RGB", (imgxOutput, imgyOutput)) pixelsOutput = imageOutput.load() # define a sphere behind the screen xc = (imgxOutput - 1.0) / 2 yc = (imgyOutput - 1.0) / 2 zc = min((imgxOutput - 1.0), (imgyOutput - 1.0)) / 2 r = min((imgxOutput - 1.0), (imgyOutput - 1.0)) / 2 # define eye point xo = (imgxOutput - 1.0) / 2 yo = (imgyOutput - 1.0) / 2 zo = -min((imgxOutput - 1.0), (imgyOutput - 1.0)) xoc = xo - xc yoc = yo - yc zoc = zo - zc doc2 = xoc * xoc + yoc * yoc + zoc * zoc for yi in range(imgyOutput): for xi in range(imgxOutput): xio = xi - xo yio = yi - yo zio = 0.0 - zo dio = math.sqrt(xio * xio + yio * yio + zio * zio) xl = xio / dio yl = yio / dio zl = zio / dio dot = xl * xoc + yl * yoc + zl * zoc val = dot * dot - doc2 + r * r if val >= 0: # if there is line-sphere intersection if val == 0: # 1 intersection point d = -dot else: # 2 intersection points => choose the closest d = min(-dot + math.sqrt(val), -dot - math.sqrt(val)) xd = xo + xl * d yd = yo + yl * d zd = zo + zl * d x = (xd - xc) / r y = (yd - yc) / r z = (zd - zc) / r x0=x*cxy-y*sxy;y=x*sxy+y*cxy;x=x0 # xy-plane rotation x0=x*cxz-z*sxz;z=x*sxz+z*cxz;x=x0 # xz-plane rotation y0=y*cyz-z*syz;z=y*syz+z*cyz;y=y0 # yz-plane rotation lng = (math.atan2(y, x) + pi2) % pi2 lat = math.acos(z) ix = int((imgxInput - 1) * lng / pi2 + 0.5) iy = int((imgyInput - 1) * lat / math.pi + 0.5) try: pixelsOutput[xi, yi] = pixelsInput[ix, iy] except: pass imageOutput.save("World.png", "PNG") ```