gnomonic transformation

gnomonic.py

import numpy as np
from PIL import Image
from skimage import transform


def gnomonic2equirectangular(ishape, oshape, fov):
  def inner(xy):
    ones = np.expand_dims(np.ones(xy.shape[0]), 0).transpose()
    v = np.concatenate((xy, ones), axis=1)
    v /= np.linalg.norm(v, axis=1, keepdims=True)

    xx = v[:, 0]
    yy = v[:, 1]
    zz = v[:, 2]

    lat = np.arcsin(zz)
    lon = np.arctan2(xx, yy)

    return np.c_[lon, lat]

  def outer(xy):
    osa = np.flip(np.array(oshape, np.float) - 1, 0)
    isa = np.flip(np.array(ishape, np.float) - 1, 0)
    o = inner((2 * xy / osa - 1) * np.tan(fov / 2))
    return (np.divide(o, np.array([2 * np.pi, np.pi])) + .5) * isa

  return outer


def rect2gnomonic(img, fov=np.pi / 2):
    ishape = img.shape[:2]
    oshape = np.full(2, np.ceil(np.tan(fov / 2) / np.sin(2 * np.pi / ishape[1])))
    return transform.warp(img.astype(np.float), inverse_map=gnomonic2equirectangular(ishape, oshape, fov), output_shape=oshape)