Mapping circular image onto surface

Question

I am trying to map the image "Angels and Devils" by M.C. Escher onto a cigar-like shape. The code I have now is

With[
 {
  img = Import[
    "https://upload.wikimedia.org/wikipedia/en/b/bf/Escher_circlelimit_iv-with_overlay.png"
    ]
  }
 ,
 RevolutionPlot3D[
  {Sqrt[1 + t^2/10 - 1/t^2], t}
  , {t, 0.957122, 7.5}
  , Mesh -> None
  , Axes -> False
  , PlotStyle -> Texture[img]
  , TextureCoordinateFunction -> ({#1, #2} &)
  ]
 ]

Where circle-limit-iv.jpg is the image file.

The problem is that this image has some white space around the circle, since the image is actually a rectangle.

I would like to have it so that the edge of the circle is mapped to the edge of the surface. Is there any way to do this?

Answer 1

rhermans gave you already the answer, however with your and with every image that has a uniform padding, you can simply call ImageCrop without parameters. Here is a better resolution of the image and after cropping, you can directly use it as a texture

tex = ImageCrop@Import[
   "http://www.katarte.net/wp-content/uploads/2015/10/Escher-Circle-limit-IV-1960.jpg"];

RevolutionPlot3D[{Sqrt[1 + t^2/10 - 1/t^2], t}, 
  {t, 0.957122, 7.5}, 
  Mesh -> None, 
  Axes -> False, 
  PlotStyle -> Texture[img], 
  TextureCoordinateFunction -> ({#1, #2} &), 
  Lighting -> {{"Ambient", ColorData[97, 2]}}
]

Answer 2

To crop your image into a square you can use

ImageCrop[#, Min[ImageDimensions[#]] {1, 1}] &

Example

With[
 {
  CropSquare = ImageCrop[#, Min[ImageDimensions[#]] {1, 1}] &
  }
 , CropSquare[ExampleData[{"TestImage", "Apples"}]]
 ]