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Interstellar is the first Hollywood movie to attempt depicting a black holeas it would actually be seen by somebody nearby. For this we developed a codecalled DNGR (Double Negative Gravitational Renderer) to solve the equations forray-bundle (light-beam) propagation through the curved spacetime of a spinning(Kerr) black hole, and to render IMAX-quality, rapidly changing images. Ourray-bundle techniques were crucial for achieving IMAX-quality smoothnesswithout flickering.  This paper has four purposes: (i) To describe DNGR for physicists and CGIpractitioners . (ii) To present the equations we use, when the camera is inarbitrary motion at an arbitrary location near a Kerr black hole, for mappinglight sources to camera images via elliptical ray bundles. (iii) To describenew insights, from DNGR, into gravitational lensing when the camera is near thespinning black hole, rather than far away as in almost all prior studies. (iv)To describe how the images of the black hole Gargantua and its accretion disk,in the movie \emph{Interstellar}, were generated with DNGR. There are no newastrophysical insights in this accretion-disk section of the paper, but disknovices may find it pedagogically interesting, and movie buffs may find itsdiscussions of Interstellar interesting.

Gravitational Lensing by Spinning Black Holes in Astrophysics, and in the Movie Interstellar